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

Lesson 4.14.1 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can explain a percent as a rate per 100, model it on a decimal grid or tape diagram, and interpret percents greater than 100%, explain what each part stands for, and build one for a situation I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
PercentSpanish: Porcentaje A ratio that compares a number to 100. The word means “per hundred,” and the symbol is %. 40% = 40 out of every 100
Per hundredSpanish: Por cada cien The meaning hidden inside the word percent: for every group of 100. It is why every percent can be written as a fraction over 100. 7% means 7 per hundred
Decimal gridSpanish: Cuadrícula decimal A 10-by-10 grid of 100 squares. Shading squares shows a percent directly, one square per percent. 62 shaded squares = 62%
Part-to-wholeSpanish: Parte a todo A comparison of one part against the whole amount. In a percent, the whole is always 100%. shaded squares to all squares
Greater than 100%Spanish: Mayor que 100 % More than one whole. A percent above 100 means the amount is larger than the thing it is being compared to. 150% of the gray kitten = 1.5 times its weight
Percents Greater Than 100% and Less Than 1%Spanish: Porcentajes mayores que 100% y menores que 1% Percents can describe amounts greater than one whole or smaller than one hundredth of a whole. 150% = 1.5 and 0.5% = 0.005

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 with percent is scaling only one term of the ratio: reading 7 out of 10 as 7%. A percent compares to 100, so BOTH terms must be multiplied by the same factor — 10 × 10 = 100, so 7 × 10 = 70, giving 70%. Reading it as 7% describes seats that are nearly empty when they are nearly full. A second mistake is treating a percent as an amount: 150% of a 200-point goal is 1.5 × 200 = 300 points, not 150 points.

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

Lesson 4.14.1 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can explain a percent as a rate per 100, model it on a decimal grid or tape diagram, and interpret percents greater than 100%, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    Miles run50?Plan (miles)40100× ?× ?
    The plan, 40 miles, is the whole.

    A runner planned to run 40 miles this month. She ran 50 miles. What percent of her plan did she run?

    1. 1The plan is the whole. Which number do you scale to 100?
    2. 2What number turns 40 into 100?
    3. 3Multiply 50 by 2.5 too. What percent of her plan did she run?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Team A wins13?Team A games20100Team B wins16?Team B games25100
    Scale both teams to 100 games.

    Team A won 13 out of 20 games. Team B won 16 out of 25 games. Which team won a greater percent of its games?

    1. 1Team A: 20 × 5 = 100. Multiply 13 by 5. What percent?
    2. 2Team B: 25 × 4 = 100. Multiply 16 by 4. What percent?
    3. 3Team B won more games. Why compare percents and not 13 and 16?
    Final answer:
  3. 3Complete each step, then write the final answer.
    PartWhole________________

    Write 3 out of every 50 as a percent.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    35%
    The third grid: 35 of 100 squares.

    A grid of 100 squares is one whole. Sam shades 2 full grids and 35 squares of one more grid. What percent did Sam shade?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Raised ($)Goal ($)________________

    A school wanted to raise $400 for a trip. It raised $520. What percent of its goal did the school raise?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    PartWhole________________________

    Jen says 21 out of 15 cannot be a percent, because 21 is more than 15. What percent is 21 out of 15?

    Show your work
    Final answer:

Explain your thinkingCan a test score be 120%? Can a gas tank be 120% full? Decide when a percent greater than 100% makes sense.

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