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

Lesson 4.24.2 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can write equivalent fractions, decimals, and percents for the same value — one step at a time, with support.

Start hereWords for this lesson

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

Word	What it means	Example
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.

Write the fraction, part over whole: 7/20
Twenty times five makes one hundred, so multiply both terms by five.
That gives thirty-five hundredths, written as the decimal 0.35
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.

Fraction, part over whole: /
Twenty-five times makes one hundred, so multiply both terms.
Hundredths written as a decimal: 0.
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 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target With my small group, I can write equivalent fractions, decimals, and percents for the same value — one step at a time, with support.

1Complete each step, then write the final answer.
Write 3/10 as a fraction out of 100, a decimal and a percent.
1. 1What do we multiply the denominator 10 by to get 100?
2. 2Multiply the numerator 3 by 10. What fraction out of 100 do you get?
3. 330/100 is what percent?
4. 4Write 30/100 as a decimal.
Final answer:
2Complete each step, then write the final answer.
Now go the other way. Write 65% as a fraction out of 100 and as a decimal. Then simplify the fraction.
1. 165% means 65 out of 100. Write it as a fraction.
2. 2Write 65/100 as a decimal.
3. 3Divide the top and bottom of 65/100 by 5. What fraction do you get?
Final answer:
3Complete each step, then write the final answer.

Write 7/10 as a percent.
Show your work
Hint Multiply the top and bottom by 10 to get a denominator of 100.
Final answer:
4Complete each step, then write the final answer.

Write 3/25 as a decimal.
Show your work
Hint First make an equivalent fraction out of 100. 25 × 4 = 100.
Final answer:
5Complete each step, then write the final answer.

Maya got 17/20 of the quiz questions right. What percent of the questions did she get right?
Show your work
Hint What do you multiply 20 by to get 100? Multiply 17 by the same number.
Final answer:
6Complete each step, then write the final answer.

Ben says 0.6 is the same as 6%. Is he right? Write 0.6 as a percent.
Show your work
Hint Write 0.6 as hundredths first. 0.6 is 6 tenths.
Final answer:

Explain your thinkingBen thought 0.6 is 6%. How does a hundred grid show that 0.6, 6/10 and 60% are the same amount?

Sentence starter On the grid, 0.6 shades ___ squares. · 0.6 is not 6% because ___.

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