Neft Teacher · Learn It

Unit 4 · Standard 6.AT.4

Understand Percent

Lesson 4-1 · Learn It — how the math works

Why we're learning this

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.

✱ Math Workbench

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What a percent really says

Percent means per hundred. Any part-to-whole comparison becomes a percent by rewriting it as an equivalent ratio whose second term is 100. A decimal grid makes that visible: 100 squares, one for each percent.

Picture itSee what the math looks like before you read about it

The arcade leaderboard shows one player scored 150% of the weekly goal. A rare bonus round adds a 0.5% point boost.
Where you see this in real lifeThe arcade leaderboard shows one player scored 150% of the weekly goal. A rare bonus round adds a 0.5% point boost.

Watch me solve itI do — read one step at a time

The problem looks like this
Double number line: 4 out of every 10 voters is the same as 40 out of 100.Chose tiger440Voters10100
  1. Students voted on a mascot, and 4 out of every 10 voters chose the tiger. I want to know how many that is out of 100.
  2. "4 out of every 10" is a ratio, so I write an with 100 as the second term. Multiplying both terms by 10 gives 40 out of 100.
  3. On a of 100 squares, I shade 40 squares — one square for each .
  4. 40 out of 100 is written 40%. So 40% of the students voted for the tiger.

Watch out — mistakes students make here

  • 4% would mean 4 out of every 100 voters — far fewer than 4 out of every 10.
  • 10 is the second term of the original ratio, not the percent.
  • Percents come from scaling a ratio, never from adding its two terms.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Shanice's gray kitten weighs 4 ounces. The orange kitten weighs 1.5 times as much. What of the gray kitten's weight is the orange kitten's weight?
  2. The gray kitten is the whole, so its weight is 100%.
  3. Draw a : one full tape is 100%. The orange kitten needs 1.5 tapes — one whole tape plus half of another.
  4. One whole is 100% and half a whole is 50%, so 100% + 50% = 150%. The orange kitten weighs 150% of the gray kitten's weight — more than one whole, which matches it being the heavier kitten.100% + 50% = 150%

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the same vote, 23 out of every 100 voters chose the eagle.
  • Write that comparison as a , and say how you would shade it on a .
  • Now a player scores twice the weekly goal. Is that more or less than 100%?
  • Explain how you know, using the words whole and .

Solve: The orange kitten weighs 1.5 times as much as the gray kitten. What of the gray kitten's weight is that?

My answer

Stuck? Open one hint at a time.

Hint 1

Which kitten is the whole?

Hint 2

One whole is 100%. What is half a whole?

Hint 3

Add the whole and the half.

Check my answer
✅ Answer: 150%
The gray kitten is the whole, or 100%. One and a half wholes is 100% + 50% = 150%.

Turn & TalkSay it out loud with a partner

The leaderboard shows one player hit 150% of the goal and a bonus round gives a 0.5% boost. How can a be more than the whole, and how can one be a tiny sliver?

Try starting with:

  • ___% means ___ because it is more / less than 100%.___% significa ___ porque es más / menos que 100%.
  • A percent over 100% means ___, and a percent under 1% means ___.Un porcentaje mayor que 100% significa ___, y uno menor que 1% significa ___.
Use these wordspercentgreater than 100%less than 1%equivalent