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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: 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. The tram needs 50 rides to move 4,000 passengers, and 625 minutes is 625 ÷ 60 hours — about 10.42 hours. A tape diagram of 4,000 cut into equal rides shows WHY we divide, and the table shows how minutes grow with rides. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhat is 1/2 of 60?

   1. A30
   2. B20
   3. C40
   4. D120

   How do you know?
3. 3

   Warm restartWhat is 1/4 of 20?

   1. A5
   2. B4
   3. C16
   4. D80

   How do you know?
4. 4

   Warm restartYou multiply a whole number by a fraction smaller than 1. The answer is:

   1. ASmaller than the number you started with
   2. BBigger than the number you started with
   3. CExactly the same
   4. DAlways zero

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughThe tram problem asks how many round trips fit in 10 hours. What is the FIRST thing you must find before you can read the answer off your table?

   1. AHow many minutes are in 10 hours, so the units match the table
   2. BHow many miles the tram travels in total
   3. CHow many passengers ride each trip
   4. DThe price of a ticket

   Why is that the answer?
2. 6

   Think it throughUsing the table (35→1, 175→5, 350→10, 525→15, 700→20 minutes→trips), why does the answer end up being 17 round trips, not 18?

   1. A17 trips take 595 minutes, which fits within 600, but an 18th trip would need 630 minutes, past the limit
   2. B18 trips is closer to 600 minutes, so it is the better estimate
   3. CA round trip can be counted as complete even if it is only partly finished
   4. DThe table only lists rows up to 20, so 17 is the safe middle choice

   How do you know? Give a second reason as well.
3. 7

   Think it through600 ÷ 35 ≈ 17.14. Why is it risky to round this quotient down to 17 WITHOUT also checking the table?

   1. ARounding down happens to work here, but only the table confirms 17 × 35 stays under 600 while 18 × 35 does not
   2. BRounding down never works for time problems
   3. C17.14 should round up to 18 because .14 rounds upward
   4. DThe table and division always disagree with each other

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelThe aerial tram must move 4,000 passengers, and each ride carries 80 passengers. What operation tells you how many rides are needed, and why?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Find how many rides are needed for 4,000 passengers if each ride carries 80
• Find the total minutes for 50 rides at 12.5 minutes each
• Find how many 35-minute round trips fit in 600 minutes
• Find the total miles a tram car travels in 17 round trips of 5 miles each
• Split 2,000 passengers into equal rides of 80
• Find how many passengers ride in 25 rides of 80 passengers each

Use the words

Fill each blank with a word from the bank.

• A drawing, table, or equation that shows the math in a situation is a ___.
• A rectangle cut into equal parts that shows how a total breaks apart is a ___ ___.
• Anything you choose to help you see relationships and solve is a ___.
• Two numbers that go together and can be plotted as a point are an ___ ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: Converting minutes to hours by moving the decimal point — 625 minutes is NOT 6.
2. 10

   Say moreYou sorted 'find how many rides are needed for 4,000 passengers' under division and 'find the total minutes for 50 rides at 12.5 minutes each' under multiplication. What tells you which operation a tram task needs?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: An aerial tramway car glides on a cable high above a valley, carrying passengers from the station below toward the mountain top.

   Show your work

Last check

These two come from Lesson 1.2. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which statement best shows what this lesson means by "math is in my world"?

   1. AWe visualize real problems, use tools to show relationships among quantities, and choose our tools strategically
   2. BReal-world problems can only be solved with a calculator
   3. CTables and diagrams are decorations we add after solving
   4. DEvery problem must be solved with the same one tool

   Explain your choice.
2. 13

   From Lesson 1.2Explain your thinking — Which statement best shows what this lesson means by "math is exploring and thinking"?

   1. AWe make sense of problems, plan a strategy, check our progress, and try other strategies at dead ends
   2. BWe compute as fast as possible and move on to the next problem
   3. CWe wait for someone to show us the one correct method
   4. DWe only check our work when the answer looks wrong

   How do you know?
3. 14

   From Lesson 1.2Building height problem: which statement shows you are CHECKING your solution against the relationship in the problem?

   1. A“5/6 is less than 1, so my answer for London should be less than 540 meters”
   2. B“My answer is 650 meters, and that seems like a big number so it's probably right”
   3. C“I don't need to check once I've multiplied”
   4. D“Since I used a fraction, the answer must be exact”

   How do you know?

Be honest — this tells your teacher what to do next