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

Lesson 4.1Understand Percent

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%.

Why This Matters The arcade posts every result as a percent of the weekly goal. A percent compares a number to 100 — so 40% means 40 out of every 100. Some players land under the goal, and some blow past it: a score of 150% means one and a half times the whole goal. Your job is to read and model each result as a comparison to 100.

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
Equivalent ratioSpanish: Razón equivalente A ratio with the same value, made by multiplying or dividing both terms by the same number. 2 : 5 → 40 : 100

How it worksWorked example

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

3 out of 4 students bring lunch. What percent?

  1. What times 4 makes 100? 25.
  2. 3 × 25 = 75 and 4 × 25 = 100.
  3. 75 out of 100 = 75%.

Answer: 75% bring lunch

Now you trySame steps, your turn

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

Shanice's gray kitten weighs 4 ounces. The orange kitten weighs 1.5 times as much. What percent of the gray kitten's weight is the orange kitten's weight?

Answer:

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 out!A 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

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

Lesson 4.1Understand Percent

Level 0Most support · every hint printed

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%.

Why This Matters The arcade posts every result as a percent of the weekly goal. A percent compares a number to 100 — so 40% means 40 out of every 100. Some players land under the goal, and some blow past it: a score of 150% means one and a half times the whole goal. Your job is to read and model each result as a comparison to 100.

How it worksWorked example

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

3 out of 4 students bring lunch. What percent?

  1. What times 4 makes 100? 25.
  2. 3 × 25 = 75 and 4 × 25 = 100.
  3. 75 out of 100 = 75%.

Answer: 75% bring lunch

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

    What does the word percent mean?

    1. APer ten
    2. BPer thousand
    3. CPer hundred
    4. DPer part
    Steps to try
    1. Look at the second half of the word: cent.
    2. A century is 100 years; a cent is 1/100 of a dollar.
    3. Percent = per 100.
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    3 out of every 10 arcade players reach the bonus level. What percent is that?

    1. A3%
    2. B10%
    3. C13%
    4. D30%
    Steps to try
    1. A percent compares to 100, so rewrite the ratio out of 100.
    2. What do you multiply 10 by to get 100?
    3. Multiply BOTH terms by that same number.
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    A decimal grid has 100 squares and 65 are shaded. What percent is shaded?

    1. A6.5%
    2. B35%
    3. C65%
    4. D100%
    Steps to try
    1. How many squares are in the whole grid?
    2. Each square stands for 1%.
    3. Count the shaded squares.
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Which percent means MORE than one whole?

    1. A0.8%
    2. B80%
    3. C100%
    4. D120%
    Steps to try
    1. What percent stands for one whole?
    2. Anything above that is more than the whole.
    3. Compare each choice to 100.
    Show your work

Explain your thinkingA friend says "a percent can never be more than 100, because you cannot have more than all of something." How would you answer using the mascot vote and the kittens?

Sentence starter A percent compares a number to ___, so ___% just means the amount is ___ than the whole it is compared to.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help