Illustrative Mathematics
Illustrative Mathematics: Longer and Heavier? Shorter and Heavier?
Learners will compare the length and weight of several pairs of objects to learn that weight and length are separate measurable attributes, and not always related.
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 Eratosthenes and the Circumference of the Earth
For this task, students must investigate an experiment by Eratosthenes where he estimated the circumference of the Earth. It requires collaboration with at least one other school. Aligns with G-MG.A.
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 Mg Running Around a Track Ii
An Olympic 400 meter track is made up of two straight sides and two semi-circular curves. For this task, students are asked to examine the perimeters of the different runners' tracks and the starting places that must be assigned in order...
Illustrative Mathematics
Illustrative Mathematics: G Mg Running Around a Track I
An Olympic track is made up of two straight sides and two semi-circular curves. For this task, students are asked to calculate the perimeters at two places on the first lane and to determine the span of a 400-meter lap. Aligns with G-MG.A.
Illustrative Mathematics
Illustrative Mathematics: G Mg, a Ced Regular Tessellations of the Plane
This task examines the ways in which a plane can be covered by regular polygons in a regular tessellation arrangement. The problem uses the formula for the measure of the interior angles of a regular polygon and the goal of the task is...
Illustrative Mathematics
Illustrative Mathematics: S id.a.3 Identifying Outliers
In this task, students are asked to construct a box plot of the distances they live from school and describe the main features of the distribution. The purpose of this task is to develop students' understanding of how extreme data points...
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...
Illustrative Mathematics
Illustrative Mathematics: G Gpe Explaining the Equation for a Circle
This problem examines equations defining different circles in the x-y plane. Students must use the Pythagorean Theorem to find equations whose solutions are points on the circle and explain why they work. Includes a GeoGebra worksheet...
Illustrative Mathematics
Illustrative Mathematics: G Gpe Equal Area Triangles on the Same Base Ii
This task has students apply their knowledge of parallel lines to solve a geometric problem on areas of triangles. The task is open-ended in that students can choose their method of completing the task. Aligns with G-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Equal Area Triangles on the Same Base I
This task is a relatively easy application of the formula for the area of a triangle and the use of parallel lines. Aligns with G-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: Shape Hunt Part 2
The objective of this game is for students to find and identify shapes by going on a scavenger hunt. Students go to the assigned area with a blank paper with 6 empty slots. When the student finds a shape they can copy it onto their paper...
Illustrative Mathematics
Illustrative Mathematics: Shape Sequence Search
This activity tests the student's understanding of patterns. The teacher will read a pattern and the student will find the row or column that contains each sequence. Example included.
Illustrative Mathematics
Illustrative Mathematics: Shape Hunt Part 1
Young scholars will take part in a scavenger hunt for shapes. Teachers will hide numbered, pre-cut shapes around the classroom. Students will hunt for the shapes with a blank paper with 6 empty slots. When the student finds a shape they...