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  • Illustrative Mathematics
Compounding with a 5% Interest Rate
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CC BY
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This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically addresses the standard (F-BF), building functions from a context, a auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (F-LE) domain of tasks.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Computing Volume Progression 1
Unrestricted Use
CC BY
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The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. The purpose of this first task is to see the relationship between the side-lengths of a cube and its volume.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Computing Volume Progression 2
Unrestricted Use
CC BY
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The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. In this iteration, we do away with the lines that delineate individual unit cubes (which makes it more abstract) and generalize from cubes to rectangular prisms.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Computing Volume Progression 3
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CC BY
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The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. Here, we are given the volume and are asked to find the height.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Computing Volume Progression 4
Unrestricted Use
CC BY
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The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. This problem is based on ArchimedesŐ Principle that the volume of an immersed object is equivalent to the volume of the displaced water.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Congruent Rectangles
Unrestricted Use
CC BY
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This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
11/12/2012
Congruent Segments
Unrestricted Use
CC BY
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Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Congruent Triangles
Unrestricted Use
CC BY
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This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
12/18/2012
Connor and Makayla Discuss Multiplication
Unrestricted Use
CC BY
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The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and to use this understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
07/14/2012
Construction of Perpendicular Bisector
Unrestricted Use
CC BY
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The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/11/2013
Converse of the Pythagorean Theorem
Unrestricted Use
CC BY
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This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/17/2012
Converting Decimal Representations of Rational Numbers to Fraction Rep
Unrestricted Use
CC BY
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Standard 8.NS.1 requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of choice of representation. For example, 0.333 and 1/3 are two different ways of representing the same number.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Converting Fractions of a Unit into a Smaller Unit
Unrestricted Use
CC BY
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This task gives students word problems with a given a set of a specified size and a specified number of subsets. The questions ask the student to find out the size of each of the subsets.

Subject:
Mathematics
Measurement and Data
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Cooking with the Whole Cup
Unrestricted Use
CC BY
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While the task as written does not explicitly use the term "unit rate," most of the work students will do amounts to finding unit rates. A recipe context works especially well since there are so many different pair-wise ratios to consider.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Counting Dots in Arrays
Unrestricted Use
CC BY
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Students who work on this task will benefit in seeing that given a quantity, there is often more than one way to represent it, which is a precursor to understanding the concept of equivalent expressions.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012