New Boxes From Old

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things.

Material Type: Activity/Lab, Lesson Plan

Author: Mary R. Hebrank

Calculus: AP Calculus Practice Questions

This series of videos focusing on calculus covers sample questions from the A.P, Calculus AB and AC exams (both multiple choice and free answer).

Material Type: Lecture

1.G Grandfather Tang's Story

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Materials * A copy of Grandfather Tang's Story by Ann Tompert * One set of tangrams for each student (see note in commentary) * A set of tangrams for t...

Material Type: Activity/Lab

Author: Illustrative Mathematics

Grade 7 Mathematics Module 1: Ratios and Proportional Relationship

In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality.  Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions.  Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing.

Material Type: Module

5.NBT Which number is it?

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Netta drew a picture on graph paper: She said, In my picture, a big square represents 1. Since ten rectangles make a big square, a rectangle represents...

Material Type: Activity/Lab

Author: Illustrative Mathematics

A-CED Regular Tessellations of the plane

This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Painting a Barn

The purpose of this task is to provide students an opportunity to use mathematics addressed in different standards in the same problem.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Giantburgers

This task requires students to use exponents and figure out percentages.

Material Type: Activity/Lab

Author: Illustrative Mathematics

2.NBT Many Ways to do Addition 2

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Materials For each student: * A large index card * A pencil Action Part 1 The teacher will put up the following addition problem: \begin{align} 24 &\ \...

Material Type: Activity/Lab

Author: Illustrative Mathematics

Prime Factorization

This short video and interactive assessment activity is designed to teach third graders about prime factorization.

Material Type: Assessment, Interactive, Lecture

Describe Place Values to 1000

This short video and interactive assessment activity is designed to teach fourth graders about completing the expanded forms of numbers (place values to 1,000).

Material Type: Assessment, Interactive, Lecture