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Visualizing Percent Problems with a Hundredths Square

Visualizing Percent Problems with a Hundredths Square. Place the Unit Square-Hundredths Square UNDER your communicator. Unit Square – Hundredths Square. The square on the left represent a unit. The square on the right has been divided into 100 smaller squares.

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Visualizing Percent Problems with a Hundredths Square

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  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. Let’s Change the Unit Square 200 • 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? • 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. On the hundredths square shade in 1 square or 1% Let the unit square represent 1200 400 150 50 Try these combinations: • 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. Let’s 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. Let’s 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. Let’s 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. Let’s 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. Let’s 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. 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. Study the last two problems Why didn’t 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 doesn’t 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 can’t be visualized? NONE

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