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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: Try 200 quarters: 200 × $0.25 = $50.00. Add 25 dimes: 25 × $0.10 = $2.50, bringing the total to $52.50. Add 15 nickels: 15 × $0.05 = $0.75, and 25 pennies: 25 × $0.01 = $0.25. $50.00 + $2.50 + $0.75 + $0.25 = $53.50. It works — and 25 pennies is a multiple of 5, just as the pattern predicted. Now use the patterns to find a different combination. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhich box holds more — one that holds 20 cubic inches, or one that holds 30 cubic inches?

   1. AThe 30 cubic inch box
   2. BThe 20 cubic inch box
   3. CThey hold the same
   4. DYou cannot tell

   How do you know?
3. 3

   Warm restartA cube is 2 cm long on every edge. What is its volume?

   1. A8 cubic cm
   2. B6 cubic cm
   3. C4 cubic cm
   4. D12 cubic cm

   How do you know?
4. 4

   Warm restartA box is 2 cm long, 3 cm wide, and 2 cm tall. What is its volume?

   1. A12 cubic cm
   2. B7 cubic cm
   3. C10 cubic cm
   4. D24 cubic cm

   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 throughPlayer A had scored 18 points before making 10 two-pointers in a row. Using the pattern rule of adding 2 points per shot, what is Player A's final score?

   1. A28
   2. B38
   3. C20
   4. D36

   Why is that the answer?
2. 6

   Think it throughPlayer B had 6 points before scoring 10 three-pointers in a row. Using the pattern rule of adding 3 points per shot, what is Player B's final score?

   1. A16
   2. B30
   3. C38
   4. D36

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

   Think it throughAfter using the pattern rules to find both players' final scores, how can the players check that their totals are reasonable?

   1. AMultiply the two final scores together
   2. BList the score after each shot in a table of values and confirm the sequence lands on the final totals
   3. CRound both totals to the nearest ten
   4. DCompare the players' shooting percentages

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

   Back to the modelAkela's change jar has coins worth $53.50. Why is 'every 100 of a coin is worth 100 times one coin's value' a pattern, while 'Akela's jar holds $53.50' is not?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Each number in Player A's points is 2 greater than the number before it.
• The pattern rule for Player B is to add 3.
• Every 100 of a coin is worth 100 times one coin's value.
• The number of pennies in the jar must be a multiple of 5.
• Player A had 18 points before the streak started.
• Akela's jar holds $53.50.
• Player B finished with 36 points.
• A sei whale measures 4.5 meters long at birth.

Use the words

Fill each blank with a word from the bank.

• Something that repeats or changes in a predictable way is a ___.
• The instruction for getting from one term to the next is the ___ ___.
• A statement true for a whole pattern, not just the cases you tried, is a ___.
• A table listing each step of a pattern in order is a ___ ___ ___.

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 only the points from the streak (20 or 30) and forgetting to add the points each player had before the streak began.
2. 10

   Say moreThe whale card was tricky: 'a sei whale measures 4.5 meters at birth' is a starting value, and the growth pattern adds about 2.5 centimeters each day. Why does a pattern need BOTH a starting value and a rule?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Rows of shoes fill a set of shoe racks. Nobody wants to count them one at a time.

   Show your work

Last check

These two come from Lesson 1.4. 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 Finding Patterns'?

   1. AWe look for patterns and relationships, use them to solve problems and make generalizations, and check our solutions for reasonableness
   2. BPatterns are decorations that make problems look nicer
   3. CA pattern rule only works if you also count every item one at a time
   4. DOnce you spot a pattern you never need to check your answer

   Explain your choice.
2. 13

   From Lesson 1.4Explain 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

   How do you know?
3. 14

   From Lesson 1.4The 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

   How do you know?

Be honest — this tells your teacher what to do next