Illustrative Mathematics
Illustrative Mathematics: A sse.b.3: Ice Cream
This task illustrates the process of rearranging the terms of an expression to reveal different aspects about the quantity it represents. Aligns with A-SSE.B.3.
Illustrative Mathematics
Illustrative Mathematics: A sse.b.3.c Forms of Exponential Expressions
This task can be used for assessment, practice or even to motivate students via an in-class discussion of why it is useful to rewrite exponential expressions in equivalent forms. Aligns with A-SSE.B.3.c.
Illustrative Mathematics
Illustrative Mathematics: 3.oa Making a Ten
This task builds on that knowledge by asking them to study more carefully the make-a-ten strategy that they should already know and use intuitively. Aligns with CCSS.Math.Content.3.OA.D.9 Identify arithmetic patterns, and explain them...
Illustrative Mathematics
Illustrative Mathematics: 3.oa Addition Patterns
The purpose of this task is to study some patterns in a small addition table. Aligns with CCSS.Math.Content.3.OA.D.9 Identify arithmetic patterns, and explain them using properties of operations.
Illustrative Mathematics
Illustrative Mathematics: 3.oa the Stamp Collection
This task uses language, half of the stamps, that students associate with multiplication by the fraction 1/2. Students will understand half of 120 to mean the number obtained by dividing 120 by 2. For students who are unfamiliar with...
Illustrative Mathematics
Illustrative Mathematics: A sse.b: Taxes and Sales
This task is not about computing the final price of the shirt but about using the structure in the computation to make a general argument. Aligns with A-SSE.B.
Illustrative Mathematics
Illustrative Mathematics: A sse.b.3.b: Rewriting a Quadratic Expression
The goal of this task is to complete the square in a quadratic expression in order to find its minimum or maximum value. Aligns with HSA-SSE.B.3.b.
Illustrative Mathematics
Illustrative Mathematics: A Sse.4: You Tube Explosion
This task, commentary, and solutions, were authored by Lacey Dixon and Jonathan Utegaard of The University of Arizona. The purpose of this task is to have students derive the formula for the sum of a specific finite geometric series....
Illustrative Mathematics
Illustrative Mathematics: 8.g Circle Sandwich
Eighth graders are presented with a drawing of a large square inscribed by a circle which is itself inscribed by a second square. They are asked to find the area of the circle outside the smaller square and compare it to the area of the...
Illustrative Mathematics
Illustrative Mathematics: 8.g Area of a Trapezoid
Eighth graders are given various dimensions of a trapezoid and are asked to find its area. This requires them to use the Pythagorean Theorem and to decompose the trapezoid into other polygons. Aligns with 8.G.B.7.
Illustrative Mathematics
Illustrative Mathematics: 8.g Two Triangles' Area
In this task, 8th graders are given the dimensions of two isosceles triangles and are asked to compare their areas. They must draw them and use the Pythagorean Theorem and the triangle area formula to solve the problem. Aligns with 8.G.B.7.
Illustrative Mathematics
Illustrative Mathematics: 8.g Comparing Snow Cones
This task asks students to compare the volume of a cone to a truncated cone when they are the same height. They must calculate volumes for a cone, a truncated cone, and a hemisphere. Aligns with 8.G.C.9.
Illustrative Mathematics
Illustrative Mathematics: 8.g Flower Vases
This task asks students to compare the volumes of three vases that are different shapes - a cylinder, a cone, and a sphere - as well as one with a combination of shapes. They are then asked to create a vase with composite shapes, find...
Illustrative Mathematics
Illustrative Mathematics: 8.g Finding Isosceles Triangles
This task asks students to examine three triangles in the coordinate plane and explain why they are isosceles triangles. Aligns with 8.G.B.8.
Illustrative Mathematics
Illustrative Mathematics: 8.g Converse of the Pythagorean Theorem
This task asks students to explain what the Pythagorean Theorem and its converse are, how the converse works, and why it is true. Aligns with 8.G.B.6.
Illustrative Mathematics
Illustrative Mathematics: 8.g Congruence of Alternate Interior Angles
Eighth graders are presented with a labeled drawing of two parallel lines intersected by a transversal line. They are asked to discuss congruency of angles when the picture is rotated about a point on the transversal. Aligns with 8.G.A.5.
Illustrative Mathematics
Illustrative Mathematics: 8.g Bird and Dog Race
In this race between a bird and a dog, 8th graders are provided with information about their starting locations on a map and their speeds. They are asked to predict a winner, draw the paths they might follow, decide how to determine who...
Illustrative Mathematics
Illustrative Mathematics: 8.g Point Reflection
In this task, 8th graders are given the coordinates of a point and are asked to find the coordinates of its reflection across a line parallel to the x-axis. Aligns with 8.G.A.3.
Illustrative Mathematics
Illustrative Mathematics: 8.g.7 Running on the Football Field
This task asks students to apply the Pythagorean Theorem to find the approximate number of yards two players ran during a football game and compare their distances. Aligns with 8.G.B.7.
Illustrative Mathematics
Illustrative Mathematics: 8.g Congruent Segments
Eighth graders are shown two line segments that are the same length and must describe a sequence of reflections that exhibits a congruence between them. Aligns with 8.G.A.2.
Illustrative Mathematics
Illustrative Mathematics: 8.g Pythagorean Theorem in Mathematical Context
Eighth graders are shown a drawing of a rectangle with a central triangle bordered by three right triangles. They are asked to prove whether or not the middle triangle is also a right triangle. Aligns with 8.G.B.
Illustrative Mathematics
Illustrative Mathematics: 8.g Find the Angle
In this task, 8th graders have to reason with angles and angle measurements, including the sum of the angles in a triangle, to deduce information from a picture. Includes a GeoGebra worksheet that the teacher can use for demonstration...
Illustrative Mathematics
Illustrative Mathematics: 8.g Triangle Congruence With Coordinates
For this task, 8th graders explore congruence and transformations of two triangles on a coordinate grid. Aligns with 8.G.A.2.
Illustrative Mathematics
Illustrative Mathematics: 8.g Congruent Triangles
In this task, 8th graders investigate congruence and transformations of two triangles on a coordinate grid. Includes a GeoGebra worksheet that the teacher can use for demonstration purposes. Aligns with 8.G.A.2.