Lesson 1.3Math is In My World
Start hereWords, worked example, and sentence starters
Learning target I can represent a real-world situation with a tape diagram or table and use decimal operations to solve it.
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 at a time. About how many coins are in the pile?
- I do not count every coin — I find a small stack I CAN count, about 10 coins.
- Then I estimate how many stacks like that are in the pile. I count about 15.
- 15 stacks of about 10 is 15 × 10 = 150, so my estimate is about 150 coins — reasoned, not random.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
One tram ride takes 12.5 minutes, so 10 rides take 12.5 × 10 = 125 minutes and 50 rides take 12.5 × 50 = 625 minutes.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- This situation needs because we are a total, not it.
- First I counted .
- Then I estimated about because .
- My tape diagram shows .
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 1.3Math is In My World
Version ASupported practice
Learning target I can represent a real-world situation with a tape diagram or table and use decimal operations to solve it.
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1Circle the letter of the best answer. Show how you know.
One tram ride takes 12.5 minutes. How many minutes do 10 rides take?
- A1.25 minutes
- B22.5 minutes
- C125 minutes
- D1,250 minutes
Hint You need 10 equal groups of 12.5.
Show your work -
2Circle the letter of the best answer. Show how you know.
Five Breaks: which of these is a correct way to decompose 12.5?
- A1 + 2.5
- B10 + 2.5
- C10 + 2.05
- D12 + 5
Hint Add each option and compare to 12.5.
Show your work -
3Circle the letter of the best answer. Show how you know.
How many minutes do 50 tram rides take, at 12.5 minutes per ride?
- A62.5 minutes
- B600 minutes
- C625 minutes
- D6,250 minutes
Hint Use the table pattern: 10 rides take 125 minutes.
per 1 - 1LabelWrite what each column is.
- 2Find per 1Divide to get one.
- 3ScaleMultiply up to what is asked.
- 4CheckDoes the size make sense?
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4Circle the letter of the best answer. Show how you know.
Each tram ride carries 80 passengers. How many rides are needed to transport 4,000 passengers?
- A50 rides
- B500 rides
- C3,920 rides
- D320,000 rides
Hint You are splitting 4,000 into equal groups of 80.
Show your work
-
5Answer in complete sentences.
A coin display has about 15 stacks that look the same size. You count 10 coins in one stack. About how many coins are in the display? Explain how to estimate without counting every coin.
Sentence starter First I counted ___ .
Then I estimated about ___ because ___ .Write your answer -
6Answer in complete sentences.
A tram carries 80 passengers per ride. How can a tape diagram show how many rides transport 4,000 passengers?
Sentence starter My tape diagram shows ___ .
It helps because ___ .Write your answer
Explain your thinkingFind a card where you and your partner chose different operations. What is it about the situation — not the numbers — that tells you whether division or multiplication helps?
Sentence starter This situation needs ___ because we are ___ a total, not ___ it.
Lesson 1.3Math is In My World
Version BCore practice
Learning target I can represent a real-world situation with a tape diagram or table and use decimal operations to solve it.
-
1Circle the letter of the best answer. Show how you know.
The 50 rides take 625 minutes. About how many HOURS is that?
- AAbout 6.25 hours
- BAbout 10.42 hours
- CAbout 12.5 hours
- DAbout 62.5 hours
Show your work -
2Circle the letter of the best answer. Show how you know.
How does the answer change for 2,000 passengers? Each ride carries 80 passengers and takes 12.5 minutes. How many MINUTES are needed?
- A31.25 minutes
- B300 minutes
- C312.5 minutes
- D3,125 minutes
Show your work -
3Circle the letter of the best answer. Show how you know.
One round trip takes 35 minutes. Using the table (35 → 1, 350 → 10, 525 → 15, 700 → 20), how many round trips does a tram car complete in 10 hours?
- A15 round trips
- B17 round trips
- C18 round trips
- D20 round trips
Show your work -
4Circle the letter of the best answer. Show how you know.
The round trip is 5 miles. How far does a tram car travel in 5 round trips?
- A1 mile
- B10 miles
- C25 miles
- D50 miles
Show your work
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5Answer in complete sentences.
Compare these tram problems. A: A tram carries 80 passengers per ride and each ride takes 35 minutes. How long would 4,000 passengers take? B: A different tram completes a round trip in 12.5 minutes. How many round trips fit in 10 hours? How are the problems alike and different?
Write your answer -
6Answer in complete sentences.
How does the answer change if the tram must transport 6,000 passengers? (Each ride carries 80 passengers and takes 12.5 minutes.) Show your steps.
Write your answer
Explain your thinkingFind a card where you and your partner chose different operations. What is it about the situation — not the numbers — that tells you whether division or multiplication helps?
Lesson 1.3Math is In My World
ChallengeExtension
Learning target I can represent a real-world situation with a tape diagram or table and use decimal operations to solve it.
-
1Write the letter of the matching item on each line.
Match each tram question to the operation that answers it.
- Minutes for 40 rides (12.5 min each)
- Rides needed for 400 passengers (80 per ride)
- Hours in 625 minutes
- Passengers on 30 full rides
- A40 × 12.5
- B400 ÷ 80
- C625 ÷ 60
- D30 × 80
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2Circle the letter of the best answer. Show how you know.
Apply — What Time Is It? The new year starts at midnight on January 1st. What time will it be 2,022 minutes after midnight?
- A8:22 p.m. on January 1
- B9:42 a.m. on January 2
- C9:42 a.m. on January 1
- D9:42 p.m. on January 2
Show your work -
3Circle the letter of the best answer. Show how you know.
How many rides would the tram need for 10,000 passengers, at 80 passengers per ride?
- A12.5 rides
- B125 rides
- C250 rides
- D1,250 rides
per 1
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4Answer in complete sentences.
The lesson says we make strategic decisions about which tool to use. For the 10-hour round-trip question, would you choose a table of values, a coordinate plane, or an equation? Defend your choice.
Write your answer -
5Answer in complete sentences.
Math is in YOUR world. Describe a real situation from your life that works like the tram problem — a total split into equal groups, or a time built from equal chunks — and show the math.
Write your answer