# Lesson 7

One Hundred Percent

### Lesson Narrative

In this second lesson about percent increase and percent decrease, students work with problems where they are given the final amount after a percent increase or decrease and must calculate the original amount, or are given the final and original amounts and must calculate the percent increase or decrease. They use double number lines to visualize such situations in order to help see clearly which of the two amounts involved, the starting amount or the final amount, is to be regarded as the whole, or 100%. They explore common misconceptions resulting from getting confused about which amount is the whole. For example, if you are given the final amount after a 10% decrease, a common error is to regard that final amount as the whole and and calculate the original amount by adding 10% of the final amount. Being clear about which quantity is the whole is a good example of attending to precision (MP6).

### Learning Goals

Teacher Facing

• Critique (orally and in writing) double number line diagrams that represent situations involving percent increase or decrease.
• Generalize (orally) that the original amount corresponds to 100% and the new amount corresponds to more or less than 100%, depending on whether the situation involves an increase or decrease.
• Interpret a description of a situation to identify the original amount, the new amount, the change, and corresponding percentages. Label these on a double number line diagram.

### Student Facing

Let’s solve more problems about percent increase and percent decrease.

### Student Facing

• I can use a double number line diagram to help me solve percent increase and decrease problems.
• I understand that if I know how much a quantity has grown, then the original amount represents 100%.
• When I know the new amount and the percentage of increase or decrease, I can find the original amount.

Building Towards

### Glossary Entries

• percentage decrease

A percentage decrease tells how much a quantity went down, expressed as a percentage of the starting amount.

For example, a store had 64 hats in stock on Friday. They had 48 hats left on Saturday. The amount went down by 16.

This was a 25% decrease, because 16 is 25% of 64.

• percentage increase

A percentage increase tell how much a quantity went up, expressed as a percentage of the starting amount.

For example, Elena had $50 in the bank on Monday. She had$56 on Tuesday. The amount went up by \$6.

This was a 12% increase, because 6 is 12% of 50.