Lesson 1.31.3 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can represent a real-world situation with a tape diagram or table and use decimal operations to solve it — 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 |
|---|---|---|
| representationSpanish: representación | A picture, diagram, table, or equation that shows the mathematics in a situation. | The same 12 shown three ways: a tape diagram, a table, and 3 × 4. |
| tape diagramSpanish: diagrama de cintas | A rectangle cut into equal parts that helps you visualize how a total breaks apart. | One bar of 4,000 passengers cut into equal groups of 80. |
| toolSpanish: herramienta | Anything you choose to help you see relationships and solve a problem — a table, a diagram, a graph. | A table, a number line, or a tape diagram — whichever shows the relationship. |
| ordered pairSpanish: par ordenado | Two numbers that go together, like a time and a number of trips, that you can plot as a point. | (4, 60): 4 hours costs $60 — the hours always come first. |
| round tripSpanish: viaje de ida y vuelta | A complete journey from the start, to the destination, and back to the start. | 5 miles out plus 5 miles back = 10 miles in all. |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A pile of coins is too big to count one by one. One small stack has about 10 coins. About 15 stacks like it make the pile. About how many coins are in the pile?
- Count one small stack: about 10 coins
- Count how many stacks make the pile: about 15 stacks
- Multiply the stacks by the coins in each: 15 × 10 = 150
- About 150 coins are in the pile.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A tram must move 4,000 passengers. Each ride carries 80 passengers. One ride takes 12.5 minutes. How long do all the rides take?
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- First I counted .
- Then I estimated about because .
Word bank representationtape diagramtoolordered pairround trip
Watch outA common mistake
Converting minutes to hours by moving the decimal point — 625 minutes is NOT 6.25 hours. An hour is 60 minutes, so divide by 60: 625 ÷ 60 ≈ 10.42 hours.
Lesson 1.31.3 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can represent a real-world situation with a tape diagram or table and use decimal operations to solve it — one step at a time, with support.
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1Complete each step, then write the final answer.
One trip carries 30 people and takes 8.5 minutes. A boat must carry 600 people. Each trip carries 30 people. One trip takes 8.5 minutes. How long do all the trips take?
- 1What is the scale factor from 30 people to 600 people?
- 2Multiply 1 trip by the same factor. How many trips?
- 3Multiply 8.5 minutes by 20. How many minutes?
Final answer: -
2Complete each step, then write the final answer.
One ride takes 7.5 minutes. One ride takes 7.5 minutes. How many hours do 40 rides take?
- 1What is the scale factor from 1 ride to 40 rides?
- 2Multiply 7.5 minutes by 40. How many minutes?
- 3There are 60 minutes in an hour. How many hours is 300 minutes?
Final answer: -
3Complete each step, then write the final answer.
One ride takes 3.5 minutes. How many minutes do 10 rides take?
Show your workHint Multiply 3.5 × 10. Each digit moves one place to the left.
Final answer: -
4Complete each step, then write the final answer.
Each ride carries 80 passengers. A tram must move 2,400 passengers. Each ride carries 80 passengers. How many rides are needed?
Show your workHint The passengers split into equal groups of 80. Divide to count the groups.
Final answer: -
5Complete each step, then write the final answer.
A ferry carries 50 cars on each trip. It must carry 500 cars. Each trip takes 9.5 minutes. How many minutes do all the trips take?
Show your workHint First divide to find the number of trips. Then multiply by 9.5 minutes.
Final answer: -
6Complete each step, then write the final answer.
One ride takes 12.5 minutes. Jen says 30 rides take 37.5 minutes. Is that reasonable? How many minutes do 30 rides take?
Show your workHint 10 rides alone take more than 100 minutes. Use the table: 10 rides, then 30 rides.
Final answer:
Explain your thinkingWhich tool helped you more today, a tape diagram or a table? Tell what it shows.
Sentence starter A tape diagram shows ___. · A table helps me ___.