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

Lesson 4.24.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write equivalent fractions, decimals, and percents for the same value, 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 way to compare a number to 100, shown with the % sign. 45% = 45 out of 100
DecimalSpanish: Decimal A number with a dot, like 0.5, that shows a part less than one. 0.45 = 45 hundredths
EquivalentSpanish: Equivalente Having the same value, just written a different way. 3/4 = 0.75 = 75%
BenchmarkSpanish: Referencia A familiar number you use to guess, like 50% or 1/2. 50% = one half
DiscountSpanish: Descuento Money taken off the first price to make it cheaper. $40 shirt at 25% off: discount = $10
HundredthsSpanish: Centésimos The second place after the decimal point; parts out of 100. 0.09 = 9 hundredths

How it worksWorked examplewriting one value three ways

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

A survey found 7 out of 20 students walk to school. Write that as a fraction, a decimal, and a percent.

  1. Write the fraction, part over whole: 7/20
  2. Twenty times five makes one hundred, so multiply both terms by five.
  3. That gives thirty-five hundredths, written as the decimal 0.35
  4. Hundredths read straight across into percent form: 0.35 is 35%

Answer: 7/20, 0.35, and 35% all name the very same amount.

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, 9 out of 25 students ride the bus. Write it as a fraction, a decimal, and a percent.

  1. Fraction, part over whole: /
  2. Twenty-five times makes one hundred, so multiply both terms.
  3. Hundredths written as a decimal: 0.
  4. Percent form: %
Answer:the bus riders as a fraction, decimal, and percent

Say it and write itSentence starters

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

  • / is the same value as written as a decimal.
  • To change a decimal into a percent I .
  • % means out of every hundred.
  • I know these three forms are equivalent because .

Word bank percentdecimalfractionequivalenthundredthsdenominatornumeratorsimplest formbenchmarkscalewholepart

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 4.24.2 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can write equivalent fractions, decimals, and percents for the same value, 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.
    Part1??Whole81100÷ ?÷ ?× ?× ?

    Write 1/8 as a decimal and a percent.

    1. 1Can 8 scale to 100 with a whole number? Find 100 ÷ 8.
    2. 212.5 is not whole. Divide 1 and 8 by 8. What goes over the 1?
    3. 3Multiply both terms by 100. What percent is it?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Part2??Whole31100÷ ?÷ ?× ?× ?

    Write 2/3 as a decimal and a percent. Round the percent to the nearest whole percent.

    1. 1Divide 2 and 3 by 3. What goes over the 1? What repeats?
    2. 2Multiply by 100 and round. What percent is it?
    3. 3Why can't you scale 2/3 to a fraction out of 100?
    Final answer:
  3. 3Complete each step, then write the final answer.
    PartWhole________________

    Write 3/40 as a decimal.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    PartWhole________________

    A fraction with a denominator of 20 is equal to 35%. What is its numerator?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Part asleepWhole day________________________

    A koala sleeps 7/8 of a day. A sloth sleeps 80% of a day. Write the koala's sleep as a percent. Which animal sleeps more?

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

    Lily says 1/4 is 0.4, because the 4 moves after the decimal point. Write 1/4 as a decimal.

    Show your work
    Final answer:

Explain your thinkingCompare 7/25 and 5/6. For which one can you scale to 100? For which one must you divide? Explain how you decide.

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