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.
Illustrative Mathematics
Illustrative Mathematics: G Gmd Doctor's Appointment
In preparation for some medical tests, Jared must drink 3 liters of water today, but he has forgotten his water bottle at home and must use paper cone cups at work. Students are asked to calculate how many of these he must drink if that...
Illustrative Mathematics
Illustrative Mathematics: G Gmd Centerpiece
This problem presents a wedding reception scenario. The bride is creating centerpieces for the tables and must calculate how many marbles she needs to partly fill the vases and stay within her budget at the same time. Aligns with G-GMD.A.3.
Illustrative Mathematics
Illustrative Mathematics: G Gmd, G Mg Tennis Balls in a Can
In this task, students investigate the volume of tennis balls and their cylindrical container, the empty space around the balls, different ways of slicing them, and what their visualizations will look like. Aligns with G-GMD.B.4 and...
Illustrative Mathematics
Illustrative Mathematics: G Gmd Volume Estimation
In this task, students are asked to estimate the volume of a non-standard 3D solid by referencing either a cone or a cylinder. Aligns with G-GMD and G-GMD.A.3.
Illustrative Mathematics
Illustrative Mathematics: G Gmd Area of a Circle
For this task, learners investigate and develop an understanding of the formula for the area of a circle. Aligns with G-GMD.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Gmd Circumference of a Circle
For this task, students are asked to explain the formula for finding the circumference of a circle. Aligns with G-GMD.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Mg Archimedes and the King's Crown
The King of Syracuse reportedly requested Archimedes' advice for determining if a crown was made with the appropriate mixture of gold and silver. The problem asks young scholars to find the amount of water displaced in Archimedes'...
Illustrative Mathematics
Illustrative Mathematics: G Mg Satellite
This task models a satellite orbiting the Earth in communication with two control stations located miles apart on Earth's surface. Students determine distances between various locations and, given a rate of travel, they determine the...
Illustrative Mathematics
Illustrative Mathematics: G Mg the Lighthouse Problem
For this task, students are asked to calculate the height above sea level of a lamp on top of a lighthouse that is visible to a boat, and to examine two other interpretations of the distance from the lighthouse to the boat. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: G Mg a Ton of Snow
In this task, students are asked to find out how much snow has been shoveled using the concepts of area, depth, density, and rate. Aligns with HSG-MG.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Mg Indiana Jones and the Golden Statue
The goal of this task is to provide an introduction to the sometimes subtle use of density and units related to density, in a simple and fun context with minimal geometric complexity. Includes video showing the opening scene of Raiders...
Illustrative Mathematics
Illustrative Mathematics: G Mg, G Gmd Global Positioning System Ii
Satellites communicate with a GPS device and establish the distance between them and their locations. The set of points at a fixed distance from a satellite form a sphere so when the GPS receives its distance from a given satellite, this...
Illustrative Mathematics
Illustrative Mathematics: G Mg How Thick Is a Soda Can? Variation Ii
In this task, learners are given an aluminum soda can and are simply asked how they could determine how thick the can is. Aligns with G-MG.A.1 and G-MG.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Mg How Thick Is a Soda Can? Variation I
For this task, students are given the dimensions of a soda can and are asked to estimate its thickness. They must first find the surface area and the volume of aluminum. Aligns with G-MG.A.1 and G-MG.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Mg Solar Eclipse
In this task, students investigate why total solar eclipses are rare. They will learn that, in addition to requiring the positioning of the Sun, Moon, and Earth, the Moon can only completely block out the Sun when it is closest to the...
Illustrative Mathematics
Illustrative Mathematics: G Mg Tilt of Earth's Axis and the Four Seasons
This task gives students a chance to explore the effects of the Earth's tilt and rotation using a simple geometric model of Earth-Sun interaction that shows why the seasons occur. Aligns with G-MG.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Mg How Many Leaves on a Tree? (Version 2)
For this task, students must estimate the number of leaves on a large tree, taking into account various complex factors such as the area shaded by the tree, the area of irregularly shaped leaves, the uneven distribution of leaves, the...
Illustrative Mathematics
Illustrative Mathematics: G Mg How Many Leaves on a Tree?
This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree, taking into account the tree size and the density of the leaves. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: G Gpe Slopes and Circles
The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever angle AXB is a right angle. This consists of...