This is the first of three lessons about the distributive property. In this lesson students recall the use of rectangle diagrams to represent the distributive property, and work with equations involving the distribute property with both addition and subtraction.
- Generate equivalent numerical expressions that are related by the distributive property, and explain (orally or using other representations) the reasoning.
- Use an area diagram to make sense of equivalent numerical expressions that are related by the distributive property.
Let's use the distributive property to make calculating easier.
- I can use a diagram of a rectangle split into two smaller rectangles to write different expressions representing its area.
- I can use the distributive property to help do computations in my head.
Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.
For example, \(3x+4x\) is equivalent to \(5x+2x\). No matter what value we use for \(x\), these expressions are always equal. When \(x\) is 3, both expressions equal 21. When \(x\) is 10, both expressions equal 70.
A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together. For example, the expression \(5x + 18\) has two terms. The first term is \(5x\) and the second term is 18.