Visualizing Percent Problems with a Hundredths Square

1
Visualizing Percent Problems with a Hundredths
Square
2

• Place the Unit Square-Hundredths Square UNDER
  your communicator

3
Unit Square Hundredths Square

• The square on the left represent a unit.
• The square on the right has been divided into 100
  smaller squares.

4
Unit Square Hundredths Square

• The unit square can represent any number
• The hundredths square will always divide the unit
  square into 100 equal parts.

5
Unit Square Hundredths Square

• Trace the Unit Square
• Slide the traced Unit Square on top of the
  hundredths square.
• What does the hundredths square do to the Unit
  Square?

6
Unit Square Hundredths Square

• Let the Unit Square represent 100

100
7
Using the Hundredths Square

• Shade in 1 small square. What does 1 small
  square represent?
• How many names does this square have?

8
What if I shade in more than 1 square?

• If 1 square is 1, what is another name for 5
  squares?
• 10 squares?
• 25 squares?
• 50 squares?
• 75 squares.
• What are the other names for these?
• You now have a visual for percent.
• What statements could you make about these
  different pictures?

9
How much do I shade?

• What will you shade in if you are asked to shade
  in 20 of the squares?
• How many ways can you describe what you have
  shaded in?
• Do these names make sense to you?

10
Thinking about the squares

• 20 squares was 20 of the whole board.
• Another way to say this is 20 squares is 20 of
  the 100 squares.
• What statement could you make about 55 squares?

11
Lets Change the Unit Square

• Suppose we had 200 pieces of candy in the unit
  box. Shade in 1 small square. How many pieces
  of candy will be in each small square?

200

• If 1 square is 1, what is 1 of 200?

• If 5 squares is 5, what is 5 of 200?

• If 10 squares is 10, what is 10 of 200?

12
With the whole board representing 200

• Shade in 20 squares.

• Write a statement about the 20 squares.

40 is 20 of 200
200

• Explain why this makes sense.

13
What proportion does this visual illustrate?
200
14
Try these combinations

• On the hundredths square shade in
• 1 square or 1

• Let the unit square represent
• 1200
• 400
• 150
• 50

• Write a statement about 1 of the unit square.

• On the hundredths square shade in
• 60
• 75
• 90

15
Picture these statements

• 20 of 250
• 30 of 150.00
• 49 of 3000 voters

• How much is 1?
• How much does 20, 30, 49 represent?
• How many squares did you color in for each part?
• Explain your reasoning for each statement.

16
Represent this problem on the template

• In New Jersey residents pay 7 sales tax.
• We want to find the amount of tax paid on a 50
  item, what shape should be used for the 50?
• What does 1 represent?
• How can you determine the tax?

17
Lets change things slightly

• Suppose a farm owns 900 chickens.

• Of these chickens, 135 are red.

900

• What shape should be represented by the 900?

• How many chickens are represented by 1?

• What percent is represented by 135 red chickens?

18
Think about it

• Does it make sense that 135 is 15 of 900?

• Explain why this statement makes sense.

900
19
Try another problem

• A surf team owns 150 surfboards
• Of these boards, 27 surf boards are long boards.
• If you want to know what percent of the surf
  boards are long boards, how can you think about
  the 150 surfboards and 27 long board surfboards
  with the hundredths grid and unit square?

150
20
What have you learned?

• What does each square of the board always
  represent?
• Unit square
• Hundredths Square
• If the unit square represent any number other
  than 100 how can you figure out what 1 of the
  number represents?
• Explain what 10 looks like? 20? 30, 40?
• Explain what 15, 25, 75 look like?

21
Lets change things slightly

• Suppose a contractor owns fifty acres of land,
  but she will only be able to build on forty seven
  of the acres.
• Shade in the hundredths to represent this
  problem.
• What percent of the land cannot be developed?

50
22
Represent this problem on your template

• If a store discounts a sofa costing 1250 by
  375, what percent discount did the store offer?
• Where would you place the 1250?
• Where would you place the 375?
• How much of a discount would 1 be?
• Write a percent statement that makes sense.
• Explain your reasoning.

1250
23
Lets change things slightly

• If 90 represents a 15 discount on an item, how
  much did the item originally cost?
• How would you represent 15?
• Where will you place the 90?
• Explain how you would find the original cost of
  the item.
• Write a statement that describes what you have
  just pictured.

?
?
90 is 15 of 600
24
Try another one

• Suppose a convention is planning to use several
  different colored ballons in their celebration.
• Suppose 4000 of the balloons are red. If these
  4000 balloons represent 75 of the balloons, how
  many balloons are their altogether?
• How will you represent 75?
• Where will you put the 4000 balloons?
• Write 2 statements that describes what you have
  just pictured.

?
25
Represent this problem on your template

• A store marks up an item they are selling by 25.
  If they marked up an item 30, how much did they
  buy the item for?
• Where will you place the 30?
• Can you determine how much 1 represent? 25?
• Explain how you will determine the cost of the
  item?
• How much will they sell the item for?

?
26
Representing discount

• If you usually sell a cd for 20.00. But today
  you are offering a 30 discount on the cd. How
  much will you take off the cost of the cd? How
  much will the cd cost?

27
Representing increase

• If you usually buy a cd for 10.00 from the
  record company, but you want to make a 15
  profit, how much should you add to the 1000 to
  make a 15 profit. How much should you charge
  for the cd?

28
Representing more than 100

• If one board represent 100, how will we
  represent more than 100?

29
Lets try some of these

• Show how to represent 20 profit on 50
• Show how to represent 50 profit on 200
• Show how to represent 60 profit on loaning
  someone 400

30
Lets try some of these

• Show how to represent 120 of 50
• Show how to represent 150 of 200
• Show how to represent 160 of 400

31
How do I represent this problem?

• Suppose I wanted to add a 30 profit on an item I
  purchased for 150. How much would the item now
  cost.
• Explain how you would use two boards to represent
  this situation.

32
Be careful with this one

• Suppose an item cost 195 dollars but that day
  they were offering a 30 discount. How much
  would the item cost?
• Picture this on the board.
• How many hundredths grids do you need to use?

33
Study the last two problems

• When a 30 profit was add to the cost of a 150
  item the item was sold for 195.

• When 30 was discounted off a items costing 195,
  the item cost 136.50.

Why didnt the cost of the item return to 150?
34
How does it work?

• If I add 20 to a price and then remove 20
  explain why doesnt the price return to the
  original price?

35
Try this

• Can you picture these questions without marking
  your board?
• Is 30 more or less than ¼?
• If I owe you 20 of 300 dollars, how much do I
  owe you?
• How much do have I paid?
• 135 is about what percent of 450?
• 30 is 15 of what number?

36
What percent problems cant be visualized?

• NONE