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

Lesson 4.13.2 · 4.1 · 4.2 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 3.2 · 4.1 · 4.2 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Rates and Unit RatesSpanish: Tasas y tasas unitarias A rate compares different units; a unit rate compares a quantity to 1 unit. 180 miles in 3 hours = 60 miles per 1 hour.
RateSpanish: Tasa A ratio comparing two amounts with different units, like miles per hour. $12 for 4 games is a rate
Unit RateSpanish: Tasa unitaria A rate for just 1 of something, like cost for 1 item. $3 per 1 game
PerSpanish: Por For each one. Example: 5 dollars per book. 60 miles per hour means 60 miles for every 1 hour
RatioSpanish: Razón A way to compare two amounts, like 3 to 2. 5 to 3 or 5:3
Unit priceSpanish: Precio unitario A unit rate that gives the cost of exactly 1 item, like $0.60 per game. $3 for 5 games → $0.60 per 1 game

How it worksWorked exampleturning a ratio into a percent

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

In a survey, 18 out of every 50 sixth graders pack their lunch. What percent pack their lunch?

  1. Write the ratio: 18 out of 50.
  2. Ask: what times 50 makes 100? 50 × 2 = 100
  3. Multiply BOTH terms by 2: 18 out of 50 → 36 out of 100
  4. 36 out of 100 means 36%.

Answer: 36% of the sixth graders pack their lunch.

Now you trySame steps, your turn

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

In the same survey, 3 out of every 10 students ride a scooter. What percent ride a scooter?

  1. Write the ratio: out of
  2. What times 10 makes one hundred?
  3. Multiply BOTH terms: out of one hundred
  4. Write the percent: %
Answer:percent of students who ride a scooter

Say it and write itSentence starters

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

  • % means out of every hundred.
  • To compare to a hundred, I multiplied both terms by .
  • The part is and the whole is .
  • A percent is a ratio because .

Word bank percentper hundredratiopartwholeequivalentmultiplytermsgridcompare

Watch outA common mistake

A common mistake in Relate Fractions, Decimals, and Percents is treating the numerator and denominator as the percent's digits — turning 3/5 into "35%" by just reading the 3 and the 5. Percent means out of 100, so the fix is to build an equivalent fraction with denominator 100: 5 × 20 = 100, so multiply the top by 20 too — 3/5 = 60/100 = 60%. A second version of this mistake is scaling only ONE part of the fraction (writing 3/5 = 3/100 or 60/5). Whatever you multiply the denominator by, you must multiply the numerator by the same number. When a denominator will not reach 100 evenly (8, 3, 7), divide the numerator by the denominator instead and then multiply by 100.

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

Lesson 4.13.2 · 4.1 · 4.2 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 3.2 · 4.1 · 4.2 by using each lesson's big idea in mixed practice.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 4.1) What does the word percent mean?

    1. APer hundred
    2. BPer ten
    3. CPer thousand
    4. DPer part

    Hint Look at the second half of the word: cent.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    (Lesson 3.2) A booth charges $4.50 for 9 games. What is the unit rate?

    1. A$0.45 per game
    2. B$0.50 per game
    3. C$2.00 per game
    4. D$4.50 per game

    Hint You know the total cost ($4.50) and the total games (9). A unit rate tells the cost of just ONE game.
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 3Circle the letter of the best answer. Show how you know.

    (Lesson 3.2) A car travels 180 miles using 6 gallons of gas. What is the unit rate in miles per gallon?

    1. A6 miles per gallon
    2. B30 miles per gallon
    3. C36 miles per gallon
    4. D180 miles per gallon

    Hint Notice the units in the question: miles PER gallon. That tells you miles go on top and gallons on the bottom.
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  3. 4Circle the letter of the best answer. Show how you know.

    (Lesson 4.1) 3 out of every 10 students walk to school. What percent is that?

    1. A3%
    2. B10%
    3. C13%
    4. D30%

    Hint A percent compares to 100, so rewrite the ratio out of 100.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    (Lesson 4.2) Convert 3/5 to a percent.

    1. A35%
    2. B53%
    3. C60%
    4. D65%

    Hint Percent means out of 100. What do you multiply the denominator 5 by to get 100?

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.

Explain your thinkingWhat number did you multiply by to turn each denominator into 100, and how did that fraction out of 100 give you the percent?

Sentence starter I multiplied the top and bottom of ___ by ___ to get ___/100, so the percent is ___%.

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