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K-8 Mathematics StandardsContent Training

Addition and Subtraction

Valerie Adams, Math Coach, Intervention Specialist, Virgie Robinson Elementary School, Pasco School District

vadams@psd1.org

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Develop understanding of addition and subtraction concepts for your grade band.

Develop understanding of different problem types for addition and subtraction.

Learn a variety of strategies for solving addition and subtraction problems.

Experience models that support students’ thinking about strategies.

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Allow ourselves and others to be seen as learners.

Monitor own airtime and sidebar conversations.

Allow for opportunities for equitable sharing.

Presume positive intentions.

Be respectful when giving and receiving opinions, ideas and approaches.

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For all students to learn significant mathematics, content should be taught and assessed in meaningful situations.

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Conceptual Understanding◦ Making sense of mathematics

Procedural Proficiency◦ Skills, facts, and procedures

Mathematical Processes◦ Using mathematics to reason and think

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At each grade level:◦ 3-4 Core Content areas◦ Additional Key Content◦ Core Processes (reasoning, problem solving, communication)

For each of these:◦ Overview paragraph◦ Performance Expectation◦ Comments/Examples

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Use either your Standards Document or Strands Document to find all K-8 references to area and perimeter.

Go back and carefully read the Performance Expectations and Explanatory Comments and Examples for your grade level.

Note the expectations for the grade level above and below yours.

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What should your students already know?What do you need to teach this year?What do they need to know for next year?

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Lydia has 7 candies. She eats two of them. How many does she have left?

Lydia has 7 candies and Juan has 2 candies. How many more candies does Lydia have?

Lydia has 2 dollars. She wants to buy something that costs 7 dollars. How many more dollars does she need?

Yesterday Lydia had 7 balloons. Some of them burst last evening. Today she has 2 left. How many balloons burst?

Yesterday Lydia had some balloons. Today Juan gave her 2 more balloons. Now she has 7 altogether. How many balloons did she have yesterday?

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Read the chart showing types of problems. Using the sheet of problems and Problem Types

Framework, work with a partner to determine where problems fit on the framework.

Discuss at your table: How are these problems alike or different? Which type do we see most often?• Which type of problems might be easier for

children?

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1.2.H 2.2.G

Yesterday Lydia had some balloons. Today Juan gave her 2 more balloons. Now she has 7 altogether. How many balloons did she have yesterday?

Think about how you modeled this problem. What buttons would you use on the calculator to solve

this problem?

? + 2 = 7 7 – 2 = ? How are these problems alike?

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1.2.D 2.2.G

What are common definitions of Addition and Subtraction?

John Van de Walle defines Addition and Subtraction as:◦Addition is used to name the whole when the parts of

the whole are known◦Subtraction is used to name a part when the whole

and the remaining part are known. Understanding the Part – Whole Relationship

enables students to use inverse relationships to solve problems.

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30 minutes

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K.2.C 1.2.A 1.2.C

Keeping the quantity constant helps children to more easily see parts and whole.

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K.1.CK.2.C 1.1.F

Counting on4 + 2 4 5, 6

Doubles 2 + 2, 3 + 3, 4 + 4, 5+ 5………….

Near Doubles or Doubles +/- 1◦ 6 + 5 5 + 5 + 1 or 6 + 6 -1

Making Ten◦ 7 + 3 = 10 7 + 4 = 7 + 3 + 1=10 +1 = 11

Compensating6 + 8 Move one from 8 to 6 6 + 8 = 7 + 7

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1.2.D1.2.F1.2.G2.2.A

Simple story problems

Focused Collection of facts or strategies

Both of these approaches use carefully selected numbers designed to encourage various strategies.◦ Joe ate 7 carrots on Monday and 8 carrots on Tuesday. How

many carrots did he eat? 7 + 8 = 7 + 7 +1◦ Carrie had 8 blue marbles. She got some more red marbles.

Now she has 16 marbles. How many red marbles did she get? 8 + ? = 16 or 16 – 8 =

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Rekenrek Using 5 & 10 structures

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v

v

v

7 + 6 = 7 + 6 = 5 + 5 + 2 + 1

K.1.CK.1.HK.2.C1.2.F1.2.F2.2.A

Make two Rekenrek Strings using two sets of string with 5 red and 5 white beads on each string.

Using the number strings (related facts) page: Choose a strategy appropriate for your grade level

standards. Model with a partner at your table how you would use

the rekenrek to model mental strategies.

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Counting on4 + 2 4 5, 6

Doubles 2 + 2, 3 + 3, 4 + 4, 5+ 5………….

Near Doubles or Doubles +/- 1◦ 6 + 5 5 + 5 + 1 or 6 + 6 -1

Making Ten◦ 7 + 3 = 10 7 + 4 = 7 + 3 + 1=10 +1 = 11

Compensating6 + 8 Move one from 8 to 6 6 + 8 = 7 + 7

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1.2.D1.2.F1.2.G2.2.A

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3 + 4 = 5 + 2

K.1.C1.1.A1.2.E

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9 + 5 = 10 + 4 1.2.F1.2.G2.2.A

15 – 9 =

25 – 17 =

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9 + = 15?

17 + 3 = 2020 + 5 = 253 + 5 = 8

Students with good Part –Whole Relationship understanding will flexibly use inverse operation.

1.2.D1.2.G

Mini- Lessons for Extending Addition and Subtraction ( Fosnot)

During short 10-15 minute lessons students solve a string of related problems designed to develop mental strategies.

25 + 15 = 30 + 15 =29 + 16 =

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2.2.C,2.2.D

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On a 3X5 index card please write:

Something new I learned

Something I want to try

Something I am still wondering about

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Young Mathematicians at Work, Catherine Twomey Fosnot

Teaching Student-Centered Mathematics, John A. Van de Walle www.ablongman.com

MiniLessons for Early Addition and Subtraction, Minilessons for Extending Addition and Subtraction, Catherine Twomey Fosnot

First Steps in Mathematics, Number

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3 + 4 = 5 + 2

K.1.C1.1.A1.2.E