This video looks at Intuition as to why subtracting a negative number is equivalent to adding the absolute value of that number

This lesson uses a number line to clarify how to add integers with different signs.

This lesson reviews absolute value and uses a number line to show what happens when negative numbers are added.

This arithmetic lesson shows how to carry digits to add multiple digits numbers.

In this lesson students use a rule of thumb about the weight of babies to practice doubling and halving numbers. They complete an organized table and compare data using vertical and horizontal double bar graphs. The lesson includes a student activity sheet and extension ideas.

This short video and interactive assessment activity is designed to teach third graders about balancing the equations.

This short video and interactive assessment activity is designed to teach second graders about balancing the equations (numbers to 1,000).

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet.

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet.

In this Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf).

In this lesson from Illuminations, students explore and discover linear relationships. Linear patterns are identified, extended and described verbally, numerically and algebraically through three investigations. Using manipulatives and the linked applet, "Chairs", learners determine the number of chairs needed when the number of tables is known, and vice versa. Instructional plan, questions for the students, assessment options, extensions and teacher reflections are provided.

This short video and interactive assessment activity is designed to teach second graders about challenging flow chart (numbers to 1,000).

This short video and interactive assessment activity is designed to teach third graders about challenging flow chart (numbers to 1,000).

This lesson develops number skills, understanding of coin values, and the concept of equivalence. Students use coin blocks, concrete representations of the value of coins (pennies, nickels, dimes, and quarters), to compose and decompose values up to a dollar. The resource includes a 3-minute video for teachers on how to build the coin blocks prior to the lesson. An interactive game, Coin Box, provides additional practice for students and is cataloged separately.

In this Flash game, students may use a variety of activities to practice counting, collecting, exchanging, and making change for coins. Coin representations may show their amounts or not; coins may also be represented by coin tiles on a 10x10 grid, to help visualize their values. The five activities are: count, in which students determine the value of a given set of coins; collect, in which students choose coins to represent a given value; exchange, in which students use the smallest number of coins to represent a given value; change from coins, in which students are given a set of coins and asked how much change would be for a dollar (essentially counting up); and change from value, in which students are given a price owed (from a dollar) and asked to make change. There is a "bank" at the lower left side of the applet in which coins may be exchanged for other coins of the same value.

In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lesson activities focus on the comparative mode of subtraction as children investigate the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts. The lessons include printable student activity sheets, a bibliography of children's counting books, questions for student discussion and teacher reflection, assessment options, extensions, and links to online applets (cataloged separately).

The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning.