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.

Why This Matters This is your challenge small group for Lesson 4.5. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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 example

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

24 stickers are 40% of a pack. How many stickers are in the pack?

  1. 40% ÷ 4 = 10%, so 24 ÷ 4 = 6.
  2. 10% × 10 = 100%, so 6 × 10 = 60.
  3. Check: 0.40 × 60 = 24.

Answer: 60 stickers

Now you trySame steps, your turn

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

Sheng's car is now worth $26,600. That is 70% of what his parents paid for it. What did they pay for the car?

Answer:

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 out!A 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

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.

Why This Matters This is your challenge small group for Lesson 4.5. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  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.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help