Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.54.5 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can determine the whole when I know a part and the percent that part represents, explain why the method works, and use it on a problem I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
PartSpanish: Parte The amount you already know — the piece of the whole that the percent describes. $42 is the sale price
WholeSpanish: Total The full amount the percent is measured against. The whole is always 100%. the original price
Double number lineSpanish: Recta numérica doble Two lines lined up — dollars on one, percents on the other — so matching marks show the same amount two ways. $0, $7, $70 · 0%, 10%, 100%
EquationSpanish: Ecuación A math sentence with an equal sign. Here it says percent × whole = part, with the whole unknown. 0.7v = 26,600 — the percent times the unknown whole equals the part
PercentSpanish: Porcentaje A ratio comparing a number to 100. To compute with it, write it in decimal form: 60% = 0.6. 60% = 0.6 · 70% = 0.7
Percent Problem SolvingSpanish: Resolución de problemas con porcentajes Use a percent to find a part, a whole, or a percent change in a real situation. Sale price = original price − discount.

How it worksWorked examplefinding the whole from a part and its percent

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A team has won 24 games, and that is 40% of the games it played. How many games did the team play?

  1. Pair up what you know: 24 games matches 40%.
  2. Step down to ten percent: divide both terms by four, giving 6 games.
  3. Step up to one hundred percent: multiply both terms by ten.
  4. Check forward: forty percent of your total should return the 24 wins.

Answer: The team played 60 games in all.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A club collected 35 cans, and that is 25% of its collection goal. How many cans is the goal?

  1. Pair up what you know: cans matches %.
  2. Divide both terms by five: cans matches five percent.
  3. Multiply both terms by twenty: cans matches one hundred percent.
  4. Check forward: one quarter of your total should return cans.
Answer:the club's full collection goal

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The part is and it matches %.
  • Ten percent of the whole is .
  • The whole is because .
  • I checked my answer by finding % of it.

Word bank partwholepercentdouble number lineequivalent ratioscaledividemultiplyten percentone hundred percenttablecheck

Watch outA common mistake

A common mistake when finding the whole is multiplying by the percent instead of dividing. For "$42 is 60% of the original price," computing 0.6 × 42 = $25.20 makes the original price SMALLER than the sale price — impossible for a discount. Since percent × whole = part, the whole is found by dividing: 42 ÷ 0.6 = $70. Whenever the percent is less than 100%, the whole must come out larger than the part, so a smaller answer is the tell.

Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.54.5 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can determine the whole when I know a part and the percent that part represents, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    Percent (%)6020100Price ($)27??÷ ?÷ ?× ?× ?
    Ray pays 60% of the price.

    A lamp is 40% off. Ray pays $27 for it. What was the original price?

    1. 1What percent of the price does Ray pay?
    2. 2Divide both by 3. What amount matches 20%?
    3. 3What do you multiply 20% by to reach 100%?
    4. 4Do the same to the other row. What is the whole?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Percent (%)12020100People3,600??÷ ?÷ ?× ?× ?
    3,600 people go with 120%.

    A town has 3,600 people now. That is 120% of its population ten years ago. What was the population ten years ago?

    1. 1What amount goes with 120% in the first column?
    2. 2Divide both by 6. How many people match 20%?
    3. 3Multiply both by 5 to reach 100%. What was the population?
    4. 4Why is the old population less than 3,600?
    Final answer:
  3. 3Complete each step, then write the final answer.
    Percent (%)Number________________________

    27 is 45% of what number?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    Percent (%)Price ($)________________________

    A shirt is on sale for 35% off. Mia pays $13. What was the original price?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Percent (%)Price ($)________________________

    A used bike sells for $252. That is 84% of its price when it was new. What was the new price?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    Percent (%)Pounds________________

    A puppy weighs 26 pounds. That is 200% of its weight 3 months ago. Leo says it weighed 52 pounds then. Find the correct weight.

    Show your work
    Final answer:

Explain your thinkingBefore you fill in the table, how do you choose the percent that matches the part you know? Use a sale price to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help