Illustrative Mathematics
Illustrative Mathematics: G Srt Tangent Line to Two Circles
The purpose of this task is to use similar triangles and setting up a proportion in order to calculate a side length. Aligns with G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg Coins in a Circular Pattern
In this task, students investigate how many coins will fit around a central coin when they are all of the same denomination, and if there is room left over. The teacher is given a chart of four coin denominations and their diameters, but...
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg Seven Circles Iii
For this task, students are shown circle formations where an inner circle is surrounded by a set of circles and all circles are touching. In the first situation, all circles have the same diameter. In the second, the inner circle is...
Illustrative Mathematics
Illustrative Mathematics: G Srt Pythagorean Theorem
The purpose of this task is to prove the Pythagorean Theorem using similar triangles. Aligns with G-SRT.B.4.
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg How Far Is the Horizon?
Some friends are at the beach looking out onto the ocean on a clear day and they wonder how far away the horizon is. A second problem asks how far the horizon would be from the top of a mountain. Students must also answer a question...
Illustrative Mathematics
Illustrative Mathematics: G Srt Similar Triangles
This task works toward establishing the AA criterion for similarity of triangles. Students are asked to provide a detailed sequence of transformations that moves one of the given triangles onto the other. Aligns with G-SRT.A.3.
Illustrative Mathematics
Illustrative Mathematics: G Srt Ask the Pilot
In the July 2013 issue of United Airlines' Hemisphere Magazine, a pilot responded to a question about how far in the distance he could see at different altitudes. The solution involved right triangles, lines of tangency to a circle, and...
Illustrative Mathematics
Illustrative Mathematics: G Srt Mt. Whitney to Death Valley
In this task, learners are asked to make a mathematical model and determine if it is possible to see a point on the surface of the Earth that is 85 miles away, and well below sea level, from the top of a mountain. The curvature of the...
Illustrative Mathematics
Illustrative Mathematics: 6.sp4, 5c Puzzle Times
A performance task asking students to create a graph of provided information and then find the mean and the median of the data.
Illustrative Mathematics
Illustrative Mathematics: 7.ee Equivalent Expressions
A performance task asking learners to determine if two equations show an equivalent expression.
Illustrative Mathematics
Illustrative Mathematics: 7.ee Discounted Books
A performance task asking students to see two different ways to look at percentages, as an increase and as a decrease of an original amount.
Illustrative Mathematics
Illustrative Mathematics: G Srt Similar Triangles
The goal of this task is to examine similarity of triangles from the point of view of proportional sides, showing that this is sufficient to conclude that two triangles are similar. Aligns with HSG-SRT.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Srt Folding a Square Into Thirds
The goal of this task is to apply knowledge about similar triangles in order to understand an origami construction: trisection of the side of a square. Aligns with G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: 6.sp.1 Identifying Statistical Questions
A task asking students to determine which of the seven questions listed are statistical questions and which are not.
Illustrative Mathematics
Illustrative Mathematics: G Srt Bank Shot
This task asks students to use similarity to solve a pool table problem. Students must use the fact from physics that when an object bounces off of a wall, the angle of incidence equals the angle of reflection. Aligns with G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: 6.rp, 7.rp.3 Climbing the Steps of El Castillo
A performance task in which students solve a problem involving a proportional relationship. The problem is: The temple at the top of the pyramid is approximately 24 meters above the ground, and there are 91 steps leading up to the...
Illustrative Mathematics
Illustrative Mathematics: 6.sp Buttons: Statistical Questions
A task asking students to determine which of the six questions listed are statistical questions and which are not. Students are then asked to write a statistical question of their own.
Illustrative Mathematics
Illustrative Mathematics: 6.sp Puppy Weights
A performance task asking students to create a graph of provided information and then answer two questions about the information provided with that graph.
Illustrative Mathematics
Illustrative Mathematics: G Srt Are They Similar?
In this task, students are shown two triangles that appear to be similar, but whose similarity cannot be proven without further information. Students are asked to provide a sequence of similarity transformations that maps one triangle to...
Illustrative Mathematics
Illustrative Mathematics: G Srt Dilating a Line
In this task, students investigate a dilation of a line segment and how the length of the dilation relates to the scale factor. Aligns with G-SRT.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Srt Joining Two Midpoints of Sides of a Triangle
In this task, students must prove that angles and triangles are congruent and that a parallel line passes through the midpoints of two sides of the larger triangle. Aligns with G-SRT.B.4.
Illustrative Mathematics
Illustrative Mathematics: G Srt Extensions, Bisections, Dissections in Rectangle
In this task, students must draw a diagram from a verbal description and use their understanding of similar triangles to find the area of a quadrilateral. Aligns with G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Srt Similar Quadrilaterals
The goal of this task is to study if the analog of the AA criterion for similarity of triangles holds for different types of quadrilaterals. Aligns with HSG-SRT.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Srt Finding the Area of an Equilateral Triangle
This task examines how to calculate the area of an equilateral triangle two ways: using triangle congruence and using trigonometric ratios. Aligns with G-CO.C.10 and G-SRT.C.