lesson 12: percents and tape diagrams essential question: how can we represent percents visually to...

Lesson 12: Percents and Tape Diagrams

Essential Question: How can we represent

percents visually to help us solve problems?

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

Each square represents 2 people.

Let’s Discuss…Let’s Discuss…

Percent: 25% 25% 25% 25%

People: 50 50 50 50

What is similar and different between the two visual models?

How could a tape diagram represent 200 people?

Remember…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 represen

ted 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 represen

ted 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 represen

ted 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 represen

ted 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 represen

ted by the tape diagram

?Express the quantity in the diagram as follows:

25% of ______ = _______

Partner WorkPartner Work1.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, 500100, 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…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 Ticket to LeaveLeave

In your math journal/notebook, explain why 25% does not always

represent the same amount.