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Illustrative Mathematics

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Operations on the number line
Unrestricted Use
CC BY
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The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Operations with Rational and Irrational Numbers
Unrestricted Use
CC BY
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This task has students experiment with the operations of addition and multiplication, as they relate to the notions of rationality and irrationality.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
02/11/2014
Painting a Wall
Unrestricted Use
CC BY
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The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/21/2012
Paper Clip
Unrestricted Use
CC BY
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This high level task is an example of applying geometric methods to solve design problems and satisfy physical constraints. This task is accessible to all students. In this task, a typographic grid system serves as the background for a standard paper clip.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/19/2013
Paper Folding
Conditional Remix & Share Permitted
CC BY-NC-SA
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This is a very open-ended task designed for students to develop some of the basic ideas surrounding exponential growth. While implementations will vary (as discussed below), the core idea is that each fold of the piece of paper doubles the height of the stack. Combined with an estimate of the original thickness of the paper and the distance to the moon, this is enough information to deduce the minimum number of folds to get there. The solution uses the estimate of 0.1 mm for the thickness of paper and 385,000 km for the distance to the moon.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Date Added:
05/02/2023
Parabolas and Inverse Functions
Unrestricted Use
CC BY
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This task assumes students have an understanding of the relationship between functions and equations. Using this knowledge, the students are prompted to try to solve equations in order to find the inverse of a function given in equation form: when no such solution is possible, this means that the function does not have an inverse.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
06/08/2012
The Parking Lot
Unrestricted Use
CC BY
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The purpose of this task is to investigate the meaning of the definition of function in a real-world context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Patterns in the Multiplication Table
Unrestricted Use
CC BY
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The goal of this task is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/27/2012
Peaches
Unrestricted Use
CC BY
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This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/07/2012