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Adding and Subtracting Within 10
Students build fluency with addition and subtraction within 10 using various strategies. Students solve familiar story problem types within 10 using objects, pictures, and equations to represent the mathematics in the problem.
Math
Unit 1
1st Grade
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
Print the Student Observational Spreadsheet to use as a formative tool to monitor the progress of students throughout the unit.
Post-Unit
Use the resources below to assess student understanding of the unit content and action plan for future units.
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. 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
- 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.
Materials
- 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 A (1 per student)
- Number Talk with Rekenrek (Doubles) Slides (Grade 1 Unit 1)
- Twin Trains Game Board A (Doubles) (1 per pair of students)
- Twin Trains Recording Sheet A (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)
Vocabulary and Models
Models
| Model | Example |
| number bond | A number bond for 10 = 3 + 7 |
| ten frame | A ten frame showing 8 + 1 |
Unit Practice
Lesson Map
Topic A: Building a Math Community
Topic B: Strategies to Add and Subtract Within 10
Topic C: Story Problems Within 10
Common Core Standards
Key
Major Cluster
Supporting Cluster
Additional Cluster
Core Standards
Number and Operations in Base Ten
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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
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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.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.C.5 — Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
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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.
Foundational Standards
Counting and Cardinality
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K.CC.A.1
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K.CC.B.4
Operations and Algebraic Thinking
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K.OA.A.1
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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
Expressions and Equations
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6.EE.A.3
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6.EE.A.4
Measurement and Data
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4.MD.C.7
Number and Operations in Base Ten
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2.NBT.B.9
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3.NBT.A.2
Number and Operations—Fractions
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4.NF.B.3
Operations and Algebraic Thinking
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2.OA.A.1
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2.OA.B.2
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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