1 K-8 Mathematics Standards Content Training Addition and Subtraction

 Valerie Adams, Math Coach, Intervention Specialist, Virgie Robinson Elementary School, Pasco School District 2

 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. 3

 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. 4

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For all students to learn significant mathematics, content should be taught and assessed in meaningful situations. 6

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 Conceptual Understanding ◦ Making sense of mathematics  Procedural Proficiency ◦ Skills, facts, and procedures  Mathematical Processes ◦ Using mathematics to reason and think 8

 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 9

 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. 10 What should your students already know? What do you need to teach this year? What do they need to know for next year? 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? 12

 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? 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? 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. 15

16 30 minutes

17 K.2.C 1.2.A 1.2.C

Keeping the quantity constant helps children to more easily see parts and whole K.1.C K.2.C 1.1.F K.1.C K.2.C 1.1.F

 Counting on , 6  Doubles 2 + 2, 3 + 3, 4 + 4, 5+ 5………….  Near Doubles or Doubles +/- 1 ◦ or  Making Ten ◦ = = =10 +1 = 11 Compensating Move one from 8 to = D 1.2.F 1.2.G 2.2.A 1.2.D 1.2.F 1.2.G 2.2.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? = ◦ 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 = 20

 Rekenrek Using 5 & 10 structures 21 v v v = = K.1.C K.1.H K.2.C 1.2.F 2.2.A K.1.C K.1.H K.2.C 1.2.F 2.2.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. 22

 Counting on , 6  Doubles 2 + 2, 3 + 3, 4 + 4, 5+ 5………….  Near Doubles or Doubles +/- 1 ◦ or  Making Ten ◦ = = =10 +1 = 11 Compensating Move one from 8 to = D 1.2.F 1.2.G 2.2.A 1.2.D 1.2.F 1.2.G 2.2.A

= K.1.C 1.1.A 1.2.E K.1.C 1.1.A 1.2.E

= F 1.2.G 2.2.A 1.2.F 1.2.G 2.2.A

15 – 9 = 25 – 17 = = 15 ? = = = 8 Students with good Part –Whole Relationship understanding will flexibly use inverse operation. 1.2.D 1.2.G 1.2.D 1.2.G

Mini- Lessons for Extending Addition and Subtraction ( Fosnot) During short minute lessons students solve a string of related problems designed to develop mental strategies = = = 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 29

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 Young Mathematicians at Work, Catherine Twomey Fosnot  Teaching Student-Centered Mathematics, John A. Van de Walle  MiniLessons for Early Addition and Subtraction, Minilessons for Extending Addition and Subtraction, Catherine Twomey Fosnot  First Steps in Mathematics, Number 32

= K.1.C 1.1.A 1.2.E K.1.C 1.1.A 1.2.E