6.AT.4 Group 2 · Challenge

Practice Set · Part 1

Find and Compare with Percentages

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: I can find the percent of a number using an equation or a model, explain what each part stands for, and build one for a situation I have not seen before.

The big idea: A percent of a number depends on both the percent and the base, so find each part before you compare.

Model to copy — Example · Compare two discounts

  1. Prize A costs 80 tickets and is 25% off. Prize B costs 60 tickets and is 30% off. Which prize saves you more tickets?
  2. Write 100% and both prices in the first column: 100% : 80 : 60
  3. Divide by 4 to find 25% for Prize A: 80 ÷ 4 = 20
  4. Find 5%, then multiply by 6 for Prize B: 60 ÷ 20 = 3; 3 × 6 = 18
  5. Compare the two discounts: 20 > 18
  6. Prize A saves more: 20 tickets, compared with 18 tickets for Prize B.

Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

  1. 1

    Same stepsFinish what the group started. Use the model above, step for step.

    Try it together — then prove it: Find 40% of 80. What number matches 100% in the first column? (80) Divide both by 5. What is 20% of 80? (16) What do you multiply 20% by to reach 40%? (× 2) Do the same to the other row. What is 40% of 80? (32) Why must 40% of 80 be less than 80? (100% matches 80. 40% is less than 100%, so its part is less than 80.)
    Show your work
  2. 2

    Warm restartWhich benchmark percent is closest to 9%?

    1. A1%
    2. B10%
    3. C25%
    4. D50%

    How do you know?

  3. 3

    Warm restartEstimate 24% of 80 using a benchmark percent.

    1. Aabout 8
    2. Babout 20
    3. Cabout 24
    4. Dabout 40

    How do you know?

  4. 4

    Warm restartA jacket costs $39.75. Estimate a 20% discount.

    1. Aabout $2
    2. Babout $4
    3. Cabout $8
    4. Dabout $20

    How do you know?

4.4 Small Group · Group 2 · Practice SetPart 1 of 4
6.AT.4 Group 2 · Challenge

Practice Set · Part 2

Find and Compare with Percentages

Keep going

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

  1. 5

    Think it throughWhat is 12% written as a decimal?

    1. A0.012
    2. B0.12
    3. C1.2
    4. D12

    Why is that the answer?

  2. 6

    Think it throughWhat is 12% of 1,500 tickets?

    1. A1.8
    2. B18
    3. C180
    4. D1,800

    How do you know? Give a second reason as well.

  3. 7

    Think it throughCheck with a benchmark: what is 10% of 1,500?

    1. A1.5
    2. B15
    3. C100
    4. D150

    Explain your thinking. What would have to change for a different choice to be right?

  4. 8

    Back to the modelWhat steps do you follow every time you find the percent of a number?

4.4 Small Group · Group 2 · Practice SetPart 2 of 4
6.AT.4 Group 2 · Challenge

Practice Set · Part 3

Find and Compare with Percentages

Words and reasoning

Word bank · Banco de palabras

Percent (Porcentaje)Base (Base)Part (Parte)Equation (Ecuación)Discount (Descuento)Double number line (Recta numérica doble)Equivalent fraction (Fracción equivalente)

Use the words

Fill each blank with a word from the bank.

Explain the thinking

  1. 9

    Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

    The mistake: A common mistake in Find the Percent of a Number is multiplying by the percent number itself instead of its decimal form — for example, finding 30% of 80 by computing 30 × 80 = 2,400 instead of 0.
  2. 10

    Say moreWhat steps did you follow every time to find the percent of a number in the discount table?

  3. 11

    Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Five phone battery icons are lined up in order. The first is full at 5 bars out of 5, and each one after it has one fewer bar. The last icon has 1 bar left, and the caption says about 1 hour remains.

    Show your work
4.4 Small Group · Group 2 · Practice SetPart 3 of 4
6.AT.4 Group 2 · Challenge

Practice Set · Part 4

Find and Compare with Percentages

Show what you know

Last check

These two come from Lesson 4.3. If they are shaky, that is the lesson to revisit — not this one.

  1. 12

    Show what you knowExplain your thinking — What is 45% of 360?

    1. A45
    2. B162
    3. C180
    4. D315

    Explain your choice.

  2. 13

    From Lesson 4.3Explain your thinking — Estimate 19% of 412 using benchmarks or compatible numbers.

    1. AAbout 8
    2. BAbout 40
    3. CAbout 80
    4. DAbout 200

    How do you know?

  3. 14

    From Lesson 4.3Photos take up 3.5 of the 4 GB of used storage. About what percent of the used storage is photos?

    1. AAbout 35%
    2. BAbout 58%
    3. CAbout 87%
    4. DAbout 99%

    How do you know?

Be honest — this tells your teacher what to do next

I can…Not yetGetting thereGot it
I can find the percent of a number using an equation or a model, explain what each part stands for, and build one for a situation I have not seen before.
I can explain why it works: A percent of a number depends on both the percent and the base, so find each part before you compare.
I can justify my answer to a skeptic and connect it to a second strategy or representation.

One question I want to ask my group next time