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Illustrative Mathematics

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Linear Functions
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This task requires students to use the fact that on the graph of the linear function h(x)=ax+b, the y-coordinate increases by a when x increases by one. Specific values for a and b were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Linear Or Exponential?
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CC BY
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This task gives a variet of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions).

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Lines of Symmetry For Circles
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This is an instructional task that gives students a chance to reason about lines of symmetry and discover that a circle has an an infinite number of lines of symmetry. Even though the concept of an infinite number of lines is fairly abstract, fourth graders can understand infinity in an informal way.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
11/11/2012
Lines of Symmetry For Quadrilaterals
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This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
11/11/2012
Lines of Symmetry For Triangles
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CC BY
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This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
10/12/2012
Listing Fractions in Increasing Size
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CC BY
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This is a challenging fraction comparison problem. The fractions for this task have been carefully chosen to encourage and reward different methods of comparison.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/22/2012
Locating Fractions Less than One on the Number Line
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CC BY
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In this number line task students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Locating Warehouse
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CC BY
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This task can be implemented in a variety of ways. For a class with previous exposure to the incenter or angle bisectors, part (a) could be a quick exercise in geometric constructions,. Alternatively, this could be part of a full introduction to angle bisectors, culminating in a full proof that the three angle bisectors are concurrent, an essentially complete proof of which is found in the solution below.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Log Ride
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CC BY
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In this instructional task students are given two inequalities, one as a formula and one in words, and a set of possible solutions. They have to decide which of the given numbers actually solve the inequalities.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Logistic Growth Model, Explicit Version
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This problem introduces a logistic growth model in the concrete setting of estimating the population of the U.S. The model gives a surprisingly accurate estimate and this should be contrasted with linear and exponential models, studied in ``U.S. Population 1790-1860.'' This task requires students to interpret data presented.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/15/2012
The Longest Walk
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CC BY
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In this task students figure out how to draw the longest line on a map of the United States without hitting a border. They use color and line plots to keep track of their results.

Subject:
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
MD Delayed Gratification
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CC BY
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The purpose of this task is for students to compare two options for a prize where the value of one is given $2 at a time, giving them an opportunity to "work with equal groups of objects to gain foundations for multiplication." This context also provides students with an introduction to the concept of delayed gratification, or resisting an immediate reward and waiting for a later reward, while working with money.

Subject:
Mathematics
Measurement and Data
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/17/2013