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, learners 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)
In this task, young scholars 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,...
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 young scholars 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
Students 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 will...
Illustrative Mathematics
Illustrative Mathematics: Alike or Different Game
Students work in pairs and take turns drawing two cards. These cards have pictures of different shapes. The students are asked to describe what is similar or different between the two shapes. This type of task lays the foundation for the...
Illustrative Mathematics
Illustrative Mathematics: Teen Go Fish
Students will play "Go Fish" using teen numbers to practice identifying these numbers.
Illustrative Mathematics
Illustrative Mathematics: Rainbow Number Line
The teacher will prepare number lines for the young scholars to trace. These number lines can be taped to the desk to be used for number recognition, sequencing, counting, "number forward", and "number backward" activities. An example is...
Illustrative Mathematics
Illustrative Mathematics: G Gpe Parallel Lines in the Coordinate Plane
The goal of this task is to prove the slope criterion for parallel lines. Aligns with HSG-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe When Are Two Lines Perpendicular?
The goal of this task is to examine when two lines in the plane are perpendicular in terms of their slopes. Aligns with HSG-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Scaling a Triangle in the Coordinate Plane
The goal of this task is to apply dilations to a triangle in the coordinate plane. Students will need to find the coordinates of a point which cuts a given segment into one third and into two thirds. The two dilated triangles share a...
Illustrative Mathematics
Illustrative Mathematics: G Gpe, N Rn, F Tf Coordinates of Equilateral Triangles
In this task, students are asked if there is an equilateral triangle ABC where two vertices are on the x-axis, and all vertices have integer coordinates. Aligns with G-GPE.B, N-RN.B, and F-TF.C.9.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Squares on a Coordinate Grid
The purpose of this task is to use the Pythagorean Theorem and knowledge about quadrilaterals in order to construct squares of different sizes on a coordinate grid. Aligns with G-GPE.B.7.