The purpose of this activity is for students to understand that a percentage increase of 25% corresponds to 125% of the original amount, and a percentage decrease of 25% corresponds to 75% of the original amount. Students may be familiar with tape diagrams from earlier grades. This activity reminds students how tape diagrams show relative quantities, and illustrates how tape diagrams can show percent change. Students look for and make use of the structure (MP7) of tape diagrams to understand percent change.

The goal of this discussion is to connect the idea of percentage increase and decrease with visual representations. Share the correct matches and ensure everyone understands how the given diagrams are connected to the descriptions. Then ask students to share their diagrams for the second question and explain their thinking. Here are some questions for discussion:

• “The ducks increased by 50%. That means the new number of ducks is what percentage of the old number?” (150%)
• “The mosquitoes decreased by 20%. That means the new number of mosquitoes is what percentage of the old number?” (80%)

In the Algebra 1 lessons, students will need to be able to express a quantity that changes by a given percentage repeatedly. For example, a credit card has a $100 balance, and is charged 12% interest each year. How much does a cardholder owe after 5 years? An expression representing the new balance is . In order for this to make sense, students first need to express the result of a percentage increase or decrease using only multiplication. This activity helps to build that capacity. Recognizing that the distributive property can be used to rewrite an expression is an example of noticing and making use of structure (MP7).

The purpose of this activity is for students to practice rewriting expressions representing percent change so that they only use multiplication. Students use the structure of the distributive property to rewrite expressions (MP7).