Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

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

   Try it together — then prove it:

   1. Write 78.5 in different ways. Then explain why a subtraction can name the same number.
   2. Write 78.5 as 70 plus a number. (78.5 = 70 + 8.5)
   3. Write 78.5 as 80 minus a number. (78.5 = 80 − 1.5)
   4. Write 78.5 as a number times 2. (78.5 = 39.25 × 2)
   5. Why do 70 + 8.5 and 80 − 1.5 name the same number? (Both land on the same point. 78.5 is 8.5 more than 70 and 1.5 less than 80.)

   Show your work
2. 2

   Quick reviewWhich expression shows 4 groups of 5 students?

   1. A4 × 5
   2. B4 + 5
   3. C5 − 4
   4. D5 ÷ 4

   How do you know?
3. 3

   Quick reviewWhat is 40 ÷ 10?

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

   How do you know?
4. 4

   Quick reviewYou have 3 bags with 5 apples in each bag. How many apples in all?

   1. A2 apples
   2. B8 apples
   3. C15 apples
   4. D35 apples

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughThe lesson says, “What we believe about ourselves, about others, and about what we are learning shapes us.” Why does the Strengths Inventory ask you to name a growth area, not only a strength?

   1. AGrowth areas are only for students who are behind in math
   2. BNaming what you want to grow shapes how you approach learning all year, just as naming a strength does
   3. CThe growth area replaces the strength, since you can only claim one
   4. DNaming a growth area has nothing to do with your beliefs about yourself

   Why is that the answer?
2. 6

   Think it throughOne student's math story says she liked math more once she started drawing problems; another's says he liked it more once he memorized steps. What is the point of hearing a classmate's story that is DIFFERENT from yours?

   1. AIt shows there is more than one valid way to be a doer of math, and you might borrow a new strategy
   2. BWhichever method is faster is the “right” one, so you should switch to it
   3. CIf a classmate's story differs from yours, one of you must be doing math wrong
   4. DIt doesn't matter — you only need to hear stories similar to your own

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

   Think it throughWhich 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”

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

   Back to the modelThe Ferris wheel has 20 cars, and you estimated about 4 riders fit in each car. Why is 20 × 4 an estimate and not an exact count?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Deciding if you have enough time to walk or need to run
• Splitting a pizza so everyone gets a fair share
• Checking whether $12 is enough for two snacks
• Guessing how many people fit on a Ferris wheel
• Following a recipe and doubling it
• Keeping score in a game
• Choosing the shorter of two lines at the store
• Packing a bag so everything fits

Use the words

Fill each blank with a word from the bank.

• Anyone who uses mathematical thinking is a ___ ___ ___.
• Your history with mathematics — what you have done and felt — is your ___ ___.
• Something you already do well and can share with others is a ___.
• To break a number into parts that rebuild it exactly is to ___ it.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step.

   The mistake: Believing that 'doing math' only counts when it happens on paper in a classroom.
2. 10

   Say moreYou sorted cards like 'splitting a pizza fairly' and 'choosing the shorter line' as doing math. What do all eight cards have in common that makes them math, even though none of them looks like a worksheet?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A Ferris wheel turns slowly against the evening sky. Each car is filling with riders as the line moves forward.

   Show your work

Last check

1. 12

   Show what you knowExplain your thinking — 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 must solve problems the same way to be correct
   3. COnly the fastest students are really doing math
   4. DEveryone uses mathematical thinking daily, in different ways, and sharing those ways helps us grow

   Explain your choice.

Check your progress

Choose the box that best describes how you feel about each skill.