McDougal Littell Concepts and Skills: Algebra 1 and Geometry

Transcription

McDougal Littell Concepts and Skills:
Algebra 1 and Geometry
correlated to
Washington Math GLEs, Grades 8–10
TABLE OF CONTENTS
Algebra 1: Concepts and Skills correlated to the Washington Math GLEs: GRADE 8.....................................................1
Algebra 1: Concepts and Skills correlated to the Washington Math GLEs: GRADES 9/10..........................................34
Geometry: Concepts and Skills correlated to the Washington Math GLEs: GRADES 9/10..........................................68
Algebra 1: Concepts and Skills
correlated to the
Washington Math GLEs
GRADE 8
EALR 1: The student understands and applies the concepts and procedures of
mathematics.
Component 1.1: Understand and apply concepts and procedures from number sense.
Number and numeration
1.1.1 Understand the concept of rational numbers including whole number powers and
square roots of square numbers. W
PE/TE: xxi (Pre–Course Practice, #1–24), 9–14, 21 (#64–66; Quiz 1, #13–18), 29,
35 (#47–54), 41 (#34–45), 59 (#5–7), 68–73, 83 (#59–61), 149 (#55–59), 499–504,
505–510, 511–517, 767–769
• Explain the meaning of a whole number exponent. [CU]
PE/TE: 9, 10, 12 (#17–18), 21 (#66; Quiz 1, #14–17), 29 (#68, 70–71, 73), 56 (#14),
59 (#5–7), 83 (#59–61), 149 (#55–59), 441 (#1)
• Read and use exponential notation to represent large numbers (e.g., 2500 = 502 ). [MC]
PE/TE: Opportunities to address this standard can be found on the following pages:
12 (#20–33), 13 (#34–39), 430 (#45), 468 (#69)
• Identify a square number and find its root.
499–500, 502, 503 (#54, 57, 59, 62, 64), 505, 508 (#18–20, 22–23, 25–31, 33),
517 (#1–9), 553 (#1–5), 638 (#53–56), 791 (#2–4)
• Identify different representations of rational numbers and select the best representation in the
situation (e.g., percent for sales discount or sales tax, fraction for probability, and decimals for
money, distance [4.35 kilometers], batting averages).
xxi (Pre–Course Practice, #1–24), 35 (#47–54), 41 (#34–45), 165, 166 (#19),
183–185, 186 (#7–10, 16–27), 187, 193 (#27–30), 194 (#11), 347 (#70–77),
430 (#56–63), 474 (#78–83), 552 (#53–68), 735 (#71–78), 768–769,
774 (Example 3), 808–810
W=tested on WASL, SP=Solves Problems, RL=Reasons Logically, CU=Communicates Understanding, MC=Makes Connections
1
Algebra 1: Concepts and Skills correlated to the
Washington Math GLEs: GRADE 8
• Write a squared number.
PE/TE: 9, 12 (#5–8, 13–16), 21 (#64–65; Quiz 1, #13, 18), 29 (#69, 72), 56 (#12, 13),
59 (#6–7), 83 (#59–61), 149 (#56, 58–59)
1.1.2 Understand the relative values of rational numbers including whole number powers
and square roots of square numbers. W
PE/TE: 24–29, 47 (#35–43), 61 (#13–20), 64 (Study Guide #3), 66, 70, 71–76, 91 (#72–77),
118 (#71–78), 121 (#1–3), 125 (#1–3), 531 (#78–85), 629, 703 (#79–96), 770–771,
784 (#1–4)
• Compare and order rational numbers using models or implementing strategies. [RL]
PE/TE: 47 (#35–43), 66–67, 68 (#23–30), 69 (#55–59), 70 (#60–61), 112 (#73–81),
118 (#71–78), 149 (#67–74), 304 (#50–58), 319 (#5–13), 531 (#78–85),
539 (#96–101), 703 (#79–96), 739 (#45–48), 770–771
• Order different representations of rational numbers. [RL]
PE/TE: 64 (Study Guide #3), 65, 66–67, 68 (#11–13), 69 (#44–49), 70 (#62),
112 (#73–81), 121 (#1–3), 125 (#1–3), 188 (#50–53), 460 (#73–78), 629 (#1–8),
770–771, 784 (#1–4)
• Place symbolic representations of rational numbers on a number line including whole number
powers and square roots of square numbers. [CU]
PE/TE: 61 (#13–20), 66–67, 68 (#3–6, 14–22, 31–34), 69 (#35–43), 76 (#70–75),
91 (#72–77), 121 (#1–3), 125 (#1–3), 182 (#49–51), 353 (#55–57), 770–771,
784 (#1–4)
1.1.3 Apply properties of addition, multiplication, and the distributive property to the
rational number system. W
PE/TE: 77, 78–83, 84–85, 91, 92, 93–98, 99, 100, 107–111, 113–118, 138–142,
382 (#16–19, 22–23), 573 (#58–63), 616 (#1–6), 763, 784 (#38, 40–41, 43–44)
• Illustrate and explain the distributive property of multiplication over addition (e.g., using an area
model or picture). [CU]
PE/TE: 99, 100, 101 (Example 2, #3–4), 103, 104 (#17–28, 41–45, 47–48), 105 (#71–73),
106 (#14), 123 (#36–37, 40–41), 125 (#30, 32), 137 (#69, 71–72), 382 (#17–18),
784 (#38, 40–41, 43–44)
2
• Use the distributive property to simplify expressions including those using integers. [RL]
PE/TE: 102, 103, 104 (#17–28, 55–67), 105 (#68–70, 74), 123 (#36, 37, 40, 41),
125 (#30, 32), 137 (#69, 71, 72), 143 (#60–61), 382 (#16–19, 22–23),
559 (Example 1, #2, 5, 9), 573 (#58–63), 784 (#38, 40, 41)
• Use the distributive property to factor expressions (e.g., 3•9+3•1=3(9+1)). [RL]
108 (Example 2a), 117 (#43, 44), 118 (#16–18), 616 (#1–6), 627 (#32),
647 (Example 3), 649 (#9, 25–27, 30)
• Identify the multiplicative inverse of a number.
113, 139 (Example 3, #5–8), 141 (#12–14), 142 (#37–45), 146 (Example 5, #8–10)
1.1.4 Apply ratio, percent, and direct proportion in situations. W
PE/TE: 177–179, 182, 188, 631, 633–635, 636–637 (#28–39), 638, 639–644, 735 (#71–78),
769 (#16–40), 793 (#1–2), 811 (#7, 9–12)
• Solve problems involving ratio and proportion (e.g., similar figures, scale drawings, rates, find
unit pricing, increase or decrease a recipe, find the portions for a group converting between
different units of measure, or finding medicinal dosages). [SP, MC]
PE/TE: 177–179, 180 (#9–11, 20–27), 181, 182 (#44–47), 188 (#4–7), 192 (#26, 27),
193 (#24–26, 33) 194 (#10), 241 (#48), 304 (#40–42), 366 (#53–54), 383 (#38–41),
488 (#6–9), 631, 633–634, 635 (Example 5), 637, 638 (#40), 656 (#50), 682 (#26),
785 (#38–41)
• Solve problems involving percentages (e.g., percent increase/decrease, tax, commission,
discount). [SP, MC]
PE/TE: 183–187, 188 (#42–43; Quiz 3, #8–9), 192 (#28), 193 (#27–31), 194 (#11),
477 (Example 2, #2), 480 (#16–27), 644 (#45–50), 703 (#60–63), 746 (#26–29),
785 (#42–43)
• Explain advantages and disadvantages of different representations of ratios or percents in a given
situation (e.g., using 1/8 versus 12_ %). [CU, MC]
186 (#11–12, 16, 18–20, 23–26), 187 (#34, 36–39), 235 (Example, #41–42),
275 (#74–83), 347 (#70–77), 735 (#71–78), 769 (#16–40)
3
• Determine an unknown value for a dimension or a number of events or objects using ratio or
proportion.
633–634, 635 (Example 5), 636, 637 (#28–39), 681 (#1), 686 (#9), 793 (#1–2),
808 (Example 1, #1), 811 (#7, 9–12)
• Complete a proportion in a situation.
PE/TE: 631, 635 (Example 5), 636
Computation
1.1.5 Understand the meaning of operations on rational numbers (including square roots of
square numbers and whole number powers). W
PE/TE: 78–83, 84–85, 86–91, 92, 93–98, 113–118, 132–137, 138–143, 144–149, 151–156,
157–162, 163–169, 443–448, 449–454, 462–468, 469–474
• Create a problem situation to match a given rational number equation. [CU, MC]
25 (#1–4), 27 (#34–48), 57 (#28–33), 134, 135 (#7–15, 25–42), 136 (#43–56),
137 (#65–68), 141 (#6–14, 22–36), 142 (#37–45), 147 (#7–39), 166 (#15–17),
508 (#9, 18–19, 25, 29–31, 33–34, 37–38, 40–41, 44–46, 48)
• Explain the meaning of negative and zero exponents. [CU]
PE/TE: 449, 450 (Example 2), 451 (Example 4, #8–10), 452, 453 (#41–48, 65–66),
490 (#9–12), 790 (#9–10)
• Demonstrate or describe the meaning of multiplication and division of integers using words,
visual, or physical models. [CU]
92–93, 94 (Properties of Multiplication Table), 94 (Example 2, #5–7), 95–97,
98 (#60), 113, 114 (#1, The Sign of a Quotient Rule), 116 (#7, 19–26),
118 (#10–15), 125 (#21–23, 36), 137 (#65–66, 68), 143 (#54), 162 (#54–57)
• Create a problem situation involving multiplication or division of integers. [CU, MC]
96 (#6–9, 13–14, 17–31, 32–40), 97 (#41–46), 116 (#7, 19–26), 118 (#10–11),
125 (#21–23, 36, 40–41), 141 (#6–14, 22–36), 143 (#63–68), 149 (#1–6),
784 (#28–29, 52–53)
4
• Explain solutions when dividing by fractions (e.g., when dividing by a number between 0 and 1,
the result is larger than the dividend). [CU]
PE/TE: 114 (Example 2b, #4), 116 (#8–9, 27–28, 31–34), 125 (#40–41),
766 (#41–43, 45, 51, 54, 59, 64), 784 (#54–55)
1.1.6 Apply computational procedures with fluency on rational numbers including whole
number powers and square roots of square numbers. W
PE/TE: 9–14, 21, 29 (#80–82), 30–35, 36–41, 61 (#1–12), 78–80, 81 (#6–35), 82 (#54–55),
97 (#41–46), 105 (#68–70), 113, 114 (#1–4), 116 (#31–38), 124 (#51–58),
125 (#12–15, 17–24, 39–42), 221 (#37–42), 227 (#57–72), 249 (#81–88),
312 (#59–70), 335 (#62–73), 414 (#49–56), 430 (#46–50), 443–448, 449–454,
465 (#3, 11–12, 25), 469–474, 477, 480 (#16–27, 32, 34), 485 (#16–21),
486 (#20–30, 35–38), 499–503, 517 (#106–113), 573 (#65–70), 601 (#70–77),
608 (#69–76), 644 (#62–69), 657 (#73–80), 676 (#66–71), 677 (#84–95),
709 (#60, 62–64)
• Compute with rational numbers using order of operations.
PE/TE: 15–16, 18 (#3–35), 29 (#74–79), 41 (#74–79), 56 (#18–23), 97 (#41–46), 99 (#1–3),
149 (#61–63), 156 (#64–66), 221 (#37–42), 265 (#9–14), 608 (#69–76)
• Compute fluently with rational numbers in all forms except exponential.
PE/TE: 15 (#1–4), 16 (#5–7), 18 (#3–35), 19 (#36–41), 21 (#20–22), 29 (#80–82),
54 (#38–46), 56 (#18–23), 61 (#1–12), 78–80, 81 (#6–35), 83 (#13–18), 91 (#78–83),
93, 99 (#1–3), 104 (#55–66), 106 (#8–13), 112 (# 61–66), 113, 114 (#1–4),
116 (#31–38), 124 (#51–58), 125 (#12–15, 17–24, 39–42), 149 (#61–66),
156 (#68–73, 78–86), 162 (#54–57, 64–6
9), 208 (#58–66), 215 (#60–63),
227 (#57–72), 249 (#81–88), 265 (#9–14), 290 (#50–58), 312 (#59–70),
335 (#62–73), 353 (#73–81), 366 (#62–67), 394 (#45–50), 414 (#49–56),
468 (#89–94), 517 (#106–113), 573 (#72–83), 580 (#90–98), 587 (#67–74),
601 (#70–77), 608 (#69–76), 644 (#62–69), 651 (#51–54, 67–72), 657 (#73–80),
677 (#84–95), 746 (#40–45)
• Write and solve problems that involve computation with rational numbers. [CU, MC]
PE/TE: 17 (#8–9), 19 (#47–48), 20 (#51–52), 80 (Example 4, #12–13), 82 (#54–55),
90 (#56–57), 104 (#67), 105 (#68–70), 125 (#38), 126 (#11), 479 (#10–15), 482 (#1),
485 (#16–21), 486 (#29–30, 35–38), 492 (#43–46), 493 (#27–30)
5
• Solve problems using rational numbers with whole number powers. [SR]
PE/TE: 430 (#46–50), 443–444, 446 (#4–5, 10), 447 (#37–39, 65–68), 462 (#1–2), 463 (#5),
465 (#3, 11–12, 25), 474 (# 1, 3), 477, 480 (#16–27, 32, 34), 483 (#2), 486 (#22–28),
488 (#1–10), 492 (#44, 46), 493 (#28, 30), 517 (#96, 99), 573 (65–70), 676 (#66–71),
790 (#55–58)
• Solve problems using rational numbers with square roots of perfect squares (e.g., given a square
garden with an area of nine square meters, how much fence would be needed to encompass a
garden twice the size of the original garden). [SR]
503 (#84–85), 507 (#9), 508 (#15–17), 509 (#61–66), 709 (#60, 62–64)
1.1.7 Understand and apply strategies and tools to complete tasks involving computation
on rational numbers.
PE/TE: 3–8, 9–14, 15–21, 25, 27 (#34–48), 39 (#4, 6–9), 83 (#74–79), 98 (#63–68), 100–105,
156 (#67), 338, 374, 452 (#11–14, 29–31, 34), 453 (#41, 43–44, 46),
483 (Example 3b, #4), 508 (#23, 25, 27, 30), 510 (#67–68), 528, 530 (#47–50, 52),
722–723, 791 (#2, 4)
• Select and justify appropriate strategies and tools (e.g., mental computation, estimation,
calculators, and paper and pencil) to compute in a problem situation. [SP, RL]
14 (#88–93), 25 (#1–4), 27 (#34–48), 29 (#60), 39 (#4, 6–8), 40 (#11, 16),
82 (#50–53), 83 (#74–79), 102 (#11), 103 (#11–12), 104 (#55–66), 118 (#56–61),
134 (#7–8), 156 (#67), 167 (#37–42), 214 (#49–51), 250–251, 338, 341 (#59–60),
374, 400 (#32–33), 451 (Example 4, #8–10), 452 (# 11–14), 453 (#41–48), 480 (#35),
483 (Example 3b, #4), 501 (#15–18), 503 (#75–83), 509 (#50–55), 510 (#67–68),
528, 530 (#47–50, 52), 573 (#65–70), 643 (#35), 645, 722–723
• Describe strategies for mentally solving problems involving integers and exponents. [CU]
14 (#88–93), 25, 27 (#34–48), 28 (#50, 57), 29 (#60), 34 (#32–35), 35 (#10), 39 (#9),
40 (#14, 19), 41 (#33), 57 (#28–33), 70 (# 66–71), 72 (#5–7), 83 (#74–79),
98 (#63–68), 103 (#11–12), 104 (#55–66), 118 (#56–61), 155 (#43–46), 456 (#67)
• Use calculators to compute with whole number powers beyond the cubed numbers.
12 (#5, 7–9, 15, 21, 23–25, 27, 30–31), 13 (#34–39, 44, 47, 51), 451,
452 (#11–14, 29–31, 34), 453 (# 41, 43–44, 46)
6
• Use calculators to compute square roots of perfect squares greater than 100.
502 (#16, 19, 21, 25, 27–28, 31, 33–36, 39–40), 503 (# 56, 58, 62, 64),
508 (#23, 25, 27, 30), 791 (#2, 4)
Estimation
1.1.8 Apply estimation strategies to predict or determine the reasonableness of answers in
situations involving computation on rational numbers in any form including whole number
powers and square roots of square numbers. W
PE/TE: 14 (#88–93), 163–165, 166 (#7–35), 167, 170, 173 (Examples 4 and 5), 197 (#54–59),
251, 298–304, 390–393, 395, 431, 453 (#41–48), 458 (# 23–30), 458 (#23–30), 483,
500 (Example 3, #10–12), 503 (#53–64), 507 (Example 5), 508 (#15–17), 526–527,
530 (#22–33), 532, 774–776
• Identify when an approximation is appropriate. [MC]
163–165, 166 (#7–35), 167, 169 (#16–21), 170, 173 (Examples 4 and 5),
175 (#19, 21), 180 (#9–10), 182 (# 52–54), 197 (#54–59), 447 (#61–62),
451 (Example 4, #8–10), 453 (#41–48), 458 (# 23–30), 460 (#13),
477 (Example 2, #2), 479 (#5), 480 (#34–35), 500 (Example 3, #10–12), 503 (#53,
55–56, 58, 60–61, 63), 507 (Example 5), 508 (#15–17), 509 (#50–55, 60), 528
• Explain situations involving rational numbers where estimates are sufficient and others for
which exact value is required. [CU]
14 (#88–93), 25 (#1–4), 27 (#34–48), 46 (#11, 16), 179 (#6), 180 (#11),
244 (Examples 3 and 4), 453 (#63–64), 483, 500 (Example 3, #10–12), 503 (#53–64),
526–527, 528 (Example 3), 530 (#22–33), 637 (#36–37), 791 (#1, 5–6, 8)
• Justify why an estimate would be used rather than an exact answer in a given situation. [CU]
179 (#6), 180 (#11), 453 (#63–64), 483, 500 (Example 3, #10–12), 503 (#53–64),
507 (Example 5), 508 (#15–17), 526–527, 557 (#32–33), 637 (#36–37),
791 (#1, 5–6, 8)
• Describe various strategies used during estimation involving integers. [CU]
46, 180 (#11), 244, 321, 392–393, 395, 431, 453 (#63–64), 483, 530 (#22–33),
774–776
7
• Use estimation to predict or to verify the reasonableness of calculated results. [RL]
14 (#88–93), 390–391, 392 (#5–15), 393 (# 16–24), 395, 431, 483, 526–527,
530 (#22–33), 776 (#1–48)
Component 1.2: Understand and apply concepts and procedures from measurement.
Attributes, units, and systems
1.2.1 Analyze how a change in a linear dimension affects volume and surface area of
rectangular prisms and right cylinders. W
PE/TE: 772–773; More extensive coverage of this standard can be found in Geometry: Concepts
and Skills.
• Compare the impact that a change in one dimension has on volume and surface area in right
cylinders and rectangular prisms. [SP, RL]
PE/TE: 773 (#15–17); More extensive coverage of this standard can be found in Geometry:
Concepts and Skills.
• Describe the relationships among linear dimensions, volume, and surface area (e.g., changing the
length of a side affects the surface area and volume). [CU]
Opportunities to address this standard can be found in Geometry: Concepts and Skills
• Solve problems involving the effects of changes in one dimension on area (e.g., given a box with
certain dimensions, make the volume of the box y cubic units by changing only one dimension
of the box). [SP]
177, 179 (Example 5)
1.2.2. Understand and apply derived units of measurement. W
PE/TE: 173 (Example 5), 177–182, 192, 298–304, 477–481, 482–487
• Explain the concept of a rate. [CU]
PE/TE: 173 (Example 5), 177, 178 (Example 3), 179 (Example 5), 180 (#9–10, 22–27),
181 (#28, 38–40), 188 (# 4–5), 192 (#26), 197 (#62), 785 (#37–41)
8
• Explain how division of measurements produces a derived unit of measurement (e.g., miles
traveled divided by hours traveled yields the derived unit [miles per hour]). [CU]
173 (Example 5), 177 (Example 2, #2–3), 178 (Example 3), 180 (#9–10, 22–27),
181 (#28, 38–40), 188 (# 4–5), 192 (#26), 197 (#62), 785 (#37–41)
• Find a rate of change in a situation (e.g., increase per year in stamp cost) and label the results.
[SP, RL, MC]
477, 480 (#16–27, 32, 34), 481 (#42), 486 (#22–28, 30, 39), 487 (#55)
• Use unit analysis to find equivalent rates (e.g., miles per hour to feet per second). [MC]
PE/TE: 178 (Example 3, #4–5), 179 (#7), 180 (#9–10, 22–27), 181 (#28, 31–40, 42–43),
192 (Example, #26), 193 (#33), 197 (#62)
• Use rate to determine a measured outcome.
PE/TE: 177 (#2–3), 178 (#6), 179 (#6–7), 180 (#9–10, 22–27), 181 (#28, 38), 192 (#26),
197 (#62), 241 (#48), 383 (#38–41), 785 (#37–41), 790 (#55–58)
1.2.3 Understand why different situations require different levels of precision. W
PE/TE: 14 (#88–93), 163–165, 166 (#7–35), 167, 170, 173 (Examples 4 and 5),
197 (#54–59), 251, 298–304, 390–393, 395, 431, 453 (#41–48), 458 (# 23–30),
458 (#23–30), 483, 500 (Example 3, #10–12), 503 (#53–64), 507 (Example 5),
508 (#15–17), 526–527, 530 (#22–33), 532, 774–776
• Explain the relationships among units within both the customary and metric system (e.g.,
kilograms to grams, feet to inches).
PE/TE: 178 (Example 4, #4), 181 (#31–37), 304 (#40–42)
• Justify the use of a unit of measure (e.g., measuring to order fencing requires a different
precision than if one is selling land and needs to be precise about borders). [CU, MC]
5 (Example 5), 7 (#46), 11 (Example 5, #10), 13 (#52, 59), 37 (#1), 177 (#2),
178–179, 180 (#9–11, 22–27), 181 (#28–31, 38–42)
9
• Compare situations for the level of precision needed. [RL]
5 (Example 5), 7 (#40–46), 11 (Example 5, #10), 13 (#52–54, 58–60),
37 (Example 2, #1), 117 (Example), 173, 175 (#21, 23), 181 (#42–43)
• Explain and give examples of situations that require more and less precision. [CU]
PE/TE: 5 (Example 5), 6 (#16), 7 (#40–46), 11 (Example 5, #10), 13 (#52–54, 58–60),
37 (Example 2, #1), 47 (#23–25), 127 (Example 1, #1–4), 148 (#45–46), 173,
174 (#10, 13–14), 175 (#15–17, 19), 176 (#25), 178 (Example 3), 181 (#38–39),
437 (#1–4)
Procedures, precision, and estimations
1.2.5 Understand and apply formulas including the Pythagorean Theorem to right prisms,
right cylinders, and triangles. W
11, 722–723, 724–729, 730–734, 773
• Explain how to use a formula for finding the surface area and volume of a solid. [CU]
Opportunities to address this standard can be found in Geometry: Concepts and Skills.
• Find missing sides or area of right triangles (e.g., use the Pythagorean Theorem to find any of
the missing values).
PE/TE: 722–723, 724–725, 727 (#3–11, 13–30), 728 (#31–35), 749 (#29–31), 752 (#8)
• Calculate measures of objects for which no direct information is given (e.g., apply ratio,
proportion, and scale to determine the area, surface area, and/or volume of a similar figure or
solid). [SP, MC]
• Compare surface areas of shapes with given volumes (e.g., compare cost of material to make
various right cylinder and right prism containers with a given volume). [RL, MC]
10
1.2.6 Apply strategies to obtain reasonable estimates of volume and surface area
measurements for right cylinders, right prisms, and of the lengths of sides of right triangles.
W
• Estimate volume and surface area for right cylinders and right prisms.
• Estimate the length of the remaining side of a right triangle given the lengths of two sides.
724–725, 727 (#3–11, 13–30), 728 (#31–35), 749 (#29–31), 752 (#8)
• Approximate distance or height in a problem situation using similar triangles or Pythagorean
relationships (e.g., height of a flagpole using proportional reasoning, distance across a lake using
Pythagorean relationship). [SP]
PE/TE: 5 (Example 5), 7 (#46), 728 (#31, 35), 729 (#10)
• Use or describe a process for finding area of a right triangle.
Component 1.3: Understand and apply concepts and procedures from geometric sense.
Properties and relationships
1.3.1 Apply understanding of characteristics and relationships among one–dimensional,
two–dimensional, and three–dimensional figures to solve problems. W
PE/TE: 7 (#46), 11 (Example 5, #10), 12 (#19), 13 (#52–54, 58–60), 14 (#63),
37 (Example 2, #1), 105 (#73), 722–723, 724–729, 730–734, 773; More extensive
coverage of this standard can be found in Geometry: Concepts and Skills
• Identify and label rays, lines, end points, line segments, vertices, and angles. [CU]
• Match or draw three–dimensional objects from different perspectives using the same properties
and relationships (e.g., match to the correct net, draw the top view). [RL]
11
• Draw and label with names and symbols, nets of prisms, and cylinders. [RL, CU]
• Describe everyday objects in terms of their geometric characteristics. [CU]
PE/TE: 7 (#46), 11 (Example 5, #10), 12 (#19), 13 (#52–54, 58–60), 14 (#63),
37 (Example 2, #1), 105 (#73), 579 (#56–57)
• Identify the two–dimensional components of three–dimensional figures.
11 (Example 5), 13 (#53–54, 58–60), 14 (#63)
1.3.2 Apply understanding of similarity to two–dimensional figures. W
• Use properties of similarity to draw, describe, and compare two–dimensional figures.
• Find the length of a missing side or the measure of a missing angle of one of the figures, given
two similar figures. [SP, RL]
• Create symmetrical, congruent, or similar figures using a variety of tools (e.g., ruler, pattern
blocks, geoboards). [RL, CU]
• Draw a similar shape to a given shape. [RL, CU, MC]
• Use properties of circles, cylinders, and figures with rotational symmetry to compare figures.
[RL, CU]
• Create a scale drawing and label the scale and the dimensions. (SP, CU, MC).
12
Locations and transformations
1.3.3 Understand and apply procedures to find distance between points in
two–dimensional representations. W
PE/TE: 203–204, 206 (#4–26), 230–232, 233 (#4–21), 263 (#1–8, 17–20), 722–725,
727 (#3–11, 13–30), 728 (#31–35), 729 (#10), 730–732, 734
• Locate a missing vertex given the coordinates of the vertices of a regular polygon. [RL]
PE/TE: 731, 733 (#5, 6, 25, 28, 29)
• Apply the Pythagorean Theorem to find the length of a side of a right triangle or distance
between two points.
PE/TE: 722–725, 727 (#3–11, 13–30), 751 (#24–29), 794 (#37–42)
• Explain a method for finding the missing side of a triangle in a real–world setting (e.g., the
height of a totem pole or building). [CU]
728 (#31–35), 729 (#10)
• Describe the relationship of any two or more points on a coordinate grid. [CU]
PE/TE: 203–204, 206 (#4–26), 208 (#36–38), 211 (Example 3), 212 (Example 4),
213 (#13–15), 216 (Example 1), 217 (Examples 2 and 3), 221 (#1–8),
223 (Example 3), 224 (Example 4), 225 (#33–35), 230–232, 233 (#4–21),
234 (#23–28) 241 (#7–12) 263 (#1–8, 17–20), 733 (#5–8, 25–30)
• Find the distance between two points on a coordinate grid including lines that are non–parallel
with either axis (oblique). [RL, MC]
PE/TE: 730–732, 733 (#9–24), 734, 751 (#33), 754 (#34–50)
1.3.4 Understand and apply transformations to figures. W
• Identify and explain how a shape has been translated, reflected, or rotated with or without a grid
(e.g., location of the North Star, rotate the Big Dipper). [CU]
13
• Use transformations (rotations, reflections, and translations) to draw or locate congruent
two–dimensional figures. [RL, CU]
• Find the image of a given shape after a combination of transformations. [RL]
• Tessellate a plane by using transformations. [RL, MC]
• Create a design using a combination of two or more transformations with one or two
two–dimensional figures. [SP, RL]
.
Component 1.4: Understand and apply concepts and procedures from probability and
statistics.
Probability
1.4.1 Understand the concept of compound events. W
PE/TE: 808–810; More extensive coverage of this standard can be found in Data Analysis
Sourcebook on the following pages: 15–21
• Determine and explain when events are compound. [CU]
This standard is taught in Data Analysis Sourcebook on the following pages: 15–21
• Explain the difference between compound events involving ‘and’ and ‘or’ (e.g., rolling a six and
rolling an odd number vs. rolling a six or rolling an odd number). [CU]
14
1.4.2 Understand and apply the procedures for comparing theoretical probability and
empirical results for independent or compound events. W
Sourcebook on the following pages: 2–7, 15–16, 19–21
• Calculate the probability of two independent events occurring simultaneously using various
methods (e.g., organized list, tree diagram, counting procedures, and area model).
This standard is taught in Data Analysis Sourcebook on the following pages: 2–7, 15–16, 19–21
• Explain the relationship between theoretical and empirical probability of compound events. [CU]
This standard is taught in Data Analysis Sourcebook on the following pages: 9–10, 13
• Predict the probability of outcomes of experiments and compare the predictions to empirical
results. [RL]
PE/TE: 808, 811 (#17–19); More extensive coverage can be found in Data Analysis
Sourcebook on the following pages: 9–10, 13
• Design or create a situation that would produce a given probability (e.g., how many of each
colored marble would it take to have a given probability of selecting one particular color). [SP,
MC]
This standard is taught in Data Analysis Sourcebook on the following pages: 8, 10, 12–13
• Design a game using compound probabilities with equal chances of winning for all players. [SP,
MC]
This standard is taught in Data Analysis Sourcebook on the following pages: 10, 19–21
Statistics
1.4.3 Analyze how different samples of a population affect the data. W
• Identify sources of sampling bias given a situation (e.g., interviewing only girls, only a certain
age group, or too few people). [CU, MC]
15
• Describe a procedure for selecting an unbiased sample. [CU, MC]
• Compare the results of a survey given two different sample groups. [RL, CU]
• Identify the appropriate population for a given research question.
• Describe how sampling may have affected the resulting data. [CU]
1.4.4 Analyze variations in data to determine the effect on the measures of central tendency.
W
• Identify clusters and outliers and determine how clusters or outliers may affect measures of
central tendency. [RL]
This standard is taught in Data Analysis Sourcebook on the following pages: 64–68, 69–72
• Alter a set of data so that the median is a more reasonable measure than the mean. [RL, CU,
MC]
• Use and interpret the most appropriate measure of central tendency and the range to describe a
given set of data (e.g., the model hourly wage earned by eighth graders is $5.75 per hour and the
range is $5.00 to $6.50; therefore, there are very small differences in hourly wages for eighth
graders). [RL, CU, MC]
16
1.4.5 Understand and apply data techniques to interpret bivariate data. W
PE/TE: 43–47, 813–816; More extensive coverage of this standard can be found in Data
Analysis Sourcebook on the following pages: 37 (#17–18), 40–51, 86–89, 91–97,
100–101
• Interpret graphic and tabular representations of bivariate data.
PE/TE: 43–46, 47 (#21–22); More extensive coverage of this standard can be found in Data
Analysis Sourcebook on the following pages: 37 (#17–18), 40–51
• Use a line of best fit to predict a future value of a variable. [ RL]
• Use a line of best fit to interpolate between existing data values. [RL]
• Draw trend lines with or without technology and make predictions about real–world situations
(e.g., population trends, socio–economic trends). [CU, MC, RL]
This standard is taught in Data Analysis Sourcebook on the following pages: 87–89, 92–95,
96–101
• Examine data in a two–column table to interpolate or extrapolate additional values. [RL]
100–101
• Use observations about differences between two or more samples to make conjectures about the
populations from which the samples were taken (e.g., age groups, regions of the U.S., genders,
racial/ethnic distributions). [RL, MC, CU]
100–101
17
1.4.6 Evaluate how statistics and graphic displays can be used to support different points
of view. W
PE/TE: 42–47, 813–816; More extensive coverage of this standard can be found in Data
Analysis Sourcebook on the following pages: 29–32, 36–37, 40–51, 63 (#18)
68 (#20), 87–89, 95
• Critique the use of data and data displays for bivariate data. [RL]
PE/TE: 43; More extensive coverage of this standard can be found in Data Analysis
• Judge the reasonableness of conclusions drawn from a set of data and support that position with
evidence (e.g., from newspapers, web sites, opinion polls). [MC, RL]
This standard is taught in Data Analysis Sourcebook on the following pages: 36–37, 63 (#18),
68 (#20), 87
• Determine whether a prediction is reasonable based on a trend line and explain the rationale. [RL]
• Determine whether claims made about results are based on biased representations of data (e.g.,
whether a scale has been intentionally used to support a point of view).
Component 1.5: Understand and apply concepts and procedures from algebraic sense.
Patterns, functions, and other relations
1.5.1 Apply understanding of linear and non–linear relationships to analyze patterns,
sequences, and situations. W
PE/TE: 1, 22 (#2, 3), 50 (#1–2), 51 (#4–5, 13–14) 52 (#20–21), 134, 209, 211–212,
213 (#13–15), 214 (#40–48, 51–52), 227 (#52–54), 250–251, 395,
459 (#31–41, 53–54), 461, 528, 532, 645
• Extend, represent, or create linear and non–linear patterns and sequences using tables and graphs.
[RL]
1, 22 (#2, 3), 49 (Example 2) 51 (#4–5, 13–14), 52 (#20–21),
211 (Examples 2 and 3), 212 (Example 4, #5–7), 213 (#10–15), 242 (#3),
255 (#7–8, 13, 16–17), 455–456, 483 (Example 3, #2–3), 486 (#39–40),
478 (Examples 4 and 5), 518 (#1–2)
18
• Explain the difference between linear and non–linear relationships. [CU]
134, 209, 211–212, 213 (#13–15), 214 (#40–48), 216–217, 219 (#8–9, 24–29), 456,
457 (#3–4, Example 5), 458 (#2–6), 459 (#31–41, 53–54), 461
• Predict an outcome given a linear relationship (e.g., from a graph of profit projections, predict the
profit). [RL]
49 (Example 2), 50 (#1–2), 51 (#4–5, 13–14) 52 (#20–21), 214 (#51–52),
215 (#55–56), 226 (Example, #48–51), 227 (#52–54), 244 (#4), 282 (#45), 299
• Use technology to generate linear and non–linear relationship. [SP, RL]
PE/TE: 250–251, 395, 461, 524 (Example, #45), 525 (#48), 528, 530 (#51–52), 532,
544 (#47–49), 645
1.5.2 Analyze a pattern, table, graph, or situation to develop a rule. W
49, 51 (#1–3), 210–211, 212 (Summary), 214 (#49–53), 215 (#54–56), 228, 229–231,
232 (#7–9), 238 (Summary), 239 (#3–11, 16–26), 455 (#1), 457 (#3–4), 459 (#34–41),
• Use technology to help develop a table or graph from an iterative definition (e.g., the number of
cells doubles every hour starting with one cell at noon). [CU, MC]
455 (#1), 456, 457 (#3–4), 458 (#2–4), 459 (#34–41)
• Explain the nature of changes in quantities in linear relationships using graphs, tables, or
expressions. [CU, MC]
214 (#49–53), 215 (#54–56), 227 (#73), 228, 229–231, 232 (#7–9), 233 (#4–9, 22),
234 (#29–34), 236, 237 (Example 2), 239 (#3–11, 16–26), 240 (#36, 39)
• Develop recursive equations that describe linear relations in terms of current and previous values
(e.g., start = 7; Current = Previous + 5 would give a set of values (1,7),(2,12),(3,17) …).
Opportunities to address this standard can be found in McDougal Littell Algebra 2.
19
• Use words or algebraic symbols to describe a rule for a linear relationship between two sets of
numbers (e.g., given a table, describe a rule). [CU]
PE/TE: 49, 51 (#1–3), 210–211, 212 (Summary), 216 (Example 1), 217 (Example 2),
218 (Summary), 229–230, 231 (Examples 3 and 4), 232 (Example 5, Summary), 236,
238 (Summary)
Symbols and representations
1.5.3 Understand relationships between quantities including whole number exponents,
square roots, and absolute value. W
PE/TE: 9–14, 35 (#47–54), 47 (#35–43), 61, 65–70, 71–76, 359 (#48–49), 365 (#42–46),
455–456, 461, 475 (#78–83), 502 (#25–40), 691–694, 703 (#79–96), 770 (#1–21)
• Represent relationships between quantities using exponents (squares) and radicals (roots). [CU]
PE/TE: 11 (Example 5, #10), 14 (#63), 455–456, 457 (Example 5), 458 (#2–4), 459 (#31–41),
461, 691, 692–694
• Explain the placement of numbers including square roots and exponents on a number line. [CU]
• Model or describe a real–life situation using absolute value (e.g., the taxi–cab distance from one
point to another can be represented by the sum of two absolute values). [CU, MC]
PE/TE: 73, 75 (#41–42), 357 (Example 5), 359 (#48–49), 363 (Example 5, #8), 365 (#42–46)
• Use relational symbols to express relationships between rational numbers including percents,
square roots, absolute value, and exponents. [CU]
PE/TE: 35 (#47–54), 47 (#35–43), 68 (#23–30), 72 (#1–4), 74 (#25–32), 106 (#94–101),
118 (#71–78), 304 (#50–58), 319 (#5–13), 475 (#78–83), 500 (#5–12), 502 (#25–40),
703 (#79–96), 770 (#1–21)
20
1.5.4 Apply understanding of concepts of algebra to represent situations involving
single–variable relationships. W
PE/TE: 3, 6 (#17–20), 32 (Example 6, #7, 8), 33, 34 (#24–31), 36–38, 40 (#18, 21), 48–53,
137 (#60, 62–63, 65–68), 161 (#40–41, 43), 205, 207, 214 (#49–53), 211–212,
214 (#50, 52), 215 (#54–55), 220 (#33–34), 226 (#36–38), 240 (#31–33), 299–300,
301 (#3–11), 302–303, 323, 325 (Example 4, #11–12), 326 (#23–28), 327 (#56–60),
455–457, 459 (#31–33, 50–51, 53–54), 475, 483–484
• Represent variable quantities, through expressions, linear equations, inequalities, tables, and
graphs of situations. [CU]
PE/TE: 6 (#17–20), 30–33, 34 (#24–31), 48–53, 54 (#4–6), 159, 161 (#41–43), 162 (#50–51),
168 (#50–52), 181 (#38), 207 (#33), 211–212, 214 (#50, 52), 215 (#54–55),
257 (#55, 57–58), 323, 326 (#23–28)
• Write an expression, equation, or inequality with a single variable representing a situation or
real–world problem. [SP, RL, MC]
PE/TE: 32 (Example 6, #7, 8), 34 (#37), 36–38, 40 (#18, 21), 41 (#22),
134 (Example 3, #8–9), 135 (#16), 136 (#58–59), 137 (#60, 62–63, 65–68),
140 (Example 4, #9), 142 (#48–50), 143 (#53, 69), 145 (Example 2, #4), 149 (#7–8),
154 (#15), 159 (Example 4, #5), 161 (#40–41, 43), 325 (Example 4, #11–12),
327 (#56–60), 334 (#54–55), 338 (Example 5), 340 (#47), 341 (#59–60, Quiz 1 #10)
• Identify and use variables to read and write relationships involving rational numbers.
PE/TE: 3, 6 (#17–20), 30–34, 35 (Quiz 1 #11–14), 57 (#34–37), 59 (#10–15), 783 (#28–29)
• Model a given description or situation involving relationships with a graph or table. [CU, MC]
PE/TE: 48–53, 205, 207, 214 (#49–53), 215 (#54–55), 238, 239 (#36–37),
244 (Example 3, #4), 248 (#59–60), 249 (#79), 257 (#54–58), 299–300, 301 (#3–11),
302–303, 455–457, 458 (#2, 15–22), 459
• Describe a situation involving relationships that matches a given graph. [CU, MC]
PE/TE: 53 (#29), 215 (#59), 217 (#7–8), 219 (#8–9), 220 (#33–34), 226 (#36–38),
240 (#31–33), 247 (#43–45), 256 (#31–36), 459 (#31–33, 53–54), 487 (#42–43, 56),
494 (#5)
• Create a table or graph given a description of, or an expression for, a situation involving a linear
or non–linear relationship. [CU, MC]
PE/TE: 207, 214 (#49–53), 215 (#54–55), 238, 239 (#36–37), 244 (Example 3, #4),
248 (#59–60), 249 (#79), 257 (#54–58), 299–300, 301 (#3–11), 302–303, 455–457,
458 (#2, 15–22), 459, 475, 483–484
21
Evaluating and solving
1.5.5 Understand and apply the procedures for simplifying single–variable expressions. W
PE/TE: 4–5, 100–106, 107–112, 124, 145-149, 511–517, 763
• Simplify expressions and evaluate formulas involving integers. [RL, MC]
PE/TE: 6 (#16), 7, 11 (#10), 13 (#52–59), 14 (#63–66), 21 (#10–12), 29 (#68–82),
47 (#23–25), 55 (#7–11), 100 (#1–2), 101 (#3–6), 104 (#17–52), 112 (#56–58),
117 (#43–48), 118 (#4–9, 16–18), 123 (#36–44), 124 (#45–50), 125 (#25–28, 30–37),
127 (#1–4), 137 (#69–74), 143 (#57–62), 196 (#32–39), 215 (#64–69), 382 (#16–23),
401 (#38–41), 784 (#38–51)
• Match expressions to equivalent simplified expressions. [MC]
PE/TE: 21 (#13–18), 100 (#2), 101 (#3–6), 102 (#7–10), 103, 105 (#74–76),
110 (#9–14, 30–38), 111 (#45–46, 48–49, 51)
• Explain a simplification of an expression involving integers. [CU]
8 (#55–57), 19 (#36–41), 29 (#68–73), 56 (#12–14), 108–109, 110 (#39–40),
382 (#16–23)
• Simplify expressions by combining like terms.
PE/TE: 107–109, 110 (#3–14, 21–38), 111 (#41–44, 46, 49, 51), 118 (#4–9), 124 (#45–50),
125 (#34–37), 143 (#58–62), 162 (#58–63), 196 (#34, 39), 215 (#64–69),
382 (#21–23), 401 (#38–41), 784 (#46–51)
• Simplify expressions using mathematical properties (distributive, commutative, associative,
etc.). [RL]
PE/TE: 100 (#1–2), 101 (#3–6), 102 (#7–10), 103, 104 (#17–52), 108 (#6–8), 109 (#9),
110 (#9–14, 30–40), 111 (#41–44, 46, 49, 51), 118 (#7–9, 16–18), 123 (#36–44),
125 (#30–33, 35–37), 126 (#12), 137 (#69–74), 143 (#60–62), 196 (#32–39),
382 (#16–23), 401 (#38–41), 573 (#58–63), 784 (#38–45)
• Determine the expression that represents a given situation. [MC, CU]
PE/TE: 103 (#13–16), 105 (#71–73, 77), 109, 111, 197 (#42)
• Describe a situation that fits with a given expression. [RL, MC, CU]
6 (#21–32), 18 (#28–30, 33–35), 104 (#17–52)
22
1.5.6 Understand and apply a variety of strategies to solve multi–step equations and
one–step inequalities with one variable. W
PE/TE: 144–149, 151–156, 157–162, 163–169, 323–328, 329, 330–335
• Solve multi–step equations and one–step inequalities with one variable.
PE/TE: 144 (#1–3), 145 (#4), 146 (#5–10), 147 (#7–39), 148, 149 (#1–6, 9–14), 150,
152 (#1–5), 154 (#9–15, 21–34), 155 (#47–48), 156 (#50–56), 158 (#1–4), 160–161,
163–165, 166 (#15–35), 167, 168 (#44, 47, 49), 169 (#5–22), 170, 215 (#70–73),
235 (#45–47), 241 (#40–45), 249 (#70–78), 324 (#5–7), 325 (#8–10), 328 (#65–73),
331 (#1–4), 335 (#74–77), 347 (#59–66), 353 (#58–63), 382 (#24–35), 394 (#32–37),
454 (#78–83), 481 (#48–51), 488 (#61–64), 785 (#1–35)
• Solve single variable equations involving parentheses, like terms, or variables on both sides of
the equal sign.
PE/TE: 147 (#7–39), 148 (#47–54), 150 (#1–7), 152 (#1–5), 153 (#6–9), 154 (#21–34),
158 (#1–4), 160 (#11–36), 161 (#44–49), 163 (#1–3), 164 (#4–7), 166 (#20–35),
335 (#74–77), 353 (#62–63), 382 (#31–35), 394 (#35–37), 481 (#48–51),
488 (#61–64), 785 (#19–35)
• Solve one–step inequalities (e.g., 2x<6, x+4>10).
PE/TE: 327 (#41–55), 331–332, 333 (#15–22), 334 (#35–46, 54–58), 353 (#64–72),
539 (#92–94), 788 (#1–8)
• Solve real–world situations involving single variable equations and proportional relationships
and verify that the solution is reasonable for the problem. [SP, RL, CU]
PE/TE: 145 (#4), 148 (#44–45), 149 (#7–8, 15), 155 (#47–49), 159 (#5), 161 (#40–43),
165 (#8), 167 (#36–38), 347 (#68–69), 383 (#70–74), 448 (#86–87), 481 (#52)
23
EALR 2: The student uses mathematics to define and solve problems.
Component 2.1: Understand problems.
Example: The following information was provided to a group of students. They were asked to
interpret this information for someone that has a speed of 19 feet per second and also for
someone who takes 5 steps per second. How would you answer these questions?
Speed (ft/s)
Steps per second
15.86
3.05
16.88
3.12
17.50
3.17
18.62
3.25
19.97
3.36
21.06
3.46
22.11
3.55
2.1.1 Analyze a situation to define a problem. W
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
• Use strategies to become informed about the situation (e.g., listing information, asking
questions).
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
• Summarize the problem (e.g., we have information about the relationship between the number of
steps per second and the speed in feet per second; we wish to find approximate speed or stride
rates).
PE/TE: 36–40, 198–199, 384–385, 782 (#1–9)
• Determine whether enough information is given to find a solution (e.g., list what is needed to
find the relationship between stride rate and speed; list known and unknown information).
PE/TE: 36–40, 198–199, 384–385, 782 (#1–9)
• Determine whether information is missing or extraneous (e.g., compare the list of known things
to the list of needed things to see if there are things that are not needed ? names, location).
PE/TE: 36–40, 198–199, 384–385, 782 (#1–9)
• Define the problem (e.g., find the relationship between the steps per second and speed).
PE/TE: 36–40, 198–199, 384–385, 782 (#1–9)
24
Component 2.2: Apply strategies to construct solutions.
2.2.1 Apply strategies, concepts, and procedures to devise a plan to solve the problem. W
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
• Organize relevant information from multiple sources.
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
• Select and apply appropriate mathematical tools for a situation (e.g., plot steps per second vs.
speed; check to see if model is linear; calculate successive differences or quotients to see if a
pattern emerges; find an equation for a line that approximates the relationship or extend the
pattern to approximate the speed at 5 steps per second).
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
2.2.2 Apply mathematical tools to solve the problem. W
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
• Implement the plan devised to solve the problem or answer the question posed (e.g., in a table of
values of lengths, widths, and areas find the one that shows the largest area; check smaller
increments to see if this is the largest that works).
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
• Identify when an approach is unproductive and modify or try a new approach (e.g., if an additive
model didn’t work, try a multiplicative model).
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
• Check the solution to see if it works (e.g., if the solution for a speed of 19 feet per second is 5
steps per second, perhaps the assumption of linearity was incorrect).
PE/TE: 36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
25
EALR 3: The student uses mathematical reasoning.
Component 3.1: Analyze information.
3.1.1 Analyze information from a variety of sources to interpret and compare information.
W
PE/TE: 50 (#1–2), 52 (#20–23), 299 (Example 2, #2, 3), 301 (#11), 302 (#15, 17, 22–23),
303 (#33–34), 809; Additional coverage of this standard can be found in Data
Analysis Sourcebook on the following pages: 9–10, 13
• Predict the probability of outcomes of experiments and compare the predication to empirical
results. [1.4.2]
PE/TE: 809; Additional coverage of this standard can be found in Data Analysis Sourcebook
on the following pages: 9–10, 13
• Predict an outcome given a linear relationship and a particular input (e.g., from a graph of profit
projections, predict the profit in 2005). [1.5.1]
50 (#1–2), 52 (#20–23), 53 (#24), 226 (#48–50), 227 (#52–53), 273 (#40–42),
274 (#53), 275 (#55), 282 (#45), 283 (#47–48), 299 (Example 2, #2, 3),
300 (Example 3), 301 (#11), 302 (#15, 17, 22–23), 303 (#33–34),
Component 3.2: Make predictions, inferences, conjectures, and draw conclusions.
3.2.1 Apply prediction and inference skills to make or evaluate conjectures. W
PE/TE: 198–199, 207, 384–385, 740–746
racial/ethnic distribution). [1.4.6]
PE/TE: 198–199, 207, 384–385
26
3.2.2 Apply the skill of drawing conclusions and support those conclusions using evidence.
W
PE/TE: 22, 77, 92, 99, 120, 198–199, 207, 209, 214, 242, 276–277, 329, 354, 384–385,
440–441, 475, 562–563, 594, 691, 715, 756–757
• Draw conclusions from displays, texts, or oral discussions and justify those conclusions with
logical reasoning or other evidence (e.g., read an editorial or ad, draw a conclusion and support
that conclusion with evidence in the article or elsewhere).
PE/TE: 120, 198–199, 207, 214, 384–385, 562–563, 756–757
3.2.3 Analyze procedures and results in various situations. W
PE/TE: 22, 77, 92, 99, 120, 198–199, 207, 209, 214, 242, 276–277, 329, 354, 384–385,
440–441, 475, 562–563, 594, 691, 715, 756–757
• Critique conclusions drawn from a set of data and support with evidence (e.g., from magazines,
newspapers, web sites, opinion polls). [1.4.6]
PE/TE: 198–199, 207, 214, 384–385, 562–563
Component 3.3: Verify results.
3.3.1 Analyze procedures and information used to justify results using evidence. W
PE/TE: 22, 77, 92, 99, 120, 198–199, 207, 209, 214, 242, 276–277, 329, 334 (#47–49), 354,
384–385, 440–441, 422 (#46, 48–49), 468 (#89–94), 475, 562–563, 594, 691, 715,
756–757, 774–776
• Use estimation to predict or to verify the reasonableness of calculated results. [1.1.8]
PE/TE: 14 (#88–93), 37 (#1), 38 (#2–3), 40 (#19–20), 83 (#74–79), 334 (#47–49), 390–391,
392 (#5–15), 393 (#16–24), 395, 422 (#46, 48–49), 431, 468 (#89–94), 483, 526–527,
530 (#22–33), 776
27
3.3.2 Analyze thinking and mathematical ideas using models, known facts, patterns,
relationships, or counter examples. W
PE/TE: 22, 77, 92, 99, 120, 198–199, 207, 209, 214, 242, 276–277, 329, 354, 384–385,
440–441, 475, 562–563, 594, 691, 715, 756–757
• Explain why a given rational number is greater than or less than another rational number. [1.1.2]
47 (#35–43), 66–67, 68 (#23–30), 69 (#55–59), 70 (#60–61), 112 (#73–81),
118 (#71–78), 149 (#67–74), 304 (#50–58), 319 (#5–13), 531 (#78–85),
539 (#96–101), 703 (#79–96), 739 (#45–48), 770–771
28
EALR 4: The student communicates knowledge and understanding in both everyday and
mathematical language.
Component 4.1: Gather information.
4.1.1 Apply a planning process to collect information for a given purpose. W
PE/TE: 119–120, 198–199, 384–385, 562–563, 740–746, 756–757, 803–807, 808–811;
Additional coverage of this standard can be found in Data Analysis Sourcebook on
the following pages: 28–34
• Describe a procedure for selecting an unbiased sample. [1.4.3]
4.1.2 Synthesize information from multiple sources using reading, listening, and
observation. W
PE/TE: 198–199, 384–385, 562–563, 756–757, 808–811; Additional coverage of this
standard can be found in Data Analysis Sourcebook on the following pages: 35–37
• Compare the results of a survey given two different sample groups. [1.4.3]
• Model the relationship with a table or graph given a description of, or an equation for, a situation
involving an inequality or linear relationship. [1.5.4]
PE/TE: 207, 214 (#49–53), 215 (#54–55), 238, 239 (#36–37), 244 (Example 3, #4),
248 (#59–60), 249 (#79), 257 (#54–58), 299–300, 301 (#3–11), 302–303, 455–457,
458 (#2, 15–22), 459, 475, 483–484
Component 4.2: Organize, represent, and share information.
4.2.1 Apply organizational skills for a given purpose. W
PE/TE: 19–120, 198–199, 384–385, 562–563, 740–746, 756–757, 803–807, 808–811;
the following pages: 10, 13
29
• Design and conduct a simulation, with and without technology, to determine the probability of an
event occurring. [1.4.2]
PE/TE: Opportunities to address this standard can be found on the following page:
811 (#17–19); More extensive coverage of this standard can be found in Data Analysis
Sourcebook on the following pages: 10, 13
4.2.2 Apply communication skills to clearly and effectively express or present ideas and
situations using mathematical language or notation. W
PE/TE: 14 (#88–93), 22–23, 25 (#1–4), 27 (#34–48), 46, 198–199, 299–300, 301 (#3–11),
302–303, 384–385, 392–393, 395, 431, 500 (Example 3, #10–12), 503 (#53–64),
562–563, 756–757, 774–776, 791 (#1, 5–6, 8)
• Articulate various strategies used during estimation involving integers. [1.1.8]
46, 180 (#11), 244, 321, 392–393, 395, 431, 453 (#63–64), 459, 483, 530 (#22–33),
562–563, 756–757, 774–776
• Clearly explain, describe, or represent mathematical information in a pictorial, tabular, graphical,
two– or three–dimensional drawing, or other form as appropriate for the mathematical
information (e.g., time, distance, categories), audience, and/or purpose, such as to perform or
persuade, with notation and labels as needed.
7 (#40–46), 13 (#58), 14 (#63–66), 22–23, 42–43, 47 (#21–25), 48–53, 198–199, 205,
207, 214 (#49–53), 215 (#54–55), 238, 239 (#36–37), 244 (Example 3, #4),
248 (#59–60), 249 (#79), 257 (#54–58), 299–300, 301 (#3–11), 302–303, 384–385,
455–457, 458 (#2, 15–22), 459, 562–563, 756–757
• Explain situations involving real numbers where estimates are sufficient and others for which
exact value is required. [1.1.8]
14 (#88–93), 25 (#1–4), 27 (#34–48), 179 (#6), 180 (#11), 453 (#63–64), 483,
500 (Example 3, #10–12), 503 (#53–64), 507 (Example 5), 508 (#15–17), 526–527,
557 (#32–33), 637 (#36–37), 791 (#1, 5–6, 8)
30
EALR 5: The student understands how mathematical ideas connect within mathematics, to
other subject areas, and to real–life situations.
Component 5.1: Relate concepts and procedures within mathematics.
5.1.1 Apply concepts and procedures from a variety of mathematical areas in a given
problem or situation. W
PE/TE: 177–179, 180 (#9–11, 20–27), 181, 631, 633–634, 637, 785 (#38–41)
• Solve problems involving ratio and proportion (e.g., similar figures, scale drawings, rates, find
unit pricing, increase or decrease a recipe, find the portions for a group converting between
different units of measure, or finding medicinal dosages). [1.1.4]
PE/TE: 177–179, 180 (#9–11, 20–27), 181, 182 (#44–47), 188 (#4–7), 192 (#26–27),
193 (#24–26, 33) 194 (#10), 241 (#48), 304 (#40–42), 366 (#53–54),
383 (#38–41), 631, 633–634, 635 (Example 5), 637, 638 (#40), 656 (#50),
682 (#26), 785 (#38–41)
• Find the area of a circle given the coordinates of the center and a point on the circle. [1.3.3]
5.1.2 Apply different mathematical models and representations to the same situation. W
27 (#34–48), 57 (#28–33), 135 (#7–15, 25–42), 141 (#6–14, 22–36), 147 (#7–39),
205, 214 (#54–55, 59), 226 (#36–38), 256 (#31–36), 459 (#31–33, 53–54),
508 (#9, 18–19, 25, 29–31, 33–34, 37–38, 40–41, 44–46, 48)
• Create a problem situation to match a given rational number equation. [1.1.5]
25 (#1–4), 27 (#34–48), 57 (#28–33), 134, 135 (#7–15, 25–42), 136 (#43–56),
137 (#65–68), 141 (#6–14, 22–36), 142 (#37–45), 147 (#7–39), 166 (#15–17),
508 (#9, 18–19, 25, 29–31, 33–34, 37–38, 40–41, 44–46, 48)
• Match a situation with a data set or graph. [1.5.4]
PE/TE: 53 (#29), 205, 207 (#33), 214 (#50, 52), 215 (#54–55, 59), 217 (#7–8), 219 (#8–9),
220 (#33–34), 226 (#36–38), 240 (#31–33), 247 (#43–45), 256 (#31–36),
459 (#31–33, 53–54), 487 (#42–43, 56), 494 (#5)
31
Component 5.2: Relate mathematical concepts and procedures to other disciplines.
5.2.1 Analyze mathematical patterns and ideas to extend mathematical thinking and
modeling to other disciplines. W
4, 13, 52, 102, 175, 400, 447, 722–723; More extensive coverage of this standard can
be found in Data Analysis Sourcebook on the following pages: 86–89, 93–95,
100–101
racial/ethnic distribution). [1.4.6]
PE/TE: This standard is taught in Data Analysis Sourcebook on the following pages: 86–89,
93–95, 100–101
• Check to see if a corner is square using the Pythagorean Theorem. [1.2.5]
PE/TE: 722–723
• Calculate the one repetition maximum for strength training of one muscle group.
• Monitor/track a diet and evaluate the relationship to physical performance (e.g., does it meet daily
nutritional requirements/energy for various populations and energy requirements based on
lifestyle, safe–work practices, and leisure activities).
5.2.2 Know the contributions of individuals and cultures to the development of
mathematics.
PE/TE: 311, 741
• Recognize the contributions of a variety of people to the development of mathematics (e.g.,
research the history of the Pythagorean Theorem).
PE/TE: 311, 741
32
Component 5.3: Relate mathematical concepts and procedures to real–world situations.
5.3.1 Understand that mathematics is used in daily life and extensively outside the
classroom.
PE/TE: 18 (#32–39), 25, 28 (#49, 57–58), 40 (#16–20), 111 (#48–52), 198–199, 214 (#49–51),
340 (#44–45), 384–385, 459 (#50), 526–527, 776 (#1–48)
• Use estimation to predict or to verify the reasonableness of calculated results. [1.1.8]
PE/TE: 14 (#88–93), 37 (#1), 38 (#2–3), 40 (#19–20), 83 (#74–79), 334 (#47–49), 390–391,
392 (#5–15), 393 (#16–24), 395, 422 (#46, 48–49), 431, 468 (#89–94), 483, 526–527,
530 (#22–33), 776
• Evaluate conclusions drawn from a set of data and support with evidence (e.g., from
newspapers, web sites, opinion polls). [1.4.6]
198–199, 207, 214, 384–385, 562–563; More extensive coverage of this standard can
be found in Data Analysis Sourcebook on the following pages: 33–37
• Analyze data from a newspaper article to see if the conclusions are reasonable.
This standard is taught in Data Analysis Sourcebook on the following page: 36
• Research how coding and decoding has played a part in history.
5.3.2 Understand that mathematics is used within many occupations or careers.
PE/TE: 26, 38, 187, 198–199, 207, 340, 384–385, 544, 562–563, 756–757
•Explain how mathematics is used in careers or occupations of interest (e.g., complete a
mathematically–based project).
PE/TE: 198–199, 384–385, 562–563, 756–757
33
Algebra 1: Concepts and Skills
correlated to the
GRADES 9/10
mathematics.
1.1.1 Understand and apply scientific notation. W
PE/TE: 9–13, 21 (#13–22), 29 (#68–73, 80–82), 443–446, 447 (#37–45, 52–60),
465 (#3–18, 25–32), 466 (#39–57), 467, 469–472, 473 (#47–69), 474 (#11–22),
491 (#21–42), 580 (#65–76), 593 (#54–61), 676 (#66–71), 790 (#1–54)
• Read and use scientific and exponential notation. [MC, RL]
PE/TE: 9–13, 21 (#13–22), 29 (#68–73, 80–82), 56 (#12–23), 59 (#1–7), 83 (#62),
91 (#66–67), 196 (#3, 5, 6), 441–442, 443–447, 448 (#69–72), 449–453,
454 (#68–70), 466 (39–46), 469–472, 474 (#11–22), 490 (#9–12), 491 (#29–42),
510 (#83–86), 573 (#65–70), 593 (#54–61), 676 (#66–71), 784 (32–34), 790 (#1–54)
• Identify a real–life situation to match a particular number written in scientific or exponential
notation and justify the answer. [MC, RL]
PE/TE: 453 (Example), 467, 471 (Example 5, #17), 473 (#62–69)
• Use scientific or exponential notation to simplify a problem. [RL, MC]
PE/TE: 443–446, 447 (#37–45, 52–60), 448 (#73), 453 (#51–62), 460 (#7–12), 462 (#1–4),
463 (#5–8), 464 (#9–11), 465 (#3–18, 25–32), 466 (#39–57),
470 (Example 2, #7–10), 472, 473 (#47–61), 474 (#1–10, 17–22), 481 (#53–58),
489 (#1–8), 491 (#21–24), 494, 517 (#96–103), 580 (#65–76), 587 (#60–63),
784 (#50), 790 (#1–8, 21–34)
• Illustrate the meaning of scientific notation using pictures, diagrams, or numbers. [CU]
PE/TE: 469 (Example 1), 470 (Example 2), 472 (#1)
• Read and translate numbers represented in scientific notation from calculators and other
technology, tables, and charts.
PE/TE: 471 (Example 4, #14–16), 473 (#56–61)
34
Washington Math GLEs, GRADES 9/10
1.1.4 Apply understanding of direct and inverse proportion to solve problems. W
PE/TE: 177–182, 183–188, 633–638, 639–644, 645, 681
• Explain a method for determining whether a real–world problem involves direct proportion or
inverse proportion. [SP, CU, MC]
PE/TE: 635 (Example 5), 637, 639, 640 (Example 3, #1–2), 643
• Explain a method for solving a real–world problem involving direct proportion. [CU, MC]
PE/TE: 635 (Example 5), 637, 640 (Example 3, #1–2)
• Explain a method for solving a real–world problem involving inverse proportion. [CU, MC]
PE/TE: 640 (Example 3, #1–2), 641, 643
• Solve problems using direct or inverse models (e.g., similarity, age of car vs. worth). [SP, MC]
PE/TE: 637, 642 (#12–26), 643, 644 (#40–42)
• Explain, illustrate, or describe examples of direct proportion. [CU]
PE/TE: 639, 642–643, 682 (#5–10), 685 (#5, 7), 793 (#7–10)
• Explain, illustrate, or describe examples of inverse proportion. [CU]
PE/TE: 640, 642–643, 682 (#11–16), 685 (#6, 8), 793 (#11–14)
• Use direct or inverse proportion to determine a number of objects or a measurement in a given
situation.
PE/TE: 636–637, 643
Computation
1.1.6 Apply strategies to compute fluently with rational numbers in all forms including
whole number exponents. W
PE/TE: 10, 13 (#40–51), 15 (#1–4), 16 (#5–7), 19 (#36–42, 47–48), 20, 29 (#74–82),
80 (#9–13), 82 (#41–53), 83 (#13–18, 62–67), 91 (#64–69, 78–83), 96 (#1–5, 17–31),
103, 104 (#17–52), 265 (9–14), 511 (#1–4), 512 (#5–8), 514 (#5–16, 21–44),
515 (#59–74), 517 (#106–113), 573 (#72–83), 608 (#69–76), 657 (#73–80),
677 (#84–95), 783 (#10–17)
35
• Complete multi–step computations using order of operations in situations involving
combinations of rational numbers including whole number exponents and square roots of
square numbers. [MC]
PE/TE: 10, 13 (#40–51), 15 (#1–4), 16 (#5–7), 17 (#8–9), 18 (#3–35), 19 (#36–41),
21 (#20–22), 29 (#79–82), 41 (#27–29), 54 (#38–46), 56 (#18–23), 61 (#1–12),
78–80, 81 (#6–35), 83 (#13–18, 62–67), 91 (#64–69, 78–83), 93, 99 (#1–3),
104 (#55–66), 106 (#8–13, 78–83), 112 (# 61–72), 113, 114 (#1–4), 116 (#31–38),
124 (#51–58), 125 (#12–15, 17–24, 39–42), 149 (#61–66), 156 (#68–73, 78–86),
162 (#54–57, 64–69), 208 (#58–66), 215 (#60–63), 227 (#57–72), 249 (#81–88),
265 (#9–14), 290 (#50–58), 312 (#59–70), 335 (#62–73), 353 (#73–81),
366 (#62–67), 394 (#45–50), 414 (#49–56), 468 (#89–94), 510 (#71–74),
517 (#106–113), 573 (#72–83), 580 (#90–98), 587 (#67–74), 601 (#70–77),
608 (#69–76), 644 (#62–69), 651 (#51–54, 67–72), 657 (#73–80), 677 (#84–95),
746 (#40–45), 783 (#10–17)
• Calculate using order of operations on all forms of rational numbers (e.g., (3•2+5)2–8, 22+
32).
PE/TE: 10, 11 (Example 4), 13 (#40–51), 15–18, 19 (#36–42, 47–48), 20, 29 (#74–82),
41 (#27–29, 74–79), 56 (#18–23), 83 (#62–67), 97 (#41–46), 99 (#1–3),
149 (#61–63), 156 (#64–66), 221 (#37–42), 265 (#9–14), 608 (#69–76)
• Use properties to reorder and rearrange expressions to compute more efficiently. [ RL]
PE/TE: 79, 80 (#9–13), 81 (#1–4, 12–14), 82 (#41–53), 95 (#8–11), 96 (#1–5, 17–31),
97 (#41–46), 101 (#3–6), 102 (#7–11), 103–104, 105 (#68–72), 123 (#36–37, 40–41),
125 (#30, 32), 137 (#69, 71, 72), 143 (#60–61), 382 (#16–19, 22–23), 511 (#1–4),
512 (#5–8), 514 (#5–16, 21–44), 515 (#59–74), 559 (Example 1, #2, 5, 9),
573 (#58–63), 784 (#38, 40, 41)
Estimation
1.1.8 Apply estimation strategies to determine the reasonableness of results in situations
involving multi–step computations with rational numbers including whole number powers
and square and cube roots. W
PE/TE: 5 (Example 5, #11), 14 (#88–93), 163–169, 173 (Examples 4 and 5),
178 (Example 3), 179 (Example 5, #6–7), 197 (#54–59), 251, 395, 458 (#23–30), 497,
500 (Example 3, #10–12), 503 (#53–64), 507 (Example 5), 508 (#15–17),
509 (#50–55, 60), 532, 774–776
36
163–165, 166 (#7–35), 167, 169 (#16–21), 170, 173 (Examples 4 and 5),
175 (#19, 21), 180 (#9–10), 182 (# 52–54), 197 (#54–59), 447 (#61–62),
451 (Example 4, #8–10), 453 (#41–48), 458 (# 23–30), 460 (#13),
477 (Example 2, #2), 479 (#5), 480 (#34–35), 500 (Example 3, #10–12), 503 (#53,
55–56, 58, 60–61, 63), 507 (Example 5), 508 (#15–17), 509 (#50–55, 60), 528
exact value is required. [CU]
5 (Example 5, #11), 7 (#46), 14 (#88–93), 25 (#1–4), 27 (#34–48), 46 (#11, 16),
178 (Example 3), 179 (#6), 180 (#11), 244 (Examples 3 and 4), 453 (#63–64), 483,
500 (Example 3, #10–12), 503 (#53–64), 526–527, 530 (#22–33), 637 (#36–37),
791 (#1, 5–6, 8)
163–165, 179 (#6), 180 (#11), 453 (#63–64), 483, 500 (Example 3, #10–12),
503 (#53–64), 507 (Example 5), 508 (#15–17), 526–527, 557 (#32–33),
637 (#36–37), 791 (#1, 5–6, 8)
• Describe various strategies used during estimation involving integers, rational numbers. [CU]
PE/TE: 46, 180 (#11), 244, 299 (#2–3), 321, 334 (#47–49), 392–393, 395, 431,
453 (#63–64), 483, 530 (#22–33), 774–776
14 (#88–93), 83 (#74–79), 163 (#1–3), 164 (#4–7), 165 (#8), 166 (#15–35),
167 (#37–42), 169 (#16–21), 390–391, 392 (#5–15), 393 (# 16–24), 395, 431,
468 (#89–94), 483, 526–527, 530 (#22–33), 544 (#49), 729 (#57–62), 776 (#1–48)
37
1.2.1 Analyze how changes in one or two dimensions of an object affect perimeter, area,
surface area, and volume. W
PE/TE: 5–8, 11–14, 22–23, 103 (#5–6, 13–16), 105 (#71–73), 174 (#10, 13–14), 175 (#15–17),
437, 772–773
• Describe and compare the impact that a change in one or more dimensions has on objects (e.g.,
how doubling one dimension of a cube affects the surface area and volume). [CU, MC]
13 (#55–57), 773 (#13–17)
• Describe how changes in the dimensions of objects affect perimeter, area, and volume in real
world situations (e.g., how does the change in the diameter of an oil drum affect the area and
volume). [CU, MC]
11 (Example 5, #10), 13 (#52–54, 58, 60), 14 (#63)
• Solve problems by deriving the changes in two dimensions necessary to obtain a desired
surface area and/or volume (e.g., given a box with certain dimensions, make the volume of the
box y cubic units by changing two dimensions of the box). [SP]
13 (#55–57, 60)
• Compare a given change in one or two dimensions on the perimeter, area, surface areas, or
volumes of two objects.
100 (Example 1, #1–2), 103 (#5–6, 13–16), 105 (#71–73), 143 (#53), 437 (#1–4),
773 (#1–12)
• Determine the change in one dimension given a change in perimeter, area, volume, or surface
area.
172 (Example 3, #2), 174 (#10, 13–14), 175 (#15–17)
38
1.2.3 Understand how to convert units of measure within systems (U.S. or metric). W
PE/TE: 8, 171, 174 (#12), 176 (#26), 177–182, 193 (#24–26)
• Understand how to convert units of measure within U.S. or within metric systems to achieve
an appropriate level of precision.
PE/TE: 178 (Example 4, #1–2), 181 (#31–37, 39), 193 (#24–26)
• Convert within a system to a unit size appropriate to a given situation.
PE/TE: 178 (#1–2), 181 (#31–37, 39, 41–43), 188 (#4–7), 193 (#24–26)
• Convert to a larger unit within a system while maintaining the same level of precision (e.g.,
represent 532 centimeters to 5.32 meters).
PE/TE: 181 (#31, 34–35, 37, 39, 41), 188 (#5), 193 (#24)
• Convert to a smaller unit within a system to increase the precision of a derived unit of
measurement.
PE/TE: 181 (#33, 36), 188 (#4), 193 (#25–26)
Procedures, precision, and estimation
1.2.5 Apply formulas to calculate measurements of right prisms or right circular cylinders.
W
PE/TE: 11–14, 437, 773; More extensive coverage of this standard can be found in
Geometry: Concepts and Skills
• Explain how to use a formula for finding the volume of a prism or cylinder. [CU, MC]
• Use a formula to find the volume of a prism or cylinder. [RL, MC]
PE/TE: An introduction to volume of solids can be found on page 437; More extensive
coverage of this standard can be found in Geometry: Concepts and Skills.
• Use a formula to derive a dimension of a right prism or right cylinder given other measures.
• Use formulas to describe and compare the surface areas and volumes of two or more right
prisms and/or right cylinders. [RL]
39
• Use formulas to obtain measurements needed to describe a right cylinder or right prism.
1.2.6 Understand and apply strategies to obtain reasonable measurements at an
appropriate level of precision. W
PE/TE: 5, 14 (#88–93), 163–165, 166 (#7–35), 169 (#16–21), 173 (Examples 4 and 5),
174 (#12), 175 (#19, 21), 177 (#2–3), 179 (Example 5, #6–7), 197 (#54–59), 251,
298–304, 251, 395, 458 (# 23–30), 480 (#34–35), 497, 503 (#53, 55–56, 58, 60–61,
63), 509 (#50–55, 60), 532, 773 (#1–6), 785 (#40–41)
• Identify situations in which approximate measurements are sufficient.
163–165, 166 (#7–35), 167, 169 (#16–21), 170, 173 (Examples 4 and 5),
175 (#19, 21), 180 (#9–10), 182 (# 52–54), 197 (#54–59), 447 (#61–62),
451 (Example 4, #8–10), 453 (#41–48), 458 (# 23–30), 460 (#13),
477 (Example 2, #2), 479 (#5), 480 (#34–35), 500 (Example 3, #10–12),
503 (#53, 55–56, 58, 60–61, 63), 507 (Example 5), 508 (#15–17), 509 (#50–55, 60),
528
• Estimate a reasonable measurement at an appropriate level of precision. [MC]
173 (Examples 4 and 5), 174 (#12), 175 (#19, 21), 773 (#1–6)
• Estimate quantities using derived units of measure (e.g., distance or time using miles per hour,
cost using unit cost). [MC]
177 (#2–3), 178 (Example 3), 179 (Examples 5, #6), 180 (#9–11), 181 (#28, 38),
182 (#46–47), 192 (#27), 785 (#38–39)
• Estimate derived units of measure (e.g., miles per hour, people/year, grams/cubic centimeters).
[MC]
PE/TE: 177 (#2–3), 180 (#22–27), 181 (#39–40), 192 (#26), 785 (#40–41)
• Apply a process that can be used to find a reasonable estimate for the volume of prisms,
pyramids, cylinders, and cones.
40
1.3.1 Understand the relationship among characteristics of one–dimensional,
two–dimensional, and three–dimensional figures. W
PE/TE: 7 (#46), 11 (Example 5), 12 (#19), 14 (#63), 37 (Example 2, #1), 105 (#73),
233 (#1–3), 722–723, 724–729, 730–734, 773
• Identify and label one– and two–dimensional characteristics (rays, lines, end points, line
segments, vertices, and angles) in three–dimensional figures. [CU]
• Draw and label with names and symbols nets of right prisms and right cylinders. [RL, CU]
PE/TE: 7 (#46), 11 (Example 5), 12 (#19), 14 (#63), 37 (Example 2, #1), 105 (#73),
143 (#53), 229, 233 (#1–3), 234 (#35)
• Describe or classify various shapes based on their characteristics.
• Make and test conjectures about two–dimensional and three–dimensional shapes and their
individual attributes and relationships using physical, symbolic, and technological models
(e.g., diagonal of a rectangle or prism is the longest interior segment; what figures make up
cross–sections of a given three–dimensional shape). [SP, RL, CU, MC]
1.3.2 Apply understanding of geometric properties and relationships. W
PE/TE: 772–723, 724–729, 730–735, 736–739; More extensive coverage of this standard can
be found in Geometry: Concepts and Skills
• Use geometric properties and relationships to describe, compare, and draw two–dimensional
and three–dimensional shapes and figures.
41
• Construct geometric figures using a variety of tools and technologies (e.g., angle bisectors,
perpendicular bisectors, triangles given specific characteristics). [MC]
• Draw a plane shape and justify the answer given a set of characteristics. [RL, CU]
• Use the properties of two–dimensional and three–dimensional shapes to solve mathematical
problems (e.g., find the width of a river based on similar triangles; given a set of parallel lines,
a transversal, and an angle, find the other angles). [SP, RL, CU, MC]
• Compare two–dimensional and three–dimensional shapes according to characteristics
including faces, edges, and vertices, using actual and virtual modeling. [RL, CU]
• Use technology to generate two and three dimensional models of geometric figures with given
geometric characteristics (e.g., generate a two–dimensional animation using pentagons with
fixed coordinates for one edge). [RL, SP]
• Create a three–dimensional scale drawing with particular geometric characteristics. [SP, CU,
MC]
1.3.3 Apply understanding of geometric properties and location of points to figures. W
PE/TE: 203–208, 210–215, 216–221, 222–227, 229–236, 694 (#11), 730–735, 736–739
• Use coordinates to describe or identify the location of objects on coordinate grids.
732 (Example 3, #8), 733 (#9)
• Describe geometric characteristics of two–dimensional objects using coordinates on a grid.
[MC]
731 (#5–7), 733 (#5–8, 25–30), 734 (#31–32, 38–39), 738 (#34)
42
• Describe the location of points that satisfy given conditions (e.g., the set of points equidistant
from a given point; a point equidistant from a given set of points). [CU]
207 (#28, 30, 34), 214 (#51), 736 (Example 1, #4), 737 (Example 3 #5), 738 (#3–33)
• Represent situations on a coordinate grid or describe the location of points that satisfy given
conditions (e.g., locate a gas station to be equidistant from given cities; locate a staking point
to maximize the grazing area of a tethered goat). [MC, SP, RL]
205 (#10), 207 (#33), 214 (#50, 52), 694 (#11), 732 (Example 3, #8),
733 (#2–4, 10–24), 734 (#33–37), 739 (#36–37)
• Use tools and technology to draw objects on a coordinate grid based on given conditions. [CU]
• Identify, interpret, and use the meaning of slope of a line as a rate of change using physical,
symbolic, and technological models. [SP, RL, MC]
PE/TE: 228, 229–232, 233 (#10–12, 19–21), 234 (#23–28, 35–37, 39),
235 (Example, #41–42)
1.3.4 Apply understanding of multiple transformations. W
• Apply multiple transformations to create congruent and similar figures in any or all of the four
quadrants.
• Use multiple transformations (combinations of translations, reflections, or rotations) to draw
an image. [RL]
• Use dilation (expansion or contraction) of a given shape to form a similar shape. [RL, CU]
• Determine the final coordinates of a point after a series of transformations. [RL, CU]
• Examine figures to determine rotational symmetry about the center of the shape. [RL, MC]
43
• Define a set of transformations that would map one onto the other given two similar shapes.
[SP, RL]
• Create a design with or without technology using a combination of two or more
transformations with one or two two–dimensional figures. [SP, RL]
• Use technology to create two– and three–dimensional animations using combinations of
transformations. [MC, SP, RL]
statistics.
Probability
1.4.1 Understand the concept of conditional probability. W
• Compare the probabilities of dependent and independent events. [CU, MC]
• Determine and justify whether the outcome of a first event affects the probability of a later
event (e.g., drawing cards from a deck with or without replacement). [CU]
• Explain the difference between dependent and independent events. [CU]
• Explain and give examples of compound events. [CU]
44
1.4.2 Apply understanding of dependent and independent events to calculate probabilities.
W
Sourcebook on the following pages: 2–7, 9–10, 13, 15–21
• Determine probabilities of dependent and independent events. [SP]
• Generate the outcomes and probability of multiple independent and dependent events using a
model or procedure (e.g., tree diagram, area model, counting procedures).
• Generate the outcomes and probability of events using a counting procedure (e.g., the number
of license plates that can be made with three letters and three numbers; winning the lottery).
[MC]
This standard is taught in Data Analysis Sourcebook on the following pages: 2–7, 8, 12
• Explain the relationship between theoretical probability and empirical frequency of dependent
events using simulations with and without technology. [CU]
• Create a simple game based on independent probabilities wherein all players have an equal
probability of winning. [MC, SP]
• Create a simple game based on compound probabilities. [MC, SP]
• Determine the sample space for independent or dependent events.
45
Statistics
1.4.3 Apply appropriate methods and technology to collect data or evaluate methods used
by others for a given research questions. W
PE/TE: 42–47, 384–385, 809–811, 813–815; More extensive coverage of this standard can
be found in Data Analysis Sourcebook on the following pages: 29–37
• Identify sources of bias in data collection questions, samples, and/or methods and describe
how such bias can be controlled. [RL, CU]
• Evaluate methods and technology used to investigate a research question. [CU, MC]
• Collect data using appropriate methods.
• Use technology appropriately to collect data. [RL, MC]
• Identify appropriate data collection methods that might impact the accuracy of the results of a
given situation. [RL, CU]
• Determine whether the sample for a given study was from a representative sample.
• Determine whether the methods of data collection used were appropriate for a given question
or population. [RL]
46
1.4.4 Understand and apply techniques to find the equation for a reasonable linear model.
W
PE/TE: 49–52, 53 (#24–25), 87 (#5), 209, 211, 212 (Example 4, #5–7), 213 (#3–6, 10–21),
214 (#40–50, 52), 217 (#7–8), 218, 219 (#4–7, 14–29), 224 (#6–9), 226 (#36–48),
239 (#9–11, 16–24), 240 (#27–30, 36, 39), 247 (#35–45), 250–251, 261 (#22–25),
270 (#3–5), 271 (#6–8), 272 (#22–27), 274 (#47, 49–52), 276–277, 278 (#1–3),
281 (#5–7, 14–19), 286, 288 (#3–5, 18–23), 289 (#6–38), 294 (#6–11),
295 (#39–44, 52–53), 296 (#57–58), 297 (#4–5, 12–14), 300, 302 (#14, 20, 25–26),
308 (#7–10), 310 (#20–39), 313 (#1–9), 314 (#10–12), 315 (#14–28),
786 (#7–18, 33–46), 787 (#6–27, 34–36)
• Determine the equation for a reasonable line to describe a set of bivariate data. [RL, MC]
PE/TE: 214 (#49), 271 (Example 3), 273 (#40), 274 (#47, 49–52), 275 (#54), 282 (#44),
283 (#46), 285 (#1), 289 (#6–38)
• Determine the equation of a line that fits the data displayed on a scatter plot. [SP, RL]
PE/TE:
814–815; More extensive coverage of this standard can be found in Data Analysis
• Use technology to determine the line of best fit for a set of data. [MC]
• Match an equation with a set of data. [MC]
49–52, 53 (#24–25, 27), 54 (#4), 87 (#5), 209, 210 (#1), 211, 212 (#5–7), 213 (#3–6,
10–12, 16–21), 214 (#49–50), 216 (#1–3), 217 (#4–6), 219 (#14–23), 221 (#12–17),
238 (Example 4), 239 (#16–24), 240 (#36, 39), 241 (#13–15), 257 (#56–58),
261 (#22–25), 286, 289 (#24–32, 37–38), 290 (#41), 294 (#6–11), 296 (#57–58),
300, 301 (#5, 9), 302 (#14, 20, 25–26), 303 (#28, 31), 304 (#35), 308 (#7–10),
310 (#20–25, 32–39), 313 (#1–6), 314 (#13), 315 (#14–28), 317 (#22–28),
786 (#33–40), 787 (#6–27, 34–36)
• Match an equation with a graphic display. [MC]
PE/TE: 53 (#29), 211 (Example 3), 214 (#59), 217 (#7–8), 218, 219 (#8–9), 220,
226 (#36–38), 247 (#43–45), 256 (#34–36), 270 (#3–5), 271 (#6–8), 272 (#22–27),
273 (#28–39), 274 (#44–47, 49, 52), 276–277, 278 (#1–3), 281 (#5–7, 14–19),
282 (#41–43), 283, 284 (#3–5), 285, 287 (#5–6), 288 (#3–5, 18–23), 289 (#33–35),
290 (#42), 293 (#6–7), 294 (#12–14), 295 (#39–44, 52–53), 296 (#61),
297 (#4–5, 12–14), 308, 309 (#17–19), 310 (#26–31), 313 (#7–9), 314 (#10–12)
47
• Create a graph based on the equation for the line.
PE/TE: 50 (#2), 51 (#4, 13–14), 52 (#21), 53 (#24–25), 54 (#5), 209, 211 (Example 3),
212 (Example 4, #5–7), 213 (#13–15), 214 (#40–48, 50, 52), 216 (#1–3), 217 (#4–6),
219 (#4–7, 24–29), 221 (#18–20), 223 (Example 3), 224 (#6–9), 226 (#39–48),
237 (#4–6), 239 (#9–11), 240 (#27–30), 241 (#16–18), 247 (#35–42), 250–251,
254 (#5–7), 256 (#37–45), 257 (#56–58), 260 (#6–13), 261 (#14–17), 262 (#31–34),
275 (#68–73), 302 (#15, 22), 786 (#7–18, 41–46)
1.4.5 Analyze a linear model to judge its appropriateness for a data set. W
PE/TE: 44 (Example 3, #3), 46 (#18–19), 51 (#5, 13–14), 49–52, 87 (#5), 211,
212 (Example 4, #5–7), 213 (#3–6, 16–21), 214 (#52–53), 215 (#54–55),
219 (#14–17), 239 (#16–24), 240 (#36, 39), 257 (#54–55, 58), 261 (#22–25), 286,
289 (#24–32, 37–38), 294 (#6–11), 296 (#57–58), 300, 302 (#14, 20, 25–26),
308 (#7–10), 310 (#20–25, 32–39), 313 (#1–6), 315 (#14–28), 786 (#33–40),
787 (#6–27, 34–36)
• Determine whether a straight line is an appropriate way to describe a trend in a set of bivariate
data. [MC, RL]
44 (Example 3, #3), 46 (#18–19), 49 (Example 2), 50 (#1–2), 51 (#5, 13–14),
53 (#24), 207 (#27–29, 31, 33), 214 (#52), 215 (#54–55), 257 (#54–55), 302 (#26);
the following pages: 50, 88–89
• Determine whether the underlying model for a set of data is linear. [RL, MC]
44 (Example 3, #3), 46 (#18–19), 206 (#13–18), 207 (#27–29, 33), 214 (#52),
215 (#54–55), 257 (#54–55, 58), 302 (#26); Additional coverage of this standard can
be found in Data Analysis Sourcebook on the following pages: 50, 88–89
• Decide and explain whether it is appropriate to extend a given data set following a line of best
fit. [RL, MC]
46 (#18–19), 205 (Example 4, #10), 207 (#27–29, 33), 214 (#52), 215 (#54–55),
257 (#54–55), 302 (#26); Additional coverage of this standard can be found in Data
Analysis Sourcebook on the following pages: 86–89
48
• Determine whether a linear prediction from a given set of data is appropriate for the data and
support the decision with data. [MC].
49–52, 53 (#24–25, 27), 54 (#4), 87 (#5), 209, 210 (#1), 211, 212 (#5–7),
213 (#3–6, 10–12, 16–21), 214 (#49–50, 52–53), 216 (#1–3), 217 (#4–6),
219 (#14–23), 221 (#1–4, 12–17), 238 (Example 4), 239 (#16–24), 240 (#36, 39),
241 (#13–15), 257 (#56–58), 261 (#22–25), 286, 289 (#24–32, 37–38), 290 (#41),
294 (#6–11), 296 (#57–58), 300, 301 (#5, 9), 302 (#14, 20, 25–26), 303 (#28, 31),
304 (#35), 308 (#7–10), 310 (#20–25, 32–39), 313 (#1–6), 314 (#13), 315 (#14–28),
317 (#22–28), 786 (#33–40), 787 (#6–27, 34–36)
• Determine whether an equation for a line is appropriate for a given set of data and support the
judgment with data. [RL, MC]
50 (#2), 51 (#4, 13–14), 52 (#21), 53 (#24–25), 54 (#5), 209, 211 (Example 3),
212 (Example 4, #5–7), 213 (#3–6,13–21), 214 (#40–48, 50, 52), 216 (#1–3),
217 (#4–6), 219 (#4–7, 24–29), 221 (#18–20), 223 (Example 3), 224 (#6–9),
226 (#39–48), 237 (#4–6), 239 (#9–11), 240 (#27–30), 241 (#16–18), 247 (#35–42),
250–251, 254 (#5–7), 256 (#37–45), 257 (#56–58), 260 (#6–13), 261 (#14–17),
262 (#31–34), 275 (#68–73), 302 (#15, 22), 786 (#7–18, 41–46)
• Use technology to generate data to fit a linear model. [SP, MC]
250–251, 395; Additional coverage of this standard can be found in Data Analysis
1.4.6 Apply understanding of statistics to make, analyze, or evaluate a statistical argument.
W
PE/TE: 46 (#14, 18–19), 207 (#29, 31–35), 214 (#50–52); Additional coverage of this
standard can be found in Data Analysis Sourcebook on the following pages:
40–51, 60–76, 86–101
• Identify trends in a set of data in order to make a prediction based on the information. [CU,
MC]
46 (#14, 18–19), 53 (#25), 207 (#29, 31–35), 214 (#50, 52); Additional coverage of
this standard can be found in Data Analysis Sourcebook on the following pages:
46–51, 60–63, 64–68, 86–89, 90–93
49
• Justify a prediction or an inference based on a set of data. [CU, MC]
46 (#14, 18–19), 53 (#25), 207 (#29, 31–33), 214 (#50–51, 53); Additional coverage
of this standard can be found in Data Analysis Sourcebook on the following pages:
63, 67–68, 86–89, 94–95
• State possible factors that may influence a trend but not be reflected in the data (e.g.,
population growth of deer vs. availability of natural resources or hunting permits). [MC, CU,
RL]
46 (#11, 18–19), 47 (#21), 207 (#32, 34–35), 214 (#50–52); Additional coverage of
86–87, 90–93
• Use statistics to support different points of view. [RL]
• Analyze a set of statistics to develop a logical point of view. [RL. CU, MC]
• Justify or refute claims and supporting arguments based on data. [CU, MC]
86–101
• Determine whether statistics have been used or misused to support a point of view or argument
and support the evaluation with data. [RL]
60–76
1.5.1 Apply processes that use repeated addition (linear) or repeated multiplication
(exponential). W
PE/TE: 22–23, 50, 52 (#23), 51 (#4–5, 7–14), 53 (#24), 58 (#40), 92 (#1–4), 98 (#69–70),
256 (#25–33, 37–45), 257 (#56–58), 439, 441–442, 452 (#19–20), 781
50
• Recognize, extend, or create a pattern or sequence between sets of numbers and/or linear
patterns. [RL, CU, MC]
PE/TE: 1, 22–23, 48 (Example 1), 92 (#1–4), 119, 120 (#5), 212 (Example 4, #5–7),
213 (#10–15), 439, 441–442, 452 (#19–20), 781
• Identify, extend, or create a geometric or arithmetic sequence or pattern. [RL, CU]
PE/TE: 22–23, 48 (Example 1), 119, 120 (#5), 168 (#50), 781
• Translate among equivalent numerical, graphical, and algebraic forms of a linear function. RL,
MC]
PE/TE: 48, 49 (Example 2), 50, 51 (#4–5, 7–14), 52 (#23), 53 (#24, 27–29), 58 (#40),
60 (#5), 70 (#73–74), 98 (#69–70), 195 (Example 2, #2), 196 (#23), 252, 254 (#5–7),
255 (#7, 13–14), 256 (#25–33, 37–45), 257, 262 (#39, 41–42), 263, 783 (#32–34)
• Make predictions based on a pattern or sequence.
48 (Example 1), 51 (#7–14), 58 (#40), 70 (#74–75), 98 (#69–70), 196 (#23),
257 (#54–59), 439, 457 (Example 5), 781, 783 (#32–34),
1.5.2 Analyze a pattern, table, graph, or model involving repeated addition (linear) or
repeated multiplication (exponential) model to write an equation or rule. W
PE/TE: 52 (#23), 53 (#24), 110 (#3–38), 143 (#57–66), 214 (#40–48), 215 (#59),
217 (Example 3, #7–8), 218, 219 (#8–9, 24–29), 220 (#30–33), 226 (#36–38),
240 (#27–30), 252–254, 255 (#7–18), 256 (#19–24), 269–273, 274 (#47, 49–50, 52),
276–283, 284 (#1–15), 288–289, 294 (#3–29), 295 (#30–44, 52–54),
297 (#4–5, 9–14), 301–303, 313 (#1–9), 315 (#14–28), 393, 395, 427 (#2–4, 9–11),
428–429, 431 (#1–6), 434 (#23–28), 435 (#1–3, 17–22), 468 (#73–78),476–478,
479 (#10–15), 480, 482–484, 485 (#16–21), 486, 638 (#44–52), 787 (#1–26)
• Find the equation of a line in a variety of ways (e.g., from a table, graph, slope–intercept,
point–slope, two points). [RL, MC]
PE/TE: 215 (#59), 217 (Example 3, #7–8), 218, 219 (#8–9), 220 (#30–33), 226 (#36–38),
256 (34–36), 269–273, 274 (#47, 49, 50, 52), 275 (#54), 276–283, 284 (#1–15),
285–289, 290 (#40–42), 293, 294 (#3–29), 295 (#30–44, 52–54), 296 (#60–62),
297 (#1–5, 9–14), 304 (#47–49), 313 (#1–9), 314 (#10–13), 315 (#14–28), 317,
383 (#58–53), 394 (#38–43), 408 (#49–54), 468 (#73–78), 525 (#55–57),
539 (#89–91), 638 (#44–52), 787 (#1–26)
• Generate and use rules for a pattern to make predictions about future events (e.g., population
growth, future sales, growth of corn stalks, future value of savings account). [SP, RL, MC]
PE/TE: 257 (#56–58), 274 (#51, 53), 275 (#55), 298–303, 459 (#50–51), 476–478,
479 (#10–15), 480, 482–484, 485 (#16–21), 486
51
• Identify or write an equation or rule to describe a pattern, sequence, and/or a linear function.
[RL, CU, MC]
252–254, 255 (#7–18), 256 (#19–24)
• Write an equation for a line given a set of information (e.g., two points, point–slope, etc.).
[CU, MC]
PE/TE: 269–273, 274 (#47, 49–50, 52), 275 (#54), 276–283, 284 (#1–15), 285–289,
290 (#40–42), 293, 294 (#3–11, 15–29), 295 (#30–38), 296 (#60–62),
297 (#4–5, 9–14), 304 (#47–49), 313 (#1–6), 314 (#10–13), 315 (#14–28), 317,
787 (#1–26)
• Write a recursive definition of a geometric pattern (e.g., Start and New = Old * Number). [CU,
MC]
• Represent systems of equations and inequalities graphically. [RL, MC]
389–391, 393, 394 (#29, 31), 395, 408 (#1–3), 424–426, 427 (#2–4, 9–11), 428–429,
431 (#1–6), 434 (#23–28), 435 (#1–3, 17–22), 460 (#67–72), 468 (#79–88),
474 (#72–77), 504 (#99–101), 525 (#55–57), 531 (#56–61), 608 (#60–62),
615 (#69–78), 789 (#1–4, 38–45)
• Write a story that represents a given linear equation or expression. [CU, MC]
110 (#3–38), 118 (#4–9), 141 (#6–14, 22–36), 143 (#57–66), 147 (#7–39),
154 (#21–34), 214 (#40–48), 219 (#24–29), 240 (#27–30)
• Write an expression, equation, or inequality with two variables representing a linear model of a
real–world problem. [CU, MC]
PE/TE: 52 (#23), 53 (#24), 240 (#36), 273 (#40), 274 (#47, 49, 50, 52), 282 (#44), 283 (#46),
289 (#36–38), 300 (#4), 301 (#6), 302 (#20, 25), 303 (#27, 31), 372 (Example, #53),
379 (#38)
52
1.5.4 Apply understanding of equations, tables, or graphs to represent situations involving
relationships that can be written as repeated addition (linear) or repeated multiplication
(exponential). W
PE/TE: 36–38, 40 (#18, 21), 105 (#71–72), 111 (#45–52), 123 (#32–35),
137 (#60, 62–63, 65–68), 142 (#48–50), 161 (#40–41, 43), 196 (#33–34),
239 (#25–26), 240 (#34–37), 274 (#47, 49–50, 52), 289 (#36–38), 302 (#20, 25),
441–447, 448 (#69–73), 466 (#39–57), 479–480, 485–487, 493 (#1–8, 14–17),
502 (#65–74), 710–713, 790 (#1–8, 21–34)
• Represent variable quantities through expressions, equations, inequalities, graphs, and tables to
represent linear situations involving whole number powers and square and cube roots. [CU,
MC]
PE/TE: 11 (#10), 13 (#52–54, 58–60), 21 (#14–17), 29 (#68, 70–71, 73), 59(#5), 118 (#6),
123 (#32–35), 124 (#46), 125 (#26–28), 196 (#33–34), 215 (#33–34), 441–447,
448 (#69–73), 462–465, 466 (#39–57), 474 (#1–10), 480 (#16–27), 489 (#1–8),
491 (#21–28), 493 (#1–8, 14–17), 494 (#1–4, 6–8), 501, 502 (#65–74), 710–713,
790 (#1–8, 21–34)
• Identify and use variable quantities to read and write expressions and equations to represent
situations that can be described using repeated addition (e.g., models that are linear in nature).
[CU, MC]
PE/TE: 32 (Example 6, #7–8), 34 (#37), 36–38, 40 (#18, 21), 41 (#22), 53 (#24),
134 (Example 3, #8–9), 135 (#16), 136 (#58–59), 137 (#60, 62–63, 65–68),
140 (Example 4, #9), 142 (#48–50), 143 (#53, 69), 145 (Example 2, #4), 149 (#7–8),
154 (#15), 159 (Example 4, #5), 161 (#40–41, 43), 167 (#37), 240 (#36), 273 (#40),
274 (#47, 49, 50, 52), 282 (#44), 283 (#46), 289 (#36–38), 300 (#4), 301 (#6),
302 (#20, 25), 303 (#27, 31), 372 (Example, #53), 379 (#38)
situations that can be described using repeated multiplication (e.g., models that are exponential
such as savings accounts and early stages of population growth). [CU, MC]
447 (#61–62, 65–68), 453 (Example, 63–64), 459 (#50–51), 476–480, 481 (#40–43),
482–487, 493 (#27–30)
• Recognize and write equations in recursive form for additive models (e.g., starting value,
New=Old + some number). [CU, MC]
New=Old _ some number). [CU, MC]
53
• Select an expression or equation to represent a given real world situation. [MC]
PE/TE: 95 (Example 4, #12), 97 (#50–55), 105 (#71–72), 109 (Example 4, #9–10),
111 (#45–52), 237 (Example 3), 238 (Example 4), 239 (#25–26), 240 (#34–37),
274 (#47, 49–50, 52), 282 (#44), 283 (#46–48), 289 (#36–38), 302(#20, 25)
1.5.5 Apply procedures to simplify expressions. W
PE/TE: 13 (#52–54, 58–60), 21 (#14–17), 29 (#68, 70–71, 73), 101 (#3–6), 104 (#17–52),
108 (#3–8), 110–111, 112 (#55–58), 118 (#4–9, 16–18), 123 (#32–35),
125 (#25–28, 34), 196 (#33–34), 444 (#9–12), 446 (#10–12), 447 (#52–62), 462–465,
474 (#1–10), 480 (#16–27), 489 (#1–8), 493 (#1–8, 14–17), 784 (#38–45),
790 (#1–8, 21–34)
• Simplify expressions and evaluate formulas involving exponents.
PE/TE: 11 (#10), 13 (#52–54, 58–60), 21 (#14–17), 29 (#68, 70–71, 73), 59 (#5), 107–111,
112 (#55–58), 118 (#6), 123 (#32–35), 124 (#46), 125 (#25–28, 34), 196 (#33–34),
215 (#66–69), 444 (#9–12), 445 (#13–16), 446 (#10–12), 447 (#52–62), 462–465,
466 (#39–57), 474 (#1–10), 476 (#1), 480 (#16–27), 482 (#1), 483 (#2),
484 (#22–28), 489 (#1–8), 491 (#21–28), 493 (#1–8, 14–17), 494 (#1–4, 6–8),
696 (#59), 790 (#1–8, 21–34)
• Justify a simplification of an expression involving exponents. [RL, CU]
21 (#14–17), 29 (#68, 70–71, 73), 59 (#5), 110–111, 112 (#55–58), 123 (#32–35),
124 (#46), 125 (#25–28, 34), 196 (#33–34), 215 (#66–69), 462–465, 466 (#39–57),
474 (#1–10), 476 (#1), 480 (#16–27), 482 (#1), 483 (#2), 484 (#22–28), 489 (#1–8),
491 (#21–28), 493 (#1–8, 14–17), 494 (#1–4, 6–8), 696 (#59), 790 (#1–8, 21–34)
• Use multiple mathematical strategies and properties to simplify expressions.
PE/TE: 100 (#1–2), 101 (#3–6), 102 (#7–10), 103, 104 (#17–52), 107–109,
110 (#3–14, 21–40), 111 (#41–44, 46, 49, 51), 112 (#55–58), 118 (#4–9, 16–18),
123 (#36–44), 124 (#45–50), 125 (#30–33, 35–37), 126 (#12), 137 (#69–74),
143 (#58–62), 162 (#58–63), 196 (#32–39), 215 (#64–69), 382 (#16–23),
401 (#38–41), 573 (#58–63), 784 (#38–45)
54
1.5.6 Apply procedures to solve equations and systems of equations. W
PE/TE: 147–148, 154–155, 160–161, 166–167, 174–175, 273 (#41–43), 192 (#23–25),
193 (#21–23), 274 (#51, 53), 283 (#47–48), 371 (#51–52), 383(#70–74), 390 (#1–3),
393 (#25–28), 398 (#4), 400 (#28–33), 407 (#43–45), 410 (#1–2), 413 (#31–34),
431 (#1–6), 435 (#1–9, 11–16), 454 (#78–83), 460 (#67–72), 481 (#48–57),
509 (#60–66), 785 (#1–35), 789 (#1–28, 30–37)
• Rearrange formulas to solve for a particular variable (e.g., given A = 0.5bh, solve for h). [MC,
CU]
PE/TE: 171–175, 188 (#1–3), 192 (#23–25), 193 (#21–23), 382 (#36), 507 (Example 5, #9),
509 (#60–66)
• Solve real–world situations involving linear relationships and verify that the solution makes
sense in relation to the problem. [SP, RL, CU, MC]
PE/TE: 145 (#4), 148 (#44–45), 149 (#7–8, 15), 155 (#47–49), 159 (#5), 161 (#40–43),
165 (#8), 167 (#36–38), 273 (#41–43), 274 (#51, 53), 275 (#55), 282 (#45),
283 (#47–48), 301 (#7–11), 347 (#68–69), 371 (#51–52), 372 (#54), 383 (#70–74),
448 (#86–87), 481 (#52)
• Find the solution to a system of linear equations using tables, graphs, and symbols. [CU, MC]
PE/TE: 389, 390 (#1–3), 392–393, 394 (#29, 31), 395, 408 (#1–3), 430 (#4), 431 (#1–6),
435 (#1–9, 11–16), 460 (#67–72), 468 (#79–88), 474 (#72–77), 504 (#99–101),
525 (#55–57), 531 (#56–61), 608 (#60–62), 615 (#69–78), 789 (#1–28, 30–37)
• Interpret solutions of systems of equations. [CU, MC]
PE/TE: 389, 390 (#1–3), 392–393, 394 (#29, 31), 395, 398 (#4), 400 (#28–33),
406 (Example), 407 (#43–45), 408 (#1–3), 409 (Example 1), 410–411, 430 (#4),
431 (#1–6), 435 (#1–9, 11–16), 460 (#67–72), 468 (#79–88), 474 (#72–77),
504 (#99–101), 525 (#55–57), 531 (#56–61), 608 (#60–62), 615 (#69–78),
789 (#1–28, 30–37)
• Solve multi–step equations. [SP, RL]
PE/TE: 144–148, 149 (#9–15), 151–155, 156 (#50–56), 157–161, 162 (#50–51), 163–167,
168 (#43–49), 169 (#5–22), 170, 215 (#70–73), 235 (#45–47), 241 (#40–45),
249 (#70–78), 328 (#65–73), 335 (#74–77), 382 (#24–35), 394 (#32–37),
454 (#78–83), 481 (#48–57), 488 (#61–64), 785 (#1–35)
• Use systems of equations to analyze and solve real–life problems. [SP, CU, MC]
PE/TE: 391 (Example 3, #4), 393 (#25–28), 398 (#4), 400 (#28–33), 406 (Example),
407 (#43–45), 409 (Example 1), 410–411
55
• Determine when two linear options yield the same outcome (e.g., given two different
investment or profit options, determine when both options will yield the same result).
PE/TE: 391 (#4), 393 (#25–28), 398 (#4), 400 (#28–33), 407 (#43–45), 413 (#30, 34)
• Use systems of equations to determine the most advantageous outcome given a situation (e.g.,
given two investment options, determine under what conditions each will yield the best
result.). [MC, SP]
PE/TE: 391 (#4), 393 (#25–28), 398 (#4), 400 (#28–33), 401 (#1–2), 411 (Example 3),
407 (#43–45), 413 (#31–33)
56
Component 2.1: Investigate situations.
Example: The following are the times (in seconds) of the Olympics in the given years. Using this
information, is it reasonable to believe that the women will run as fast as the men in this event?
Justify your answer using this data:
Year Men’s Women’s
1948 10.3 11.9
1976 10.06 11.08
1952 10.4 11.5
1980 10.25 11.06
1956 10.5 11.5
1984 9.99 10.97
1960 10.2 11.0
1988 9.92 10.54
1964 10
11.4
1992 9.96 10.82
1968 9.95 11.0
1996 9.84 10.94
1972 10.14 11.07
2000 9.87 10.75
36–40, 198–199, 384–385, 562–563
• Use strategies to become informed about the situation (e.g., listing information; examine the
table for patterns; create a scatter plot to look for patterns; asking questions).
36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9)
• Summarize the problem (e.g., there are Olympic winning times over the past 50 years; both
men’s and women’s times are decreasing; will there come a time when women run faster than
men).
36–40, 198–199, 384–385, 562–563
be found; extend the pattern to see if women’s times will be less).
36–40, 198–199, 384–385, 562–563, 782 (#1–9)
• Determine whether information is missing or extraneous (e.g., compare the list of known
things to the list of needed things to see if there are things that are not needed).
36–40, 198–199, 384–385, 562–563, 782 (#1–9)
57
• Define the problem (e.g., if the pattern continues in the same fashion, will women run faster
than men and, if so, when will that occur).
36–40, 198–199, 384–385, 562–563, 782 (#1–9)
36–40, 198–199, 384–385, 562–563; Additional coverage of this standard can be
found in Data Analysis Sourcebook on the following pages: 40–45
• Organize relevant information from multiple sources (e.g., create a list of known and unknown
information; create a scatter plot of men’s and women’s times vs. time on the same coordinate
axis to analyze the patterns).
36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9); Additional coverage of
40–45
• Select and apply appropriate mathematical tools to devise a strategy in a situation (e.g., if the
data, in either tabular or graphical form, suggest a linear relationship, plan to find a linear
equation for each set of data; solve those equations simultaneously [or use technology to find
the intersection of the two lines] to answer the question). If the data pattern suggests a
non–linear model, plan to project what the pattern is and extend that pattern.
36–40, 198–199, 384–385, 562–563, 756–757, 782 (#1–9); Additional coverage of
40–45
36–40, 198–199, 384–385, 390 (#1–3), 392–393, 431 (#1–6), 435 (#1–9, 11–16),
460 (#67–72), 562–563, 789 (#1–28, 30–37)
• Implement the plan devised to solve the problem (e.g., solve the set of simultaneous equations
to arrive at a time where the two times are the same).
36–40, 198–199, 384–385, 562–563, 756–757
58
• Use mathematics to solve the problem (e.g., use algebra to write equations for the two linear
models, solve the system of equations using either symbols or technology).
198–199, 384–385, 389, 390 (#1–3), 392–393, 394 (#29, 31), 395, 408 (#1–3),
430 (#4), 431 (#1–6), 435 (#1–9, 11–16), 460 (#67–72), 468 (#79–88), 474 (#72–77),
504 (#99–101), 525 (#55–57), 531 (#56–61), 562–563, 608 (#60–62), 615 (#69–78),
789 (#1–28, 30–37)
• Identify when an approach is unproductive and modify or try a new approach (e.g., if the result
does not make sense in the context, return to the plan to see if something has gone wrong and
adjust accordingly).
198–199, 384–385, 562–563, 782 (#1–9)
• Check the solution to see if it works (e.g., the solution may be a partial year [i.e., 2003.6];
decide how to deal with this and also if the year is reasonable [i.e., 1925 does not make sense
given the context]).
198–199, 384–385, 562–563, 756–757, 782 (#1–9)
59
3.1.1. Synthesize information from multiple sources in order to answer questions. W
PE/TE: 7 (#46), 90 (#56–57), 105 (#71–73), 143 (#53), 572 (#51–52), 728 (#31–35)
• Use the properties of two–dimensional and three–dimensional figures to solve mathematical
a transversal, and an angle, find the other angles).
5 (Example 5), 7 (#46), 90 (#56–57), 105 (#71–73), 143 (#53), 162 (#50–51),
234 (#35), 247 (#55), 570 (Example 5), 572 (#51–52), 728 (#31–35), 729 (#10)
3.2.1 Apply skill of conjecturing and analyze conjectures by formulating a proof or
constructing a counter example. W
PE/TE: 119–120, 740–745
• Make and test conjectures about two–dimensional and three–dimensional figures and their
cross–sections of a given three–dimensional shape). (1.3.1)
PE/TE:
745 (#18, 22–23)
3.2.2 Analyze information to draw conclusions and support them using inductive and
deductive reasoning. W
PE/TE: 119–120; Additional opportunities to address this standard can be found in
Geometry: Concepts and Skills and McDougal Littell Algebra 1
• Compare and describe the volume of cylinders, cones, and prisms when an attribute is changed
(e.g., the area of the base, the height of solid). (1.2.4)
• Draw a plane shape of a given set of characteristics and justify the answer. (1.3.2)
60
• Identify trends in a set of data in order to make a prediction based on the information. (1.4.6)
46 (#14, 18–19), 53 (#25), 207 (#29, 31–35), 214 (#50, 52); Additional coverage of
46–51, 60–63, 64–68, 86–89, 90–93
• Use statistics to support different points of view. (1.4.6)
3.2.3 Analyze procedures to determine appropriateness of claims and arguments. W
86–101
• Examine claims and supporting arguments based on data and make needed revisions. (1.4.6)
86–101
3.3.1 Analyze results using inductive and deductive reasoning.
Geometry: Concepts and Skills.
• Compare and contrast similar two–dimensional figures and shapes using properties of
two–dimensional figures and shapes. (1.3.2)
• Find a reasonable estimate for the volume of prisms, pyramids, cylinders, and cones. (1.2.6)
relationships, counter examples, or proportional reasoning. W
46–51, 60–76
61
• Examine a set of data, research other sources to see if the data is consistent, find articles
written to see if the data makes sense, to develop a logical point of view and to support that
view. (1.4.6)
46–51, 60–76
62
4.1.1 Understand how to develop or apply an efficient system for collecting mathematical
information for a given purpose. W
PE/TE: 198–199, 384–385, 502–503, 756–757, 808–811
• Collect data efficiently on the outcomes of first events and later events to determine and justify
how the first event affects the probability of later events (e.g., drawing cards from a deck with
or without replacement). (1.4.1)
PE/TE:
198–199, 384–385, 502–503, 756–757, 808–811
4.1.2 Synthesize mathematical information for a given purpose from multiple, self–selected
sources. W
PE/TE: 198–199, 384–385, 502–503, 756–757, 808–811
population growth of deer vs. availability of natural resources or hunting permits). (1.4.6)
PE/TE: 198–199, 384–385, 502–503, 756–757, 808–811
4.2.1 Analyze mathematical information to organize, clarify, and refine an argument. W
• Develop an argument to support a given point of view and set of statistics. (1.4.6)
63
4.2.2 Understand how to express ideas and situations using mathematical language and
notation. W
13 (#52–54, 58, 60), 177, 178 (Example 3), 181 (#28, 38–40), 207 (#28, 30, 34),
214 (#51), 733–734, 738, 739 (#35–38), 785 (#37–41), 808–812; Additional
coverage of this standard can be found in Data Analysis Sourcebook on the
following pages: 9–10, 13
traveled divided by hours traveled yields the derived unit [miles per hour]). (1.2.2)
173 (Example 5), 177, 178 (Example 3), 180 (#9–10, 22–27), 181 (#28, 38–40),
188 (#4–5), 192 (#26), 197 (#62), 785 (#37–41)
from a given point; a point equidistant from a given set of points). (1.3.3)
203–204, 207 (#28, 30, 34), 214 (#51), 730–734, 736–738, 739 (#35–38)
doubling the edge of a cube affects the surface area). (1.2.1)
11 (Example 5, #10), 13 (#52–54, 58, 60), 14 (#63); More extensive coverage of this
standard can be found in Geometry: Concepts and Skills
events using simulations with and without technology. (1.4.2)
PE/TE: 808–812; Additional coverage of this standard can be found in Data Analysis
Sourcebook on the following pages: 9–10, 13
64
5.1.1 Apply multiple mathematical concepts and procedures in a given problem or
situation. W
PE/TE: 177–182
(1.2.6)
PE/TE: 177 (#2–3), 180 (#9–10, 22–27), 181 (#39–40), 192 (#26), 785 (#40–41)
• Determine the final coordinates of a point after a series of transformations. (1.3.4)
5.1.2 Understand how use different mathematical models and representations in the same
situation. W
PE/TE: 215 (#59), 217 (Example 3, #7–8), 218, 219 (#8–9), 220 (#30–33), 226 (#36–38),
228–232, 233 (#10–12, 19–21), 233 (#10–12, 19–21), 269–273,
274 (#47, 49–50, 52), 276–277, 294 (#3–29), 295 (#30–44, 52–54), 313 (#1–9),
314 (#10–13), 315 (#14–28), 390 (#1–3), 391 (#4), 393 (Example 3, #4), 431 (#1–6),
435 (#1–9, 11–16), 460 (#67–72), 468 (#73–88), 474 (#72–77), 525 (#55–57),
638 (#44–52), 787 (#1–26), 789 (#1–28, 30–37)
• Identify, interpret, and use the meaning of slope of a line as a rate of change using concrete,
symbolic, and technological models. (1.2.2)
PE/TE: 228–232, 233 (#10–12, 19–21), 234 (#23–28, 35–37, 39), 235 (Example, #41–42)
• Construct one–dimensional, two–dimensional, and three–dimensional geometric figures using
a variety of tools and technologies (e.g., angle bisectors, perpendicular bisectors, triangles
given specific characteristics). (1.3.2)
65
point–slope, two points). (1.5.1)
PE/TE: 215 (#59), 217 (Example 3, #7–8), 218, 219 (#8–9), 220 (#30–33), 226 (#36–38),
256 (34–36), 269–273, 274 (#47, 49, 50, 52), 275 (#54), 276–283, 284 (#1–15),
285–289, 290 (#40–42), 293, 294 (#3–29), 295 (#30–44, 52–54), 296 (#60–62),
297 (#1–5, 9–14), 304 (#47–49), 313 (#1–9), 314 (#10–13), 315 (#14–28), 317,
383 (#58–53), 394 (#38–43), 408 (#49–54), 468 (#73–78), 525 (#55–57),
539 (#89–91), 638 (#44–52), 787 (#1–26)
• Find the solution to a system of linear equations using tables, graphs and symbols. (1.5.6)
PE/TE: 389, 390 (#1–3), 392–393, 394 (#29, 31), 395, 408 (#1–3), 430 (#4), 431 (#1–6),
435 (#1–9, 11–16), 460 (#67–72), 468 (#79–88), 474 (#72–77), 504 (#99–101),
525 (#55–57), 531 (#56–61), 608 (#60–62), 615 (#69–78), 789 (#1–28, 30–37)
5.2: Relate mathematical concepts procedures to other disciplines.
modeling in other disciplines.
PE/TE: 1, 119, 120, 242; Additional coverage of this standard can be found in Data
Analysis Sourcebook on the following pages: 63, 67–68, 88–89, 94–95
• Justify a prediction or an inference based on a set of data. (1.4.6)
PE/TE: 1, 119–120, 242, 244 (#4), 248 (#60, 65), 299 (#2–3); Additional coverage of this
standard can be found in Data Analysis Sourcebook on the following pages: 63,
67–68, 88–89, 94–95
• Create a physical activity plan that results in a specified number of calories over a specified
time. [PE]
5.2.2 Know contributions of individuals and cultures to the development of mathematics.
PE/TE: 201, 311 (#44), 722
• Recognize the mathematical contribution of a person or culture (e.g., create a report or
presentation that highlights a mathematical contribution related to current mathematical study).
PE/TE: 311 (#44), 722, 741 (Example 2)
66
5.3.1 Understand situations in which mathematics can be used to solve problems with local,
national, or international implications.
PE/TE: 639–644, 645, 730–735, 736–739
• Explain a method for determining whether a real world problem involves direct proportion or
inverse proportion. (1.1.4)
PE/TE: 639, 640 (Example 3, #1–2), 635 (Example 5), 637, 641, 643
• Describe how changes in the dimensions of objects affect perimeter, area, and volume in
real–world situations (e.g., how does the change in the diameter of an oil drum affect the area
and volume). (1.2.1)
PE/TE: 11 (Example 5, #10), 13 (#52–54, 58, 50), 14 (#63)
to maximize the grazing area of a tethered goat). (1.3.3)
PE/TE: 205 (#10), 207 (#33), 214 (#50, 52), 694 (#11), 732 (Example 3, #8),
733 (#2–4, 10–24), 734 (#33–37), 739 (#36–37)
5.3.2 Understand the mathematical knowledge and training requirements for
occupational/career areas of interest.
PE/TE: 26, 38, 44, 53, 97, 105, 136, 173, 187, 207, 302, 371, 421, 447, 466, 509, 544, 579,
586, 598, 621, 675, 734, 737, 742
• Select a career and research the mathematics necessary to get the job and the mathematics used
in the job.
36, 38, 97, 173, 207, 302, 371, 391, 421, 428, 466
67
Geometry: Concepts and Skills
correlated to the
GRADES 9/10
mathematics.
1.1.1 Understand and apply scientific notation. W
This standard is taught in Algebra 1: Concepts and Skills.
• Read and use scientific and exponential notation. [MC, RL]
• Identify a real–life situation to match a particular number written in scientific or exponential
notation and justify the answer. [MC, RL]
• Use scientific or exponential notation to simplify a problem. [RL, MC]
• Illustrate the meaning of scientific notation using pictures, diagrams, or numbers. [CU]
• Read and translate numbers represented in scientific notation from calculators and other
technology, tables, and charts.
68
Geometry: Concepts and Skills correlated to the
1.1.4 Apply understanding of direct and inverse proportion to solve problems. W
PE/TE: 218 (#52–57), 341 (#27–34), 360, 361 (#9–12), 362 (#38–45), 369 (#11–13, 16),
370 (#17–21), 377 (#30, 38), 379–381, 382 (#2–10), 384 (#19–26), 386–388,
390 (#7–19), 401 (#8–14), 404 (#2–6, 9–11), 687 (#7–14)
• Explain a method for determining whether a real–world problem involves direct proportion or
inverse proportion. [SP, CU, MC]
PE/TE: 360, 370 (#21), 374 (Example 3), 377 (#30, 38), 383 (#14), 384 (#29)
• Explain a method for solving a real–world problem involving direct proportion. [CU, MC]
PE/TE: 367 (Example 4), 370 (#21), 374 (example 3), 377 (#30, 38), 383 (#14), 384 (#29)
• Explain a method for solving a real–world problem involving inverse proportion. [CU, MC]
Opportunities to address this standard can be found in Algebra 1: Concepts and Skills.
• Solve problems using direct or inverse models (e.g., similarity, age of car vs. worth). [SP, MC]
PE/TE: 365–367, 369 (#11–13, 16), 370 (#17–20), 374 (#3–4), 376 (#18–19, 21–26),
386–388
• Explain, illustrate, or describe examples of direct proportion. [CU]
PE/TE: xxiii (#9–16), 218 (#52–57), 341 (#27–34), 349, 359, 361 (#9–12), 362 (#38–45),
377 (#30, 33–34, 38), 378 (#43–45, Quiz #1: #4–6), 379–381, 382 (#2–10),
383 (#11–13, 15–18), 384 (#19–26), 385 (#33, 38–41), 388 (#1–4), 390 (#7–19),
395 (#4–5), 396 (#11–14), 398 (#3–5), 401 (#8–14), 402 (#18–20), 403 (#21–23),
404 (#2–6, 9–11), 445 (#43–45), 455 (#7–8), 457 (#31–32), 490 (#53–58),
687 (#7–14)
• Explain, illustrate, or describe examples of inverse proportion. [CU]
• Use direct or inverse proportion to determine a number of objects or a measurement in a given
situation.
PE/TE: 369 (#11–13, 16), 370 (#17–20), 374 (#3–4), 376 (#18–19, 21–26), 380 (#1–2),
381 (#3–4), 382 (#2–10), 383 (#11–13, 15–18), 384 (#19–26), 385 (#33, 38–41),
388 (#1–4), 390 (#3–19), 395 (#4–5), 396 (#11–14), 398 (#3–5), 401 (#8–14),
402 (#18–20), 403 (#21–23), 404 (#2–6, 9–11), 445 (#43–45), 687 (#17–19),
688 (#31–33)
69
Computation
1.1.6 Apply strategies to compute fluently with rational numbers in all forms including
whole number exponents. W
PE/TE: 33 (#40–45), 49 (#1–20), 59 (#55–63), 149 (#37–42), 280 (#54–62), 308 (#37–42),
280 (#54–62), 480 (#69–74), 541 (#63–68), 562 (#44–49), 619 (#50–55)
• Complete multi–step computations using order of operations in situations involving
combinations of rational numbers including whole number exponents and square roots of
square numbers. [MC]
PE/TE: 33 (#40–45), 49 (#1–20), 59 (#55–63), 66 (#42–47), 101 (#7–12), 113 (#55–62),
125 (#47–49), 135 (#51–56), 149 (#37–42), 178 (#67–72), 263 (#40–45),
271 (#30–35), 280 (#54–62), 323 (#35–44), 459 (#47–55), 480 (#69–74),
499 (#56–61), 507 (#51–56), 555 (#51–56), 562 (#44–49), 619 (#50–55),
632 (#49–51), 670 (#1–9)
• Calculate using order of operations on all forms of rational numbers (e.g., (3•2+5)2–8, 22+
32).
PE/TE:
xxv (Evaluate Expressions: #1–8, 11–16; Solving Equations: #1–6), 33 (#40–45),
49 (#1–20), 59 (#55–63), 66 (#42–47), 101 (#7–12), 113 (#55–62), 125 (#47–49),
135 (#51–56), 149 (#37–42), 178 (#67–72), 263 (#40–45), 271 (#30–35),
280 (#54–62), 323 (#35–44), 459 (#47–55), 480 (#69–74), 499 (#56–61),
507 (#51–56), 555 (#51–56), 562 (#44–49), 619 (#50–55), 632 (#49–51), 670 (#1–9)
• Use properties to reorder and rearrange expressions to compute more efficiently. [ RL]
PE/TE: xxv (Distributive Property: #1–16), 33 (#40–45), 49 (#1–20), 59 (#55–63),
66 (#42–47), 101 (#7–12), 113 (#55–62), 125 (#47–49), 135 (#51–56), 149 (#37–42),
178 (#67–72), 263 (#40–45), 271 (#30–35), 280 (#54–62), 323 (#35–44),
459 (#47–55), 480 (#69–74), 499 (#56–61), 507 (#51–56), 555 (#51–56),
562 (#44–49), 619 (#50–55), 632 (#49–51), 670 (#1–9)
70
Estimation
1.1.8 Apply estimation strategies to determine the reasonableness of results in situations
involving multi–step computations with rational numbers including whole number powers
and square and cube roots. W
exact value is required. [CU]
• Describe various strategies used during estimation involving integers, rational numbers. [CU]
1.2.1 Analyze how changes in one or two dimensions of an object affect perimeter, area,
surface area, and volume. W
PE/TE: 496 (#23–28), 498 (#46), 503 (#11–16), 504 (#22–24), 506 (#39–40), 514 (#23–24),
528 (#18–20)
how doubling one dimension of a cube affects the surface area and volume). [CU, MC]
448 (#4), 481–482, 488 (#20), 502 (Example 3), 506 (#39–40), 528 (#18–20)
71
• Describe how changes in the dimensions of objects affect perimeter, area, and volume in real
world situations (e.g., how does the change in the diameter of an oil drum affect the area and
volume). [CU, MC]
367 (Example 4), 378 (#5), 425 (Example 2), 429 (#31), 442 (#14), 504 (#22–24),
514 (#23–24), 528 (#21)
• Solve problems by deriving the changes in two dimensions necessary to obtain a desired
surface area and/or volume (e.g., given a box with certain dimensions, make the volume of the
box y cubic units by changing two dimensions of the box). [SP]
486 (#4–5), 498 (#46), 503 (#11–16), 504 (#22–24)
• Compare a given change in one or two dimensions on the perimeter, area, surface areas, or
volumes of two objects.
367 (Example 4), 378 (#5), 425 (Example 2), 429 (#31), 433 (Example 4), 435 (#15),
438, 442 (#8–14), 443 (#23–28), 447 (#1–3), 449 (#15), 487 (#5–7), 488 (#17–19),
496 (#23–28), 498 (#46), 514 (#23–24)
• Determine the change in one dimension given a change in perimeter, area, volume, or surface
area.
435 (#16–20), 437 (#7–9), 440 (#4–6), 443 (#18–20), 447 (#4–7), 449 (#18–20),
507 (#47)
1.2.3 Understand how to convert units of measure within systems (U.S. or metric). W
• Understand how to convert units of measure within U.S. or within metric systems to achieve
an appropriate level of precision.
• Convert within a system to a unit size appropriate to a given situation.
72
• Convert to a larger unit within a system while maintaining the same level of precision (e.g.,
represent 532 centimeters to 5.32 meters).
• Convert to a smaller unit within a system to increase the precision of a derived unit of
measurement.
Procedures, precision, and estimation
1.2.5 Apply formulas to calculate measurements of right prisms or right circular cylinders.
W
PE/TE: 483–490, 500–507, 508–509, 523 (#1–3), 526 (#18–33), 692 (#19–24)
• Explain how to use a formula for finding the volume of a prism or cylinder. [CU, MC]
PE/TE: 500–502, 508–509
• Use a formula to find the volume of a prism or cylinder. [RL, MC]
PE/TE: 501 (#1–3), 502 (#4–6), 503 (#5–6, 11–13, 17–18), 504 (#19–22, 25),
505 (#27–34, 36), 506 (#39, 41–46), 507 (#50–51), 523 (#1–3), 526 (#18–33),
528 (#12–13, 15), 533 (#31–33), 562 (#41–42), 651 (#36, 38), 692 (#19–24)
• Use a formula to derive a dimension of a right prism or right cylinder given other measures.
507 (#47–49, 51)
• Use formulas to describe and compare the surface areas and volumes of two or more right
prisms and/or right cylinders. [RL]
484 (Example 2), 485 (#33), 486 (Example 3), 487 (#6), 488 (#19, 24, 26),
501 (Example 2b), 502 (Example 3), 503 (#11–13), 504 (#19–22), 505 (#27–32),
516 (#50), 691 (#10, 12), 692 (#22–24)
• Use formulas to obtain measurements needed to describe a right cylinder or right prism.
501 (Example 2, #1–3), 505 (#28–29), 507 (#47–49, 51), 692 (#21–24)
73
1.2.6 Understand and apply strategies to obtain reasonable measurements at an
appropriate level of precision. W
• Identify situations in which approximate measurements are sufficient.
• Estimate a reasonable measurement at an appropriate level of precision. [MC]
• Estimate quantities using derived units of measure (e.g., distance or time using miles per hour,
cost using unit cost). [MC]
[MC]
• Apply a process that can be used to find a reasonable estimate for the volume of prisms,
pyramids, cylinders, and cones.
1.3.1 Understand the relationship among characteristics of one–dimensional,
two–dimensional, and three–dimensional figures. W
PE/TE: 14–17, 35–36, 38 (#15–17), 64 (#14–16), 75, 178 (#42–47), 288 (#21–23), 303,
307 (#24–27), 339, 473–479, 481–485, 488 (#21–23, 27–31), 489 (#33–36, 38),
497 (#32–33), 504–505, 508–509, 515 (#36–39), 524 (#6–8), 636 (#13–15)
74
• Identify and label one– and two–dimensional characteristics (rays, lines, end points, line
segments, vertices, and angles) in three–dimensional figures. [CU]
PE/TE: 14–17, 18 (#56–57), 35–36, 38 (#15–17), 41 (#1–3), 175 (#2–3), 178 (#42–47), 417
PE/TE: 191, 481–482, 483–485, 488 (#21–23), 489 (#33–35), 497 (#32–37), 508–509
• Draw and label with names and symbols nets of right prisms and right cylinders. [RL, CU]
PE/TE: 489 (#33–36, 38), 497 (#32–33)
PE/TE: 63 (#7–8), 64 (#14–16), 75, 80 (#37), 111 (#30–33), 116 (Example 2), 120 (#1–2),
124 (#22), 196 (#26), 277 (#20), 287 (#5–7), 288 (#21–23), 303, 307 (#24–27),
341 (#4–5), 367 (Example 4), 383 (#14), 384 (#27–28), 477, 488 (#27–31),
489 (#42–44), 490–491, 497–498, 502, 504–505, 515 (#36–39), 516, 528 (#21–22),
546 (#18), 547 (#32–33), 554 (#42), 561 (#31), 596 (Example 2), 636 (#13–15)
• Describe or classify various shapes based on their characteristics.
PE/TE: 303, 307 (#24–27), 339, 341 (#4–5), 383 (#14), 384 (#27–28), 436 (#31), 473–479,
524 (#6–8)
• Make and test conjectures about two–dimensional and three–dimensional shapes and their
cross–sections of a given three–dimensional shape). [SP, RL, CU, MC]
PE/TE: 141 (#30), 191, 364, 386, 439, 481–482, 508–509, 594
1.3.2 Apply understanding of geometric properties and relationships. W
PE/TE: 16–17, 19 (#60–61, 63–65), 32 (#2–3), 40 (#45), 66, 74, 77 (#1–6), 78–80,
81 (#57–59), 93 (#27), 107, 112 (Example, #36–38), 122 (#1–6), 123–124, 126–127,
129 (#1–6), 130 (#7–15), 143–144, 150–151, 173–177, 183 (#15–17, 22), 190 (#32),
191, 217 (#41–43), 240–241, 276 (#7–8), 279 (#30–31), 324, 331, 337, 340 (#20–23),
385 (#30–31), 393, 416, 427, 438, 468–469, 476–477, 478 (#43–51), 546,
567 (#33–35), 624, 626, 640
75
• Use geometric properties and relationships to describe, compare, and draw two–dimensional
and three–dimensional shapes and figures.
PE/TE: 16–17, 19 (#60–61, 63–65), 20 (#70), 36, 38 (#1–4), 39 (#24–26), 41 (#46–48), 66,
74, 107, 183 (#22), 185, 190 (#32), 191, 279 (#30–31), 306, 308 (#28), 324,
340 (#24), 385 (#30–31), 392 (#38–39), 393, 416, 427, 438, 449 (#16–17),
449 (#15), 474, 478 (#43–51), 503 (#17–18), 546, 567 (#33–35), 584–585, 624, 626,
640
• Construct geometric figures using a variety of tools and technologies (e.g., angle bisectors,
perpendicular bisectors, triangles given specific characteristics). [MC]
PE/TE: 66, 143–144, 148 (#22–24), 150–151, 183 (#22), 187, 190 (#32), 206, 240–241, 250,
272, 279 (#30–31), 308 (#28), 321 (#23), 324, 331, 340 (#24), 385 (#30–31),
392 (#38–39), 393, 438, 449 (#16–17), 449 (#15), 546, 567 (#33–35), 624, 626, 640
• Draw a plane shape and justify the answer given a set of characteristics. [RL, CU]
PE/TE: 150–151, 216 (Example, #34–36), 275 (Example 4), 276 (#7–6), 321 (#23),
567 (#33–35)
• Use the properties of two–dimensional and three–dimensional shapes to solve mathematical
a transversal, and an angle, find the other angles). [SP, RL, CU, MC]
PE/TE: 74, 77 (#1–6), 78–80, 81 (#57–59), 119 (#28–30), 122 (#1–6), 123–124,
125 (#33–35), 126–127, 129 (#1–6), 130 (#7–15), 131 (#16–18), 132 (#1–8),
133 (#25), 134 (#38), 135 (#1–12), 183 (#15–17), 188 (#5–6), 197 (#33–34),
217 (#41–43), 377 (#30, 38), 561 (#31), 562 (#38), 567 (#31), 584–585
• Compare two–dimensional and three–dimensional shapes according to characteristics
including faces, edges, and vertices, using actual and virtual modeling. [RL, CU]
32 (#2–3), 40 (#45), 93 (#27), 173–177, 269 (#10–11), 281, 325, 337, 340 (#20–23),
473, 475, 476–479, 521 (#29–32)
• Use technology to generate two and three dimensional models of geometric figures with given
geometric characteristics (e.g., generate a two–dimensional animation using pentagons with
fixed coordinates for one edge). [RL, SP]
PE/TE: 66 (#31), 158 (#46–47), 183 (#22), 190 (#32), 199, 264, 308 (#28), 324, 331,
340 (#24), 385 (#30–31), 392 (#38–39), 393, 438, 449 (#16–17), 567 (#33–35), 546,
624, 626, 640
76
• Create a three–dimensional scale drawing with particular geometric characteristics. [SP, CU,
MC]
PE/TE: 112 (Example, #36–38), 399, 438, 468–469
1.3.3 Apply understanding of geometric properties and location of points to figures. W
PE/TE: 156 (#22–31), 157 (#32–35, 38–44), 158 (#46–47), 197 (#33–34), 199, 211 (#19–21),
392 (#44–52), 399, 516 (#52–57), 591 (#8–12), 592 (#40–44), 593 (#45, 7), 626–630,
632 (#43–46), 637 (#27–30), 639 (#10–12), 640651 (#54–56), 695 (#7–8)
• Use coordinates to describe or identify the location of objects on coordinate grids.
153 (Example 2), 154 (Example 4, #6–7), 155 (#7–8), 156 (#22–31),
157 (#32–35, 38–44), 158 (#48–50), 159 (#8–9), 163 (#31–32), 165 (#8), 191,
193 (Example 3), 197 (#33–34), 211 (#19–21), 283 (Example 3, #1–3),
287 (#14–16), 289 (#40–42), 297 (#7–8), 399, 590 (Example 3), 591 (#8–12),
592 (#40–44), 632 (#43–46), 635 (Example 3, #4), 637 (#27–30), 638 (#37),
639 (#10–12), 645 (#53–55), 651 (#54–56), 695 (#7–8), 696 (#42–44)
• Describe geometric characteristics of two–dimensional objects using coordinates on a grid.
[MC]
150–151, 153–154, 155 (#8), 156, 157 (#38–41), 158 (#46–47), 159 (#8–9),
163 (#31–32), 165 (#8), 191, 193 (Example 3), 197 (#33–34), 211 (#19–21),
287 (#14–16), 289 (Example, #40–41), 399, 591 (#8–12), 592 (#40–44),
593 (#45–47), 627–630, 635 (#4), 637 (#27–30), 639 (#10–12), 645 (#53–55),
651 (#54–56), 695 (#7–8), 696 (#42–44)
from a given point; a point equidistant from a given set of points). [CU]
55 (#3–5), 193 (Example 3), 211 (#19–21), 283 (Example 3, #1–3), 287 (#14–16),
297 (#7–8), 399, 590 (Example 3), 591 (#8–12), 592 (#40–44), 593 (#45–47),
632 (#43–46), 635 (Example 3, #4), 637 (#27–30), 638 (#37), 646 (18), 651 (#56),
695 (#7–8)
77
to maximize the grazing area of a tethered goat). [MC, SP, RL]
153–154, 155 (#8), 156–157, 158 (#45, 48), 159 (#8–9), 163 (#31–32), 165 (#8),
191, 193 (Example 3, #1–3), 197 (#33–34), 283 (Example 3, #1–3), 287 (#14–16),
289 (#40–42), 297 (#7–8), 399, 590 (Example 3), 591 (#8–12), 592 (#40–44),
637 (#27–30), 638 (#37), 639 (#10–12), 645 (#53–55), 651 (#54–56), 695 (#7–8),
696 (#42–44)
• Use tools and technology to draw objects on a coordinate grid based on given conditions. [CU]
157 (#38–41), 158 (#46–47), 199, 264, 324, 331, 399, 438, 626, 640
• Identify, interpret, and use the meaning of slope of a line as a rate of change using physical,
symbolic, and technological models. [SP, RL, MC]
150–151, 299 (Example 2, #7–12), 315 (#50–55), 392 (#44–52), 516 (#52–57),
600 (#40–45), 665 (#1–15)
1.3.4 Apply understanding of multiple transformations. W
PE/TE: 153–154, 155 (#6–8), 156 (#24–31), 281, 282–283, 287 (#20), 297 (#7–9), 393–397,
399, 403 (#24–26), 633, 636–638, 640
• Apply multiple transformations to create congruent and similar figures in any or all of the four
quadrants.
281, 282–283, 286 (#12–13), 289, 297 (#7–9)
• Use multiple transformations (combinations of translations, reflections, or rotations) to draw
an image. [RL]
287 (#20), 640, 696 (#42–44)
78
• Use dilation (expansion or contraction) of a given shape to form a similar shape. [RL, CU]
393–397, 399, 403 (#24–26), 404 (#13–14), 405 (#7), 632 (#47–48)
• Determine the final coordinates of a point after a series of transformations. [RL, CU]
PE/TE: 153–154, 155 (#6–8), 156 (#24–31), 157 (#32–35, 42–44), 637 (#27–30),
639 (#10–12), 640, 696 (#42–44)
• Examine figures to determine rotational symmetry about the center of the shape. [RL, MC]
633–638, 639 (#7–12)
• Define a set of transformations that would map one onto the other given two similar shapes.
[SP, RL]
281–283, 399
• Create a design with or without technology using a combination of two or more
transformations with one or two two–dimensional figures. [SP, RL]
287 (#20), 640, 651 (#54–56)
• Use technology to create two– and three–dimensional animations using combinations of
transformations. [MC, SP, RL]
640
statistics.
Probability
1.4.1 Understand the concept of conditional probability. W
• Compare the probabilities of dependent and independent events. [CU, MC]
• Determine and justify whether the outcome of a first event affects the probability of a later
event (e.g., drawing cards from a deck with or without replacement). [CU]
79
• Explain the difference between dependent and independent events. [CU]
• Explain and give examples of compound events. [CU]
1.4.2 Apply understanding of dependent and independent events to calculate probabilities.
W
This standard is taught in Data Analysis Sourcebook on the following pages: 2–10, 13, 19–21,
28–29
• Determine probabilities of dependent and independent events. [SP]
• Generate the outcomes and probability of multiple independent and dependent events using a
model or procedure (e.g., tree diagram, area model, counting procedures).
• Generate the outcomes and probability of events using a counting procedure (e.g., the number
of license plates that can be made with three letters and three numbers; winning the lottery).
[MC]
events using simulations with and without technology. [CU]
• Create a simple game based on independent probabilities wherein all players have an equal
probability of winning. [MC, SP]
This standard is taught in Data Analysis Sourcebook on the following page: 13
• Create a simple game based on compound probabilities. [MC, SP]
• Determine the sample space for independent or dependent events.
80
Statistics
1.4.3 Apply appropriate methods and technology to collect data or evaluate methods used
by others for a given research questions. W
• Identify sources of bias in data collection questions, samples, and/or methods and describe
how such bias can be controlled. [RL, CU]
• Evaluate methods and technology used to investigate a research question. [CU, MC]
P This standard is taught in Data Analysis Sourcebook on the following pages: 28–32
• Collect data using appropriate methods.
• Use technology appropriately to collect data. [RL, MC]
• Identify appropriate data collection methods that might impact the accuracy of the results of a
given situation. [RL, CU]
• Determine whether the sample for a given study was from a representative sample.
• Determine whether the methods of data collection used were appropriate for a given question
or population. [RL]
1.4.4 Understand and apply techniques to find the equation for a reasonable linear model.
W
• Determine the equation for a reasonable line to describe a set of bivariate data. [RL, MC]
81
• Determine the equation of a line that fits the data displayed on a scatter plot. [SP, RL]
• Use technology to determine the line of best fit for a set of data. [MC]
• Match an equation with a set of data. [MC]
• Match an equation with a graphic display. [MC]
• Create a graph based on the equation for the line.
Algebra 1: Concepts and Skills.
1.4.5 Analyze a linear model to judge its appropriateness for a data set. W
This standard is taught in Data Analysis Sourcebook on the following pages: 50, 86–89, 95
• Determine whether a straight line is an appropriate way to describe a trend in a set of bivariate
data. [MC, RL]
• Determine whether the underlying model for a set of data is linear. [RL, MC]
• Decide and explain whether it is appropriate to extend a given data set following a line of best
fit. [RL, MC]
• Determine whether a linear prediction from a given set of data is appropriate for the data and
support the decision with data. [MC].
• Determine whether an equation for a line is appropriate for a given set of data and support the
judgment with data. [RL, MC]
82
• Use technology to generate data to fit a linear model. [SP, MC]
This standard is taught in Data Analysis Sourcebook on the following pages: 89, 95
1.4.6 Apply understanding of statistics to make, analyze, or evaluate a statistical argument.
W
86–101
• Identify trends in a set of data in order to make a prediction based on the information. [CU,
MC]
64–68, 86–89, 90–93
•
Justify a prediction or an inference based on a set of data. [CU, MC]
This standard is taught in Data Analysis Sourcebook on the following pages: 63, 67–68,
86–89, 94–95
population growth of deer vs. availability of natural resources or hunting permits). [MC, CU,
RL]
• Use statistics to support different points of view. [RL]
• Analyze a set of statistics to develop a logical point of view. [RL. CU, MC]
• Justify or refute claims and supporting arguments based on data. [CU, MC]
86–101
• Determine whether statistics have been used or misused to support a point of view or argument
and support the evaluation with data. [RL]
60–76
83
1.5.1 Apply processes that use repeated addition (linear) or repeated multiplication
(exponential). W
PE/TE: 3–6, 7 (#33–37), 11 (#8–12), 43 (#13–15), 46 (#1–4), 81 (#60–63), 666–667,
675 (#1–8)
• Recognize, extend, or create a pattern or sequence between sets of numbers and/or linear
patterns. [RL, CU, MC]
PE/TE: 3–6, 7 (#33–37), 8, 9 (Example 2), 11 (#8–12), 12 (#13–14), 13 (#21, 24), 20 (#1–2),
43 (#18), 46 (#1–4, 6–7), 66 (#34–37), 81 (#60–63), 675 (#1–8)
• Identify, extend, or create a geometric or arithmetic sequence or pattern. [RL, CU]
PE/TE: 3 (Example 2, #3–4), 4 (#7–8), 5 (#5–10, 17–22), 6 (#26–30, 32), 7 (#36–37), 8,
9 (Example 2), 12 (#14), 13 (#21), 43 (#13–15), 46 (#1–4), 66 (#34–37),
81 (#60–63), 675 (#3–8)
• Translate among equivalent numerical, graphical, and algebraic forms of a linear function. RL,
MC]
PE/TE: 666–667; More extensive coverage of this standard can be found in Algebra 1:
• Make predictions based on a pattern or sequence.
3 (Example 2, #3–4), 4 (#7–8), 5 (#5–10, 17–22), 6 (#26–30, 32), 7 (#36–37), 8,
9 (Example 2), 12 (#14), 13 (#21), 43 (#13–15), 46 (#1–4), 66 (#34–37),
81 (#60–63), 675 (#3–8)
1.5.2 Analyze a pattern, table, graph, or model involving repeated addition (linear) or
repeated multiplication (exponential) model to write an equation or rule. W
PE/TE: 666–667; More extensive coverage of this standard can be found in Algebra 1:
point–slope, two points). [RL, MC]
PE/TE: 666–667
84
• Generate and use rules for a pattern to make predictions about future events (e.g., population
growth, future sales, growth of corn stalks, future value of savings account). [SP, RL, MC]
• Identify or write an equation or rule to describe a pattern, sequence, and/or a linear function.
[RL, CU, MC]
• Write an equation for a line given a set of information (e.g., two points, point–slope, etc.).
[CU, MC]
• Write a recursive definition of a geometric pattern (e.g., Start and New = Old * Number). [CU,
MC]
• Represent systems of equations and inequalities graphically. [RL, MC]
• Write a story that represents a given linear equation or expression. [CU, MC]
• Write an expression, equation, or inequality with two variables representing a linear model of a
real–world problem. [CU, MC]
1.5.4 Apply understanding of equations, tables, or graphs to represent situations involving
relationships that can be written as repeated addition (linear) or repeated multiplication
(exponential). W
PE/TE: 41 (#53–60), 49, 87 (#38–43), 135 (#51–56), 280 (#54–62), 323 (#35–44),
507 (#58–63), 666–667, 670–673
• Represent variable quantities through expressions, equations, inequalities, graphs, and tables to
represent linear situations involving whole number powers and square and cube roots. [CU,
MC]
PE/TE: 13 (#31–41), 41 (#53–60), 49, 66 (#42–47), 81 (#66–71), 87 (#38–43), 125 (#47–49),
135 (#51–56), 167, 178 (#67–72), 271 (#30–35), 280 (#54–62), 323 (#35–44),
398 (#24–29), 507 (#58–63), 562 (#44–49), 593 (#63–68), 619 (#50–55), 666–667,
670–673
85
situations that can be described using repeated addition (e.g., models that are linear in nature).
[CU, MC]
situations that can be described using repeated multiplication (e.g., models that are exponential
such as savings accounts and early stages of population growth). [CU, MC]
New=Old + some number). [CU, MC]
New=Old _ some number). [CU, MC]
• Select an expression or equation to represent a given real world situation. [MC]
13 (#31–41), 41 (#53–60), 49, 66 (#42–47), 81 (#66–71), 87 (#38–43), 125 (#47–49),
135 (#51–56), 167, 178 (#67–72), 271 (#30–35), 280 (#54–62), 323 (#35–44),
398 (#24–29), 507 (#58–63), 562 (#44–49), 593 (#63–68), 619 (#50–55), 666–667,
670–673
1.5.5 Apply procedures to simplify expressions. W
PE/TE: 81 (#66–71), 407 (#1–12), 445 (#49–56), 455 (#9–11), 456 (#15–21),
488 (#17–20, 24–31), 494 (#4–6), 496 (#23–28), 517–521, 671 (#9–17),
669 (#29–40)
• Simplify expressions and evaluate formulas involving exponents.
PE/TE: 81 (#66–71), 101 (#1–8), 407 (#1–12), 445 (#49–56), 451, 453, 455 (#9–11),
456 (#15–21), 480 (#75–80), 486 (#4–6), 487 (#5–7), 488 (#17–20, 24–31),
494 (#4–6), 496 (#23–28), 502, 505 (#27–32, 36), 512, 517–521, 671 (#9–17),
669 (#29–40)
• Justify a simplification of an expression involving exponents. [RL, CU]
86
• Use multiple mathematical strategies and properties to simplify expressions.
PE/TE: 81 (#66–71), 101 (#1–8), 407 (#1–12), 445 (#49–56), 451, 453, 455 (#9–11),
456 (#15–21), 480 (#75–80), 486 (#4–6), 487 (#5–7), 488 (#17–20, 24–31),
494 (#4–6), 496 (#23–28), 502, 505 (#27–32, 36), 512, 517–521, 671 (#9–17),
669 (#29–40)
1.5.6 Apply procedures to solve equations and systems of equations. W
PE/TE: 49 (#13–20), 66 (#42–47), 280 (#54–62), 407 (Example 2, #9–12), 443 (#18–22),
449 (#18–22), 457 (#24–29), 507 (#58–63), 562 (#44–49), 583, 593 (#63–68),
677 (#1–33)
• Rearrange formulas to solve for a particular variable (e.g., given A = 0.5bh, solve for h). [MC,
CU]
PE/TE: 407 (Example 2, #9–12), 435 (#19–20), 440 (Example 2, #4–6), 443 (#18–22),
447 (Example 2, #4–7), 449 (#18–22), 453 (Example 3), 457 (#24–29), 464 (#20–23)
• Solve real–world situations involving linear relationships and verify that the solution makes
sense in relation to the problem. [SP, RL, CU, MC]
• Find the solution to a system of linear equations using tables, graphs, and symbols. [CU, MC]
PE/TE: 583; More extensive coverage of this standard can be found in Algebra 1: Concepts
and Skills.
• Interpret solutions of systems of equations. [CU, MC]
• Solve multi–step equations. [SP, RL]
PE/TE: 49 (#13–20), 66 (#42–47), 87 (#38–43), 135 (#51–56), 178 (#67–72), 280 (#54–62),
507 (#58–63), 562 (#44–49), 593 (#63–68), 677 (#1–33)
• Use systems of equations to analyze and solve real–life problems. [SP, CU, MC]
87
• Determine when two linear options yield the same outcome (e.g., given two different
investment or profit options, determine when both options will yield the same result).
• Use systems of equations to determine the most advantageous outcome given a situation (e.g.,
given two investment options, determine under what conditions each will yield the best
result.). [MC, SP]
88
Component 2.1: Investigate situations.
Example: The following are the times (in seconds) of the Olympics in the given years. Using this
information, is it reasonable to believe that the women will run as fast as the men in this event?
Justify your answer using this data:
1948 10.3 11.9
1976 10.06 11.08
1952 10.4 11.5
1980 10.25 11.06
1956 10.5 11.5
1984 9.99 10.97
1960 10.2 11.0
1988 9.92 10.54
1964 10
11.4
1992 9.96 10.82
1968 9.95 11.0
1996 9.84 10.94
1972 10.14 11.07
2000 9.87 10.75
PE/TE: 228–229, 352–353, 468–469, 584–585, 653–654
• Use strategies to become informed about the situation (e.g., listing information; examine the
table for patterns; create a scatter plot to look for patterns; asking questions).
228–229, 352–353, 468–469, 584–585
• Summarize the problem (e.g., there are Olympic winning times over the past 50 years; both
men’s and women’s times are decreasing; will there come a time when women run faster than
men).
228–229, 352–353, 468–469, 584–585
be found; extend the pattern to see if women’s times will be less).
468–469, 584–585
• Determine whether information is missing or extraneous (e.g., compare the list of known
things to the list of needed things to see if there are things that are not needed).
468–469, 584–585
89
• Define the problem (e.g., if the pattern continues in the same fashion, will women run faster
than men and, if so, when will that occur).
228–229, 352–353, 468–469, 584–585
PE/TE: 468–469, 584–585, 653–654
• Organize relevant information from multiple sources (e.g., create a list of known and unknown
information; create a scatter plot of men’s and women’s times vs. time on the same coordinate
axis to analyze the patterns).
468–469, 584–585
• Select and apply appropriate mathematical tools to devise a strategy in a situation (e.g., if the
data, in either tabular or graphical form, suggest a linear relationship, plan to find a linear
equation for each set of data; solve those equations simultaneously [or use technology to find
the intersection of the two lines] to answer the question). If the data pattern suggests a
non–linear model, plan to project what the pattern is and extend that pattern.
468–469, 584–585
PE/TE: 468–469, 584–585, 653–654
• Implement the plan devised to solve the problem (e.g., solve the set of simultaneous equations
to arrive at a time where the two times are the same).
468–469, 584–585, 653–654
• Use mathematics to solve the problem (e.g., use algebra to write equations for the two linear
models, solve the system of equations using either symbols or technology).
468–469, 584–585, 653–654
90
• Identify when an approach is unproductive and modify or try a new approach (e.g., if the result
does not make sense in the context, return to the plan to see if something has gone wrong and
adjust accordingly).
468–469, 584–585
• Check the solution to see if it works (e.g., the solution may be a partial year [i.e., 2003.6];
decide how to deal with this and also if the year is reasonable [i.e., 1925 does not make sense
given the context]).
468–469, 584–585, 653–654
91
3.1.1. Synthesize information from multiple sources in order to answer questions. W
PE/TE: 77 (#1–6), 78–80, 119 (#28–30), 122 (#1–6), 123–124, 129 (#1–6), 130 (#7–15),
131 (#16–18), 135 (#1–12), 584–585
• Use the properties of two–dimensional and three–dimensional figures to solve mathematical
a transversal, and an angle, find the other angles).
PE/TE: 74, 77 (#1–6), 78–80, 81 (#57–59), 119 (#28–30), 122 (#1–6), 123–124,
125 (#33–35), 126–127, 129 (#1–6), 130 (#7–15), 131 (#16–18), 132 (#1–8),
133 (#25), 134 (#38), 135 (#1–12), 183 (#15–17), 188 (#5–6), 197 (#33–34),
217 (#41–43), 377 (#30, 38), 561 (#31), 562 (#38), 567 (#31), 584–585
3.2.1 Apply skill of conjecturing and analyze conjectures by formulating a proof or
constructing a counter example. W
PE/TE: 8–12, 191, 364, 508–509, 594
• Make and test conjectures about two–dimensional and three–dimensional figures and their
cross–sections of a given three–dimensional shape). (1.3.1)
PE/TE: 8–12, 13 (#20–22), 191, 364, 386, 439, 481–482, 508–509, 594
3.2.2 Analyze information to draw conclusions and support them using inductive and
deductive reasoning. W
PE/TE: 4–6, 7 (#33–37), 8–9, 150–151, 505 (#30–34), 512 (#4–8), 567 (#33–35); Additional
coverage of this standard can be found in Data Analysis Sourcebook on the following
pages: 46–51, 60–63, 64–68, 86–89, 90–93
92
• Compare and describe the volume of cylinders, cones, and prisms when an attribute is changed
(e.g., the area of the base, the height of solid). (1.2.4)
PE/TE: 504 (#22), 505 (#30–34), 512 (#4–8)
• Draw a plane shape of a given set of characteristics and justify the answer. (1.3.2)
PE/TE: 150–151, 216 (Example, #34–36), 275 (Example 4), 276 (#7–6), 321 (#23),
567 (#33–35)
• Identify trends in a set of data in order to make a prediction based on the information. (1.4.6)
PE/TE: 4–6, 7 (#33–37), 8–9, 11–12, 13 (#20–23); Additional coverage of this standard can
be found in Data Analysis Sourcebook on the following pages: 46–51, 60–68,
86–101
• Use statistics to support different points of view. (1.4.6)
3.2.3 Analyze procedures to determine appropriateness of claims and arguments. W
86–101
• Examine claims and supporting arguments based on data and make needed revisions. (1.4.6)
86–101
3.3.1 Analyze results using inductive and deductive reasoning.
PE/TE: 17, 19 (#60–61, 63–65), 191, 279 (#30–31), 364–365, 370 (#17–25), 372, 373 (#1–2),
374 (#3–4), 375–376, 382–384, 502 (#4–6), 503 (#5, 7, 11–13, 17–18),
504 (#19–22, 25), 505 (#27–36), 514 (#17–22), 515 (#30–36, 39), 523 (#1–4, 7),
692 (#19–30)
93
• Compare and contrast similar two–dimensional figures and shapes using properties of
two–dimensional figures and shapes. (1.3.2)
PE/TE: 17, 19 (#60–61, 63–65), 20 (#70), 36, 38 (#1–4), 39 (#24–26), 41 (#46–48), 66, 74,
107, 183 (#22), 185, 190 (#32), 191, 279 (#30–31), 306, 308 (#28), 324, 340 (#24),
364–365, 366 (#1–2), 369 (#11–16), 370 (#17–25), 372, 373 (#1–2), 374 (#3–4),
375–376, 378 (#7–9), 380 (#1–2), 381 (#3–4), 382–384, 385 (#30–31),
392 (#38–39), 393, 416, 427, 438, 449 (#16–17), 449 (#15), 474, 478 (#43–51),
503 (#17–18), 546, 567 (#33–35), 584–585, 624, 626, 640
• Find a reasonable estimate for the volume of prisms, pyramids, cylinders, and cones. (1.2.6)
PE/TE: 501 (#1–3), 502 (#4–6), 503 (#5, 7, 11–13, 17–18), 504 (#19–22, 25), 505 (#27–36),
506 (#41–46), 507 (#50), 510 (Example 1), 511 (Example 2, #1–3),
512 (Example 3, #4–8), 513 (#5–7, 12–16), 514 (#17–22), 515 (#30–36, 39),
516 (#42–44), 523 (#1–4, 7), 692 (#19–30)
relationships, counter examples, or proportional reasoning. W
• Examine a set of data, research other sources to see if the data is consistent, find articles
written to see if the data makes sense, to develop a logical point of view and to support that
view. (1.4.6)
94
4.1.1 Understand how to develop or apply an efficient system for collecting mathematical
information for a given purpose. W
• Collect data efficiently on the outcomes of first events and later events to determine and justify
how the first event affects the probability of later events (e.g., drawing cards from a deck with
or without replacement). (1.4.1)
4.1.2 Synthesize mathematical information for a given purpose from multiple, self–selected
sources. W
population growth of deer vs. availability of natural resources or hunting permits). (1.4.6)
4.2.1 Analyze mathematical information to organize, clarify, and refine an argument. W
60–76, 86–101
• Develop an argument to support a given point of view and set of statistics. (1.4.6)
60–76, 86–101
95
4.2.2 Understand how to express ideas and situations using mathematical language and
notation. W
PE/TE: 211 (#19–21), 399, 481–482, 506 (#39–40), 591 (#8–12), 592 (#40–44), 593 (#45–47),
632 (#43–46), 637 (#27–30), 651 (#56), 695 (#7–8)
traveled divided by hours traveled yields the derived unit [miles per hour]). (1.2.2)
from a given point; a point equidistant from a given set of points). (1.3.3)
55 (#3–5), 193 (Example 3), 211 (#19–21), 283 (Example 3, #1–3), 287 (#14–16),
297 (#7–8), 399, 590 (Example 3), 591 (#8–12), 592 (#40–44), 593 (#45–47),
632 (#43–46), 635 (Example 3, #4), 637 (#27–30), 638 (#37), 646 (18), 651 (#56),
695 (#7–8)
doubling the edge of a cube affects the surface area). (1.2.1)
PE/TE: 448 (#4), 481–482, 488 (#20), 502 (Example 3), 506 (#39–40), 528 (#19)
events using simulations with and without technology. (1.4.2)
96
5.1.1 Apply multiple mathematical concepts and procedures in a given problem or
situation. W
PE/TE: 153–154, 155 (#7–8), 157 (#32–35, 38–44), 637 (#27–30), 639 (#10–12), 640,
696 (#42–44)
(1.2.6)
• Determine the final coordinates of a point after a series of transformations. (1.3.4)
PE/TE: 153–154, 155 (#6–8), 156 (#22–31), 157 (#32–35, 38–44), 159 (#8–9),
283 (Example 3), 399, 632 (#43–46), 635 (Example 3, #4), 637 (#27–30), 638 (#37),
639 (#10–12), 640, 696 (#42–44)
5.1.2 Understand how use different mathematical models and representations in the same
situation. W
PE/TE: 66, 143–144, 150–151, 240–241, 299 (Example 2, #7–12), 324, 331, 385 (#30–31),
392 (#44–52), 438, 546, 600 (#4–45), 624, 626, 640, 666–667
• Identify, interpret, and use the meaning of slope of a line as a rate of change using concrete,
symbolic, and technological models. (1.2.2)
PE/TE: 299 (Example 2, #7–12), 315 (#50–55), 392 (#44–52), 516 (#52–57), 600 (#4–45),
665 (#1–15)
• Construct one–dimensional, two–dimensional, and three–dimensional geometric figures using
a variety of tools and technologies (e.g., angle bisectors, perpendicular bisectors, triangles
given specific characteristics). (1.3.2)
PE/TE: 66, 143–144, 148 (#22–24), 150–151, 183 (#22), 187, 190 (#32), 206, 240–241, 250,
272, 279 (#30–31), 308 (#28), 321 (#23), 324, 331, 340 (#24), 385 (#30–31),
392 (#38–39), 393, 438, 449 (#16–17), 449 (#15), 546, 567 (#33–35), 583, 624, 626,
640, 666–667
97
point–slope, two points). (1.5.1)
PE/TE: 666–667
• Find the solution to a system of linear equations using tables, graphs and symbols. (1.5.6)
PE/TE: 583; More extensive coverage of this standard can be found in Algebra 1: Concepts
and Skills.
5.2: Relate mathematical concepts procedures to other disciplines.
modeling in other disciplines.
PE/TE: 4–6, 7 (#33–37), 8–9, 11–12, 13 (#20–23), 126–127
• Justify a prediction or an inference based on a set of data. (1.4.6)
PE/TE: 4–6, 7 (#33–37), 8–9, 11–12, 13 (#20–23), 65 (#27), 114 (Geo–Activity), 126–127,
150, 185 (Geo–Activity), 191, 384 (#29), 399, 508–509
• Create a physical activity plan that results in a specified number of calories over a specified
time. [PE]
5.2.2 Know contributions of individuals and cultures to the development of mathematics.
PE/TE: 192, 479
• Recognize the mathematical contribution of a person or culture (e.g., create a report or
presentation that highlights a mathematical contribution related to current mathematical study).
PE/TE: 192, 479
98
5.3.1 Understand situations in which mathematics can be used to solve problems with local,
national, or international implications.
PE/TE: 153–154, 156–157, 197 (#33–34), 287 (#14–16), 360, 377 (#30, 38), 378 (#5),
429 (#31), 442 (#14), 504 (#22–24), 514 (#23–24), 591 (#8–12), 592 (#40–44),
639 (#10–12), 645 (#53–55), 696 (#42–44)
• Explain a method for determining whether a real world problem involves direct proportion or
inverse proportion. (1.1.4)
PE/TE: 360, 370 (#21), 374 (Example 3), 377 (#30, 38), 383 (#14), 384 (#29)
• Describe how changes in the dimensions of objects affect perimeter, area, and volume in
real–world situations (e.g., how does the change in the diameter of an oil drum affect the area
and volume). (1.2.1)
367 (Example 4), 378 (#5), 425 (Example 2), 429 (#31), 442 (#14), 504 (#22–24)
514 (#23–24), 528 (#21)
to maximize the grazing area of a tethered goat). (1.3.3)
153–154, 155 (#8), 156–157, 158 (#45, 48), 159 (#8–9), 163 (#31–32), 165 (#8),
191, 193 (Example 3, #1–3), 197 (#33–34), 283 (Example 3, #1–3), 287 (#14–16),
289 (#40–42), 297 (#7–8), 399, 590 (Example 3), 591 (#8–12), 592 (#40–44),
637 (#27–30), 638 (#37), 639 (#10–12), 645 (#53–55), 651 (#54–56), 695 (#7–8),
696 (#42–44)
5.3.2 Understand the mathematical knowledge and training requirements for
occupational/career areas of interest.
PE/TE: 62, 86, 134, 183, 288, 329, 335, 370, 414, 497, 505, 553, 559, 574, 638
• Select a career and research the mathematics necessary to get the job and the mathematics used
in the job.
PE/TE: 62, 71, 86, 126, 134, 329, 360, 370, 497, 553, 638
99
WA 85
9/2004
2004/05
CC2

McDougal Littell Concepts and Skills: Algebra 1 and Geometry

Transcription

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