Manipulating basic expressions with rational coefficients

The topic  appears under the 7th Grade Math Mission. This exercise

Types of Problems
There are three types of problems in this exercise:


 * 1) Distribute the expression: This problem has an expression that can be multiplied out. The student is asked to distribute the constant through and write the expression in the space provided.Mlewrc1.png
 * 2) Factor the expression: This problem is backwards from the first type of problem. It provides an expression and asks the student to factor out something to make the expression simpler.Mlewrc2.png
 * 3) Perform requested operation: This problem provides two linear expressions. The student is asked to perform an operation on those expressions.Mlewrc3.png

Strategies
The distributive property and an ability to collect like terms efficiently can help increase speed and accuracy on this exercise.
 * 1) The distributive property for multiply through addition is $$ a(b+c)=ab+ac $$ and factoring is this rule in reverse.
 * 2) The problems for Perform requested operation will have to be only add or subtract, because otherwise it will cease to be linear (unless constants are used).