Numeracy Resources
Content Resources
180 Ways to Use Estimation 180: Inequalities
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.
22? 30? 50? 100?
A teacher of children blogs about a challenging experience working with a student learning to count. An ABE teacher of basic numeracy may find many suggestions in the comments of this blog entry very useful.
3-Act Lesson: Volume of a Cylinder
A 3-act lesson starts with a quick video or visual that makes students wonder. In the videos for this 3-act lesson, Jenn Vadnais offers students a chance to consider the volume of a cylinder of Playdoh.
8 Math Skills Students Must Be Able to Do Without A Calculator (on the GED)
The GED test includes a section on the math test where students cannot access the calculator. Here the GED Testing Services explicitly breaks down skills students should be able to perform without a calculator on the test.
An Excellent Lesson for Long Division
This blog post offers some important aspects to consider in how we teach long division to our students. How does place value play a role in long division, and how do I teach long division so my students strengthen that understanding? The post includes video, a word problem, and a lesson plan that you could use tomorrow!
Another Blog Post About Fraction Division
This blog post was created to help teachers understand a strategy for making division with fractions visual and meaningful for students.
AREA: Big Cheez-its & Multiplication and Rectangles
Two children discuss whether "Big Cheez-its" are really twice as big as regular Cheez-its. While the learners in this case are children, numeracy students of all ages could enjoy exploring area with a similar question.
Barbie Bungee: Illuminations
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.]
Concept, Method, Procedure (The Secret Formula for Math Success)
Max Ray, of The Math Forum, explores developing procedures from conceptual understanding. His 5-minute video uses dividing by fractions as the topic for instruction.
Conservation: The More Things Change The More They Stay the Same
This blog post from Graham Fletcher (Gfletchy) shares series of very short and very accessible videos for exploring the concept of conservation in weight, length, liquid, and number. Perfect for learners at many levels of math and language to discuss what they notice and wonder.
Desmos: Graphing
What if students could "play" with graphs and quickly see what changing a single component would do to a graph (such as changing the b in y =mx+b)? Desmos is user friendly and thoughtfully uses color and layout in ways that support students' understanding.
Desmos: Linear Inequalities in Standard Form
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.
Estimating
This workbook has activities to help students develop their number sense through estimation. As they work through the activities, they will look at different strategies for estimating in different contexts. Some of those strategies include partitioning, using your own body as a benchmark, as well as multiple strategies for estimating with numbers. The workbook offers strategies, examples for students to develop their own strategies, and then space to reflect on their learning. An optional video and asynchronous mini-course are also available.
Fast Growing Plant
An activity where students must determine how tall the plant was x time ago if it is a certain height now and how fast it will grow.
Fluency Without Fear
Turns out memorization, timed tests and flash cards are not the most effective ways to learn math facts! This article from Jo Boaler addresses developing students' fluency with math facts (such as times tables), including confidence and how some common approaches to math facts can be related to anxiety and loss of perseverance.
For Teachers: Please Don’t Teach Exponent Rules
A teacher writes about how he approaches operations with exponents so that the students make meaning and discover the rules for operations with exponents for themselves.
Fraction Talk (and Pie)
Math teacher Chase Orton lays out the instruction he used, starting with pictures of pies, in order to get students to use benchmark fractions.
- Advanced ABE
- Beginning ABE
- CCRS Level B
- Intermediate ABE
- Number Sense
- One-Room Schoolhouse/Multilevel
Fraction Talks
A Fraction Talk is a discussion-rich routine that invites multiple ways of identifying fractions. They are similar to number talks, but instead of drawing out strategies through mental calculations, students evaluate images of shapes and identify fractions. The Fraction Talks website has a huge collection of images to inspire discussion and exploration, as well as suggestions for using this routine in your class.
GED Math Video App
Students can either use this GED math prep resource on the computer or download the app to their phone.
Geometric Subitizing: A Different Kind of Number Talk
The discussion cards posted on this site can be used to discuss counting and grouping strategies with students. This could be a great way to engage students using vocabulary around numbers and shapes.
Geometric Subitizing: Counting Discussion Cards
The discussion cards posted on this site can be used to discuss counting and grouping strategies with students. This could be a great way to engage students using vocabulary around numbers and shapes.
Graphing Stories
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.
How Big Is the Guatemala Sinkhole?
A fun and short activity from Robert Kaplinsky to find the volume of a sinkhole.
How much did the temperature drop? Absolute Value
Robert Kaplinsky describes the lesson this way: "This lesson uses a time lapse thermometer video as a context for discussing integer operations and absolute value. The video should provide some added meaning to the classic temperature drop problem."
If Graphing Linear Inequalities Is Aspirin, Then How Do You Create the Headache?
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.
Instructional Strategies for Counting
These three blog posts from an elementary math coach describe instructional strategies around basic counting that may be useful for some ABE teachers addressing very basic numeracy.
Introducing the Orangamallow
A quick reading about a quick strategy a teacher uses to make "like terms" meaningful to her students.
Labor Mediator
"In this problem, student groups serve as mediators to settle a dispute between the owner and the union of a small manufacturing company. ... This is a really engaging problem that raises important questions about the way data, often perceived as being completely objective, can be biased and informed by perspective."
Linear Matching
A printable matching activity for matching graphs to equations.
Math Antics: Negative Numbers
This video introduces negative numbers on a number line, demonstrates comparing positive and negative numbers by comparing position on a number line. The video also models negative numbers using a picture representing sea level.
Math Antics: Types of Fractions
This video presents types of fractions (proper, improper, etc.) and addresses how students can use the structure of a fraction to make sense of where it belongs on the number line. The video points out that the relationship between the numerator and denominator is division.
Math Snacks: Counting
Online activities and videos for supporting students' understanding of math concepts such as ratios, scale factors, fractions, number lines, and so on. Some activities may need additional language learning supports (i.e. for beginning English learners). Videos are also available in Spanish and in a printable "comic book" form.
Math Snacks: Fractions
Online activities and videos for supporting students' understanding of math concepts such as ratios, scale factors, fractions, number lines, and so on. Some activities may need additional language learning supports (i.e. for beginning English learners). Videos are also available in Spanish and in a printable "comic book" form.
Math Snacks: Ratios
Online activities and videos for supporting students' understanding of math concepts such as ratios, scale factors, fractions, number lines, and so on. Some activities may need additional language learning supports (i.e. for beginning English learners). Videos are also available in Spanish and in a printable "comic book" form.
Math Visuals
Imagine that a math teacher made simple, attractive visuals to spark student discussion around counting and basic operations. Berkeley Everett did - and here it is!
Mean, Median, and Range: Open Middle
Students are asked to find a data set to satisfy certain criteria. There is a worksheet provided on the right-hand side of the website where students can record their attempts at answering this question and what they learned from each attempt.
Multiplication Representation Card
A printable matching activity for making connections between different representations of multiplication. Great to use as an ice breaker, a way to make groups, or just to get students out of their seats and talking to each other.
Multiply without Memorizing
This workbook has activities to help students develop their conceptual understanding of multiplication. As they work through the activities, they will look at different strategies for grouping, including arrays and decomposing larger multiplication problems into friendlier numbers. The workbook offers strategies, examples for students to develop their own strategies, and then space to reflect on their learning. An optional video and asynchronous mini-course are also available.
Number Lines and the Coordinate Grid, Part 1
Every number can be thought of as a point on the number line. Because of this, number lines are important for all kinds of mathematics - they are used in algebra, geometry, statistics, and many other kinds of mathematics. In Part 1, students study (1) plotting points on a number line, including fractions, decimals, and signed numbers; (2) measurement and distance on a number line; and (3) absolute value. For teachers wishing to build on number line concepts to connect to the coordinate grid, there is a Part 2 for these materials.
Number Lines and the Coordinate Grid, Part 1 – Integers
Every number can be thought of as a point on the number line. Because of this, number lines are important for all kinds of mathematics - they are used in algebra, geometry, statistics, and many other kinds of mathematics. In Part 1, students study (1) plotting points on a number line, including fractions, decimals, and signed numbers; (2) measurement and distance on a number line; and (3) absolute value. For teachers wishing to build on number line concepts to connect to the coordinate grid, there is a Part 2 for these materials.
Number Lines and the Coordinate Grid, Part 2
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.
Number Lines and the Coordinate Grid, Part 2 – Data
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.
One Formula to Rule Them All
Before you teach another formula for area of a 2-D shape, check out the "applets" on this page. Teachers who do not have access to internet in their classroom can learn from the animations and do a similar demonstration with paper.
Piles of Tiles (3-Act Lesson)
A 3-act lesson starts with a quick video or visual that makes students wonder. This one from Graham Fletcher (gfletchy) is set up to ponder the concept of area.
Playing Uno: The “Combine Like Terms” Version
Instructions and printables for a "combine like terms" UNO game, with some hints for using the game with your students.
Playing with Patterns
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.
Progression of Addition and Subtraction
What is a progression that builds to a conceptual understanding of addition and subtraction? In this 7-minute video, Gfletchy demonstrates strategies that teachers can use to develop students' conceptual understanding as a building block to fluency.
Progression of Division
What is a progression that builds to a conceptual understanding of division? In this 8-minute video, Gfletchy demonstrates strategies that teachers can use to develop students' conceptual understanding as a building block to fluency.
Progression of Early Number and Counting
What is an instructional progression that leads to conceptual understanding of counting and numbers? This 8-minute video lays out a progression for children learning these concepts, but ABE teachers of students with beginning numeracy will find useful ideas here.
Progression of Multiplication
What is a progression that builds to a conceptual understanding of multiplication? In this 6-minute video, Gfletchy demonstrates strategies that teachers can use to develop students' conceptual understanding as a building block to fluency.
Progressions: Illustrative Mathematics
Videos and tasks on math content progressions related to fractions in the Common Core standards.
Pythagorean Theorem Visual Model
This YouTube video shows a visual model to help students understand the Pythagorean Theorem.
Rational Number Project: Fraction Operations and Initial Decimal Ideas
Free lessons from the Rational Number Project about fraction concepts: adding, subtracting, multiplying, and dividing. Understanding of decimals is introduced as well. Teacher's guide, worksheets and colored fraction templates included. These resources help develop conceptual understanding.
Rational Number Project: Initial Fraction Ideas
Free lessons about fractions: concept, equivalencies, ordering, adding and subtracting. Teacher's guide, worksheets and colored fraction templates included. These resources help develop conceptual understanding.
Representing Data with Grouped Frequency Graphs and Box Plots
"This lesson unit is intended to help you assess how well students are able to interpret frequency graphs that use grouped data and their associated box plots. In particular this unit aims to identify and help students who have difficulty interpreting information from frequency graphs and box plots; such as minimum and maximum values, medians and quartiles."
Representing Variability with Mean, Median, Mode, and Range
This resource gives students practice with calculating the mean, median, mode, and range from a frequency chart. It also requires students to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.
The Power of Exponents, Part 1
In these materials, students learn about exponents and roots as well as how to break numbers down and examine how they work. Topics in part 1 include: (1) multiplication, including factors, multiples, and arrays; (2) characteristics of numbers, including factors, prime factorization, and finding common factors between numbers; (3) an introduction to exponents, square roots and cube roots, with connections to geometry; and (4) what it means when an exponent is 1 or less (fractional exponents, to the power of zero, and negative exponents).
The Power of Exponents, Part 1 – Introductory
In these materials, students learn about exponents and roots as well as how to break numbers down and examine how they work. Topics in part 1 include: (1) multiplication, including factors, multiples, and arrays; (2) characteristics of numbers, including factors, prime factorization, and finding common factors between numbers; (3) an introduction to exponents, square roots and cube roots, with connections to geometry; and (4) what it means when an exponent is 1 or less (fractional exponents, to the power of zero, and negative exponents).
The Power of Exponents, Part 2
In these materials, students learn about exponents and roots as well as how to break numbers down and examine how they work. Part 2 focuses on (1) place value, powers of ten, and scientific notation; (2) powers of two and exponential growth; (3) variables and exponents; and (4) operations with exponents (multiplication, division, and raising a power to a power).
Three-Dimensional Geometry: Area
In these materials, students explore concepts in three-dimensional (3D) geometry and measurement, including: identifying the types of solids in the world around us, measuring the surface area and volume of solids, and understanding where the geometric formulas on the HSE come from.
Three-Dimensional Geometry: Shapes
In these materials, students explore concepts in three-dimensional (3D) geometry and measurement, including: identifying the types of solids in the world around us, measuring the surface area and volume of solids, and understanding where the geometric formulas on the HSE come from.
Three-Dimensional Geometry: Volume
In these materials, students explore concepts in three-dimensional (3D) geometry and measurement, including: identifying the types of solids in the world around us, measuring the surface area and volume of solids, and understanding where the geometric formulas on the HSE come from.
Tools of Algebra: Expressions, Equations, & Inequalities, Part 1
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.
Tools of Algebra: Expressions, Equations, & Inequalities, Part 1 – Functions
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.
Tools of Algebra: Expressions, Equations, & Inequalities, Part 2
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.
Tools of Algebra: Expressions, Equations, & Inequalities, Part 2 – Functions
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.
Tools of Algebra: Linear Functions, Part 1
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.
Tools of Algebra: Linear Functions, Part 2
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.
Two-Dimensional Geometry: Area
In these materials, student explore concepts in two-dimensional (2D) geometry and measurement, including: categorizing 2D shapes; measures and units of length (perimeter and circumference); measures and units of area; where the geometric formulas come from; the Pythagorean Theorem; and scale factors.
Two-Dimensional Geometry: Perimeter
In these materials, student explore concepts in two-dimensional (2D) geometry and measurement, including: categorizing 2D shapes; measures and units of length (perimeter and circumference); measures and units of area; where the geometric formulas come from; the Pythagorean Theorem; and scale factors.
Two-Dimensional Geometry: Pythagorean Theorem
In these materials, student explore concepts in two-dimensional (2D) geometry and measurement, including: categorizing 2D shapes; measures and units of length (perimeter and circumference); measures and units of area; where the geometric formulas come from; the Pythagorean Theorem; and scale factors.
Two-Dimensional Geometry: Shapes
In these materials, student explore concepts in two-dimensional (2D) geometry and measurement, including: categorizing 2D shapes; measures and units of length (perimeter and circumference); measures and units of area; where the geometric formulas come from; the Pythagorean Theorem; and scale factors.
- Add-Subtract-Multiply-Divide
- Coherence
- Decimals
- Exponents
- Expressions
- Factors
- Fractions
- Levels of Knowing
Uncovering Coherence Using Area Models
When is area more than area? In this recorded webinar, presenters Connie Rivera and Amy Vickers from the Adult Numeracy Network (ANN) explore coherent mathematical content that can be addressed using mathematical arrays.
Using The Change Agent in Math Class – Data
The SABES Math & Numeracy Team in Massachusetts started this online collection of math lessons and activities with connections to student articles from The Change Agent, a social justice journal written by and for adult education students and teachers. Explore the site and check out two recommended lessons to get started.
Virtual Math Manipulatives
This resource contains numerous math manipulatives to use in your virtual classroom. Everything from coins to fraction pieces to number lines to algebra tiles – this resource has it all!
Visual Patterns
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.
Weird Conversation About Perimeter
A teacher's conversation with a student about what perimeter means.
What Michaels’ coupon should you use?
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.
Which Mistake to Pursue?
This blog post describes a class's exploration of an open-ended perimeter problem.
Which toilet uses less water?
Fun and applicable real life activity from Robert Kaplinsky that compares the amount of water used with different toilets.
College & Career Readiness (CCR) Math Standards
Looking for more specific information about the College & Career Readiness (CCR) Math Standards? Check out the CCRS Math Resources section of the CCR Standards resource library!