Lesson 12 Percents and Tape Diagrams Essential Question

Lesson 12: Percents and Tape Diagrams Essential Question: How can we represent percents visually to help us solve problems?

Let’s Discuss… How could a 10 x 10 square grid represent 200 people? Each square represents 2 people.

Let’s Discuss… How could a tape diagram represent 200 people? Percent: 25% 25% People: 50 50 What is similar and different between the two visual models?

Remember… • Tape diagram segment divisions will vary depending upon the percent. Example: To find 20%, it is useful to divide 100 into 5 segments; to find 10%, it is useful to divide 100 into 10 segments, etc.

Complete the tape diagram. Shade in 25% on the tape diagram where the whole represents different amounts. Percent: 100% Whole: 100 What fraction is represented by the tape diagram? Express the quantity in the diagram as follows: 25% of ______ = _______

Complete the tape diagram. Shade in 25% on the tape diagram where the whole represents different amounts. Percent: 100% Whole: 200 What fraction is represented by the tape diagram? Express the quantity in the diagram as follows: 25% of ______ = _______

Complete the tape diagram. Shade in 25% on the tape diagram where the whole represents different amounts. Percent: 100% Whole: 60 What fraction is represented by the tape diagram? Express the quantity in the diagram as follows: 25% of ______ = _______

Complete the tape diagram. Shade in 25% on the tape diagram where the whole represents different amounts. Percent: 100% Whole: 20 What fraction is represented by the tape diagram? Express the quantity in the diagram as follows: 25% of ______ = _______

Complete the tape diagram. Shade in 25% on the tape diagram where the whole represents different amounts. Percent: 100% Whole: 500 What fraction is represented by the tape diagram? Express the quantity in the diagram as follows: 25% of ______ = _______

Partner Work 1. You will be given a percent: (such as 10%, 20%, 50%, or 75%). 2. With your partner, label the given tape diagrams in which you must find the assigned percent of the following wholes: 100, 200, 60, 20, 500

What pattern can you see from the fractions represented by each tape diagram? What conclusion can be drawn? • All fractions are equivalent and equal to 25% or ¼. • 25% represents different quantities (depending upon the amount of the whole).

Let’s Review… • The quantity represented by a percent depends upon the size of the whole. • Visual representations of percents are useful in solving percent problems.

Ticket to Leave In your math journal/notebook, explain why 25% does not always represent the same amount.