1 Pull It All Together

BIG idea Variable

You can use variables to represent variable quantities in real-world situations and in patterns.

BIG idea Properties

You can use the properties of real numbers to simplify algebraic expressions.

Task 1

The tables below show the same set of inputs and outputs using two different process columns.

1. Copy and complete each table. Write an algebraic expression for each rule using n.
2. Show that the two algebraic expressions are equivalent.
3. Describe a pattern using a third rule.

BIG idea Solving Equations and Inequalities

You can use properties of numbers and equality to solve an equation by finding increasingly simpler equations that have the same solution as the original equation.

Task 2

Find all possible values of a and b in the figures below, given the following conditions.

• The perimeters are equal.
• The rectangle has an area between 80 and 100 square units.
• The values of a and b are integers.

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