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Adding and Subtracting With Story Problems
Students solve new story problem types within 10 using objects, pictures, and equations to represent the mathematics in the problem. They explore the relationship between addition and subtraction and develop flexibility relating equations to story problems.
Math
Unit 2
1st Grade
Unit Summary
In Unit 2, students build on their addition and subtraction work, learning to solve new story problem types. Students will use appropriate tools, including ten frames, linking cubes, counters, and drawings, strategically throughout the unit MP.5 Use appropriate tools strategically. . They will make sense of problems and persevere in solving them MP.1 Make sense of problems and persevere in solving them. .
In Unit 1, students strengthened their addition and subtraction fluency within 10. They reviewed the addition and subtraction problem types introduced in Kindergarten: add to with result unknown, take from with result unknown, and put together/take apart with total unknown and both addends unknown. Students showed their thinking with objects, pictures, and equations.
In this unit, students are introduced to most of the story problem types that are new to them in Grade 1: add to with change unknown, take from with change unknown, put together/take apart with addend unknown and compare with difference unknown. All story problems are introduced within 10 to keep the student focus on making sense of the story problems. Students will see story problems represented in multiple ways, including using both situation and solution equations (see p. 22 of the Progressions for the CCSS for an explanation of situation and solution equations). In all instances, the focus is on student understanding of the relationship between the equations and the story MP.2 Reason abstractly and quantitatively. . Students continue to develop computational fluency within 10 as they make sense of the quantities and their relationships in problem situations.
The work that students engage with in this unit continues to build the strong foundation, started in Unit 1, for the development of problem solving skills throughout 1st grade and beyond. In Units 3 and 4, students will learn the remaining new problem types, with Unit 4 extending problem solving to the full focus of the standard: using addition and subtraction within 20 to solve word problems 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. . As students build proficiency, they prepare for the work of Grade 2, adding and subtracting within 100 to solve one- and two-step problems 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. .
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Assessment
The following assessments accompany Unit 2.
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. 44-51, Appendices 1 and 2 of The Progressions for the Common Core State Standards in Mathematics.
Essential Understandings
- 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.
- Counting on is an effective Level 2 strategy to solve problems involving adding to find the total, finding an unknown addend, and subtracting by thinking of subtraction as finding the unknown addend.
- In all problem solving, students’ ability to explain how a representation connects to a story problem context is more important than the representation separate from its context. The goal is to foster conceptual understanding and problem-solving skills.
Materials
- Optional: Two-sided counters (10 per student)
- Linking cubes (2 different color towers of 10 per student and 6 for teacher)
- Ten Frame Template (1 per student) –These can be laminated and cut apart for individual use
- Chart Paper (1 per pair of students)
- Capture the Number Game Board A (1 per pair of students)
- Capture the Number Recording Sheet A (1 per student)
- Tiny Ten Frame Cards
- Pete the Cat and the Missing Cupcakes by Kimberly & James Dean
- Bears in the Cave Game Board A (1 per pair of students)
- Bears in the Cave Recording Sheet A (1 per student)
- Numeral Cards 6-10 (1 set of 6-10 per pair of students)
- Counting bears (10 per pair of students)
- Plastic cup (1 per pair of students) –Alternatively could use a bowl
- In and Out Game Board B (Three Parts) (1 per pair of students)
- In and Out (Three Parts) Recording Sheet B (1 per student)
- Pompoms (10 per pair of students)
- In and Out Game Board C (Hide and Count) (1 per pair of students)
- In and Out (Hide and Count) Recording Sheet C (1 per student)
- Ladybug Spots Game Board A (1 per pair of students)
- Ladybug Spots Recording Sheet A (1 per student)
- Dice (1 per pair of students)
- Twin Trains Game Board B (Compare) (1 per pair of students)
- Twin Trains Recording Sheet B (1 per student)
- Brad (1 per Twin Trains Game Board)
- Paper clips (1 per Twin Trains Game Board)
- Colored Pencils –For students for Problem Set
- Race to 10 Game Board (1 per pair of students)
- Race to 10 Recording Sheet (1 per student)
- Game piece or token (2 per pair of students) –Counter, linking cube, etc.
- What's Missing? Version A
- What's Missing? Version B
- One is a Snail, Ten is a Crab by April Pulley Sayre and Jeff Sayre and illustrated by Randy Cecil
- One is a Snail, Ten is a Crab Cards (1 set per pair of students)
- One is a Snail, Ten is a Crab Table (1 per student)
- Tape –For teacher use in creating class chart
- Numeral Cards 1-10 (1 set per pair of students)
Vocabulary and Models
Unit Vocabulary
difference
expression
To see all the vocabulary for Unit 2, view our 1st Grade Vocabulary Glossary.
Models
| Model | Example |
| number path | |
| tape diagram | |
Unit Practice
Lesson Map
Topic A: Add To/Take From with Change Unknown
Topic B: Put Together/Take Apart with Addend Unknown
Topic C: Compare with Difference Unknown
Topic D: Plenty of Problems (mixed problem types)
Common Core Standards
Key
Major Cluster
Supporting Cluster
Additional Cluster
Core Standards
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.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.
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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
Counting and Cardinality
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K.CC.A.1
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K.CC.A.2
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K.CC.B.4
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K.CC.C.6
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
Expressions and Equations
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6.EE.A.3
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6.EE.A.4
Number and Operations in Base Ten
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2.NBT.B.9
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3.NBT.A.2
Operations and Algebraic Thinking
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2.OA.A.1
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2.OA.B.2
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2.OA.C.3
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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