Numeracy Resources

Estimation 180 is an incredibly rich resource that offers photographs that we can use in meaningfully developing students' number sense. In this blog post, the author uses 4 of the images (and the students' estimates about those images) to quickly and meaningfully introduce (or review) graphing and writing inequalities.

From the posting: "In this lesson, students model a bungee jump using a Barbie® doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions." Appropriate for CCRS Level D, Level E. [Note: Resource only accessible for NCTM members.]

Desmos is an online graphing calculator. Many teachers have created activities for their classes using the calculator. Activities on the site are created by teachers and Desmos staff and will vary. You can also create your own activities.

These are 15-second videos that show a real-life event. Students are encouraged to graph the event. The video reveals the suggested graph at the end. The site allows you to sort by type of graph and offers a printable graphing handout. Appropriate for CCRS Level C, Level D, Level E.

Brief blog post by Dan Meyer that addresses teaching students not just the procedure for how to graph linear inequalities, but providing the opportunity for them to consider why the conventional representation (graph) is an efficient way to go.

A quick reading about a quick strategy a teacher uses to make "like terms" meaningful to her students.

A printable matching activity for matching graphs to equations.

In these materials, students will learn how to (1) plot points and interpret points on the coordinate grid; (2) draw lines and shapes on the coordinate grid; and (3) make sense of data on the coordinate grid (including scatter plots) and correlation. NOTE: There is a "Number Lines and the Coordinate Grid, Part 1" that helps students get comfortable with number lines.

Instructions and printables for a "combine like terms" UNO game, with some hints for using the game with your students.

This workbook has activities for students to develop their algebraic reasoning through an investigation of patterns. As they work through the activities, they will look at different kinds of patterns, find rules for how those patterns work, and use what they notice to guess what comes next. The workbook offers different ways of looking at patterns, examples for students to develop their own ways of seeing, and then space to reflect on their learning. An optional video and asynchronous mini-course are also available.

Teachers can use these materials to help students develop algebraic reasoning and learn how to use algebra as a tool in problem-solving. Students also learn about mathematical symbols and how they are used. Part 1 focuses on (1) mathematical equality; (2) how to evaluate equations and expressions and solve equations using visual models like area models, hanger diagrams, and balance scales; (3) the distributive property of multiplication and the order of operations; and (4) how to write equations to describe real-life situations.

Teachers can use these materials to help students develop algebraic reasoning and learn how to use algebra as a tool in problem-solving. Students also learn about mathematical symbols and how they are used. Part 1 focuses on (1) mathematical equality; (2) how to evaluate equations and expressions and solve equations using visual models like area models, hanger diagrams, and balance scales; (3) the distributive property of multiplication and the order of operations; and (4) how to write equations to describe real-life situations.

Teachers can use these materials to help students develop algebraic reasoning and learn how to use algebra as a tool in problem-solving. Students also learn about mathematical symbols and how they are used. Part 2 focuses on (1) four different uses for variables in math; (2) how to combine like terms and solve equations using tape diagrams; (3) using variables in scientific and geometric formulas, including finding the volume of three-dimensional figures and the Pythagorean Theorem; (4) evaluating systems of equations through guess and check and matching systems of equations to real-life situations; and (5) understanding, solving, evaluating, and graphing inequalities.

Teachers can use these materials to help students develop algebraic reasoning and learn how to use algebra as a tool in problem-solving. Students also learn about mathematical symbols and how they are used. Part 2 focuses on (1) four different uses for variables in math; (2) how to combine like terms and solve equations using tape diagrams; (3) using variables in scientific and geometric formulas, including finding the volume of three-dimensional figures and the Pythagorean Theorem; (4) evaluating systems of equations through guess and check and matching systems of equations to real-life situations; and (5) understanding, solving, evaluating, and graphing inequalities.

With these materials, students learn the concepts to flexibly create, interpret, and use linear functions. Part 1 focuses on (1) number patterns, repeating patterns, growing patterns, and visual patterns; (2) how to use input/output machines to understand the basic structure of functions; and (3) how functions can be represented in 4 connected ways.

With these materials, students learn the concepts to flexibly create, interpret, and use linear functions. Part 2 focuses on (1) rate of change (also known as slope) in graphs, tables, and equations; (2) starting amount (also known as the y-intercept) in graphs, tables, and equations; and (3) applying all the concepts learned about linear functions to some real-life situations, including paying bills and tracking medical antibodies.

A gallery of visual patterns can be used with students exploring algebra. Fawn Nguyen, the teacher behind the site, also documents her students' discussion of the patterns at mathtalks.net. You can also read about how ABE teachers are using the patterns.

A good activity from Robert Kaplinsky to compare when one coupon might be better than another. Can be done with or without inequalities. Can also be extended to graph the inequalities.