Grade 6 Mathematics · Pre-UnitStandard 5.NBT.B.7

Lesson 1.31.3 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can represent a real-world situation with a tape diagram or table and use decimal operations to solve it, explain what each part stands for, and build one for a situation I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
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.

One tram car makes a round trip in 35 minutes. How many full round trips can it make in 10 hours?

  1. Change 10 hours to minutes: 10 × 60 = 600
  2. Use the table to get close to 600: 10 trips → 350 minutes; 15 trips → 525 minutes
  3. Try 17 trips and 18 trips: 17 × 35 = 595; 18 × 35 = 630
  4. Find the leftover time: 600 − 595 = 5
  5. The tram car makes 17 full round trips. 5 minutes are left over.

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?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

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.

Grade 6 Mathematics · Pre-UnitStandard 5.NBT.B.7

Lesson 1.31.3 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can represent a real-world situation with a tape diagram or table and use decimal operations to solve it, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    Round trips11011Minutes45??× ?× ?
    Compare each column with the minutes in 8 hours.

    One bus makes a round trip in 45 minutes. How many full round trips can it make in 8 hours?

    1. 1Change 8 hours to minutes.
    2. 2Multiply 1 trip and 45 minutes by 10. How many minutes?
    3. 311 trips take 495 minutes. How many full round trips fit in 480 minutes?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Trips1?People40700Minutes8.5?× ?× ?
    One trip carries 40 people and takes 8.5 minutes.

    A ferry carries 40 people on each trip. Each trip takes 8.5 minutes. How many minutes does it take to move 700 people?

    1. 1What is the scale factor from 40 people to 700 people?
    2. 2The ferry cannot make half a trip. How many trips are needed?
    3. 3How many minutes do 18 trips take?
    4. 4Why do we round 17.5 up, not down?
    Final answer:
  3. 3Complete each step, then write the final answer.
    Round trips1?Minutes25180× ?× ?

    A round trip takes 25 minutes. How many full round trips fit in 3 hours?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    Rides1?Minutes12.5300× ?× ?

    One tram ride takes 12.5 minutes. How many full rides fit in 5 hours?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Trips1?Students35420Minutes9.5?× ?× ?

    A bus carries 35 students on each trip. Each trip takes 9.5 minutes. How many minutes does it take to move 420 students?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    Trips18?People12?100× 8× 8

    A van holds 12 people. 100 people need a ride. Dev says 100 ÷ 12 is about 8.3, so the van needs 8 trips. How many trips are really needed?

    Show your work
    Final answer:

Explain your thinkingWhen do you round the number of trips up, and when do you round down? Use the bus and the ferry.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help