Virtual Manipulatives

NOTE: To access some of the resources, you will need to download and install Adobe Shockwave. Go to and be sure to close all internet browsers as you install the program, or installation will fail. 

Adding Integers 

In this activity, students practice adding positive and negative integers using positive (purple) chips and negative (red) chips.

Circle Graphs 

Students build a circle graph (pie chart) using data from a bar graph. They identify the fractional amounts represented by each category and the program displays the percentages for each category.


Students can use counters in five workspaces: basic with no structure; part-part-whole; equivalence (greater than, less than and equal to); containers that show either objects or a numeral; and arrays that range from 1 by 1 to 10 by 10. Ten frames can be added to some of the workspaces to help students organize their counts. Options exist for both part-part whole and missing-part tasks.


Students have access to three workspaces. In the wedges and strips workspace, students can represent different fractional amounts by selecting unit fraction symbols in the tools menu. In the arrays workspace, an area model is used to represent multiplication of fractions. Amounts are symbolically displayed using fraction notation, percents, decimals, or number words. Students can also consider fractions greater than one.


Students can access workspaces for length, capacity, and temperature. In the length workspace, students can measure up to 12 different objects using linking cubes, paper clips, or a ruler. In the capacity workspace, students compare cups, pints, quarts, gallons, teaspoons, tablespoons, and one fluid ounce. In the temperature workspace, students can see how temperature changes in Celsius are reflected in Fahrenheit and vice versa.

Number Line

Students practice adding positive and negative integers using a number line. 


In this activity, students continue a given repeating pattern. There are three different levels of challenge, ranging from patterns with two colors to four colors and patterns between two to six blocks long.

Subtraction of Integers

In this activity, students practice subtracting positive and negative integers using positive (purple) chips and negative (red) chips.