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The Square Counting Shortcut
Unrestricted Use
CC BY
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This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas. However, students should not be discouraged from using individual counting to start if they are stuck. Often students will get tired of counting and devise the shortcut method themselves.

Subject:
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
The Stamp Collection
Unrestricted Use
CC BY
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This task uses language, "half of the stamps," that students in Grade 5 will come to associate with multiplication by the fraction 12. In Grade 3, many students will understand half of 120 to mean the number obtained by dividing 120 by 2. For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
07/05/2012
Stock Swaps, Variation 3
Unrestricted Use
CC BY
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This is a multi-step problem since it requires more than two steps no matter how it is solved. The problem is not scaffolded for the student, but each step is straightforward and should follow from the previous with a careful reading of the problem.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Sugar in Six Cans of Soda
Unrestricted Use
CC BY
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This task provides a familiar context allowing students to visualize multiplication of a fraction by a whole number. This task could form part of a very rich activity which includes studying soda can labels.

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/21/2012
Sum of Angles in a Polygon
Unrestricted Use
CC BY
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This problem provides students with an opportunity to discover algebraic structure in a geometric context. More specifically, the student will need to divide up the given polygons into triangles and then use the fact that the sum of the angles in each triangle is 180_.

Subject:
Algebra
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/21/2013
Sum of Even and Odd
Unrestricted Use
CC BY
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Parts (d) and (e) of this task constitute a very advanced application of the skill of making use of structure: in (d) students are being asked to use the defining property of even and odd functions to manipulate expressions involving function notation. In (e) they are asked to see the structure in the system of two equations involving functions.

Subject:
Algebra
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Support for a Longer School Day?
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CC BY
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

Subject:
Mathematics
Statistics and Probability
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/06/2015
Symmetry of the Addition Table
Unrestricted Use
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
Tangent Lines and the Radius of a Circle
Unrestricted Use
CC BY
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This task presents a foundational result in geometry, presented with deliberately sparse guidance in order to allow a wide variety of approaches. Teachers should of course feel free to provide additional scaffolding to encourage solutions or thinking in one particular direction. We include three solutions which fall into two general approaches, one based on reference to previously-derived results (e.g., the Pythagorean Theorem), and another conducted in terms of the geometry of rigid transformations.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
11/13/2012
Tangent to a Circle from a Point
Unrestricted Use
CC BY
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The construction of the tangent line to a circle from a point outside of the circle requires knowledge of a couple of facts about circles and triangles. First, students must know, for part (a), that a triangle inscribed in a circle with one side a diameter is a right triangle. This material is presented in the tasks ''Right triangles inscribed in circles I.'' For part (b) students must know that the tangent line to a circle at a point is characterized by meeting the radius of the circle at that point in a right angle: more about this can be found in ''Tangent lines and the radius of a circle.''

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/21/2013