Start here

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: Not every good reason is an equation. Finish this argument: “I recommend buying two jumbo boxes because …” The book offers two word-based reasons: there is less packaging with two boxes, and two boxes are easier to store than three boxes. Now listen to the other side. One student recommends the three large boxes because the cereal will stay fresher — each box is open for less time — and because greater volume does not always mean more cereal inside. How convincing is each argument? That judgment is math too. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartA tram carries 10 passengers each trip. How many trips move 40 passengers?

   1. A4 trips
   2. B10 trips
   3. C30 trips
   4. D400 trips

   How do you know?
3. 3

   Warm restartWhat is 2.5 × 10?

   1. A25
   2. B2.5
   3. C250
   4. D12.5

   How do you know?
4. 4

   Warm restartMultiplying a whole number by 10 makes the number…

   1. Aten times as large
   2. B10 more than it was
   3. Cten times smaller
   4. Dexactly the same

   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 group needs to order soil to fill the garden beds. Which unit should they use to express the amount of soil?

   1. Afeet
   2. Bsquare feet
   3. Ccubic inches
   4. Dcubic feet

   Why is that the answer?
2. 6

   Think it throughAfter finding the volume of the garden beds one way, what should the group do to be confident their total of 48 cubic feet is accurate?

   1. ARound the answer to the nearest ten
   2. BDecompose the figure a second, different way and check that both totals match
   3. CMultiply the total by 2 just to be safe
   4. DAsk a classmate if the number sounds right

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

   Think it throughThe group decides to decompose the garden bed design into simpler shapes to find its volume. What does that method involve?

   1. AAdding the areas of each face of the figure
   2. BBreaking the figure into rectangular prisms, finding each prism's volume, then adding them
   3. CMultiplying the total length by the total width only
   4. DAveraging the volumes of similar containers they've seen before

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

   Back to the modelYuzuki can buy three large boxes (240 cubic inches each) or two jumbo boxes (400 cubic inches each) for the same price. Which option gives more cereal, and how do you know?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Two jumbo boxes hold 800 cubic inches, and 800 > 720.
• 8 × 3 × 10 = 240, so each large box holds 240 cubic inches.
• 400 × 2 = 800 cubic inches for the two jumbo boxes.
• There is less packaging with two boxes.
• Two boxes are easier to store than three boxes.
• The cereal stays fresher because each box is open for less time.
• 240 × 3 = 720 cubic inches for the three large boxes.
• Greater volume does not always mean more cereal inside the box.

Use the words

Fill each blank with a word from the bank.

• A chain of reasons used to defend your thinking is an ___.
• A statement you believe is true but have not yet proven is a ___.
• A single case that shows a statement is not always true is a ___.
• The amount of space a solid figure takes up, in cubic units, is its ___.

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: Reporting volume without cubic units — saying the garden needs '48 feet' of soil, which is a length, or '48 square feet', which is an area.
2. 10

   Say moreYou sorted '800 > 720' as an equation argument and 'the cereal stays fresher' as a word argument. Why are both considered legitimate math arguments, even though only one uses numbers?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A breakfast plate holds a stack of egg muffins. Each egg muffin is about 60 calories.

   Show your work

Last check

These two come from Lesson 1.3. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which statement best captures what this lesson means by 'Math is Explaining and Sharing'?

   1. AWe communicate our reasoning, listen to classmates' arguments, decide whether they are convincing, and check our calculations for accuracy
   2. BWe keep our methods private so nobody can copy our answers
   3. CAn argument only counts in math if it uses equations
   4. DOnce you have an answer, checking it a second way is a waste of time

   Explain your choice.
2. 13

   From Lesson 1.3Explain 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

   How do you know?
3. 14

   From Lesson 1.3600 ÷ 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

   How do you know?

Be honest — this tells your teacher what to do next