Lesson 12: Percents and Tape Diagrams

1
Lesson 12 Percents and Tape Diagrams

• Essential Question
• How can we represent percents visually to help us
  solve problems?

2
Lets Discuss
How could a 10 x 10 square grid represent 200
people?










Each square represents 2 people.
3
Lets Discuss
How could a tape diagram represent 200 people?
Percent 25 25 25 25
People 50 50 50 50
What is similar and different between the two
visual models?
4
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.

5
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 ______ _______
6
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 ______ _______
7
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 ______ _______
8
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 ______ _______
9
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 ______ _______
10
Partner Work

• 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

11
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).

12
Lets Review

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

13
Ticket to Leave
In your math journal/notebook, explain why 25
does not always represent the same amount.