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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: Claire burned 123 Calories on a 30-minute jog and 246 Calories on a 60-minute jog. Which did Claire choose — the minutes, or the Calories? She chose how long to jog. So time is independent, and Calories burned is dependent. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartA ticket costs $8. Which equation represents "8 tickets cost $56"?

   1. A8t = 56
   2. Bt + 8 = 56
   3. Ct − 8 = 56
   4. Dt ÷ 8 = 56

   How do you know?
3. 3

   Warm restartSolve: 4x = 32

   1. Ax = 8
   2. Bx = 28
   3. Cx = 36
   4. Dx = 128

   How do you know?
4. 4

   Warm restartMaya needs at least 20 points to win a prize. Which inequality shows this?

   1. Ap ≥ 20
   2. Bp > 20
   3. Cp ≤ 20
   4. Dp < 20

   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 number of pizzas made each week determines other costs at the shop. Which variable is the independent variable in this relationship?

   1. Athe number of pizzas made
   2. Bthe cost of cheese used
   3. Cthe number of employees
   4. Dthe number of toppings allowed

   Why is that the answer?
2. 6

   Think it throughWhich two quantities have a dependent relationship in this scenario?

   1. Acost of cheese and number of pizzas made
   2. Bnumber of employees and number of pizzas made
   3. Cnumber of toppings allowed and cost of sauce
   4. Dnumber of employees and number of toppings allowed

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

   Think it throughThe shop makes 20 pizzas in a week. Which of these does NOT depend on the number of pizzas sold?

   1. Athe total cost of cheese
   2. Bthe total cost of sauce
   3. Cthe number of employees
   4. Dthe total spent on cheese and sauce combined

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

   Back to the modelAkela put her three bean trays in three different spots, so each got a different amount of sunlight. After three weeks she measured the height of the plants. Which of those two quantities did Akela choose, and which one responded?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Hours of sunlight a tray receives each day
• Average height of the bean plants after 3 weeks
• Number of minutes Claire spends jogging
• Number of Calories Claire burns
• Number of tickets you decide to buy
• Total cost of the tickets
• Number of months you keep a gym membership
• Total amount you have paid the gym

Use the words

Fill each blank with a word from the bank.

• The quantity that is subject to choice is the ___ ___.
• The quantity that changes in response to the other is the ___ ___.
• Say it in order: the responding quantity ___ ___ the chosen one.
• Something that can be counted or measured 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: Naming the variables backward — calling the responding quantity 'independent' because it is the one the question asks about.
2. 10

   Say moreWhen you sorted the eight cards into independent and dependent, how did you decide where 'number of Calories Claire burns' belonged?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Three trays of bean seedlings sit on a windowsill. The tray closest to the glass is tall and leafy. The tray in the middle is shorter. The tray pushed back into the corner is barely up out of the soil.

   Show your work

Last check

These two come from Lesson 8.7. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A dog walker charges by the hour. Which sentence is correct?

   1. AThe total charge depends on the number of hours, so hours is the independent variable.
   2. BThe number of hours depends on the total charge, so the charge is the independent variable.
   3. CBoth quantities are independent variables.
   4. DNeither quantity depends on the other.

   Explain your choice.
2. 13

   From Lesson 8.7Explain your thinking — A box of donuts has some donuts. After giving away 7, there are fewer than 5 left. Which inequality represents the starting number of donuts d?

   1. Ad − 7 < 5
   2. Bd + 7 < 5
   3. Cd − 7 > 5
   4. Dd − 7 = 5

   How do you know?
3. 14

   From Lesson 8.7Why is one an equation and the other an inequality?

   1. AThe flashlights cost exactly $60, but the budget is a limit she must stay under
   2. BBecause equations are for money and inequalities are for counting
   3. CBecause 4 is smaller than 320
   4. DThere is no real difference

   How do you know?

Be honest — this tells your teacher what to do next