Distributing Constants over Linear Expressions

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In this activity students will use the integers one through nine along with linear expressions x, x+1, x+2, …, x+9 to figure out how to distribute those integers over the expression. Print Settings Printer Brand: MakerBot Printer: MakerBot Replicator Rafts: Yes Supports: No Resolution: standard Infill: 20% How I Designed This It was fairly simple to make these manipulatives. In TinkerCad I used a square for the numbers and a rectangle for the expressions. I copy and pasted to get ten copies of the square (for the numbers 1-9 and an ‘x’) and nine copies of the rectangle. I placed the numbers and the x on the squares and used the text generator for the expressions. Standards CCSS Overview and Background This activity will satisfy the following Common Core Standard: CCSS.Math.Content.6.EE.A.3 Apply the properties of operations to generate equivalent expressions. Lesson Plan and Activity Start by working through one example with students. Pick a number and an expression and place them together as shown in Figure 1. Write your new expression here: 3(x+5) Now take 3 copies of the (x+5) as shown in Figure 2. How many x’s do you see? Count them to get 3 x’s How many constants do you count? 5+5+5 = 15 What is the solution? 3x + 15 Then have students make up three of their own examples to distribute the constant over the expression. To make sure they understand the concept of distributing students are then asked to describe how they can re-write 4(x+2) directly without any intermediate steps and how they can re-write any number times (x+ any number) directly without any intermediate steps. An activity sheet as well as solutions are posted in the files section. Figure 1 Figure 2 Materials Needed For each group you will need to print one copy of the numbers one through nine and up to nine copies of the linear expressions. Duration of Lesson One day or less