Download Grade 8 Mathematics

Grade 1 Mathematics
Possible Scope and Sequence
Curriculum Cluster 2
Number, Operation, and Quantitative Reasoning
Patterns, Relationships, and Algebraic Thinking
Underlying Processes and Mathematical Tools
25 days: 45 minutes per day
1.1 Use whole numbers to describe and compare quantities.
1.3 Recognize and solve problems in addition and subtraction situations.
1.4 Use repeating patterns and additive patterns to make predictions.
1.5 Recognize patterns in numbers and operations.
1.11 Apply Grade 1 mathematics to solve problems connected to everyday experiences and activities in and outside of school.
1.12 Communicate about Grade 1 mathematics using informal language.
1.13 Use logical reasoning.
TEKS
1.1D
Read and write numbers to 99 to
describe sets of concrete objects.
TAKS
Obj.
Instructional Scope
1
Reading Numbers 0 – 40

Use sets of concrete objects to
represent quantities from 0-40.
Example:
30
Ask students, “What is the total number
of counters in the set?”
Answer: Thirty
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Possible Resources
Instruction
Assessment
1. The Number Stations, Math
Their Way, pages 166-179.
2. The 100 Chart, TERC:
Building Number Sense,
Investigation 3, Sessions 1
& 2.
3. Which Holds More?, TERC:
Building Number Sense,
Investigation 3, Sessions 3
& 4.
4. More Counting and
Comparing, TERC: Building
Number Sense,
Investigation 3, Sessions 5
and 6.
5. Number at the Concept
Level, Math Their Way
(chapter 7), pages 164-213.
District
“Rapid” Assessment
for 1.1D, Math
TEKS Connections,
http://www.tea.state.
tx.us/math/training/
materials/MTC/K2/10Lesson_Assess
mentLibrary/Rapids/
MTCK2_RapidsGra
de%201.pdf
Curriculum Cluster 2
Page 1 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Writing Numbers 0 – 40

Given a set of concrete objects,
write the corresponding
number.
Example:
Possible Resources
Instruction
Assessment
District
This chapter includes many
activities for stations.
6. Number at the Connecting
Level, Math Their Way
(chapter 8), pages 214-233.
This chapter includes many
activities for stations.
7. Number at the Symbolic
Level, Math Their Way
(chapter 9), pages 234-251.
This chapter includes many
activities for stations.
Ask students, “How would you write the
numeral that describes the number of
counters in the set?”
Answer: 36
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 2 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TAKS
Obj.
Instructional Scope
1.1A
Compare and order whole
numbers up to 99 (less than,
greater than, or equal to) using
sets of concrete objects and
pictorial models.
1
Comparing Whole Numbers 0 – 40
1.11D
Use tools such as real objects,
manipulatives, and technology to
solve problems.
6
TEKS

Given sets of concrete objects,
compare whole numbers and
describe the sets of concrete
objects using vocabulary such
as less than/fewer than, greater
than/more than, or equal to.
Example:
30
Set A
15
Set B
Ask the students, “How does the
number of counters in Set A compare to
the number of counters in Set B?”
Answer: “Set A is greater than Set B.
Set B is less than set A.”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Possible Resources
Instruction
Assessment
1. Place Value Lesson,
Region 4 TAKS
Mathematics Preparation,
Grade 1, pages 16-29.
2. The Game of Compare,
TERC: Mathematical
Thinking at Grade 1,
Investigation 2, Session 1.
3. Introducing Staircases and
Choice Time, TERC:
Mathematical Thinking at
Grade 1, Investigation 2,
Sessions 2 and 3.
4. Seven Peas and Carrots,
TERC: Mathematical
Thinking at Grade 1,
Investigation 2, Session 4.
5. Number Choices, TERC:
Mathematical Thinking at
Grade 1, Investigation 2,
Sessions 5 and 6.
6. Handfuls, Math Their Way,
page 125.
7. Stack, Tell, Spin, and Win,
Math Their Way, pages
126-127.
8. The 100 Chart, TERC:
Building Number Sense,
Investigation 3, Sessions 1
& 2. Read What to Plan
Ahead of Time in this
Investigation.
Recommended duration: 2
District
“Rapid” Assessment
for 1.1A, Math
TEKS Connections,
http://www.tea.state.
tx.us/math/training/
materials/MTC/K2/10Lesson_Assess
mentLibrary/Rapids/
MTCK2_RapidsGra
de%201.pdf
Curriculum Cluster 2
Page 3 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
class periods.

Use pictorial models to
compare whole numbers and
describe the pictorial models
using vocabulary such as less
than/fewer than, greater
than/more than, or equal to.
Example:
16
Set A
29
Set B
Ask the students, “How does the
number of apples in Set A compare to
the number of apples in Set B?”
Answer: “Set B is greater than Set A.
Set A is less than set B.”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 4 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Ordering Whole Numbers 0 – 40

Use sets of concrete objects to
order whole numbers.
Example:
40
Set A
18
Set B
20
Set C
Ask the students, “How can you put the
numbers in order from least to greatest
and/or greatest to least?”
Answer: Least to greatest 18-20-40
Greatest to least 40-20-18
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 5 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope

Possible Resources
Instruction
Assessment
District
Use pictorial models to order
whole numbers.
Example:
35
Set A
21
Set B
17
Set C
Set A
Ask the students, “How can you put the
numbers in order from least to greatest
and/or greatest to least?”
Answer: Least to greatest 17-21-35
Greatest to least 35-21-17
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 6 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
1.1B
Create sets of tens and ones
using concrete objects to
describe, compare, and order
whole numbers.
TAKS
Obj.
1
Instructional Scope
Describing Sets of Tens and Ones
0 – 40

Create sets of tens and ones
using concrete objects to
describe whole numbers.
Example:
Possible Resources
Instruction
Assessment
1. Counting Fish, Math By All
Means: Place Value, pages
56-66.
2. The King’s Commissioners,
by Aileen Friedman. Math
By All Means: Place Value,
pages 72-82.
3. Five Tower Game, Math By
All Means: Place Value,
pages 152-159.
4. Guess My Number, Math
By All Means: Place Value,
pages 160-165.
District
Region 4 TAKS
Mathematics
Preparation, Grade
1, page 50.
“Rapid” Assessment
for 1.1B, Math
TEKS Connections,
http://www.tea.state.
tx.us/math/training/
materials/MTC/K2/10Lesson_Assess
mentLibrary/Rapids/
MTCK2_RapidsGra
de%201.pdf
Ask the students, “Which number is
represented by this set of tens and
ones?”
Answer: 34
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 7 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Example:
Ask the students, “How can you
represent 38 using tens and ones?”
Answer:
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 8 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Comparing Sets of Tens and Ones
0 – 40

Create sets of tens and ones
using concrete objects to
compare whole numbers.
Example:
Ask the students to compare sets of
concrete objects that represent tens
and ones.
37
Set A
22
Set B
Ask the students, “How does the
number of counters in Set A compare to
the number of counters in Set B?”
Answer: “37 is greater than 22.
22 is less than 37.”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 9 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Ordering Sets of Tens and Ones
0 – 40

Create sets of tens and ones
using concrete objects to order
whole numbers.
Example:
Ask the students to compare sets of
concrete objects that represent tens
and ones to order whole numbers from
least to greatest or greatest to least.
32
26
16
Ask the students, “How can you put
these sets of marbles in order from
least to greatest and/or greatest to
least?”
Answer: Least to greatest 16-26-32
Greatest to least 32-26-16
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 10 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
1.5C
Compare and order whole
numbers using place value.
TAKS
Obj.
2
Instructional Scope
Use Place Value to Compare Whole
Numbers 0 – 40

Use place value to compare
whole numbers.
Example:
Prompt the students to look at the
greatest place value (tens) to see which
number has a greater value.
Tens
3
3
2
Ones
0
7
9
If the digits in the tens place are the
same, prompt the students to look at
the next largest place value (ones) to
see which number has the greatest
value.
Tens
3
3
2
Possible Resources
Instruction
Assessment
1. Comparing Tens, Math
TEKS Connections,
http://www.tea.state.tx.us/m
ath/training/materials/MTC/
K2/10Lesson_AssessmentLib
rary/Lessons/MTCK2_Using
PlaceValueK2.pdf
2. Number at the Concept
Level, Math Their Way
(chapter 7), pages 164-213.
3. Number at the Connecting
Level, Math Their Way
(chapter 8), pages 214-233.
4. Number at the Symbolic
Level, Math Their Way
(chapter 9), pages 234-251.
District
“Rapid” Assessment
for 1.5C, Math
TEKS Connections,
http://www.tea.state.
tx.us/math/training/
materials/MTC/K2/10Lesson_Assess
mentLibrary/Rapids/
MTCK2_RapidsGra
de%201.pdf
Ones
0
7
9
Prompt the student to compare the
digits in the ones place to determine
which number has the greatest value.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 11 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Ask the students, “How do you know
which number is the greatest?”
Answer: Two numbers have 3 tens but
37 has the greatest number of ones.
Ask the students, “How do you know
which number is the smallest?”
Answer: 29 only has 2 tens and the
other two numbers have 3 tens.
Use Place Value to Order Whole
Numbers 0 – 40

Use place value to order whole
numbers.
Example: Prompt the students to look
at the greatest place value (tens) to see
which number has a greater value.
Tens
3
2
3
Ones
1
5
4
If the digits in the tens place are the
same, prompt the students to look at
the next largest place value (ones) to
see which number has the greatest
value.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 12 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Tens
3
2
3
Possible Resources
Instruction
Assessment
District
Ones
1
5
4
Prompt the student to compare the
digits in the ones place to determine
which number has the greatest value.
Ask the students, “How can you put the
numbers in order from least to
greatest?”
Answer: 25-31-34
Ask the students, “How can you put the
numbers in order from greatest to
least?”
Answer: 40-34-31
1.3A
Model and create addition and
subtraction problem situations
with concrete objects and write
corresponding number
sentences.
Addition: Sums to 10
1

Use concrete objects to model
addition problem situations with
sums to 18 and write the
corresponding number
sentence.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
1. Basic Addition and
Subtraction Facts, Math
TEKS Connections,
http://www.tea.state.tx.us/m
ath/training/materials/MTC/
K2/10Lesson_AssessmentLib
rary/Lessons/MTCK2_AddS
ubBasicFacts1thru2.pdf
Region 4 TAKS
Mathematics
Preparation, Grade
1, pages 51 & 52.
Curriculum Cluster 2
Page 13 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Use tools such as a Part/Part/Whole
mat and concrete objects such as
counters to model joining/combining
sets.
Part
Part
Whole
Example:
Frank had 5 frogs in his aquarium. He
went to the store to buy 3 more frogs.
How many frogs does Frank now have
in his aquarium?
Model placing 5 counters in one “part”
of the Part/Part/Whole mat and
3 counters in the other “part” of the
Part/Part/Whole mat.
Since the question asked to find the
number of frogs Frank had all together,
move the “parts” to the “whole” section.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Possible Resources
Instruction
Assessment
District
2. Addition and Subtraction
Lesson, Region 4 TAKS
Mathematics Preparation,
Grade 1, pages 39-48.
3. Quick Images, TERC:
Building Number Sense,
Investigation 1, Session 1.
4. Copying Cubes, TERC:
Building Number Sense,
Investigation 1, Sessions 3
and 4.
5. Number Shapes, TERC:
Building Number Sense,
Investigation 1, Sessions 5
and 6.
6. Making Dot Pictures, TERC:
Building Number Sense,
Investigation 1, Sessions 7
and 8.
7. How Many Dots?, TERC:
Building Number Sense,
Investigation 1, Session 9.
8. Twelve Cats and Dogs,
TERC: Building Number
Sense, Investigation 2,
Session 1.
9. Problems about Ten,
TERC: Building Number
Sense, Investigation 2,
Session 2.
10.
Towers of 10 and
Number Choices, TERC:
Building Number Sense,
Investigation 2, Sessions 6,
Curriculum Cluster 2
Page 14 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
7, and 8.
Remind the students that Frank started
with 5 frogs and went to buy 3 frogs at
the store. He now has a total of
8 frogs.
Model for the students how to write the
corresponding number sentence.
Number Sentence: 5+3=8 or 3+5=8.

Use concrete objects to create
addition problem situations with
sums to 10 and write the
corresponding number
sentence.
Use tools such as a Part/Part/Whole
mat and concrete objects such as
counters to create addition problem
situations.
Part
Part
Whole
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 15 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Example: Provide the students with
9 color tiles. Prompt the students to
use the 9 color tiles to create an
addition problem situation and write the
corresponding number sentence.
Possible Answer:
“Lydia has 7 baby dolls and her family
gave her 2 more baby dolls for her
birthday. How many baby dolls does
Lydia have all together?”
The student places 7 color tiles in one
“part” of the Part/Part/Whole mat and
2 color tiles in the other “part” of the
Part/Part/Whole mat to represent the
number of dolls.
Since the question asks to find the
number of baby dolls she had in all, the
student then moves the “parts” to the
“whole” section.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 16 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
The student writes the corresponding
number sentence that matches the
problem.
Answer: 7 + 2 = 9
Subtraction: Differences from 10

Use concrete objects to model
subtraction problems and write
the corresponding number
sentence.
Use tools such as a Part/Part/Whole
mat and concrete objects such as
counters to model separating or
comparing sets.
Part
Part
Whole
Example:
Rhea had 9 pieces of candy. She gave
4 pieces to her friends. How many
pieces of candy does Rhea have left?
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 17 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Model placing 9 counters in the “whole”
part of the mat.
Place 4 of the counters on a “part” of
the Part/Part/Whole chart to represent
the pieces of candy that Rhea gave to
her friends.
Explain that the remaining counters
represent the number of pieces
remaining from the “whole” and the
pieces of candy that Rhea has left.
Move the remaining counters to the
other “part” of the Part/Part/Whole mat.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 18 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Remind the students that Rhea started
with 9 pieces of candy, and then she
gave 4 pieces of candy to her friends.
She now has 4 pieces of candy.
Model for the students how to write the
corresponding number sentence.
Number Sentence: 9 – 4 = 5
1.12B
Relate informal language to
mathematical language to
symbols.
6

Use concrete objects to create
subtraction problem situations
with differences from 10 and
write the corresponding number
sentence.
Use tools such as a Part/Part/Whole
mat and concrete objects such as
counters to create subtraction
problems.
Part
Part
Whole
Example: Provide the students with
10 linking cubes. Prompt the students
to use the 10 linking cubes to create a
subtraction problem situation and write
the corresponding number sentence.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Daily problem solving will
allow children to explore, to
justify, and to validate their
reasoning skills. The resource
list below has many different
types of problems that a
teacher can choose from.
Choosing problems that have
relevance to children is an
important factor in creating
enthusiasm for problem
solving. Often, the
enthusiasm of the teacher
translates into a positive
disposition toward problem
solving for children. If
statements like “Now that’s an
unusual problem. I wonder
how we can find the answer,”
are part of a teachers’
repertoire, children get the
notion that problem solving is
interesting and they are
Curriculum Cluster 2
Page 19 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Answer:
“Manuel had 10 tennis balls in a basket.
He threw 6 tennis balls over the fence.
How many tennis balls does Manuel
have left in his basket?”
The student places 10 linking cubes in
the “whole” section of the
Part/Part/Whole mat.
Possible Resources
Instruction
Assessment
District
encouraged to use their own
resources to find a path to the
solution. Teachers should
encourage children to share
their strategies and accept
many different paths to the
same solution. The teacher
can model this behavior by
thinking aloud, using many of
the same techniques used
during a shared writing
lesson.
The books listed below are
excellent resources daily
problem solving activities:
Then the student places 6 of the linking
cubes in one “part” of the
Part/Part/Whole mat. The 4 linking
cubes remaining in the “whole” section
of the Part/Part/Whole mat represent
the 4 tennis balls that Manuel has left.
Read It! Draw It! Solve It!
Grade 1, by Elizabeth D.
Miller
Read It! Draw It! Solve It!
Grade K-3:Problem Solving
with Animal Themes, by
Elizabeth D. Miller
Groundworks: Algebraic
Thinking, Grade 1, by
Greenes & Findell
Groundworks: Reasoning
About Measurement by
Findell et. al.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 20 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
The student writes the corresponding
number sentence that matches the
problem.
Possible Resources
Instruction
Assessment
District
The Problem Solver 1 by
Hoogeboom & Goodnow
Answer: 10 – 6 = 4
1.11B
Solve problems with guidance
that incorporates the process of
understanding the problem,
making a plan, carrying out the
plan, and evaluating the solution
for reasonableness.
6
Using the Problem Solving Model
with Joining and Separating Sets
Example:
Ann has 9 books and Michelle has
6 books. How many more books does
Ann have than Michelle?
Understanding the Problem:
 Ask students to restate the
problem.
 Ask, “What are we trying to find
out?”
Possible Answer: “We are trying to find
out how many more books Ann has
than Michelle.”
Making a Plan:
 Ask the students, “Are we
joining sets, separating sets, or
comparing sets?”
 Ask the students, “What is the
important information in this
problem?”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 21 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Possible Answer: “We are comparing
the number of books so we will have to
use subtraction.”
1.11C
Select or develop an appropriate
problem-solving plan or strategy
including drawing a picture,
looking for a pattern, systematic
guessing and checking, or acting
it out in order to solve a problem.
6
Carrying Out the Plan:
 Ask the students, “How are you
going to solve the problem?”
 Remind the students that they
can draw a picture, act out the
problem, look for a pattern,
and/or use guess and check.
Possible Answer: “I am going to line up
my counters and compare the number
of books that Michelle and Ann each
have.”
lllllllll
llllll
1.13A
Justify his or her thinking using
objects, words, pictures,
numbers, and technology.
6
Evaluating for Reasonableness:
 Ask the students, “Is it
reasonable to get a smaller
number than the numbers in
the problem if we are joining
sets?” Prompt the students to
explain their thinking.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 22 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope

Possible Resources
Instruction
Assessment
District
Ask the students, “Is it
reasonable to get a larger
number than the numbers in
the problem if we are
comparing sets?” Prompt the
students to explain their
thinking.
Possible Answer: “I know I did this
correctly because 9 – 6 = 3. It is
reasonable to get 3 because Ann had
9 books and Michelle had 6 books.”
Prompt the students to record in a math
journal, notebook, or on a piece of
paper their thoughts and explanations
of the problems that are modeled.
Prompt the students to write (words,
pictures, or teacher dictation) an
explanation of how the problem was
solved.
Possible Answer:
There are 3 left over and 9 – 6 = 3.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 23 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
1.3B
Use concrete and pictorial
models to apply basic addition
and subtraction facts (up to 9 + 9
= 18 and 18 – 9 = 9).
1
1.11D
Use tools such as real objects,
manipulatives, and technology to
solve problems.
6
Instructional Scope
Applying Addition Facts: Sums to 10

Use concrete models to apply
basic addition facts to sums of
10.
Example:
Give the students a problem such as
4 + 4 = ? and allow them to use
counters to solve the problem.
Answer: 4 + 4 = 8
 Use pictorial models to apply
basic addition facts to sums of
10.
Example:
6
+
3
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
=
9
Possible Resources
Instruction
Assessment
1. Basic Addition and
Subtraction Facts, Math
TEKS Connections,
http://www.tea.state.tx.us/m
ath/training/materials/MTC/
K2/10Lesson_AssessmentLib
rary/Lessons/MTCK2_AddS
ubBasicFacts1thru2.pdf
2. Collect 15 Together, TERC:
Mathematical Thinking at
Grade 1, Investigation 4,
Session 1.
3. Counting and Combining,
TERC: Mathematical
Thinking at Grade 1,
Investigation 4, Sessions 2
and 3.
4. Eleven Fruits, TERC:
Mathematical Thinking at
Grade 1, Investigation 4.
5. Making Predictions About a
Story, TERC: Mathematical
Thinking at Grade 1,
Investigation 4, Session 5.
6. How Many in All?, TERC:
Mathematical Thinking at
Grade 1, Investigation 4,
Session 6.
7. Beginning Number
Concepts, About Teaching
Mathematics, pages 161-
District
“Rapid” Assessment
for 1.3B, Math
TEKS Connections,
http://www.tea.state.
tx.us/math/training/
materials/MTC/K2/10Lesson_Assess
mentLibrary/Rapids/
MTCK2_RapidsGra
de%201.pdf
Curriculum Cluster 2
Page 24 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Possible Resources
Instruction
Assessment
Instructional Scope
District
172.
Applying Subtraction Facts:
differences from 10
1.11D
Use tools such as real objects,
manipulatives, and technology to
solve problems.
6

Use models to apply basic
subtraction facts with
differences from 10.
Example:
Give the students a problem such as
9 - 4 =? and prompt the students to use
counters to solve the problem.
Answer: 9 - 4 = 5

Use pictorial models to apply
basic subtraction facts with
differences from 10.
Example:
8
-
6
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
=
2
Curriculum Cluster 2
Page 25 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
1.5D
Use patterns to develop
strategies to solve basic addition
and basic subtraction problems.
TAKS
Obj.
2
Instructional Scope
Use Patterns to Develop Basic
Addition Facts: Sums to 10

Use patterns to develop
strategies to solve basic
addition problems.
Example:
Ask the students, “What patterns do
you notice?”
2 + 8 = 10
2+7=9
2+6=8
2+5=7
Possible Answer: “The sums decrease
by one.”
Possible Resources
Instruction
Assessment
District
1. The Game of Compare,
TERC: Mathematical
Thinking at Grade 1,
Investigation 2, Session 1.
2. Introducing Staircases and
Choice Time, TERC:
Mathematical Thinking at
Grade 1, Investigation 2,
Sessions 2 and 3.
3. Number Choices, TERC:
Mathematical Thinking at
Grade 1, Investigation 2,
Sessions 5 and 6.
4. Handfuls, Math Their Way,
page 125.
5. Two-Handed-Take-Away,
Math Their Way, page 346.
6. Patterns on the 0-99 Chart,
Developing Number
Concepts, pages 49-50.
Example:
Ask the students, “What patterns do
you notice?”
5+4=9
4+3=7
3+2=5
2+1=3
Possible Answer: “The numbers added
together are doubles plus one.” or “The
sums decrease by two.”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 26 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Use Patterns to Develop Basic
Subtraction Facts: Difference from
10

Use patterns to develop
strategies to solve basic
subtraction problems.
Example:
Ask the students, “What patterns do
you notice?”
8–5=3
8–4=4
8–3=5
8–2=6
8–1=7
Possible Answer: “The differences
increase by one.”
Example:
Ask the students, “What patterns do
you notice?”
10 – 2 = 8
10 – 4 = 6
10 – 6 = 4
10 – 8 = 2
Possible Answer: “The differences
decrease by two.”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 27 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
1.5E
Identify patterns in related
addition and subtraction
sentences (fact families for sums
to 18) such as 2+3=5, 3+2=5, 52=3, and 5-3=2.
TAKS
Obj.
2
Possible Resources
Instruction
Assessment
Instructional Scope
Identify Patterns in Related Addition
and Subtraction Sentences

Use addition facts to solve
subtraction problems.
1. Fact Families Lesson,
Region 4 TAKS
Mathematics Preparation,
Grade 1, pages 58-64.
District
Region 4 TAKS
Mathematics
Preparation, Grade
1, page 73.
Example:
Use concrete objects such as 3 red
linking cubes and 7 blue linking cubes
to create a train of linking cubes.
R
R
R
B
B
B
B
B
B
B
Prompt the students to represent the
model using 2 addition sentences and
2 subtraction sentences.
Possible Answers:
Addition Sentences
3 + 7 = 10
7 + 3 = 10
Subtraction Sentences
10 – 3 = 7
10 – 7 = 3
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 28 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Example:
Taylor had 6 baseballs. He gave some
baseballs to his friends. If he now has
2 baseballs left, how many baseballs
did he give to his friends?
Possible Solution Strategy:
6- ? = 2
2+ ? = 6
6- 2
= ?
Answer: 4 baseballs
1.4A
Identify, describe, and extend
concrete and pictorial patterns in
order to make predictions and
solve problems.
2
1.11C
Select or develop an appropriate
problem-solving plan or strategy
including drawing a picture,
looking for a pattern, systematic
guessing and checking, or acting
it out in order to solve a problem.
6
Identifying Patterns
 Identify patterns in pictorial
representations or sets of
concrete objects in order to
make predictions or solve
problems.
Example:
Show the students a set of pictures or a
set of concrete objects that create a
pattern.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
1. What Comes Next?, TERC:
Mathematical Thinking at
Grade 1, Investigation 3,
Session 1.
2. Clapping Patterns, TERC:
Mathematical Thinking at
Grade 1, Investigation 3,
Session 2.
3. Finding and Making
Patterns, TERC:
Mathematical Thinking at
Grade 1, Investigation 3,
Sessions 3 and 4.
4. What is a Pattern?, TERC:
“Rapid” Assessment
for 1.4, Math TEKS
Connections,
http://www.tea.state.
tx.us/math/training/
materials/MTC/K2/10Lesson_Assess
mentLibrary/Rapids/
MTCK2_RapidsGra
de%201.pdf
Curriculum Cluster 2
Page 29 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Pattern:
Ask the students, “What pattern do the
pictures/objects make? How do you
know?”
Possible Answer: “Butterfly, Butterfly,
Flower, Butterfly, Butterfly, Flower,
Butterfly, Butterfly, Flower. The
pictures create an AABAABAAB
pattern.”
Possible Resources
Instruction
Assessment
District
Mathematical Thinking at
Grade 1, Investigation 3,
Sessions 5 and 6.
5. Rooster's Off to See the
World, by Eric Carle.
Source: Math and Literature
(K-3) Book One, pages 5-7.
6. Unifix Snap and Clap
Patterns, Math Their Way,
pages 33-34.
7. Unifix Patterns, Math Their
Way, pages 26-28.
8. Pattern Block Walls, Math
Their Way, pages 38-39.
This is a great station
activity.
Possible Pattern:
Ask the students, “How would you
identify the pattern the picture/objects
make?”
Answer: “Each time 1 circle is added.”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 30 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Extending Patterns

Extend patterns in pictorial
representations or sets of
concrete objects in order to
make predictions or solve
problems.
Example:
Show the students a set of pictures or a
set of concrete objects that create a
pattern.
Possible Pattern:
**
**
** ?
Ask the students, “Which object or
picture comes next?”
Answer:
The arrow
Possible Pattern:
Ask the students, “What would the
object or picture look like if this pattern
is continued?”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 31 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Answer:
Example:
Show the students a set of pictures or a
set of concrete objects that create a
pattern.
Possible Pattern:
XOTXOT?OT
Ask the students, “Which object or
picture is missing from this pattern?”
Answer: The X
Describing Patterns

Describe patterns in pictorial
representations or sets of
concrete objects in order to
make predictions or solve
problems.
Example:
Show the students a set of pictures or a
set of concrete objects that create a
pattern.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 32 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Possible Resources
Instruction
Assessment
District
Possible Pattern:
Ask the students, “How can you
describe the pattern that we are
making?”
Answer: “ABABAB or dog, bone, dog,
bone, dog bone”
Possible Pattern:
Ask the students, “How can you
describe the pattern that we are
making?”
Answer: “There are 2 triangles added
each time.”
1.5A
Use patterns to skip count by
twos, fives, and tens.
2
Using Patterns to Skip Count

Use patterns to skip count by
tens.
Example:
Practice skip counting by tens.
Say “10, 20, 30, 40, {clap}, 60.”
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
1. Patterns in Numbers
Lesson, Region 4 TAKS
Mathematics Preparation,
Grade 1, pages 65-72..
2. What Comes in 2's, 3's, and
4's?, by Suzanne Aker.
Source: Math and Literature
(K-3) Book One, page 70.
3. Eyes, Math Their Way,
Region 4 TAKS
Mathematics
Preparation, Grade
1, page 75.
“Rapid” Assessment
for 1.5A, Math
TEKS Connections,
Curriculum Cluster 2
Page 33 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Instructional Scope
Ask the students, “What number is
missing?”
Answer: 50

Use patterns to skip count by
fives.
Possible Resources
Instruction
Assessment
pages 328-329.
4. Stars, Math Their Way,
page 330.
5. Labeling the Number
Pattern with Color,
Developing Number
Concepts, pages 44-48.
District
http://www.tea.state.
tx.us/math/training/
materials/MTC/K2/10Lesson_Assess
mentLibrary/Rapids/
MTCK2_RapidsGra
de%201.pdf
Example:
Practice skip counting by fives.
Say, “10,15, 20,25.”
Ask the students, “What number comes
next?”
Answer: 30

Use patterns to skip count by
twos.
Example:
Practice skip counting by twos.
Say “12, 14, 16, 18, {clap}, 22.”
Ask the students, “What number is
missing?”
Answer: 20
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 34 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
1.5B
Find patterns in numbers,
including odd and even.
Possible Resources
Instruction
Assessment
TAKS
Obj.
Instructional Scope
2
Finding Patterns in Numbers

Find patterns in numbers,
including odd and even.
Example:
Show the students a number chart.
1
6
11
16
2
7
12
17
3
8
13
18
4
9
14
19
5
10
15
20
1. Two-Handed-Take-Away,
Math Their Way, page 346.
2. Patterns on the 0-99 Chart,
Developing Number
Concepts, pages 49-50.
3. Even Steven, Odd Todd, by
Kathy Richardson.
District
“Rapid” Assessment
for 1.5B, Math
TEKS Connections,
http://www.tea.state.
tx.us/math/training/
materials/MTC/K2/10Lesson_Assess
mentLibrary/Rapids/
MTCK2_RapidsGra
de%201.pdf
Prompt the students to use sets of
objects to determine if the numbers are
odd or even.
Give each student 5 linking cubes or
Unifix cubes. Prompt the students to
put the 5 cubes in sets of 2.
Explain to the students that when there
is one cube left over and it does not
have a partner, the cubes represent an
odd number.
Prompt the students to color the 5 on
the number chart blue.
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 35 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Possible Resources
Instruction
Assessment
Instructional Scope
District
Give each student 6 linking cubes or
Unifix cubes. Prompt the students to
put the 6 cubes in sets of 2.
Explain to the students that when there
are no cubes left over and all cubes
have a partner, the cubes represent an
even number. Prompt the students to
color the 6 on the number chart red.
Repeat the process with 2,3,4,7,8,9,
and 10 cubes. Identify that numbers
ending in 1,3,5,7, or 9 are odd and that
numbers ending in 0,2,4,6, or 8 are
even. Continue coloring odd numbers
and even numbers on the number chart
until the students identify a pattern with
odd and even numbers.
Prompt the students to identify the
pattern.
1
6
11
16
2
7
12
17
3
8
13
18
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
4
9
14
19
5
10
15
20
Curriculum Cluster 2
Page 36 of 37
Grade 1 Mathematics
Possible Scope and Sequence
TEKS
TAKS
Obj.
Possible Resources
Instruction
Assessment
Instructional Scope
District
Possible Answer: ‘Starting with 2,
every other number is even. Starting
with 1, every other number is odd.”
Example:
Show the students a number chart such
as the example below.
25
30
35
26
31
36
27
32
37
28
33
38
29
34
39
Ask the students to identify the pattern
created by the shaded numbers.
Possible Answer: “The shaded
numbers increase by 3 each time.”
Ask the students, “If the number chart
were extended, what number would be
shaded next?”
Answer: 40
Number, Operation, and Quantitative Reasoning
Patterns, Relationships, and Algebraic Thinking
Underlying Processes and Mathematical Tools
*Curriculum-Based Assessment 2
*For each student expectation (SE) that incorporates the use of a concrete model/object and/or a mathematical tool, students should be encouraged to use
a concrete model/object and/or a mathematical tool to model items on the curriculum-based assessment (CBA).
Possible Scope and Sequence, Grade 1 Mathematics
© 2006 Region 4 Education Service Center. All rights reserved.
Curriculum Cluster 2
Page 37 of 37