1st Grade Mathematics | Adding and Subtracting Within 10

Unit Summary

In this first unit, students build on their experiences adding and subtracting within 10 to form a deeper conceptual understanding of these operations. Students will use appropriate tools, including Rekenreks, ten frames, linking cubes, and counters, strategically throughout the unit MP.5 Use appropriate tools strategically. . In Topic C, these tools will be used to help students make sense of problems and persevere in solving them MP.1 Make sense of problems and persevere in solving them. .

In kindergarten, students worked with the following addition and subtraction problem types: add to with result unknown, take from with result unknown, and put together/take apart with total unknown and both addends unknown. Students represented addition and subtraction situations with objects, drawings, and equations and developed fluency within 5.

The work of first grade necessarily begins with building a strong math community by developing a shared vision and establishing classroom structures for math routines and centers. Lessons provided in this unit will not only strengthen the problem solving and fluency work started in kindergarten, but will also lay the foundation for developing year-long fluency with addition and subtraction within 10 and problem solving in a variety of story problem situations. Students continue to develop these skills further in subsequent units as they extend problem solving situations to within 20 and learn new problem types not seen in kindergarten.

The work that students engage with in this unit provides a strong foundation for the development of problem solving skills throughout 1st grade, so that as students move into 2nd grade, they begin to solve one- and two-step problems of all three situations and all of their subtypes involving addition and subtraction within 100 2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. . In addition, building addition and subtraction fluency within 10 in 1st grade sets students up for success to fluently add and subtract within 20 using mental strategies in 2nd grade 2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. . Finally, the work of this unit is the beginning of the first of four critical areas of instruction in 1st grade: developing understanding of addition, subtraction, and strategies for addition and subtraction within 20 (CCSS, p. 13) and supports the foundation of the second of four critical areas of instruction in 2nd grade: building fluency with addition and subtraction (CCSS, p. 13).

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Assessment

The following assessments accompany Unit 1.

Student Observational Spreadsheet

Use the Student Observational Spreadsheet as a formative tool to monitor the progress of students throughout the unit.

Student Observational Spreadsheet

Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Unit Prep

Intellectual Prep

Suggestions for how to prepare to teach this unit

Intellectual Prep for All Units

Read and annotate the "Unit Summary" and "Essential Understandings" portions of the unit plan.
Do all the Target Tasks and annotate them with the "Unit Summary" and "Essential Understandings" in mind.
Take the Post-Unit Assessment.

Unit-Specific Intellectual Prep

Read pp. 15-36 on Operations and Algebraic Thinking in the Progressions.
Watch the video linked here for a model of how to effectively use a Rekenrek as a mathematical tool in the classroom.

Essential Understandings

The central mathematical concepts that students will come to understand in this unit

Using known number partners to add and subtract within 5 supports adding and subtracting within 10.
Counting on 1 or 2 to add and counting back 1 or 2 to subtract helps students to make sense of how counting relates to addition and subtraction.
Understanding the commutative property of addition can help students to make sense of addition equations and how they relate to one another, eventually leading students to solve problems more efficiently.
Making sense of problems and persevering in solving them is an important practice when solving story problems. Representing story problems with concrete objects, pictorial representations, and equations helps students to conceptualize and solve them.

Vocabulary and Models

Models

Models and representations that students learn or use in the unit

Model	Example
number bond	A number bond for 10 = 3 + 7
ten frame	A ten frame showing 8 + 1

Model

Example

number bond

A number bond for 10 = 3 + 7

ten frame

A ten frame showing 8 + 1

Materials

The materials, representations, and tools teachers and students will need for this unit

Rekenrek (1 per student) – Rekenreks can be purchased, or made with cardboard, string or pipe cleaners, and pony beads
Make 5 Game Board (1 per pair of students) – These can be laminated or in page protectors to reuse
Numeral Cards 0-5 (1 set per pair of students)
Linking cubes (max 2 different color towers of 10 per student)
Two-sided counters (max 10 per student)
Make 5 Recording Sheet (1 per student)
Colored Pencils (2 different colored pencils per student)
Rekenrek Slides (Grade 1 Unit 1)
Dot Cards 0-6 (1 set per pair of students)
Adding Dot Cards Game Board (1 per pair of students)
Adding Dot Cards Recording Sheet (1 per student)
Baggies of collections ranging in size up to 20 objects (at least 1 per pair of students) – These may include paperclips, marbles, erasers, or other objects that you have available
Clipboards (1 per student)
Counting Collections Recording Sheet (at least 1 per student)
Hundreds Chart – visible in the classroom
Optional: Counting Collections Folder (1 per student) – See Lesson 3 for more information.
Ten Frame Template (1 per student) – These can be laminated and cut apart for individual use
Four in a Row Game Board J (+1/+2 within 10) (1 per pair of students)
Game piece or token (1 per pair of students)
Four in a Row Game Board K (-1/-2 within 10) (1 per pair of students)
In and Out Game Board A (Count) (1 per pair of students) – These can be laminated or in page protectors to reuse
Numeral Cards 1-10 (1 set per pair of students)
Pompoms (10 per pair of students)
Plastic cup (1 per pair of students)
In and Out (Count) Recording Sheet (1 per student)
Number Talk with Rekenrek (Doubles) Slides (Grade 1 Unit 1)
Twin Trains Game Board (1 per pair of students)
Twin Trains Recording Sheet (1 per student)
Brad (1 each per Twin Trains Game Board)
Paper clips (1 each per Twin Trains Game Board)
The Ten Trail Game Board (Addition) (1 per pair of students)
The Ten Trail Game Board (Subtraction) (1 per pair of students)
Dice (1 per pair of students)

Unit Practice

Lesson Map

Topic A: Building a Math Community

1

Lesson

Count objects and make 5 in a variety of ways.

Standards

1.OA.C.6

2

Lesson

Add and subtract within 5 using number bonds.

Standards

1.OA.C.6

3

Lesson

Count and represent a number of objects within 20 with a pictorial model and a written numeral.

Standards

1.NBT.A.1

Topic B: Strategies to Add and Subtract Within 10

4

Lesson

Count on 1 or 2 to add within 10.

Standards

1.OA.C.5

5

Lesson

Count back 1 or 2 to subtract within 10.

Standards

1.OA.C.5

6

Lesson

Understand the commutative property of addition.

Standards

1.OA.B.3

7

Lesson

Add numbers within 10 using doubles facts.

Standards

1.OA.C.61.OA.D.7

8

Lesson

Solve put together/take apart with both addends unknown story problems.

Standards

1.OA.C.6

Topic C: Story Problems Within 10

9

Lesson

Solve add to/take from with result unknown story problems using objects and words.

Standards

1.OA.A.1

10

Lesson

Solve add to/take from with result unknown story problems using objects, pictures, and words.

Standards

1.OA.A.1

11

Lesson

Solve add to/take from with result unknown story problems using objects, pictures and words and write a related equation.

Standards

1.OA.A.1

12

Lesson

Solve put together/take apart with total unknown story problems using objects, pictures, and words.

Standards

1.OA.A.1

13

Lesson

Solve put together/take apart story problems with total unknown using objects, pictures and words and write a related equation.

Standards

1.OA.A.11.OA.B.3

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

Number and Operations in Base Ten

1.NBT.A.1 — Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Number and Operations in Base Ten

1.NBT.A.1 — Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Operations and Algebraic Thinking

1.OA.A.1 — Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Operations and Algebraic Thinking

1.OA.A.1 — Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.B.3 — Apply properties of operations as strategies to add and subtract. Students need not use formal terms for these properties. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)

Operations and Algebraic Thinking

1.OA.B.3 — Apply properties of operations as strategies to add and subtract. Students need not use formal terms for these properties. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)
1.OA.C.5 — Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Operations and Algebraic Thinking

1.OA.C.5 — Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.C.6 — Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Operations and Algebraic Thinking

1.OA.C.6 — Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
1.OA.D.7 — Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Operations and Algebraic Thinking

1.OA.D.7 — Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Foundational Standards

Standards covered in previous units or grades that are important background for the current unit

Counting and Cardinality

K.CC.A.1

Counting and Cardinality

K.CC.A.1 — Count to 100 by ones and by tens.
K.CC.B.4

Counting and Cardinality

K.CC.B.4 — Understand the relationship between numbers and quantities; connect counting to cardinality.

Operations and Algebraic Thinking

K.OA.A.1

Operations and Algebraic Thinking

K.OA.A.1 — Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. Drawings need not show details, but should show the mathematics in the problem (This applies wherever drawings are mentioned in the Standards.)
K.OA.A.2

Operations and Algebraic Thinking

K.OA.A.2 — Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
K.OA.A.3

Operations and Algebraic Thinking

K.OA.A.3 — Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
K.OA.A.4

Operations and Algebraic Thinking

K.OA.A.4 — For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
K.OA.A.5

Operations and Algebraic Thinking

K.OA.A.5 — Fluently add and subtract within 5.

Future Standards

Standards in future grades or units that connect to the content in this unit

Expressions and Equations

6.EE.A.3

Expressions and Equations

6.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
6.EE.A.4

Expressions and Equations

6.EE.A.4 — Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Measurement and Data

4.MD.C.7

Measurement and Data

4.MD.C.7 — Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Number and Operations in Base Ten

2.NBT.B.9

Number and Operations in Base Ten

2.NBT.B.9 — Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects.
3.NBT.A.2

Number and Operations in Base Ten

3.NBT.A.2 — Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Number and Operations—Fractions

4.NF.B.3

Number and Operations—Fractions

4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Operations and Algebraic Thinking

2.OA.A.1

Operations and Algebraic Thinking

2.OA.A.1 — Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
2.OA.B.2

Operations and Algebraic Thinking

2.OA.B.2 — Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. See standard 1.OA.6 for a list of mental strategies.

Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Adding and Subtracting Within 10

Unit Summary

Assessment

Student Observational Spreadsheet

Post-Unit

Unit Prep

Intellectual Prep

Intellectual Prep for All Units

Unit-Specific Intellectual Prep

Essential Understandings

Vocabulary and Models

Models

Materials

Unit Practice

Lesson Map

Common Core Standards

Core Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Foundational Standards

Counting and Cardinality

Counting and Cardinality

Counting and Cardinality

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Future Standards

Expressions and Equations

Expressions and Equations

Expressions and Equations

Measurement and Data

Measurement and Data

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations—Fractions

Number and Operations—Fractions

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Standards for Mathematical Practice

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