2nd Grade Math | Adding and Subtracting within 20

Unit Summary

This introductory unit helps set students up for the major work of fluently adding and subtracting within 20 which is the end-of-year goal. By reviewing, building, and refining strategies for fluently adding and subtracting mentally, this will help students as they work flexibly with larger numbers in later units. Topic A re-engages students with their fluency within 10 which was the end-of-year goal of first grade and continues on their counting work extending from 120 to 200. Topic B allows students to use advanced strategies to add and subtract flexibly within 20. They use strategies such as make a ten to add, relate addition and subtraction to subtract by using known facts and making a ten strategies, subtracting by going down over ten, and converting to easier problems using known and doubles facts. In Topic C students re-engage with story problems and use tape diagrams to represent the math of the mathematical situations while focusing on adding to and taking from, and putting together and taking apart situation types.

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Assessment

The following assessments accompany Unit 1.

Mid-Unit

Have students complete the Mid-Unit Assessment.

Post-Unit

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

Expanded Assessment Package

Use student data to drive instruction with an expanded suite of assessments. Unlock Mid-Unit Assessments and Answer Keys, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

Unit Prep

Intellectual Prep

Suggestions for how to prepare to teach this unit

Intellectual Prep for All Units

Read and annotate "Unit Summary" and "Essential Understandings" portion 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 the following table that includes models used in this unit..

number bond

A number bond for 10 = 3 + 7

tape diagram

Example: Armando buys 16 peppers for a barbeque. 7 of the peppers are red and the rest of the peppers are orange. How many orange peppers did Armando buy?

ten frame

Two ten frames showing 8 + 11

Essential Understandings

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

The number sequence can be extended beyond 120 by continuing the count by ones and by tens.
Basic tens facts can be used to to support adding and subtracting within 20.
Thinking of addition when subtracting can be a supportive strategy for fluently and flexibility subtracting within 20.
Number bonds can be used to show relationships within numbers as students use make ten strategies to add and subtract.
Making sense of problems and persevering in solving them is an important practice when solving word problems. Representing word problems with mathematical drawings, including tape diagrams, helps students model their thinking and helps them toward solutions.

Materials

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

Optional: Number Bond Template (1 per student) — These can be laminated or in page protectors to reuse
Tens Frame Template (1 per student) — These can be laminated or in page protectors to reuse
Linking cubes (2 different color towers of 10 per student)
Blank Hundreds Chart (1 per student)
Optional: Dry erase marker (1 per student) — Can continue to be used past Unit 1 for story problems but will not be referred to
Optional: White board (1 per student) — Can continue to be used past Unit 1 for story problems but will not be referred to
Optional: Manipulatives (As needed) — At teacher discretion on types used and how much are needed. Can continue to be used past Unit 1 for story problems but will not be referred to

Unit Practice

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson Map

Topic A: Adding and Subtracting within 10 and Counting

1

Solve addition and subtraction equations within 10 using various strategies.

2.OA.B.2

2

Use related facts to add and subtract within 10.

2.OA.B.2

3

Use mental math to add and subtract within 10.

2.OA.B.2

4

Count by ones and tens within 200.

2.NBT.A.2

Topic B: Strategies to Add and Subtract within 20

5

Use facts to 10 to apply make ten strategy to add within 20.

2.OA.B.2

6

Solve unknown addend equations within 20.

2.OA.B.2

7

Relate subtraction to addition to solve within 20.

2.OA.B.2

8

Subtract within 20 with strategies (going down over ten) Day 1.

2.OA.B.2

9

Subtract within 20 with strategies (going down over ten) Day 2.

2.OA.B.2

10

Use doubles facts to solve addition and subtraction problems within 20.

2.OA.B.2

11

Solve and explain strategies used to solve equations within 20.

2.OA.B.2

Topic C: Story Problems within 20

12

Represent story problems visually within 20.

2.OA.A.1

13

Solve and represent story problems using tape diagrams.

2.OA.A.1

14

Solve add to and take from word problems within 20.

2.OA.A.1

15

Solve put together and take apart problems within 20.

2.OA.A.1

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

2.NBT.A.2 — Count within 1000; skip-count by 5s, 10s, and 100s.

Number and Operations in Base Ten

2.NBT.A.2 — Count within 1000; skip-count by 5s, 10s, and 100s.

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.

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 — 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.

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.

Foundational Standards

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

Number and Operations in Base Ten

1.NBT.B.2

Number and Operations in Base Ten

1.NBT.B.2 — Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
1.NBT.C.5

Number and Operations in Base Ten

1.NBT.C.5 — Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
1.NBT.C.6

Number and Operations in Base Ten

1.NBT.C.6 — Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
K.NBT.A.1

Number and Operations in Base Ten

K.NBT.A.1 — Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Operations and Algebraic Thinking

1.OA.A.1

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.4

Operations and Algebraic Thinking

1.OA.B.4 — Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.
1.OA.C.5

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

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).
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.

Future Standards

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

Number and Operations in Base Ten

2.NBT.A.1

Number and Operations in Base Ten

2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
2.NBT.B.5

Number and Operations in Base Ten

2.NBT.B.5 — Fluently add and subtract within 100 using strategies 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

3.OA.A.1

Operations and Algebraic Thinking

3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.A.3

Operations and Algebraic Thinking

3.OA.A.3 — Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
3.OA.D.8

Operations and Algebraic Thinking

3.OA.D.8 — Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
3.OA.D.9

Operations and Algebraic Thinking

3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

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 20

Unit Summary

Assessment

Mid-Unit

Post-Unit

Unit Prep

Intellectual Prep

Intellectual Prep for All Units

Unit-Specific Intellectual Prep

Essential Understandings

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

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

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

Operations and Algebraic Thinking

Future Standards

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

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Standards for Mathematical Practice

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