Unit 4 Inequalities, Expressions, and Equations (Family Materials)

This week your student will be working with equivalent expressions (expressions that are always equal, for any value of the variable). For example, and are equivalent expressions. We can see that these expressions are equal when we try different values for .

We can also use properties of operations to see why these expressions have to be equivalent—they are each equivalent to the expression .

Here is a task to try with your student:

Match each expression with an equivalent expression from the list below. One expression in the list will be left over.

List:

Solution

1. is equivalent to , because and .

2. is equivalent to , because and .

3. is equivalent to , because and .

4. is equivalent to , because and .

This week your student will be learning to visualize, write, and solve equations. They did this work in previous grades with numbers. In grade 6, we often use a letter called a variable to represent a number whose value is unknown. Diagrams can help us make sense of how quantities are related. Here is an example of such a diagram:

Since 3 pieces are labeled with the same variable , we know that each of the three pieces represent the same number. Some equations that match this diagram are and

A solution to an equation is a number used in place of the variable that makes the equation true. In the previous example, the solution is 5. Think about substituting 5 for in either equation: and are both true. We can tell that, for example, 4 is not a solution, because does not equal 15.

Solving an equation is a process for finding a solution. Your student will learn that an equation like can be solved by dividing each side by 3. Notice that if you divide each side by 3, , you are left with , the solution to the equation.

Here is a task to try with your student:

Draw a diagram to represent each equation. Then, solve each equation.

Solution: