Lesson 4.54.5 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can determine the whole when I know a part and the percent that part represents — 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 |
|---|---|---|
| PartSpanish: Parte | The amount you already know — the piece of the whole that the percent describes. | $42 is the sale price |
| WholeSpanish: Total | The full amount the percent is measured against. The whole is always 100%. | the original price |
| Double number lineSpanish: Recta numérica doble | Two lines lined up — dollars on one, percents on the other — so matching marks show the same amount two ways. | $0, $7, $70 · 0%, 10%, 100% |
| EquationSpanish: Ecuación | A math sentence with an equal sign. Here it says percent × whole = part, with the whole unknown. | 0.7v = 26,600 — the percent times the unknown whole equals the part |
| PercentSpanish: Porcentaje | A ratio comparing a number to 100. To compute with it, write it in decimal form: 60% = 0.6. | 60% = 0.6 · 70% = 0.7 |
| Percent Problem SolvingSpanish: Resolución de problemas con porcentajes | Use a percent to find a part, a whole, or a percent change in a real situation. | Sale price = original price − discount. |
How it worksWorked examplefinding the whole from a part and its percent
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A team has won 24 games, and that is 40% of the games it played. How many games did the team play?
- Pair up what you know: 24 games matches 40%.
- Step down to ten percent: divide both terms by four, giving 6 games.
- Step up to one hundred percent: multiply both terms by ten.
- Check forward: forty percent of your total should return the 24 wins.
Answer: The team played 60 games in all.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A club collected 35 cans, and that is 25% of its collection goal. How many cans is the goal?
- Pair up what you know: cans matches %.
- Divide both terms by five: cans matches five percent.
- Multiply both terms by twenty: cans matches one hundred percent.
- Check forward: one quarter of your total should return cans.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The part is and it matches %.
- Ten percent of the whole is .
- The whole is because .
- I checked my answer by finding % of it.
Word bank partwholepercentdouble number lineequivalent ratioscaledividemultiplyten percentone hundred percenttablecheck
Watch outA common mistake
A common mistake when finding the whole is multiplying by the percent instead of dividing. For "$42 is 60% of the original price," computing 0.6 × 42 = $25.20 makes the original price SMALLER than the sale price — impossible for a discount. Since percent × whole = part, the whole is found by dividing: 42 ÷ 0.6 = $70. Whenever the percent is less than 100%, the whole must come out larger than the part, so a smaller answer is the tell.
Lesson 4.54.5 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can determine the whole when I know a part and the percent that part represents — one step at a time, with support.
-
1Complete each step, then write the final answer.
$28 goes with 70%. The whole goes with 100%. Jin paid $28 for a backpack on sale. That was 70% of the original price. What was the original price?
- 1What amount goes with 70% in the first column?
- 2Divide both by 7. What amount matches 10%?
- 3What do you multiply 10% by to reach 100%?
- 4Do the same to the other row. What is the whole?
Final answer: -
2Complete each step, then write the final answer.
15 games go with 30%. A team has played 15 games. That is 30% of its season. How many games are in the whole season?
- 1What amount goes with 30% in the first column?
- 2Divide both by 3. What amount matches 10%?
- 3What do you multiply 10% by to reach 100%?
- 4Do the same to the other row. What is the whole?
Final answer: -
3Complete each step, then write the final answer.
8 is 50% of what number?
Show your workHint Put 50% and 8 in the first column. What scale factor takes 50% to 100%?
Final answer: -
4Complete each step, then write the final answer.
$45 is 75% of the original price. What was the original price?
Show your workHint Put 75% and 45 in the first column. Find 25% first. Then multiply to reach 100%.
Final answer: -
5Complete each step, then write the final answer.
Ty has saved $36. That is 20% of the cost of a bike. How much does the bike cost?
Show your workHint Put 20% and 36 in the first column. What scale factor takes 20% to 100%?
Final answer: -
6Complete each step, then write the final answer.
9 is 30% of a number. Ella writes 0.3 × 9 = 2.7 and says the number is 2.7. Find the correct number.
Show your workHint Put 30% and 9 in the first column. 100% is more than 30%, so the whole is more than 9.
Final answer:
Explain your thinking9 is 30% of a number. Ella says the number is 2.7. Before you compute, how can you tell the number must be more than 9?
Sentence starter The whole is 100%, so it must be ___ than the part. · In the table, I scale ___% up to 100% because ___.