1. Putting Manipulatives to Work
Developing Expressions & Equations in Grades 6-8 with Algebra Tiles & Algeblocks
Tuesday, August 4, 2015
Presented by Sara Delano Moore, Ph.D.
Director of Mathematics and Science at ETA hand2mind
Join our community on edWeb.net
Building Understanding in Mathematics

2. Building Understanding in Mathematics
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5. Putting Manipulatives to Work:
Developing Expressions & Equations in Grades 6-8 with Algebra Tiles and Algeblocks
Sara Delano Moore, Ph.D.
Director of Mathematics & Science
ETA hand2mind
4 August 2015

6. Putting Manipulatives to Work: Series Overview
June 2: Developing Number Sense K-5 with Cuisenaire Rods, Rekenreks, and Place Value Chips
July 7: Developing Geometric Measurement in Grades 3-4 – Area, Perimeter, Angle Measure with Color Tiles and AngLegs
August 4: Developing Expressions & Equations Grades 6-8 with Algebra Tiles and Algeblocks

7. Send out a search party!
Are there manipulatives hiding in THAT closet?
Have you received new tools as part of new programs and you aren’t sure how to use them?

8. Understanding Expressions & Equations
Build on essential ideas of arithmetic
Meaning of operations
Properties of operations
How can manipulative models support this work?

9. Adding/Subtracting Integers
What can we do to extend student understanding of addition/subtraction to include integers?
The action associated with addition is JOINING.
The action associated with subtraction is SEPARATING.

10. Grammar and Integers
We use the symbols – and + in two different ways. This can be confusing to students.
As ADJECTIVES, - and + indicate what kind of number, positive or negative.
As VERBS, - and + indicate which operation is in use, addition or subtraction.
Helping students see both, especially in the early stages of learning, can make the mathematics more transparent.

11. Addition as Joining
John has two cars. He receives three more cars for his birthday. How many cars does John have now?

12. Addition as Joining +2 + +3 = +5 What makes these positive?
Algebra Tiles: red ~ negative, not red ~ positive
Where is the addition?
Joining the groups

13. Addition as Joining +2 + -3 = -1 Additional important idea: zero pairs
= 0
To find the sum, create zero pairs

14. Subtraction as Separating
= +2
Algeblocks
Sign ~ position on the mat
Operation ~ place on or remove

15. Subtraction as Separating
= -2
Now What?????

16. Addition and Subtraction as Inverses
Sara has $5. She went to the fair and spent $1 to purchase an ice cream cone. How much money does Sara have now?
Sara has $5. She went to the fair but left her money at home. She borrowed $1 from her friend to purchase an ice cream cone. How much money does Sara have now?
= +4
= +4

17. Multiplication & Factoring
What is x multiplied by x?

18. Multiplication & Factoring
What if I make each side one unit longer?

19. Multiplication & Factoring
What if one constant is negative?

20. With Algebra Tiles

21. More about Algeblocks

22. Putting Manipulatives to Work: Series Overview
June 2: Developing Number Sense K-5 with Cuisenaire Rods, Rekenreks, and Place Value Chips
July 7: Developing Geometric Measurement in Grades 3-4 – Area, Perimeter, Angle Measure with Color Tiles and AngLegs
August 4: Developing Expressions & Equations Grades 6-8 with Algebra Tiles and Algeblocks

24. Building Understanding in Mathematics
Join our community on edWeb.net
Building Understanding in Mathematics
Invitations to upcoming webinars
Webinar recordings and resources
CE quizzes
Online discussions
Join the community

25. Recognition for your participation today!
Attending Live?
Your CE Certificate will be
ed to you within 24 hours.
Viewing the Recording?
Join the community at
Go to the Webinar Archives folder
Take the CE Quiz to get a personalized CE Certificate
CE Certificate provided by

26. Geometric Reasoning with Shapes & Attributes
Join us for the next webinar
Tuesday, September 15th – 4 PM Eastern Time
Geometric Reasoning with Shapes & Attributes
Part 1: Laying a Strong Foundation
Presented by
Sara Delano Moore, Ph. D.,
Director of Mathematics and Science at ETA hand2mind
For an invitation to the next webinar
Join Building Understanding in Mathematics

27. Thank you!