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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.

   Let's do one together: Decompose 105.76 in five ways. Each way must equal exactly 105.76. Start at 100. What do you add to reach 105.76? (5.76, so 105.76 = 100 + 5.76) Start at 105. What do you add to reach 105.76? (0.76, so 105.76 = 105 + 0.76) Start at 110. How far down is 105.76? (4.24, so 105.76 = 110 − 4.24) Half of 105.76 is 52.88. Double is 211.52. Write two more ways. (105.76 = 52.88 × 2 and 105.76 = 211.52 ÷ 2)

   My first step is ___ , because the problem asks for ___ .

   Show your work
2. 2

   Warm restartA Ferris wheel has 10 cars. Each car holds 4 people. How many people ride at once?

   1. A14 people
   2. B20 people
   3. C40 people
   4. D44 people
3. 3

   Warm restartWhat is half of 20?

   1. A5
   2. B10
   3. C15
   4. D40
4. 4

   Warm restartA pizza is cut into 8 equal slices. You eat half of it. How many slices did you eat?

   1. A2 slices
   2. B4 slices
   3. C8 slices
   4. D16 slices

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 throughIn the Comparing Walks problem, Deon walked a shorter distance than Miguel, and Evelyn walked a longer distance than Miguel. Without any exact distances, what can you determine?

   1. ANothing — you need exact numbers before you can compare
   2. BDeon and Evelyn walked the same distance
   3. CThe order from shortest to longest: Deon, Miguel, Evelyn
   4. DEvelyn walked the shortest distance

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughA student picks Miguel = 2 miles, Deon = 2.5 miles, Evelyn = 1.5 miles. What is wrong with these values?

   1. ANothing is wrong — any three distances work
   2. BEvelyn's distance is too small compared to Deon's
   3. CDeon's distance is greater than Miguel's, which breaks “shorter than”
   4. DMiguel's distance must always be the smallest of the three

   How do you know?

   I chose ___ because ___ .
3. 7

   Think it throughBuilding 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”

   Explain your thinking.

   I chose ___ because ___ .
4. 8

   Back to the modelThe book decomposes 105.76 as one example: 100 + 5.76. Why must the parts of a decomposition always rebuild the original number exactly?

   100 + 5.76 works because ___.

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Three students walked different distances
• Deon walked a shorter distance than Miguel
• Evelyn walked a longer distance than Miguel
• How far each student walked
• The exact number of miles Deon walked
• Miguel's exact distance

Use the words

Fill each blank with a word from the bank.

• A number with a meaning attached, like 540 meters, is a ___.
• How two quantities connect or change together is a ___.
• The plan you choose before you start computing is your ___.
• An answer that makes sense in the story of the problem is ___.

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: Expecting a fraction of a number to be bigger than the number — 5/6 × 540 must be LESS than 540 because 5/6 is less than 1; only a fraction greater than 1, like 6/5, makes the product bigger.
2. 10

   Say moreYou sorted 'Deon walked a shorter distance than Miguel' as something we KNOW, even without exact numbers. How can a relationship like 'shorter than' be knowledge, if we don't know the actual distance?

   We know this because the problem states a ___, not an exact number.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   Show your work

Last check

These two come from Lesson 1.1. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: Which statement best shows what this lesson means by "math is exploring and thinking"?

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

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 1.1Quick check — you've got this: Which statement best shows what this lesson means by “we are all doers of math”?

   1. AEveryone gets the same score if they try hard enough
   2. BEveryone uses mathematical thinking daily, in different ways, and sharing those ways helps us grow
   3. CEveryone must solve problems the same way to be correct
   4. DOnly the fastest students are really doing math
3. 14

   From Lesson 1.1Which of these is the BEST example of a specific math strength for the Connect prompt?

   1. A“I'm good at math”
   2. B“I can explain my thinking out loud so others can follow my steps”
   3. C“I got an A last year”
   4. D“Math is easy for me”

Be honest — this tells your teacher what to do next