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Symmetry of the Addition Table
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CC BY
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The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers. This is important as it gives students a chance, at a young age, to do more than memorize these arithmetic facts which they will use throughout their education.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
09/05/2012
Three composing/decomposing problems
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CC BY
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The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
To Regroup or Not To Regroup
Unrestricted Use
CC BY
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This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping. This way students have to recognize the pattern and not just follow a memorized algorithm--in other words, they have to think about what happens in the subtraction process when we regroup. This task is appropriate to use after students have learned the standard US algorithm.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/12/2013
Using Benchmarks To Compare Fractions
Unrestricted Use
CC BY
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The goal of this task is to provide examples for comparing two fractions by finding a benchmark fraction which lies in between the two.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
IInstitute for Mathematics & Education funded by the Bill & Melinda Gates Foundation
Illustrative Mathematics
Date Added:
07/30/2012
Using Place Value
Unrestricted Use
CC BY
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This task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
11/13/2012
Using lengths to represent equality
Unrestricted Use
CC BY
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Students develop a physical understanding for the meaning of equality by trying to find equal lengths using rods.

Subject:
Mathematics
Measurement and Data
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
09/20/2012
Watch Out for Parentheses 1
Unrestricted Use
CC BY
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This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. It helps students see the purpose of using parentheses.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
What is 23 Ö 5?
Unrestricted Use
CC BY
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When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder or a mixed number.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/03/2013
What's Missing?
Unrestricted Use
CC BY
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The words compose and decompose are used to describe actions that young students learn as they acquire knowledge of small numbers by putting them together and taking them apart. This understanding is a bridge between counting and knowing number combinations. It is how instant recognition of small numbers develops and leads naturally to later understanding of fact families. This task helps them develop an understanding of number combinations.

Subject:
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Which Number is Greater? Which Number is Less? How Do You Know?
Unrestricted Use
CC BY
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The purpose of this task is for students to explain how they know one quantity is greater or less than another quantity. Students will easily be able to identify which number is greater or less. However, explaining their reasoning will help them solidify their number sense skills.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
10/28/2012