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 www.edweb.net/math

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 www.edweb.net/math

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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

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

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?

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

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.

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.

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

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

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

Subtraction as Separating +5 - +3 = +2 Algeblocks Sign ~ position on the mat Operation ~ place on or remove

Subtraction as Separating +3 - +5 = -2 Now What?????

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? +5 - +1 = +4 +5 + -1 = +4

Multiplication & Factoring What is x multiplied by x?

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

Multiplication & Factoring What if one constant is negative?

With Algebra Tiles

More about Algeblocks

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

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 www.edweb.net/math

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

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 www.edweb.net/math

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