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Beyond the Algorithm: Addition and Subtraction
Strategies that Make Sense!
Kimberly Rimbey, Ph.D.
Co-Founder & CEO, KP Mathematics
kpkimrimbey@gmail.com
January 20, 2018
1
MEAD 2018-Addition & Subtraction Strategies, Grades 1-4
Todays Session
Learning Goal: To understand strategies and
representations for teaching and learning
addition and subtraction.
Todays Focus
Concrete Representations
Pictorial Representations
aka, Transitional Representations
Abstract Representations
Numerals
Expressions
Equations
Not necessarily standard form!
Tips  Selecting Tools Strategically
 Start with one, then add to the tool box.
 Demonstrate appropriate use for each tool before
putting in tool box.
 Give students the opportunity to try out each tool
when first introduced.
 Keep a cumulative anchor chart.
 Discuss appropriate use frequently.
STRATEGIES FOR ADDITION
Place Value Properties Composing & Decomposing Counting Expanded Form
9
24 + 27
Addition Representations
9
10
Just because its notated in a standard format
does NOT mean students must use the
standard algorithm!
10
24
+ 27
Corrina had [ ] daisies and [ ] roses. How many
flowers did she have in all?
[4,7] [24, 27] [124, 327]
Place Value Strategy w/
Manipulatives
Decomposing Strategy w/ Number
Bonds
Counting Strategy w/ Number Lines
Expanded Form Strategy w/ Pictures
Expanded Form Strategy w/ Numbers
Place-Value Models
17 + 34 65 + 28
Strategies
Place Value
Properties
Decomposing
Counting
Expanded Form
Representations
Manipulatives
Number Bonds
Number Lines
Expanded Form - Pictures
Expanded Form - Numbers
What Strategies Might You Look For?
 Place Value
 Properties
 Composing & Decomposing
 Counting Strategies
 Expanded Form
STRATEGIES FOR SUBTRACTION
Place Value Properties Relationships Composing & Decomposing Counting
20
51  27
Subtraction Representations
20
Corrina had [ ] flowers. [ ] of them were roses.
How many were not roses?
[11,7] [51, 27] [451, 327]
Place Value Strategy w/
Manipulatives
Decomposing Strategy w/ Number
Bonds
Counting Strategy w/ Number Lines
Expanded Form Strategy w/ Pictures
Expanded Form Strategy w/ Numbers
Place-Value Models
Strategies
Place Value
Decomposing
Counting
Expanded Form
Expanded Form
Representations
Manipulatives
Number Bonds
Number Lines
Expanded Form - Pictures
Expanded Form - Numbers
43 - 26 60 - 38
What Strategies Might You Look For?
 Place Value
 Properties
 Composing & Decomposing
 Counting Strategies
 Expanded Form
Reflect
What are your next steps for
implementing these ideas?
Instructional Support
MEAD 2018-Addition & Subtraction Strategies, Grades 1-4
MEAD 2018-Addition & Subtraction Strategies, Grades 1-4
MEAD 2018-Addition & Subtraction Strategies, Grades 1-4
THANK YOU!
Kimberly Rimbey, Ph.D.
KP Mathematics
623-297-7373
www.kpmathematics.com
kpkimrimbey@gmail.com

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MEAD 2018-Addition & Subtraction Strategies, Grades 1-4

Editor's Notes

  • #2: A5: Beyond the Algorithm: Addition and Subtraction Strategies that Make Sense! By Kimberly Rimbey K-4 Making sense of multi-digit subtraction requires strong connections with addition and place value. Join us as we explore addition and subtraction using concrete and visual models, connected to written work, and grounded in problem solving. Formative assessment strategies will be included.