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Adding and Subtracting Within 20
Students extend their knowledge of addition and subtraction to within 20 using various strategies, while continuing to build fluency within 10. They are introduced to add to and take from story problems with start unknown and revisit familiar problem types using numbers within 20. Students deepen their understanding of the relationship between addition and subtraction and apply flexibility in writing equations that represent story problem situations.
Math
Unit 4
1st Grade
Unit Summary
In Unit 4, students build on prior addition and subtraction work by applying both new and familiar strategies to solve problems within 20. They explore new story problem types and extend their work with familiar problem types to the full scope of the standard 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. . Students are introduced to new tools, such as double ten frames, and continue to use familiar ones, including linking cubes, counters, Rekenreks, and drawings, strategically throughout the unit MP.5 Use appropriate tools strategically. .
In kindergarten, students began composing and decomposing numbers from 11 to 19 into 10 ones and some further ones 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. . In earlier 1st grade units, they built a strong foundation in addition and subtraction within 10. They engaged with all 1st grade story problem types within that range, except for the four subtypes identified in the Progressions as particularly challenging, which are not expected to be fully developed until 2nd grade. Students represented their thinking using objects, pictures, and equations.
In this unit, students build the foundational understanding of ten as a unit, a critical understanding that will be further explored in Unit 6. They use this understanding to develop efficient strategies for solving addition and subtraction problems. These strategies include making a ten to add (e.g., 9 + 4 = 9 + 1 + 3 = 10 + 3 = 13), making a ten to subtract (e.g., 14 – 6 = 14 – 4 – 2 = 10 – 2 = 8), using the relationship between addition and subtraction (e.g., knowing 6 + 7 = 13 helps solve 13 – 6 = 7), and creating easier or equivalent sums using known facts like doubles and near doubles (e.g., solving 5 + 6 by thinking 5 + 5 + 1 = 10 + 1 = 11). Students are introduced to add to and take from story problems with start unknown and solve all previously learned problem types within 20.
This unit lays an important foundation for work in upcoming units and future grades. In later 1st grade units, students will develop an understanding that the two digits in a two-digit number represent amounts of tens and ones. They will learn that numbers like 10, 20, 30, and so on represent one, two, three, etc., tens and zero ones 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: . Students will also begin adding within 100 using concrete models, drawings, and strategies based on place value 1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. , while building fluency for addition and subtraction within 10 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). . They will encounter the two remaining problem subtypes introduced in 1st grade, compare with bigger and smaller unknown, where the language suggests the opposite operation. Looking ahead to 2nd grade and beyond, students will add and subtract within 1,000 2.NBT.B.7 Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. and will develop fluency with these operations by 3rd grade 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. .
Unit Prep
Intellectual Prep
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. 44-47, Appendix 1 of The Progressions for the Common Core State Standards in Mathematics.
Essential Understandings
- Understanding number patterns in counting (e.g. 1 ten and 1 one = 11, 1 ten and 2 ones = 12, 1 ten and 3 ones = 13, etc.) is crucial to understanding adding and subtracting with teen numbers as the total.
- Making a ten to add and to subtract within 20 rely on (1) knowing the partner that makes 10 for any number, (2) knowing the decompositions of all numbers less than ten, and 3. understanding teen numbers as 10 + n (e.g., 13 = 10 + 3).
- 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.
Materials
- Optional: Two-sided counters (10 per student)
- Optional: Linking cubes (2 different color towers of 10 per student)
- Optional: Ten Frame Template (1 per student) — These can be laminated and cut apart for individual use
- Math Match Procedures (1 per pair of students)
- Math Match Ten Frame Cards (1 set per pair of students)
- Math Match Equation Cards (1 set per pair of students)
- Tens Go Fish Procedures (1 per pair of students)
- Tens Go Fish Cards ((1 set per pair of students))
- Tens Go Fish Recording Sheet (1 per student)
To see all the materials needed for this course, view our 1st Grade Course Material Overview.
Vocabulary and Models
Unit Vocabulary
ten
To see all the vocabulary for Unit 4, view our 1st Grade Vocabulary Glossary.
Unit Practice
Lesson Map
Common Core Standards
Key
Major Cluster
Supporting Cluster
Additional Cluster
Core Standards
Number and Operations in Base Ten
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1.NBT.B.2.A — 10 can be thought of as a bundle of ten ones — called a "ten."
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1.NBT.B.2.B — The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
Operations and Algebraic Thinking
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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.
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1.OA.A.2 — Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
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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.)
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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.
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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).
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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.
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1.OA.D.8 — Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.
Foundational Standards
Number and Operations in Base Ten
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K.NBT.A.1
Operations and Algebraic Thinking
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K.OA.A.2
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K.OA.A.3
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K.OA.A.4
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K.OA.A.5
Future Standards
Number and Operations in Base Ten
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2.NBT.B.5
Operations and Algebraic Thinking
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2.OA.A.1
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2.OA.B.2
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3.OA.D.8
Standards for Mathematical Practice
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CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
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CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
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CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
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CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
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CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
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CCSS.MATH.PRACTICE.MP6 — Attend to precision.
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CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
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CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
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