Strategy

Multiple Representations

UDL 2.5 UDL 5.1

Multiple representations allow students to see the same mathematical expression or mathematical relationship presented in more than one form. This strategy is particularly useful for helping students understand the meaning of algebraic symbols, but can be effectively utilized with most math skills and concepts. Common forms include words or verbal representations; pictures; graphs; tables of values; and symbolic representations, including expressions and equations.

Ready-to-Use Resources

Mini-Lesson

Differentiated Small Group Intervention: Multiplication

Multiple research-based mini-lessons aligned to a specific standard to use for small group instruction, reteaching, or intervention. Each mini-lesson presents a differentiated method of support for students and includes a full teacher model as well as student practice items.

Grade 3 · Math · 12 pages


Mini-Lesson

Differentiated Small Group Intervention: Place Value - Compare Decimals to the Thousandths

Multiple research-based mini-lessons aligned to a specific standard to use for small group instruction, reteaching, or intervention. Each mini-lesson presents a differentiated method of support for students and includes a full teacher model as well as student practice items.

Grade 5 · Math · 15 pages


Mini-Lesson

Differentiated Small Group Intervention: Solving One-Variable Linear Equations

Multiple research-based mini-lessons aligned to a specific standard to use for small group instruction, reteaching, or intervention. Each mini-lesson presents a differentiated method of support for students and includes a full teacher model as well as student practice items.

Grade 8 · Math · 18 pages


Implementation Tips

Using Multiple Representations Strategically
Consider the context when determining how to most powerfully utilize multiple representations. Teachers can provide more than one representation at the outset of a problem, ask students to work collaboratively to develop alternate representations while working on a problem, or give each student the choice as to which representation he or she is more comfortable using to analyze a mathematical situation.
Multiple Representations within a Given Form
It can be helpful for students to not only see multiple representations across forms, but also to see multiple representations within a given form. For example, if given a statement like, "Bob has three more dollars than Tim, and John has twice as much money as Tim," students could assign the variable x to either Bob, Tim, or John, and depending on that choice, would write different equations. Many students find it valuable to try a problem like this multiple times, using variables different ways.
Colors for Additional Support
Use colors to represent correspondences across representations. For example, if students were drawing a pictorial representation of the expression 3n + 2, students might color blocks different to show how the 2 remains constant but 3 new units are added each time.

Examples

Three Acts
When asking students to model a series [[ http://threeacts.mrmeyer.com/pixelpattern/ | in context ]], have them describe the change in the pattern first by drawing a picture, then by using words to describe how each picture changes, then by creating a table, and finally by creating an equation.
Algebraic Equations
When solving simple algebraic equations, teach students to draw visual representations of each expression and explain how the drawings correspond with different methods for solving the equation algebraically.
Slope
When teaching students about slope, illustrate a rate of change using a visual depiction that shows rise over run, a graph of a linear equation, a table, and a verbal description of how both input and output are changing.

Related Strategies