G r a d

Transcription

G r a d

2014 - 2015
Grade 7 Mathematics
Curriculum Map
Mathematics Florida State Standards
Volusia County Curriculum Maps are revised annually and updated throughout the year.
The learning goals are a work in progress and may be modified as needed.
Mathematics Florida State Standards
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. (MAFS.K12.MP.1)
Solving a mathematical problem involves making sense of what is known and applying a thoughtful and logical process which
sometimes requires perseverance, flexibility, and a bit of ingenuity.
2. Reason abstractly and quantitatively. (MAFS.K12.MP.2)
The concrete and the abstract can complement each other in the development of mathematical understanding: representing a
concrete situation with symbols can make the solution process more efficient, while reverting to a concrete context can help make
sense of abstract symbols.
3. Construct viable arguments and critique the reasoning of others. (MAFS.K12.MP.3)
A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and supporting
evidence.
4. Model with mathematics. (MAFS.K12.MP.4)
Many everyday problems can be solved by modeling the situation with mathematics.
5. Use appropriate tools strategically. (MAFS.K12.MP.5)
Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen mathematical
understanding.
6. Attend to precision. (MAFS.K12.MP.6)
Attending to precise detail increases reliability of mathematical results and minimizes miscommunication of mathematical
explanations.
7. Look for and make use of structure. (MAFS.K12.MP.7)
Recognizing a structure or pattern can be the key to solving a problem or making sense of a mathematical idea.
8. Look for and express regularity in repeated reasoning. (MAFS.K12.MP.8)
Recognizing repetition or regularity in the course of solving a problem (or series of similar problems) can lead to results more quickly
and efficiently.
Grade 7 Mathematics: Mathematics Florida Standards
In Grade 7,instructional time should focus on four critical area: (1) developing understanding of and applying proportional relationships;
(2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving
problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve
problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.
(1) Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students
use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes,
tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by
using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and
understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships
from other relationships.
(2) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation),
and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational
numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By
applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero),
students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational
numbers as they formulate expressions and equations in one variable and use these equations to solve problems.
(3) Students continue their work with area from Grade 6, solving problems involving area and circumference of a circle and surface area of threedimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional
figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationship between angles formed by
intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve
real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes and right prisms.
(4) Students build on their previous work with single data distributions to compare two data distributions and address questions about difference
between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative
samples for drawing inferences.
Fluency Recommendations
7.EE.3:
7.EE.4:
7.NS.1–2:
Students solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions and
decimals), using tools strategically. This work is the culmination of many progressions of learning in arithmetic, problem solving and
mathematical practices.
In solving word problems leading to one-variable equations of the form px + q = r and p(x + q) = r, students solve the equations
fluently. This will require fluency with rational number arithmetic (7.NS.1–3), as well as fluency to some extent with applying
properties operations to rewrite linear expressions with rational coefficients (7.EE.1).
Adding, subtracting, multiplying and dividing rational numbers is the culmination of numerical work with the four basic operations. The
number system will continue to develop in grade 8, expanding to become the real numbers by the introduction of irrational numbers,
and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers.
Because there are no specific standards for rational number arithmetic in later grades and because so much other work in grade 7
depends on rational number arithmetic (see below), fluency with rational number arithmetic should be the goal in grade 7.
The following English Language Arts LAFS should be taught throughout the course:
LAFS.68.RST.1.3:
LAFS.68.RST.2.4:
Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific
scientific or technical context relevant to grades 6–8 texts and topics.
LAFS.68.RST.3.7:
Integrate quantitative or technical information expressed in words in a text with a version of that information expressed
visually (e.g., in a flowchart, diagram, model, graph, or table).
LAFS.68.WHST.1.1: Write arguments focused on discipline-specific content. a. Introduce claim(s) about a topic or issue, acknowledge and
distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically. b. Support
claim(s) with logical reasoning and relevant, accurate data and evidence that demonstrate an understanding of the topic or
text, using credible sources. c. Use words, phrases, and clauses to create cohesion and clarify the relationships among
claim(s), counterclaims, reasons, and evidence. d. Establish and maintain a formal style. e. Provide a concluding statement or
section that follows from and supports the argument presented.
LAFS.68.WHST.2.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and
audience.
LAFS.7.SL.1.1:
Engage effectively in a range of collaborative discussions with diverse partners on grade 7 topics, texts, and issues, building
on others’ ideas and expression their own clearly.
LAFS.7.SL.1.2:
Analyze the main ideas and supporting details presented in diverse media and formats (e.g., visually, quantitatively, orally)
and explain how the ideas clarify a topic, text, or issue under study.
LAFS.7.SL.1.3:
Delineate a speaker’s argument and specific claims, evaluating the soundness of the reasoning and the relevance and
sufficiency of the evidence.
LAFS.7.SL.2.4:
Present claims and findings, emphasizing salient points in a focused, coherent manner with pertinent descriptions, facts,
details, and examples; use appropriate eye contact, adequate volume, and clear pronunciation.
Grade 7 Mathematics: Mathematics Florida Standards At A Glance
First Nine Weeks
SMT 1
Unit 1- Rational Numbers
MAFS.7.NS.1.1
MAFS.7.NS.1.2
MAFS.7.NS.1.3
DIA- Unit 1
Unit 2- Expressions and
Equations/ Inequalities
MAFS.7.EE.1.1
MAFS.7.EE.1.2
MAFS.7.EE.2.3
MAFS.7.EE.2.4
DIA – Unit 2
Second Nine Weeks
Third Nine Weeks
Fourth Nine Weeks
Unit 3-Ratios and
Proportional Relationships
MAFS.7.RP.1.1
MAFS.7.RP.1.2
MAFS.7.RP.1.3
Unit 4-Geometry
MAFS.7.G.1.1
MAFS.7.G.1.2
MAFS.7.G.1.3
MAFS.7.G.2.4
MAFS.7.G.2.5
MAFS.7.G.2.6
Unit 6- Statistics
MAFS.7.SP.1.1
MAFS.7.SP.1.2
MAFS.7.SP.2.3
MAFS.7.SP.2.4
SMT 2
DIA - Unit 4
Unit 5 – Probability
MAFS.7.SP.3.5
MAFS.7.SP.3.8
MAFS.7.SP.3.6
MAFS.7.SP.3.7
DIA- Unit 5
FSA
Grade 7 Mathematics
Year at a Glance Planning Aide
District
Assessment
Number
Standards Learning
of
Unit
# of
Per
Targets Quarters Standards
Number Days
Unit
per Unit
per
Quarter
Quarter
End
Dates
SMT 1
DIA 1
SMT 2
DIA 2
DIA 3
1
2
3
18
29
21
3
4
3
4
5
6
36
23
20
6
4
4
19
12
9
0
23
15
10
24
88
Review &
Administration
of FSA
Preparation for
next year
20
TOTAL
174
1
7
10/17/14
2
3
12/19/14
3
10
3/19/15
4
4
6/3/15
7
24
First Quarter Pacing M/J Mathematics 2
Monday
August 18
Tuesday
August 19
Wednesday
August 20
Thursday
August 21
Friday
August 22
Procedures/Course Intro; Review Prior Knowledge/Begin Unit 1; DSA
August 25
August 26
August 27
August 28
August 29
September 4
September 5
Unit 1 – Rational Numbers
September 1
September 2
September 3
Labor Day
September 8
September 9
September 10
September 11
September 12
Unit 1 - Rational Numbers
September 15
September 16
Professional
Development Day
September 22
September 17
September 18
September 19
September 23
September 24
September 25
September 26
Unit 2 – Expressions & Equations / Inequalities
Deadline for DIA 1
September 29
September 30
October 1
October 2
October 3
Unit 2 – Expressions & Equations/ Inequalities
October 6
October 7
October 8
October 9
October 10
October 13
October 14
October 15
October 16
October 17
st
Last Day of 1 Quarter
Second Quarter Pacing M/J Mathematics 2
Monday
October 20
Teacher Duty Day
Tuesday
October 21
Wednesday
October 22
Thursday
October 23
Friday
October 24
Deadline for DIA 2
Unit 2 – Expressions & Equations / Inequalities
October 27
October 28
October 29
October 30
October 31
November 3
November 4
November 5
November 6
November 7
Unit 3 – Ratios and Proportional Relationships
November 10
November 11
Unit 3
Veteran’s Day
Holiday
November 17
November 18
November 12
November 13
November 14
November 19
November 20
November 21
November 24
November 25
Unit 3
December 1
December 2
November 26
November 27
November 28
Thanksgiving
Holiday
Thanksgiving
Holiday
Thanksgiving
Holiday
December 3
December 4
December 5
December 8
December 9
December 10
December 11
December 12
December 18
Deadline for SSA
December 19
Unit 4 – Geometry
December 15
December 16
December 17
Unit 4 – Geometry
Teacher Duty Day
nd
Last Day of 2 Quarter
Third Quarter Pacing M/J Mathematics 2
Monday
January 5
Tuesday
January 6
Wednesday
January 7
Friday
January 9
Unit 4 – Geometry
Winter Holiday
January 12
Thursday
January 8
January 13
January 14
January 15
January 16
January 22
January 23
Unit 4 – Geometry
January 19
January 20
January 21
Unit 4 – Geometry
MLK Day
January 26
January 27
January 28
January 29
January 30
February 5
February 6
February 12
February 13
February 19
February 20
Unit 4 – Geometry
February 2
February 3
February 4
Unit 4 – Geometry
February 9
February 10
February 11
Unit 4 - Geometry
February 16
February 17
President’s Day
February 23
February 18
Unit 5 - Probability
February 24
February 25
Deadline for DIA 4
February 26
February 27
March 5
March 6
March 12
March 13
March 19
March 20
Last Day of 3rd Quarter
Teacher Duty
Day
March 2
March 9
March 16
March 3
March 4
Unit 5 – Probability
March 10 Unit 5 - March
11
Probability
March 17
March 18
Fourth Quarter Pacing M/J Mathematics 2
Monday
March 30
Tuesday
March 31
Wednesday
April 1
Thursday
April 2
Friday
April 3
April 9
April 10
April 16
April 17
April 23
April 24
April 30
May 1
Unit 6 - Statistics
April 6
April 7
April 8
Unit 6 - Statistics
April 13
April 14
April 15
Unit 6 - Statistics
April 20
April 21
April 22
Unit 6 - Statistics
April 27
April 28
April 29
State Test Prep/Remediation
May 4
May 5
May 6
May 7
May 8
May 11
May 12
May 13
May 14
May 15
May 18
May 19
May 20
May 21
May 22
Estimated State Test Week
May 25
May 26
May 28
May 29
Pre-Algebra Preparation
Memorial Day
June 1
May 27
June 2
Pre-Algebra Prep
June 3
Last Day of 4th Quarter
June 4
June 5
Course: Grade 7 Mathematics
Unit One: Rational Numbers
Standard
The students will:
MAFS.7.NS.1.1
Apply and extend previous understandings
of addition and subtraction to add and
subtract rational numbers; represent
addition and subtraction on a horizontal or
vertical number line diagram.
a. Describe situations in which opposite
quantities combine to make 0.
b. Understand p + q as the number located
a distance |q| from p, in the positive or
negative direction depending on whether q
is positive or negative. Show that a number
and its opposite have a sum of 0 (are
additive inverses). Interpret sums of rational
numbers by describing real-world contexts.
c. Understand subtraction of rational
numbers as adding the additive inverse, p –
q = p + (–q). Show that the distance
between two rational numbers on the
number line is the absolute value of their
difference, and apply this principle in realworld contexts.
d. Apply properties of operations as
strategies to add and subtract rational
numbers.
SMP #4
Essential Question(s):
In what ways can rational numbers be useful?
Learning Goals
I can:








describe real-world situation where opposite
quantities have a sum of zero.
use a number line or positive/negative chips
to show that an integer and its opposite will
always have a sum of zero.
use a number line to show addition as a
specific distance from a particular number in
one direction or the other, depending on the
sign of the value being added.
interpret the addition of integers by relating
the values to real-world situations.
rewrite a subtraction problem as an addition
problem by using the additive inverse.
show the distance between two integers on
a number line is the absolute value of their
difference.
describe real-world situations represented
by the subtraction of integers.
use the properties of operations to add and
subtract rational numbers.
Remarks
Resources
MARS Task: Division
http://map.mathshell.or
g/materials/tasks.php?t
askid=368&subpage=a
pprentice
a. For example, a hydrogen
atom has 0 charge because
its two constituents are
oppositely charged.
http://mathstar.lacoe.ed
u/lessonlinks/menu_ma
th/poly_power.html
http://www.funbrain.co
m/cgi-bin/cr.cgi
http://illuminations.nctm
.org/ActivityDetail.aspx
?id=64
http://www.uen.org/curri
culumsearch/searchRe
sults.action
Unit One: Rational Numbers (cont)
Standard
The students will:
In what ways can rational numbers be useful?
Learning Goals
I can:
MAFS.7.NS.1.2
Apply and extend previous understandings of
multiplication and division and of fractions to multiply and
divide rational numbers.
a. Understand that multiplication is extended from
fractions to rational numbers by requiring that operations
continue to satisfy the properties of operations, particularly
the distributive property, leading to products such as (–
1)(–1) = 1 and the rules for multiplying signed numbers.
Interpret products of rational numbers by describing realworld contexts.
b. Understand that integers can be divided, provided
that the divisor is not zero, and every quotient of integers
(with non-zero divisor) is a rational number. If p and q are
integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients
of rational numbers by describing real-world contexts.
Apply properties of operations as strategies to multiply and
divide rational numbers.
c. apply properties of operations as strategies to
multiply and divide rational numbers.
d. Convert a rational number to a decimal using long
division; know that the decimal form of a rational number
terminates in 0’s or eventually repeats.
SMP #8
MAFS.7.NS.1.3
Solve real-world and mathematical problems involving the
four operations with rational numbers.
SMP #1











use patterns and properties to explore the
multiplication of integers.
use patterns and properties to develop
procedures for multiplying integers.
describe real-world situations represented
by the multiplication of integers.
use the relationship between multiplication
and division to develop procedures for
dividing integers.
explain why the property of closure exists
for the division of rational numbers, but not
for whole numbers.
describe real-world situation represented by
the division of integers.
interpret the quotient in relation to the
original problem.
generalize the procedures for multiplying
and dividing integers to all rational numbers.
use long division to convert a rational
number to a decimal.
verify that a number is rational based on its
decimal equivalent.
solve real-world problems that involve the
addition, subtraction, multiplication, and/or
division or rational numbers.
Remarks
Resources
http://www.uen.
org/Lessonplan
/preview?LPid=
23396
Examples of
Opportunities for InDepth Focus
When students work
toward meeting this
standard (which is
closely connected to
7.NS.1.1 and
7.NS.1.2), they
consolidate their skill
and understanding
of addition,
subtraction,
multiplication and
division of rational
numbers.
Unit Two: Expressions and Equations/ Inequalities
How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?
Standard
Learning Goals
The students will:
I can:
Remarks
Resources
MAFS.7.EE.1.1
Apply properties of operations as
strategies to add, subtract, factor, and
expand linear expressions with rational
coefficients.
SMP #7



MAFS.7.EE.1.2
Understand that rewriting an
expression in different forms in a
problem context can shed light on the
problem and how the quantities in it
are related.
MAFS.7.EE.2.3
Solve multi-step real-life and
mathematical problems posed with
positive and negative rational numbers
in any form (whole numbers, fractions,
and decimals), using tools strategically.
Apply properties of operations to
calculate with numbers in any form;
convert between forms as appropriate;
and assess the reasonableness of
answers using mental computation and
estimation strategies.



use the commutative and associative
properties to add linear expressions with
rational coefficients.
use the distributive property to add and/or
subtract linear expressions with rational
coefficients.
use the distributive property to expand a
linear expression with rational
coefficients.
use equivalent expressions to understand
the relationship between quantities.
simplify an expression following and
using the order of operations.
determine and explain the solution of an
equation.
http://www.granitescho
ols.org/depart/teachingl
earning/curriculuminstr
uction/math/secondary
mathematics/Math%20
7%20Lessons/20NewMath7LessonDDec
2WritingAlgebraicExpre
ssionsForWords.pdf
For example, a + 0.05a = 1.05a
means that “increase by 5%” is the
same as “multiply by 1.05.”
For example: If a woman making $25
an hour gets a 10% raise, she will make
an additional 1/10 of her salary an hour,
or $2.50, for a new salary of $27.50.
If you want to place a towel bar 9¾
inches long in the center of a door that
is 27½ inches wide, you will need to
place the bar about 9 inches from each
edge; this estimate can be used as a
check on the exact computation.
Examples of Opportunities for In-Depth
Focus
This is a major capstone standard
for arithmetic and its application.
ols.org/depart/teachingl
earning/curriculuminstr
uction/math/secondary
mathematics/Math%20
7%20Lessons/20NewMath7LessonDDec
2WritingAlgebraicExpre
ssionsForWords.pdf
Unit Two: Expressions and Equations/ Inequalities (cont)
How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?
Standard
Learning Goals
The students will:
I can:
Remarks
Resources
MAFS.7.EE.2.4
Use variables to represent quantities
in a real-world or mathematical
problem, and construct simple
equations and inequalities to solve
problems by reasoning about the
quantities.
a. Solve word problems leading to
equations of the form px + q = r and
p(x ÷ q) = r, where p, q, and r are
specific rational numbers.
b. Solve equations of these forms
fluently. Compare an algebraic
solution to an arithmetic solution,
identifying the sequence of the
operations used in each approach.
SMP #2






use a variable to represent a unknown
quantity.
write a simple algebraic equation to
represent a real-world problem.
solve a simple algebraic equation by
using the properties of equality or
mathematical reasoning, and show or
explain my steps.
compare an arithmetic solution to an
algebraic solution.
solve a simple algebraic inequality and
graph the solution on a number line.
describe the solution to an inequality in
relation to the problem.
For example, the perimeter of a
rectangle is 54 cm. Its length is 6
cm. What is its width?
Examples of Opportunities for InDepth Focus
Work toward meeting this standard
builds on the work that led to
meeting 6.EE.2.7 and prepares
students for the work that will lead
to meeting 8.EE.3.7.
http://www.graniteschools.org
/depart/teachinglearning/curri
culuminstruction/math/second
arymathematics/Math%207%
20Lessons/23NewMath7LessonEJan1Solvi
ngEquations.pdf
ngEquationsPartII.pdf
ngInequalities.pdf
20Lessons/26NewMath7LessonEJan4Mod
elRealWorldWithEquations.pd
f
Unit Three: Ratios and Proportional Relationships
How can ratios and proportional relationships be used to determine unknown quantities?
Standard
Learning Goals
The students will:
I can:
Remarks
Resources
MAFS.7.RP.1.1
Compute unit rates associated with ratios of
fractions, including ratios of lengths, areas,
and other quantities measured in like or
different units.
MAFS.7.RP.1.2
Recognize and represent proportional
relationships between quantities.
a. Decide whether two quantities are in a
proportional relationship, e.g., by testing for
equivalent ratios in a table, or graphing on a
coordinate plane and observing whether the
graph is a straight line through the origin.
b. Identify the constant of proportionality (unit
rate) in tables, graphs, equations, diagrams,
and verbal descriptions of proportional
relationships.
c. Represent proportional relationships by
equations.
d. Explain what a point (x, y) on the graph of
a proportional relationship means in terms of
the situation, with special attention to the
points (0, 0) and (1, r ) where r is the unit
rate.

compute a unit rate by iterating (repeating)
or partitioning given rate.
 compute a unit rate by multiplying or
dividing both quantities by the same factor.
 explain the relationship between using
composed units and a multiplicative
comparison to express a unit rate.
 determine whether two quantities are
proportional by examining the relationship
given in a table, graph, equation, diagram or
as a verbal description.
 identify the constant of proportionality when
presented with a proportional relationship in
the form of a table, graph equation, diagram,
or verbal descriptions.
 write an equation that represents a
proportional relationship.
 graph proportional relationships and
indentify the unit rate as the slope of the
related linear function
For example, if a person
walks ½ mile in each ¼
hour, compute the unit rate
as the complex fraction ½/¼
miles per hour, equivalently
2 miles per hour.
For example, if total cost t is
proportional to the number n
of items purchased at a
constant price p, the
relationship between the
total cost and the number of
items can be expressed
as t = pn.
Examples of Opportunities for
In-Depth Focus
Students in grade 7 grow in
their ability to recognize,
represent, and analyze
proportional relationships in
various ways, including by using
tables, graphs, and equations.
http://www.opusmat
h.com/commoncore-clusters/7.rp.aproportionalrelationships
http://map.mathshell
.org/materials/lesson
s.php?taskid=494#ta
sk494
http://www.granitesc
hools.org/depart/tea
chinglearning/curricu
luminstruction/math/
secondarymathemat
ics/Math%207%20L
essons/27NewMath7LessonEJ
an5RatioRateAndPr
oportion.pdf
Unit Three: Ratios and Proportional Relationships (cont)
How can ratios and proportional relationships be used to determine unknown quantities?
Standard
Learning Goals
The students will:
I can:
Remarks
Resources
MAFS.7.RP.1.3
Use proportional relationships to
solve multi-step ratio and percent
problems.


use proportional reasoning to solve
real-world ratio problems, including
those with multiple steps.
use proportional reasoning to solve
real-world percent problems,
including those with multiple steps.
Examples: simple interest, tax,
markups and markdowns,
gratuities and commissions, fees,
percent increase and decrease,
percent error.
http://www.graniteschools.org/dep
art/teachinglearning/curriculuminstr
uction/math/secondarymathematic
s/Math%207%20Lessons/28NewMath7LessonEJan6SovlingPr
oblemsWithProportions.pdf
s/Math%207%20Lessons/29NewMath7LessonEJan7SolvingPe
rcentProblemsWithProportions.pdf
s/Math%207%20Lessons/31NewMath7LessonFFeb2Proportion
,ScaleFactor.pdf
Unit Four- Geometry
Standard
The students will:
How does geometry better describe objects?
Learning Goals
I can:
MAFS.7.G.1.1
Solve problems involving scale drawings of
geometric figures, including computing actual
lengths and areas form a scale drawing and
reproducing a scale drawing at a different
scale.

MAFS.7.G.1.2
Draw (freehand, with ruler and protractor, and
with technology) geometric shapes with given
conditions. Focus on constructing triangles
from three measures of angles or sides,
noticing when the conditions determine a
unique triangle, more than one triangle, or no
triangle.

MAFS.7.G.1.3
Describe the two-dimensional figures that result
from slicing three-dimensional figures, as in
plane sections of right rectangular prisms and
right rectangular pyramids.
SMP #4





use a scale drawing to determine the actual
dimensions and area of a geometric figure.
use a different scale to reproduce a similar
scale drawing.
determine actual measurements from a
scale drawing.
draw a geometric shape with specific
conditions.
construct a triangle when given three
measurement: 3 side lengths, 3 angle
measurements, or a combination of side and
angle measurements.
determine when three specific
measurements will result in one unique
triangle, more than one possible triangle or
no possible triangles.
name the two-dimensional figure that
represents a particular slice of a threedimensional figure.
Remarks
Resources
MARS Task: Which
is Bigger?
http://insidemathemat
ics.org/common-coremath-tasks/7thgrade/72004%20Which%20i
s%20Bigger.pdf
Problem of the
month: What’s
your angle?
http://insidemathem
atics.org/problemsof-the-month/pomwhatsyourangle.pdf
Unit Four- Geometry (cont)
Standard
The students will:
MAFS.7.G.2.4
Know the formulas for the area and
circumference of a circle and solve
problems; give an informal
derivation of the relationship
between the circumference and
area of a circle.
SMP #6
How does geometry better describe objects?
Learning Goals
I can:








MAFS.7.G.2.5
Use facts about supplementary,
complementary, vertical and
adjacent angles in a multi-step
problem to write and solve simple
equations for an unknown angle in
a figure.

MAFS.7.G.2.6
Solve real-world and mathematical
problems involving area, volume,
and surface area of two- and threedimensional objects composed of
triangles, quadrilaterals, polygons,
cubes, and right prisms.







state the formula for finding the circumference of a
circle.
state the formula for finding the area of a circle.
calculate the circumference of a circle using
formulas.
understand how the formula for the area of a circle
can be derived from the area of a parallelogram.
understand the relationship between area and
circumference of a circle.
calculate the area of a circle using formulas.
determine the diameter or radius of a circle when the
circumference is given.
apply a ratio and algebraic reasoning to compare the
area and circumference of a circle.
Remarks
Students may believe:
Pi is an exact number rather
than understanding that 3.14
is just an approximation of
pi.
Many students are confused
when dealing with
circumference (linear
measurement) and area.
This confusion is about an
attribute that is measured
using linear units
(surrounding) vs. an attribute
that is measured using area
units (covering).
state the relationship between supplementary,
complementary, and vertical angles.
use angle relationships to write algebraic equations
for unknown angles.
use algebraic reasoning and angle relationships to
solve multi-step problems.
determine the area of two-dimensional figures.
determine the surface area and volume of threedimensional figures.
solve real-world problems involving area, surface
area and volume.
solve problems involving a missing dimension of a
geometric figure.
draw 3-dimentional figures.
Examples of Opportunities
for In-Depth Focus
Work toward meeting this
standard draws together
grades 3–6 work with
geometric measurement.
Resources
Geometric
constructions:
http://www.opusmath.c
om/common-corestandards/7.g.1-solveproblems-involvingscale-drawings-ofgeometric-figuresincluding
om/common-corestandards/7.g.2-drawfreehand-with-rulerand-protractor-andwith-technologygeometric
om/common-corestandards/7.g.4-knowthe-formulas-for-thearea-andcircumference-of-acircle-and-use-them
om/common-corestandards/7.g.6-solvereal-world-andmathematicalproblems-involvingarea-volume-and
https://www.teachingch
annel.org/videos/prepa
ring-students-forexams
Unit Five: Probability
How is probability used to make informed decisions about uncertain events?
Standard
Learning Goals
I can:
Remarks
The students will:
MAFS.7.SP.3.5
 define probability as a ratio that compare
Understand that the probability of a chance
favorable outcomes to all possible outcomes.
event is a number between 0 and 1 that
 recognize and explain that probabilities are
expresses the likelihood of the event
expressed as a number between 0 to 1.
occurring. Larger numbers indicate greater  interpret a probability near 0 as unlikely to occur
likelihood. A probability near 0 indicates an
and a probability near 1 as likely to occur.
unlikely event, a probability around ½
 interpret a probability near ½ as being as equally
indicates an event that is neither unlikely
to occur as to not occur.
nor likely, and a probability near 1 indicates
a likely event.
MAFS.7.SP.3.8
Find probabilities of compound events
using organized lists, tables, tree diagrams
and simulation.
a. understand that , just as with simple
events, the probability of a compound event
is the fraction of outcomes in the staple
space for which the compound event
occurs.
b. represent sample spaces for compound
events using methods such as organized
lists, tables and tree diagrams. For an
event described in everyday language (eg.
“rolling double sixes”), identify the
outcomes in the sample space which
compose the event.
c. design and use a simulation to generate
frequencies of compound events.





determine outcome of events/experiments.
determine outcomes of an event with and
without replacement.
create a sample space of all possible outcomes
for a compound event by using an organized list,
a table or a tree diagram.
use the sample space to compare the number of
favorable outcomes to the total number of
outcomes and determine the probability of the
compound event.
design and utilize a simulation to predict the
probability of a compound event.
For example, use random
digits as a simulation tool to
approximate the answer to
the question: If 40% of
donors have type A blood,
what is the probability that it
will take at least 4 donors to
find one with type A blood?
Resources
http://www.granite
schools.org/depart
/teachinglearning/c
urriculuminstructio
n/math/secondary
mathematics/Math
%207%20Lessons
/42NewMath7Less
onHApril4Probabili
ty.pdf
Unit Five: Probability (cont)
Standard
The students will:
How is probability used to make informed decisions about uncertain events?
Learning Goals
I can:
Remarks
MAFS.7.SP.3.6
Approximate the probability of a chance
event by collecting data on the chance
process that produces it and observing
its long-run relative frequency, and
predict the approximate relative
frequency given the probability.

MAFS.7.SP.3.7
Develop a probability model and use it to
find probabilities of events. Compare
probabilities from a model to observed
frequencies; if the agreement is not
good, explain possible sources of the
discrepancy.
a. develop a uniform probability model by
assigning equal probability to all
outcomes, and use the model to
determine probabilities of events.

b. develop a probability model (which
may not be uniform) by observing
frequencies in data generated from a
chance process.




collect data on a chance process to
approximate its probability.
use probability to predict the number of times a
particular event will occur given a specific
number of trials.
use variability to explain why the experimental
probability will not always exactly equal the
theoretical probability.
develop a simulation to model a situation in
which all events are equally likely to occur.
utilize the simulation to determine the
probability of specific events.
determine the probability of events that may not
be equally likely to occur, by utilizing a
simulation model.
Form example, when rolling a
number cure 600 times,
predict that a 3 or 6 would be
rolled roughly 200 times, but
probably not exactly 200
times.
For example, if a student is
selected at random from a
class, find the probability that
a girl will be selected.
For example, find the
approximate probability that a
spinning penny will land
heads up or that a tossed
paper cup will land open-end
down. Do the outcomes for
the spinning penny appear to
be equally likely based on the
observed frequencies?
i) Simple events only.
Resources
ols.org/depart/teaching
learning/curriculuminst
ruction/math/secondar
ymathematics/Math%2
07%20Lessons/40NewMath7LessonHApr
2CircleGraphs.pdf
Unit Six: Statistics
How do you account for variability in the data?
What effect does the distribution of data have on its center, spread, and overall shape?
In what ways can numerical data be displayed?
Standard
Learning Goals
The students will:
I can:
Remarks
MAFS.7.SP.1.1
Understand that statistics can be used to gain
information about a population by examining a
sample of the population; generalizations about a
population from a sample are valid only if the
sample is representative of that population.
Understand that random sampling tends to
produce representative samples and support valid
inferences.
MAFS.7.SP.1.2
Use data from a random sample to draw inference
about a population with an unknown characteristic
of interest. Generate multiple samples (or
simulated samples) of the same size to gauge the
variation in estimates or predictions.
MAFS.7.SP.2.3
Informally assess the degree of visual overlap of
two numerical data distributions with similar
variability, measuring the difference between the
centers by expressing it as a multiple of a measure
of variability.
MAFS.7.SP.2.4
Use measure of center and measure of variability
for numerical data from random samples to draw
informal comparative inference about two
populations.










explain that inferences about a population can be made
by examining a sample.
explain why the validity of a sample depends on whether
the sample is a representative of the population.
explain that random sampling trends to produce
representative samples.
draw inferences about a population based on data
generated by a random sample.
generate multiple samples from the same population and
analyze the estimates or predictions based on the
variation of each sample.
find the difference in the mean or median of two
different data sets.
demonstrate how two data sets that are very different
can have similar variability’s.
draw inferences about the data sets by making a
comparison of these difference relative to the mean
absolute deviation or interquartile range of either set of
data.
compare two populations by using the means and/or
medians of data collected from random samples.
compare two populations by using the mean absolute
deviations and/or interquartile ranges of data from
random samples.
For example, estimate the mean
word length in a book by
randomly sampling words from
the book; predict the winner of a
school election based on
randomly sampled survey data.
Gauge how far off the estimate
or prediction might be.
For example, the mean height of
players on the basketball team is
1- cm greater than the mean
height of players on the soccer
team, about twice the variability
( mean absolute deviation) on
either team; on a dot plot, the
separation between the two
distributions of heights is
noticeable.
For example, decide whether the
words in a chapter of a seventhgrade science book are
generally longer than the words
in a chapter of a fourth-grade
science book.
Resources

G r a d

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