CISD Solves

Transcription

CISD Solves

CISD Solves
Committed to Excellence
Fifth Grade Mathematics
Scope and Sequence
with lessons, activities, and resources
(Document updated periodically with new information and resources.)
Grade 5: Mathematics
Scope and Sequence
PROFILE
Mathematics is the study of the measurement, properties, and relationships of quantities, sets, and patterns
using numbers and symbols. It is an intellectual endeavor that involves logic and deductive reasoning and
provides the foundation for decision-making and problem-solving. Learning mathematics requires concrete
experiences that move to an abstract level. It is a sequential process, and all students should have access to
rigorous, appropriate, stimulating, "hands-on and manipulative-based" content-rich mathematical experiences.
OUR CURRICULUM
The Conroe Independent School District offers students a rigorous mathematics curriculum that utilizes problemsolving and discovery models of instruction that provide opportunities for all students to master mathematics
concepts. Students will experience the depth of mathematics through manipulate-based lessons, labs, graphing
and other forms of technology. Our mathematics curriculum is based on the Texas Essential Knowledge and
Skills (TEKS) curriculum framework.
2010-11 Conroe Independent School District
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Scope and Sequence
CURRICULUM & INSTRUCTION STAFF
Deanna K. Martin
Director of Curriculum, Instruction, & Staff Development………………………………………[email protected]
Holly Berger
Coordinator of Mathematics..……………………………………………………………………………...……[email protected]
Kathy Collins
Mathematics Instructional Coach……...........………………………………..…..……………………[email protected]
Brandi Hatch
Mathematics Instructional Coach……...........………………………………..…..……………………[email protected]
Mary Anne Hines
Mathematics Instructional Coach……...........………...…..…………………………………………[email protected]
Vanessa Lincoln
Mathematics Instructional Coach……...........….……………………………..…..…………………[email protected]
Christina Myers
ESL Mathematics Instructional Coach.......………………………………………………………………[email protected]
Brandy Norris
Mathematics Instructional Coach……........……………..…………………………………………….…[email protected]
Marsha Raulsten
Mathematics Instructional Coach……...........……………………….………..…………………….…[email protected]
Kara Saly
Karen Tackett
Mathematics Instructional Coach………………………………………………………….. ……………[email protected]
Tricia Thacker
Mathematics Instructional Coach……...........……………………….………..…..…………………[email protected]
Nancy Trent
Tammy Zunker
Mathematics Instructional Coach………………………………………………………….. ……………[email protected]
Tammie Blake
Mathematics Department Secretary................................................................tblake@conroeisd.net
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Scope and Sequence
The following materials are tools for effective instruction that can be used to enhance the 5th grade curriculum:
1. ACESS, EducAide Software, 2003 (Database TX9)
2. Moose Math refers to TEKSas Daily Moose Grades 5 and 6, Diane McKenzie, Irving, TX: Moose Productions,
2003, P.O. Box 153062, Irving, TX 75015-3062, phone/fax 972-255-6748, located at [email protected]
3. Kamico, refers to Kamico TAKS Connection Books 1,2, and Diagnostic Series, 4413 Spicewood Springs Road,
Suite 200, Austin, TX 78759: Kamico Instructional Media, 2002 located at http://www.kamico.com (phone - 512343-0801, fax - 512-372-9204)
4. North Carolina refers to: North Carolina Resources Grade 6 located at http://www.learnnc.org/dpi/inserv.nsf
5. TAKS Busters, Longview, TX: Teachers Treasures, Inc., 2004
6. TAKS Toppers refers to TAKS Toppers Grade 6 Mathematics, Alana Sloan, Dallas,TX: Wordsmith Publishing
Company, 2004, 3603 Urban Ave., Dallas, TX 75227, fax 214-388-0035, located at [email protected]
7. TEA TAKS Study Guide, Austin, TX: Texas Education Agency, 2004
8. TEKS Target Practice - Lone Star Learning - http://www.lonestarlearning.com/
9. Target The Question - Lone Star Learning - http://www.lonestarlearning.com/
10. Matheletics -- Harcourt publications. www.harcourt.com
11. District Created Tutorial Binder: See your administrator for a copy
12. Master Rulers http://www.themasterruler.com/shop/index.php
13. Kim Sutton Materials www.creativemathematics.com
Following the scope and sequence is a list of concepts and manipulatives provided by The Charles A. Dana Center
at the University of Texas at Austin.
Benchmark Test will be administered at the end of each nine weeks.
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Scope and Sequence
EXPECTATIONS
Introduction.
1. Within a well-balanced mathematics curriculum, the primary focal points at Grade 5 are comparing and contrasting lengths, areas,
and volumes of two- or three-dimensional geometric figures; representing and interpreting data in graphs, charts, and tables; and
applying whole number operations in a variety of contexts.
2. Throughout mathematics in Grades 3-5, students build a foundation of basic understandings in number, operation, and quantitative
reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and
statistics. Students use algorithms for addition, subtraction, multiplication, and division as generalizations connected to concrete
experiences; and they concretely develop basic concepts of fractions and decimals. Students use appropriate language and
organizational structures such as tables and charts to represent and communicate relationships, make predictions, and solve
problems. Students select and use formal language to describe their reasoning as they identify, compare, and classify two- or threedimensional geometric figures; and they use numbers, standard units, and measurement tools to describe and compare objects,
make estimates, and solve application problems. Students organize data, choose an appropriate method to display the data, and
interpret the data to make decisions and predictions and solve problems.
3. Throughout mathematics in Grades 3-5, students develop numerical fluency with conceptual understanding and computational
accuracy. Students in Grades 3-5 use knowledge of the base-ten place value system to compose and decompose numbers in order to
solve problems requiring precision, estimation, and reasonableness. By the end of Grade 5, students know basic addition,
subtraction, multiplication, and division facts and are using them to work flexibly, efficiently, and accurately with numbers during
addition, subtraction, multiplication, and division computation.
4. Problem solving, language and communication, connections within and outside mathematics, and formal and informal reasoning
underlie all content areas in mathematics. Throughout mathematics in Grades 3-5, students use these processes together with
technology and other mathematical tools such as manipulative materials to develop conceptual understanding and solve meaningful
problems as they do mathematics.
5. Fifth Grade Texas Essential Knowledge and Skills
(5.1) Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and
decimals.
(A) Use place value to read, write, compare, and order whole numbers through the 999,999,999,999; and
(B) Use place value to read, write, compare, and order decimals through the thousandths place.
5
Scope and Sequence
(5.2) Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations.
(A) generate a fraction equivalent to a given fraction such as 1/2 and 3/6 or 4/12 and 1/3;
(B) generate a mixed number equivalent to a given improper fraction or generate an improper fraction equivalent to
a given mixed number;
(C) compare two fractional quantities in problem-solving situations using a variety of methods, including common
denominators;
(D) use models to relate decimals to fractions that name tenths, hundredths, and thousandths.
(5.3) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve
meaningful problems.
(A) use addition and subtraction to solve problems involving whole numbers and decimals;
(B) use multiplication to solve problems involving whole numbers (no more than three digits times two digits without
technology);
(C) use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends
without technology), including interpreting the remainder within a given context;
(D) identify common factors of a set of whole numbers; and
(E) model situations using addition and/or subtraction involving fractions with like denominators using concrete objects,
pictures, words, and numbers.
(5.4) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results.
The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition,
subtraction, multiplication, and division problems.
(5.5) Patterns, relationships, and algebraic thinking. The student makes generalizations based on observed patterns
and relationships.
(A) describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams;
(B) identify prime and composite numbers using concrete objects, pictorial models, and patterns in factor pairs.
(5.6) Patterns, relationships, and algebraic thinking. The student describes relationships mathematically.
The student is expected to select from and use diagrams and equations such as y = 5 + 3 to represent meaningful
problem situations.
(5.7) Geometry and spatial reasoning. The student generates geometric definitions using critical attributes.
The student is expected to identify essential attributes including parallel, perpendicular, and congruent parts of two- and
three-dimensional geometric figures.
(5.8) Geometry and spatial reasoning. The student models transformations.
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Scope and Sequence
(A) Sketch the results of translations, rotations, and reflections on a Quadrant I coordinate grid; and
(B) Identify the transformation that generates one figure from the other when given two congruent figures on a
Quadrant I coordinate grid.
(5.9) Geometry and spatial reasoning. The student recognizes the connection between ordered pairs of numbers and
locations of points on a plane.
The student is expected to locate and name points on a coordinate grid using ordered pairs of whole numbers.
(5.10) Measurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume,
and weight/mass to solve problems.
(A) perform simple conversions within the same measurement system (SI (metric) or customary);
(B) connect models for perimeter, area, and volume with their respective formulas; and
(C) select and use appropriate units and formulas to measure length, perimeter, area, and volume.
(5.11) Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees
Fahrenheit and Celsius).
(A) solve problems involving changes in temperature; and
(B) solve problems involving elapsed time.
(5.12) Probability and statistics. The student describes and predicts the results of a probability experiment.
(A) use fractions to describe the results of an experiment;
(B) use experimental results to make predictions; and
(C) list all possible outcomes of a probability experiment such as tossing a coin.
(5.13) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of
data.
(A) use tables of related number pairs to make line graphs;
(B) describe characteristics of data presented in tables and graphs including median, mode, and range; and
(C) graph a given set of data using an appropriate graphical representation such as a picture or line graph.
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Scope and Sequence
UNDERLYING PROCESSES AND MATHEMATICAL TOOLS
Problem solving, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie
all content areas in mathematics. Throughout mathematics, students use these processes together with technology and other
mathematical tools such as manipulative materials to develop conceptual understanding and solve meaningful problems as they do
mathematics.
These underlying processes and mathematical tools are not designed to be taught in isolation. They are to be embedded in each
instructional unit and should be practiced each time mathematics is taught.
(5.14) Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems
connected to everyday experiences and activities in and outside of school.
(A) identify the mathematics in everyday situations;
(B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and
evaluating the solution for reasonableness;
(C) select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a
pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working
backwards to solve a problem;
(D) use tools such as real objects, manipulatives, and technology to solve problems.
(5.15) Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal
language.
(A) explain and record observations using objects, words, pictures, numbers, and technology; and
(B) relate informal language to mathematical language and symbols.
(5.16) Underlying processes and mathematical tools. The student uses logical reasoning.
(A) make generalizations from patterns or sets of examples and non-examples; and
(B) justify why an answer is reasonable and explain the solution process.
These TEKS MUST be addressed EVERY nine weeks within the Scope and Sequence.
Please refer to the textbook lessons on the following page for activities to address
these TEKS.
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Scope and Sequence
Houghton Mifflin Problem-Solving Lessons
(Coded in green at the top of the page in the textbook)
Section
1-5
2-4
3-3
4-4
5-3
6-4
131
8-5
9-4
10-5
11-4
12-4
13-4
14-5
15-4
16-4
17-5
18-5
19-5
20-4
21-4
22-5
23-4
24-4
Topic
Make a Plan
Relative Size
Make a Table
Too Much or Too Little Information
Use a Table
Diagrams and Equations
More Than One Way
Interpret Results
Guess and Check
Choose an Operation
Solve a Simpler Problem
Act It Out
Multi-step Problems
Look for a Pattern
Draw a Picture
Use Formulas
Guess and Check
Use Models to Act It Out
Choose a Strategy
Interpret Quotients
Draw a Picture
Work Backwards
Choose Appropriate Data Displays
Make a Table
Pages in TE
TE Volume
16A - 19
36A - 39
54A - 55
82A - 85
98A - 101
128A - 131
146A - 149
174A - 175
190A - 193
212A - 215
236A - 239
254A - 257
272A - 273
298A - 301
318A - 319
334A - 337
362A - 365
384A - 387
412A - 413
430A - 431
454A - 457
476A - 479
502A - 505
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
522A - 525
2
9
Scope and Sequence
First Semester
Second Semester
1st 9 weeks
3rd 9 weeks
Graphing and Measures of Central Tendency
Whole Numbers Concepts
Decimal Concepts
Begin Multiplication
Fractions
Probability and Statistics
Measurement
2nd 9 weeks
4th 9 weeks
Finish Multiplication
Review for TAKS
Division
5th Grade Review
Geometry and Spatial Reasoning
6th Grade Preparation
Begin Fraction Unit
The Problem Solving TEKS MUST be addressed EVERY Nine Weeks.
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Scope and Sequence
FIRST NINE WEEKS
Unit: Graphing and Measures of Central Tendency (2 weeks)
UNDERLYING PROCESSES
PROCESSES AND
AND MATHEMATICAL
MATHEMATICAL TOOLS
TOOLS SHOULD
SHOULD BE
BE PRACTICED
PRACTICED EACH
EACH TIME
TIME MATHEMATICS
MATHEMATICS IS
IS TAUGHT.
TAUGHT.
UNDERLYING
VOCABULARY
TEKS/NOUN
Tables
Number pairs
Line Graphs
Data
Median
Mode
Range
Graphic
organizer
Lists
Charts
Diagrams
Coordinate grid
Ordered pair
Equations
TEKS/VERB
Describe
Graph
Locate
Name
Select
MATH VOCABULARY
Plot
Venn Diagram
Axis
Sequence
X-axis
Column
Y-axis
Vertical
Vertical axis
Horizontal
Horizontal axis
Analyze
Interval
Bar Graph
Pictograph
Line Plot
Related number pair
STUDENT EXPECTATIONS
(SEs)
5.13A Use tables of related
number pairs to make line graphs
HOUGHTON
MIFFLIN
CLARIFYING STATEMENTS
•
Understand x & y coordinates and
how to plot on a line graph
HM Texas Math
24-3
Time Frame for 5.13 A, B, C:
2 - 4 Days
5.13B Describe characteristics
of data presented in tables &
graphs including median, mode, &
range
HM Expressions: 2-14
•
•
2 - 4 Days
5.13C Graph a given set of data
using an appropriate graphical
representation such as a picture
or line graph
•
•
•
Collect Data
Organize Data
o
Least to greatest
o
Range (largest - smallest)
o
Median (middle number)
o
Mode (Occurs the most)
Review Bar Graphs (comparisons)
Introduce Line graphs (change over
time)
Review Pictographs
HM Expressions
2-13
HM Texas Math
5.1, 23-1
HM Expressions
2-11, 2-14
2 - 4 Days
5.5A Describe the relationship
between sets of data in graphic
organizers such as lists, tables,
charts, and diagrams
HM Texas Math
23-2, 23-3
•
•
•
Time Frame for 5.5A and 5.6:
Introduce 2 circled Venn Diagrams
Introduce Line plots
Discuss relationships of data in
table form
HM Texas Math
4-2, 4-3, 5-2, 5-4
This is an ongoing TEK for the entire
year that will be introduced at this
point
Students should understand how
write equations for problems as well
as just solving a problem
Demonstrate plotting and locating
points on a coordinate grid in
Quadrant I (positive whole numbers
only)
Practice moving points in directional
moves (north, south, east, west)
HM Texas Math
7-1, 7-2, 7-3
HM Expressions
2- 4 Days
5.6 Select from and use
diagrams and equations such as y
= 5 + 3 to represent meaningful
problem situations
Time Frame for 5.5A and 5.6:
•
•
2- 4 Days
5.9 The student is expected to
locate and name points on a
coordinate grid using ordered
pairs of whole numbers.
Time Frame for 5.9: 1 Day
•
•
HM Expressions
1-7, 1-8, 2-16, 2-17
HM Texas Math
24-1, 24-2,
RESOURCES/ACTIVITIES
Newspapers
Students bring in newspapers to use as
resource to gather data to create graphs
Region IV TAKS Book
Pages 225-238
Battleship
Give each student a piece of graph paper,
and have them number the x and y axes
to 15. The students then will put 5 X’s in
various spots on their graph. The
students then pair up with someone else
and try to sink their battleship (the x’s)
by calling out various points.
TIC TAC TOE
The students will work in pairs with a
graph (the x and y axis is numbered to
12). Each student picks a marker of
different color to use as his or her game
piece. The goal is for the students to
get three colored dots in a row and
correctly call out the coordinate pair.
Region IV TAKS Book
Page 140 – 151
Kim Sutton
Visual Tools
Math Focus Activities
The Powerful Numbers 0-100
Math Engineers
HM Expressions
D-2, D-3
11
Scope and Sequence
FIRST NINE WEEKS
UNIT: Addition and Subtraction of Whole number and Decimal Concepts (3 week Unit)
UNDERLYING PROCESSES AND MATHEMATICAL TOOLS SHOULD BE PRACTICED EACH TIME MATHEMATICS IS TAUGHT.
VOCABULARY
TEK/NOUN
Whole
number
Place value
Decimals
Fractions
Tenths
Hundredths
Thousandths
Compatible
numbers
Addition
Subtraction
Multiplication
Division
TEK/VERB
Read
Write
Compare
Order
Relate
Round
Estimate
(SEs)
5.1A Use place value to read,
write, compare, and order whole
numbers through the
999,999,999,999
Time Frame for 5.1A: 3-5 Days
5.1B Use place value to read, write,
compare, and order decimals through
the thousandths place
Time Frame for 5.1B and 5.2D:
•
•
•
•
•
•
•
3-5 Days
5.2D Use models to relate decimals
to fractions to name tenths,
hundredths, and thousandths
•
Time Frame for 5.1B and 5.2D:
3-5 Days
MATH VOCABULARY
Standard form Addend
Difference
Sum
Expanded form
Combine
Word form
Commutative property
Associative property
Identity property
Zero property
Place Value
Greater than
Less than
Decimal point
Approximate
Reasonable
Place value of whole numbers through
hundred billions
Use expanded form to write whole
numbers
Compare Whole numbers
Order whole numbers
Place value of decimals
Compare decimals
Order decimals
5.4 The student is expected to
use strategies, including rounding
and compatible numbers to
estimate solutions to addition,
subtraction, multiplication, and
division problems.
Time Frame for 5.4 and 5.3A:
2-4 Days
•
•
•
•
•
•
•
5.3A Use addition and
subtraction to solve problems
involving whole numbers and
decimals
Time Frame for 5.4 and 5.3A:
2-4 Days
•
•
•
•
Use number lines, pictoral models,
based on powers of 10 and place value
models to relate decimals to
fractions
HOUGHTON
MIFFLIN
HM Texas Math
1-1, 1-2, 1-3, 1-4, 3-1,
3-2
HM Expressions
2-1, 2-2, 2-3, 2-4, 2-5
HM Texas Math
2-1, 2-2, 2-3, 2-5, 3-4,
3-5
HM Expressions
2-1, 2-2, 2-3, 2-4, 2-5,
2-9
Round whole numbers and decimals
Estimate sums and differences of
whole numbers and decimals.
Front end estimation
Compatible numbers
Ballpark
Reasonableness
HM Texas Math
6-1, 8-1
Use addition and subtraction of whole
numbers and decimals to solve
problems.
Properties of addition
* Commutative, Associative, Identity
Talk about words used in problems
Addend + Addend = Sum
Minuend + Subtrahend = Difference
HM Texas Math
6-2, 6-3, 22-1, 22-2,
22-3, 22-4
HM Expressions
HM Expressions
2-6, 2-7, 2-8
Decimal Squares
Use overhead transparency models and
student models to demonstrate
understanding of decimal place value
Base 10 Blocks
Use blocks to model whole number and
decimal place value
Big Number
Teacher rolls a 10-sided dice.
As the teacher calls out each number,
the student places that number on the
place value chart and creates the largest
number in the class
Menu Math
Use menus from various restaurants and
estimate total cost of items purchased.
Trading Cards Trivia
Use athlete trading cards to compare,
order, add, subtract the statistics on
different players
Region IV TAKS Book
Page 40 – 51
Kim Sutton
Visual Tools
Place Value With Pizzazz
Number Line Workbook
Math Drills to Thrill
12
Scope and Sequence
FIRST NINE WEEKS
Unit: Multiplication (3 Weeks) Continues into 2nd Nine Weeks
VOCABULARY
TEKS/NOUN
Multiplication
Whole number
Digits
Problem
Prime number
Composite
Number
Factor pairs
Models
Perimeter
Area
Volume
Formula
Units
TEKS/VERB
Solve
Identify
Connect
Select
Use
STUDENT
EXPECTATIONS (SEs)
5.3B Use multiplication to solve
problems involving whole numbers
(no more than 3 digit x 2 digit w/o
technology)
•
•
Time Frame for 5.3B:
•
2-3 Days
5.10B Connect models for
perimeter, area, and volume with
their respective formulas
HM Texas Math
4-1, 8-2, 8-3, 9-1, 9-2, 9-3, 9-5,
12-1
Find perimeter and area using
models and bridge models to the
corresponding formula
HM Texas Math
15-1, 16-1
2-4 Days
5.10C select and use appropriate
units and formulas to measure
length, perimeter, area, and volume
2-4 Days
Multiply
Product
Factor
Common Factor
Greatest common factor
•
5.5B Identify prime and
composite numbers using concrete
objects, pictorial models, and
patterns in factor pairs
•
•
•
•
•
Time Frame for 5.5B & 5.3D:
HOUGHTON MIFFLIN
Factor x Factor = Product
Properties of multiplication
o
Commutative
o
Associative
o
Identity & Zero
Use calculators to investigate 4digit and larger problems
Time Frame 5.10B & 5.10C:
Time Frame 5.10B & 5.10C:
MATH VOCABULARY
Perimeter
Polygons/Irregular polygons
Area
Squares/Rectangles
Volume
Rectangular Prisms
Identify common prime factors of a
set of whole numbers
Use color tiles, arrays, and concrete
models to demonstrate prime and
composite numbers
HM Expressions
1-1, 1-2, 1-3, 1-6, 1-7, 1-9, 1-10,
4-3, 4-4, 4-5, 4-6, 4-11
HM Expressions
A-1, A-2, A-4,A-5, C-1, C-2
HM Texas Math
11-1, 16-2, 16-3
HM Expressions
A-1, A-2, A-4,A-5, C-1, C-2
HM Texas Math
17-1, 17-3
HM Expressions
1-15, 1-2
3-5 Days
5.3D Identify common factors of
a set of whole numbers
Time Frame for 5.5B & 5.3D:
3-5 Days
•
Find common factors including GCF
using multiple formats, including
venn diagrams and lists
HM Texas Math
17-4, 17-2
Region IV TAKS Book
Page 62 - 70, Page 109 – 116
Page 169-174
1-16,
Create a Product
Have the students create the
board:
______ _______ _______
X _______ _______
_______________________
The student places the number
on one of the five spots until all
spots are filled. Create the
largest or the smallest product
Manipulatives to Use to
reinforce Area and Perimeter
Geoboards
Color Tiles
Pattern Blocks
Kim Sutton
Visual Tools
HM Expressions
1-14
13
Scope and Sequence
Second Nine Weeks
Unit: Division (2 Weeks)
VOCABULARY
TEKS/NOUN
Division
Whole numbers
Divisor
Dividend
Remainder
Strategies
Rounding
Compatible
Numbers
Solutions
Addition
Subtraction
Multiplication
Division
TEKS/VERB
Solve
Interpreting
Estimate
STUDENT
EXPECTATIONS
(SEs)
CLARIFYING
STATEMENTS
5.3C Use division to solve
problems involving whole
numbers (no more than twodigit divisors and three-digit
dividends without
technology), including
interpreting the remainder
within a given context
•
Time Frame for 5.3C:
•
•
divisor
4-5 Days
•
MATH VOCABULARY
Divisor
Dividend
Quotient
Remainder
Calculate
5.4 Use strategies, including
rounding and compatible
numbers to estimate
solutions to addition,
subtraction, multiplication,
and division problems
Use division to solve
problems involving one-digit
and two digit divisors
Teach students correct
terminology of division
•
quotient
dividend
remainder
HOUGHTON MIFFLIN
HM Texas Math
8-4, 10-1, 10-2, 10-3, 10-4
HM Expressions
1-10, 4-12, 4-15, 4-16, 4-17, 4-20,
4-21
Region IV TAKS Book
Page 71 – 79
Kim Sutton
Visual Tools
Use calculators to
investigate division
involving 3-digit and larger
divisors and 4-digit and
larger dividends
REMINDER: In the past,
TAKS has only asked 1 to 2
questions on division using
smaller divisors and
dividends. Use small groups
to work with those who do
not master.
Estimate quotients
o Front end
o Compatible
numbers
o Ballpark
o reasonableness
HM Texas Math
8-1
HM Expressions
4-10, 4-11, 2-9
Time Frame for 5.4:
3-4 Days
14
Second Nine Weeks
Scope and Sequence
Unit: Geometry and Spatial Reasoning (3 Weeks)
VOCABULARY
TEKS/NOUN
Attributes
Parallel
Perpendicular
Congruent
2-Dimensional
figures
3-dimensional
figures
TEKS/VERB
Identify
5.7 Identify essential
attributes including parallel,
perpendicular, and congruent
parts of two- and threedimensional geometric figures
•
•
•
Time Frame for 5.7:
5-7 Days
MATH VOCABULARY
Point
Line segment
End point
Angle
Triangle
Ray
Plane
Regular polygon
Transformation
Acute angle
Obtuse angle
Right angle
Straight angle
Irregular polygon
Octagon
Plane figure
Decagon
Hexagon
Right triangle
Acute triangle
Equilateral triangle
Isosceles triangle
Obtuse triangle
Scalene triangle
Pentagonal Prism
Triangular prism
STUDENT
EXPECTATIONS (SEs)
Square
Pentagon
Polygon
Rectangle
Parallelogram
Trapezoid
Rhombus
Cone
Cube
Cylinder
Pyramid
Sphere
Faces
Edges
Vertices
Side
Height
Base
Tessellate
Translation
Rotation
Reflection
Vertex
Symmetry
Rectangular
prism
•
5.8A Sketch the results of
translations, rotations, and
reflections on a Quadrant I
coordinate grid
Time Frame for 5.8A & 5.8B:
Review geometry terms:
SEE VOCAB LIST
Identify faces, edges, and
vertices of 3-D shapes
Discuss essential attributes
to define geometric shapes
(sides and angles of 2-D
shapes)
Use manipulatives and
pictures to demonstrate
rotations, translations,
reflections and then
illustrate the transformation
on a coordinate plane
HOUGHTON MIFFLIN
HM Texas Math
14-1, 14-2, 14-3, 14-4
HM Expressions
B-1, B-2, B-3, B-4, B-5, E-1,
E-2, E-3, F-1
HM Texas Math
24-5
HM Expressions
D-1, D-2
Manipulatives to Use
Pattern Blocks
Tangrams
Fraction Squares/Circles
Geoboards
Color tiles
3-D models (marshmallows and
toothpicks)
Region IV TAKS Book
Page 127 - 132
Page 133 - 139
Kim Sutton
Visual Tools
2-4 Days
•
5.8B Identify the
transformation that generates
one figure from the other when
given two congruent figures on
a Quadrant I coordinate grid
Identify reflections,
rotations, and translations
using concrete models on
coordinate graphs
HM Texas Math
24-5
HM Expressions
D-1, D-2
Time Frame for 5.8A & 5.8B:
2-4 Days
15
Scope and Sequence
Second and Third Nine Weeks
Unit: Fractions (5 Weeks)
(PAGE 1 OF 2)
UNDERLYING
PROCESSES
AND
MATHEMATICAL
TOOL
UNDERLYING
PROCESSES
MATHEMATICAL
TOOLS IS
SHOULD
BE
UNDERLYING
PROCESSES
AND
MATHEMATICAL
TOOLS
SHOULD BE
PRACTICEDAND
EACH
TIME MATHEMATICS
TAUGHT.
PRACTICED EACH TIME MATHEMATICS IS TAUGHT.
VOCABULARY
HOUGHTON
TEKS/NOUN TEKS/VERB
(SEs)
MIFFLIN
Common
factor
Whole
number
Prime number
Composite
number
Models
Patterns
Fraction
Decimal
Mixed number
Improper
fraction
Identify
Generate
REVIEW 5.3D: Identify common
factors of a set of whole numbers
•
Time Frame 5.3D,5.5B, 5.2D:
3-5 Days
REVIEW 5.5B: Identify prime and
composite numbers using concrete
objects, pictorial models, and
patterns in factor pairs
•
Region IV TAKS Book
Page 34-39
HM Texas Math
17-3
Pattern Blocks
Color Tiles
Fraction Squares
Fraction Circles
Hershey Candy Bars
HM Expressions
1-14
HM Expressions
1-15, 1-2
Kim Sutton
3-5 Days
REVIEW 5.2D Use models to relate
decimals to fractions that name
tenths, hundredths, and thousandths
•
•
3-5 Days
Tenth
Hundredth
Thousandth
Factor
Common denominator
Numerator
Denominator
Equivalent fraction
Reduce
Simplest form
Simplify
Rename
Mixed Number
Review prime and composite numbers
HM Texas Math
17-1, 17-2, 17-4
MATH VOCABULARY
Review concept of factors, common
factors, and greatest common factor
5.2A Generate a fraction equivalent
to a given fraction such as 1/2 and
3/6 or 4/12 and 1/3
•
•
Time Frame 5.2A:
2-4 Days
5.2B Generate a mixed number
equivalent to a given improper
fraction or generate an improper
fraction equivalent to a given mixed
number
Time Frame 5.2B:
3-4 Days
•
•
Review converting a decimal to a
fraction with denominators of 10,
100, and 1000
Decimal conversion with reducing
the fraction: 5/10 = 1/2
HM Texas Math
20-1, 20-3
HM Expressions
2-1, 2-2, 2-3, 2-4, 2-5
Visual Tools
Math Engineers
HM Texas Math
18-1, 18-2, 18-3, 18-4,
19-2, 19-3
Generate equivalent fractions using
pictoral models, manipulatives, &
bridge to paper pencil
Show relationship between the
numerator and denominator
Reduce fractions to simplest form
HM Expressions
3-11, 3-12, 3-13, 3-14
Use concrete models to show
relationship between improper
fractions and mixed numbers and
bridge to paper/pencil
HM Texas Math
18-1, 18-2, 18-3, 18-4,
19-2, 19-3
HM Expressions
3-6
16
Scope and Sequence
S SHOU Second and Third Nine Weeks LD BE
Unit: Fractions (5 Weeks)
(PAGE 2 OF 2)
CS IS TAUGHT.
UNDERLYING PROCESSES AND MATHEMATICAL Third
TOOLSNine
SHOULD
BE PRACTICED EACH TIME MATHEMATICS IS TAUGHT.
Weeks
VOCABULARY
TEKS/NOUN
TEKS/VERB
Fractional
quantities
Common
denominators
Concrete
objects
Addition
Subtraction
Like
denominators
Compare
Model
STUDENT
EXPECTATIONS
5.2C Compare
two fractional
quantities in
problem-solving
situations using a
variety of
methods including
common
denominators
•
Compare fractions using concrete
models, pictoral models, and
bridge to paper and pencil.
HOUGHTON MIFFLIN
HM Texas Math
19-1, 19-4, 20-2
HM Expressions
3-2, 3-11, 3-12, 3-13, 3-5
5.3E Model
situations using
addition and/or
subtraction involving
fractions with like
denominators using
concrete objects,
pictures, words, and
numbers
Region IV TAKS Book
Page 101 – 108 (5.5B)
Page 34-39 (5.2B)
Pattern Blocks
Color Tiles
Fraction Squares
Fraction Circles
Hershey Candy Bars
Kim Sutton
Time Frame 5.2C:
5-7 Days
MATH VOCABULARY
Multiple
Least Common Multiple
•
Use drawings and manipulatives to
model and record addition and
subtraction of fractions with like
denominators in problem-solving
situations and bridge to paper/pencil
HM Texas Math
21-1, 21-2, 21-3
Visual Tools
Math Engineers
HM Expressions
3-1, 3-3, 3-7, 3-8, 3-9, 3-10
Time Frame 5.3E:
2-3 Days
17
Scope and Sequence
Third and Fourth Nine Weeks
Unit: Probability and Statistics (2 Weeks)
TEKS/NOUN
VOCABULARY
TEKS/VERBS
(SEs)
Experiment
Fractions
Experimental
results
Outcomes
Probability
experiment
Describe
Predict
List
5.12A Use fractions to
describe the results of an
experiment
Time Frame 5.12A-D & 5.2A:
3-5 Days
•
•
•
5.12B Use experimental results
to make predictions
3-5 Days
MATH VOCABULARY
Data
Prediction
ordered pair
Organized list
Equation
Outcome
Possible Outcomes
Least likely
Equally likely
Most likely
5.12C List all possible outcomes
of a probability experiment such
as tossing a coin
•
•
•
•
3-5 Days
Review 5.2A Generate a
fraction equivalent to a given
fraction such as 1/2 and 3/6 or
4/12 and 1/3
•
HOUGHTON MIFFLIN
Display statistical data in the
following ways:
o Part: whole
o Part/Whole
o Part to Whole
When doing fraction form, be
sure to reduce to simplest form
HM Texas Math
25-1
Use fractions to describe the
results of an experiment
o 7 of 10 marbles are red
so, 7/10
Favorable outcomes
Total outcomes
HM Texas Math
25-3
Tree diagrams
Listing Method
List outcomes in fraction form,
reduced to the simplest form
Use theoretical probability to
make predictions
o Rolling a dice
o Tossing a coin
o Spinning a spinner
Reduce all fractions to their
lowest terms when describing
outcomes of statistical data
HM Texas Math
25-2, 25-3
HM Expressions
3-14
Region IV TAKS Book
Page 219-224 (5.12A and B)
Kim Sutton
Visual Tools
Math Engineers
HM Expressions
3-14
HM Expressions
3-14
3-5 Days
18
Scope and Sequence
Fourth Nine Weeks
Unit: Measurement (4 Weeks)
VOCABULARY
TEKS/VERB
TEKS/NOUN
Models
Perimeter
Area
Volume
Measurement
system
Units
Temperature
Simple
Conversions
Metric
Customary
Elapsed time
Perform
Connect
Select
Use
Measure
Solve
(SEs)
5.10A Perform simple conversions
within the same measurement
system (SI (metric) or customary)
•
Reteach and review
5.10B Connect models for
perimeter, area, and volume with
their respective formulas;
•
Time Frame 5.10B and 5.10C:
3-5 Days
•
Reteach and Review
5.10C Select and use appropriate
units and formulas to measure
length, perimeter, area, and volume.
•
5.11A Solve problems involving
changes in temperature;
•
Time Frame 5.10A:
5-7 Days
•
•
Time Frame 5.10B and 5.10C:
3-5 Days
MATH VOCABULARY
Fahrenheit
Celsius
Centimeter
Fluid ounce
Kilogram
Kilometer
Mile
Milligram
Milliliter
Square inches
Gallon
Thermometer
Foot
Feet
Gram
Height
Inch
Length
Liter
Meter
Ton
Ounce
Pound
Quart
Cup
Weight
Mile
Yard
Convert units of time, length, weight,
capacity, and temperature in
customary and metric measurement
•
Time Frame 5.11A and 5.11B:
3-4 Days
•
5.11B Solve problems involving
elapsed time.
Time Frame 5.11A and 5.11B:
3-4 Days
•
Calculate the volume using concrete
models such as linking cubes
Connect models of area and perimeter
using color tiles to the correct formula
Students need to be able to explain
the difference between area and
Practice calculating the area,
perimeter, and volume of certain
shapes
Measure the lengths and widths of
rectangles and calculate area and
perimeter
Show temperature changes using
graphs and charts
Show temperature changes in both
Fahrenheit and Celsius
Add and subtract time including
regrouping within hours, minutes, and
seconds
Students should be able to calculate
elapsed time in problem solving
situations
HOUGHTON
MIFFLIN
HM Texas Math
11-2, 11-3, 12-2, 12-3
HM Expressions
C-3, C-4
Region IV TAKS Book
Page 162-168 (5.10A)
Page 169-207 (5.11A and B)
HM Texas Math
HM Expressions
C-1, C-2, A-1, A-2, A-3,
A-4, A-5
HM Texas Math
HM Expressions
C-1, C-2, A-1, A-2, A-3,
A-4, A-5, A-6
HM Texas Math
13-1, 13-2
HM Expressions
HM Texas Math
13-3
HM Expressions
19
Scope and Sequence
Fourth Nine Weeks
Unit IX: REVIEW For TAKS and After TAKS
VOCABULARY
TEKS/NOUN TEKS/VERB
Prime
factorization
Exponents
Multiples
Integer
Multiples
Fractions
Write
Identify
Add
Subtract
(SEs)
TAKS PREPARATION: Use flexible groupings and data from benchmarks
and unit tests to re-teach any concepts students had difficulty with
before the 1st administration of TAKS in early April.
•
Create prime factorizations using
exponents
•
Least common multiple in problem
solving situations
•
Add and subtract fractions and
mixed numbers using models
•
Add fractions and mixed numbers
with unlike denominators
Subtract fractions and mixed
numbers with unlike denominators
6.1D Write prime
factorizations using exponents
6.1F Identify multiples of a
positive integer and common
multiples and the least common
multiple of a set of positive
integers
MATH VOCABULARY
Least common multiple
Positive integers
Fractions
Decimals
6.2A Add and subtract
situations involving fractions
with objects, pictures, words,
and numbers
6.2B Use addition and
subtraction to solve problems
involving fractions and decimals.
•
HM Texas Math
Looking Ahead T71-T100
20
Scope and Sequence
Unit IX: After TAKS
VOCABULARY
TEKS/NOUN TEKS/VERB
Equation
Radius
Diameter
Circumference
Angles
Data
Formulate
Describe
Measure
Solve
(SEs)
Introduce variable equations to
represent problem-solving
situations
Introduce generating
expressions from patterns in a
table or list
Introduce the terms radius,
diameter and circumference
Discuss characteristics of a
circle
HM Texas Math
•
Introduce how to use a
protractor to measure angles
HM Texas Math
•
Introduce interpreting and
creating three circled Venn
diagrams
HM Texas Math
•
6.5 Formulate an equation from
a problem situation
•
•
6.6C Describe the relationship
between radius, diameter and
circumference of a circle
MATH VOCABULARY
•
HM Texas Math
6.8C Measure angles
6.10D Solve problems by
collecting, organizing, displaying,
and interpreting data.
21
Scope and Sequence
From Manipulative to Concepts
THE FOLLOWING IS A LISTING OF SOME OF THE CONCEPTS THAT CAN EFFECTIVELY BE TAUGHT USING THE GIVEN MANIPULATIVES The list is recommended by the
National Council of Supervisors of Mathematics, Supporting Leaders in Mathematics Education: A Source Book of Essential Information, 1994.
Manipulative
Concepts
Algebra tiles
integers, equations, inequalities, polynomials, similar terms, factoring, estimation
Attribute blocks
sorting, classification, investigation of size, shape, color, logical reasoning, sequencing, patterns, symmetry, similarity, congruence, thinking skills, geometry,
organization of data
Balance scale
Weight, mass, equality, inequality, equations, operations on whole numbers, estimation, measurement
Base-ten blocks place value, operations on whole numbers, decimals, decimal-fractional-percent equivalencies, comparing, ordering, classification, sorting, number concepts,
square & cubic numbers, area, perimeter, metric measurement, polynomials
Calculators
problems with large numbers, problem solving, interdisciplinary problems, real-life problems, patterns, counting, number concepts, estimation, equality,
inequality, fact strategies, operations on whole numbers, decimals, fractions
Capacity
containers
Measurement, capacity, volume, estimation
Clocks
times, multiplication, fractions, modular arithmetic, measurement
Color tiles
color, shape, patterns, estimations, counting, number concepts, equality, inequality, operations on whole numbers & fractions, probability, measurement,
area, perimeter, surface area, even & odd numbers, prime & composite numbers, ratio, proportion, percent, integers, square & cubic numbers, spatial
visualization
Compasses
constructions, angle measurement
Cubes
number concepts, counting, place value, fact strategies - especially turnaround facts, classification, sorting, colors, patterns, square & cubic numbers,
equality, inequalities, averages, ratio, proportion, percent, symmetry, spatial visualization, area, perimeter, volume, surface area, transformational geometry,
operations on whole numbers & fractions, even & odd numbers, prime & composite numbers, probability
Cuisenaire rods
classification, sorting, ordering, counting, number concepts,, comparisons, fractions, ratio, proportion, place value, patterns, even & odd numbers, prime &
composite numbers, logical reasoning, estimation, operations on whole numbers
Decimal
Squares
decimals - place value, comparing, ordering, operations, classification, sorting, number concepts, equality, inequality, percent, perimeter, area
Dominoes
counting, number concepts, fact strategies, classification, sorting, patterns, logical reasoning, equality, inequality, mental math, operations on whole numbers
Fraction models fractions - meaning, recognition, classification, sorting, comparing, ordering, number concepts, equivalence, operations, perimeter, area, percent, probability
Geoboards
size, shape, counting, area, perimeter, circumference, symmetry, fractions, coordinate geometry, slopes, angles, Pythagorean Theorem, estimation, percent,
similarity, congruence, rotations, reflections, translations, classification, sorting, square numbers, polygons, spatial visualization, logical reasoning
Geometric solids shape, size, relationships between area & volume, volume, classification, sorting, measurement, spatial visualization
Math balance
equality, inequality, operations on whole numbers, open sentences, equations, place value, fact strategies, measurement, logical reasoning
Invicta, number
Miras
symmetry, similarity, congruence, reflections, rotations, translations, angles, parallel & perpendicular lines, constructions
22
Scope and Sequence
Money
money, change, comparisons, counting, classification, sorting, equality, inequality, operations on whole numbers, decimals, fractions, probability, fact
strategies, number concepts
Number cubes
counting, number concepts, fact strategies, mental math, operations on whole numbers, fractions, decimals, probability, generation of problems, logical
reasoning
Numeral cards
counting, classification, sorting, comparisons, equality, inequality, order, fact strategies, number concepts, operations on whole numbers, fractions, decimals,
logical reasoning, patterns, odd & even numbers, prime & composite numbers
Pattern blocks
patterns, one-to one correspondence, sorting, classification, size, shape, color, geometric relationships, symmetry, similarity, congruence, area, perimeter,
reflections, rotations, translations, problem solving, logical reasoning, fractions, spatial visualization, tessellations, angles, ratio, proportions
Polyhedral
models
shape, size, classification, sorting, polyhedra, spatial visualization
Protractors
constructions, angle measurement
Rulers
measurement, area, perimeter, constructions, estimation, operations on whole numbers, volume
Tape measures
Spinners
counting, number concepts, operations on whole numbers, decimals, fractions, fact strategies, mental math, logical reasoning, probability, generation of
problems
Tangrams
geometric concepts, spatial visualization, logical reasoning, fractions, similarity, congruence, area, perimeter, ratio, proportion, angles, classification, sorting,
patterns, symmetry, reflections, translations, rotations
Ten-frames
fact strategies, mental math, number concepts, counting, equality, inequality, place value, patterns, operations on whole numbers
Thermometers
temperature, integers, measurement
Two-color
counters
counting, comparing, sorting, classification, number concepts, fact strategies, even & odd numbers, equality, inequality, operations, ratio, proportions,
probability, integers
23
Scope and Sequence
From Concepts to Manipulatives
THE FOLLOWING IS A LISTING OF SOME OF THE MANIPULATIVES THAT CAN EFFECTIVELY BE USED TO TEACH THE GIVEN CONCEPT.The list is recommended by the
National Council of Supervisors of Mathematics, Supporting Leaders in Mathematics Education: A Source Book of Essential Information, 1994.
Concepts
Manipulatives
Angles
protractors, compasses, geoboards, miras, rulers, tangrams, pattern blocks
Area
geoboards, color tiles, base-ten blocks, decimal squares, cubes, tangrams, pattern blocks, rulers, fraction models
Classification, sorting
attribute blocks, cubes, pattern blocks, tangrams, 2-color counters, Cuisenaire rods, dominoes, geometric solids, money, numeral cards,
base-ten materials, polyhedral models, geoboards, decimal squares, fraction models
Coordinate geometry
geoboards
Constructions
Compasses, protractors, rulers, miras
Counting
Cubes, 2-color counters, color tiles, Cuisenaire rods, dominoes, numeral cards, spinners, 10-frames, number cubes, money, calculators
Decimals
decimal squares, base-ten blocks, money, calculators, number cubes, numeral cards, spinners
Equations/inequalities
algebra tiles, math balance, calculators, 10-framers, balance scale, color tiles, dominoes, money, numeral cards, 2-color counters, cubes,
Cuisenaire rods, decimal squares, fraction models
Equality/inequality
Equivalence
Estimate
color tiles, geoboards, balance scale, capacity containers, rulers, Cuisenaire rods, calculators
Factoring
algebra tiles
Fact strategies
10-frames, 2-color counters, dominoes, cubes, numeral cards, spinners, number cubes, money, math balance, calculators
Fractions
fraction models, pattern blocks, base-ten materials, geoboards, clocks, color tiles, cubes, Cuisenaire rods, money, tangrams, calculators,
number cubes, spinners, 2-color counters, decimal squares, numeral cards
Integers
2-color counters, algebra tiles, thermometers, color tiles
Logical reasoning
attribute blocks, Cuisenaire rods, dominoes, pattern blocks, tangrams, number cubes, spinners, geoboards
Measurement
balance scale, math balance, rulers, capacity containers, thermometers, clocks, geometric solids, base-ten materials, color tiles
Mental math
10-frames, dominoes, number cubes, spinners
Money
money
Number concepts
cubes, 2-color counters, spinners, number cubes, calculators, dominoes, numeral cards, base-ten materials, Cuisenaire rods, fraction
models, decimal squares, color tiles, 10-frames, money
Odd, even, prime, composite
color tiles, cubes, Cuisenaire rods, numeral cards, 2-color counters
Patterns
pattern blocks, attribute blocks, tangrams, calculators, cubes, color tiles, Cuisenaire rods, dominoes, numeral cards, 10-frames
Percent
base-ten materials, decimal squares, color tiles, cubes, geoboards, fraction models
Perimeter/ Circumference
geoboards, color tiles, tangrams, pattern blocks, rules, base-ten materials, cubes, fraction circles, decimal squares
Place value
base-ten materials, decimal squares, 10-frames, Cuisenaire rods, math balance, cubes, 2-color counters
Polynomials
algebra tiles, base-ten materials
24
Scope and Sequence
Probability
spinners, number cubes, fraction models, money, color tiles, cubes, 2-color counters
Pythagorean Theorem
geoboards
Ratio/proportion
color tiles, cubes, Cuisenaire rods, tangrams, pattern blocks, 2-color counters
Similarity/congruence
geoboards, attribute blocks, pattern blocks, tangrams, miras
Size/shape/color
attribute blocks, cubes, color tiles, geoboards, geometric solids, pattern blocks, tangrams, polyhedral models
Spatial visualization
tangrams, pattern blocks, geoboards, geometric solids, polyhedral models, cubes, color tiles
Square/cubic numbers
color tiles, cubes, base-ten materials, geoboards
Surface area
color tiles, cubes
Symmetry
geoboards, pattern blocks, tangrams, miras, cubes, attribute blocks
Tessellations
pattern blocks, attribute blocks
Transformational geom.: translation,
rotations, reflections
geoboards, cubes, miras, pattern blocks, tangrams
Volume
capacity containers, cubes, geometric solids, rules
whole numbers
base-ten materials, balance scale, number cubes, spinners, color tiles, cubes, math balance, money, numeral cards, dominoes, rules,
calculators, 10-frames, Cuisenaire rods, clocks, 2-color counters
This site is developed and maintained by
the Charles A. Dana Center with support
from the Texas Education Agency as the
designated Mathematics Center for
Educator Development and from the
National Science Foundation.
Charles A. Dana Center
The University of Texas at
Austin
Email Questions and/or Comments to:
Mathematics TEKS Toolkit.
http://www.mathtekstoolkit.org
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at Austin
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25

CISD Solves

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