This task aims at explaining why four regular octagons can be placed around a central square, applying student knowledge of triangles and sums of angles in both triangles and more general polygons.
Material Type: Activity/Lab
The goal of this task is to use rigid motions to establish some fundamental results about angles made by intersecting lines. Both vertical angles and alternate interior angles are treated.
Material Type: Activity/Lab
This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.
Material Type: Activity/Lab
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: Quadrilateral $ABCD$ is a trapezoid, $AD = 15$, $AB = 50$, $BC = 20$, and the altitude is 12. What is the area of the trapezoid?...
Material Type: Activity/Lab
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: During the 2005 Divisional Playoff game between The Denver Broncos and The New England Patriots, Bronco player Champ Bailey intercepted Tom Brady aroun...
Material Type: Activity/Lab
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: A square is inscribed in a circle which is inscribed in a square as shown below. Note that the vertices of the inner square meet the midpoints of the o...
Material Type: Activity/Lab
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: A spider walks on the outside of a box from point A to B to C to D and finally to point E as shown in the picture below. Draw a net of the box and map ...
Material Type: Activity/Lab
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: Mrs. Lu has asked students in her class to find isosceles triangles whose vertices lie on a coordinate grid. For each student example below, explain wh...
Material Type: Activity/Lab
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 aspects of the task and its potential use.
Material Type: Activity/Lab
The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.
Material Type: Activity/Lab
This task gives students an opportunity to work with volumes of cylinders, spheres and cones. Notice that the insight required increases as you move across the three glasses, from a simple application of the formula for the volume of a cylinder, to a situation requiring decomposition of the volume into two pieces, to one where a height must be calculated using the Pythagorean theorem.
Material Type: Activity/Lab
This task requires students to determine whether a number is rational or irrational. The task assumes that students are able to express a given repeating decimal as a fraction.
Material Type: Activity/Lab
Standard 8.NS.1 requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of choice of representation. For example, 0.333 and 1/3 are two different ways of representing the same number.
Material Type: Activity/Lab
When students plot irrational numbers on the number line, it helps reinforce the idea that they fit into a number system that includes the more familiar integer and rational numbers.
Material Type: Activity/Lab
This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.
Material Type: Activity/Lab
This is a remix of https://www.oercommons.org/authoring/29037-curriculum-guide-the-pythagorean-theorem/view by Shana Friend, with a few resources added at the beginning to provide more conceptual connections. The purpose of this curriculum guide is to provide OER lesson material and support activities for Pythagorean Theorem instruction. It is geared towards GED® requirements. Both printable and online options are provided.
Material Type: Activity/Lab, Assessment, Lesson, Reading, Teaching/Learning Strategy
For many adult students, positive and negative integers are an example of when math “keeps changing the rules.” This is the fifth of six lessons guiding students in constructing the abstract concepts necessary to understand adding positive and negative integers. This lesson will review previous knowledge about negative numbers and teach adding integers with different signs. This is a time when it’s important to stress to students that understanding this lesson will help them in many future lessons.
Material Type: Lesson Plan
In Bootstrap:Data Science, students form their own questions about the world around them, analyze data using multiple methods, and write a research paper about their findings. The module covers functions, looping and iteration, data visualization, linear regression, and more. Social studies, science, and business teachers can utilize this module to help students make inferences from data. Math teachers can use this module to introduce foundational concepts in statistics, and it is aligned to state and national standards.
Material Type: Activity/Lab, Assessment, Data Set, Full Course, Homework/Assignment, Lecture Notes, Lesson Plan, Teaching/Learning Strategy
Resource suggestions to explore and consider as a way to support your family learning during school closures.
Material Type: Activity/Lab, Interactive, Teaching/Learning Strategy
The stories in Living Proof are intended to provide support and inspiration for mathematics students experiencing struggle and despair. If students keep working, if they keep seeking, they’ll be rewarded by serendipity, which is really just, as these stories remind us, the habit of mind to be engaged and to notice when something good has happened.
Material Type: Case Study
