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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: Clue: "The lookout earned less than $50." Write a model for the lookout's earnings. Equation or inequality? How do you know? (Inequality. "Less than" is a limit, not one exact amount.) Let e be the earnings. Which symbol matches "less than"? (<) Write the inequality. (e < 50) Is $30 a reasonable value? Is $50? ($30 works, because 30 < 50. $50 does not work, because 50 is not less than 50.)

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

   Show your work
2. 2

   Warm restartSolve: x − 4 < 11

   1. Ax < 7
   2. Bx > 15
   3. Cx = 15
   4. Dx < 15
3. 3

   Warm restartSolve: x + 6 > 14

   1. Ax < 8
   2. Bx = 8
   3. Cx > 8
   4. Dx > 20
4. 4

   Warm restartSolve: x + 10 ≥ 25

   1. Ax ≥ 15
   2. Bx ≤ 15
   3. Cx = 15
   4. Dx ≥ 35

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 throughSolve 320 + r ≤ 500.

   1. Ar ≤ 180
   2. Br ≥ 180
   3. Cr ≤ 500
   4. Dr ≤ 820

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughSolve 4f = 60.

   1. Af = 15
   2. Bf = 56
   3. Cf = 64
   4. Df = 240

   How do you know?

   I chose ___ because ___ .
3. 7

   Think it throughWhy is one an equation and the other an inequality?

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

   Explain your thinking.

   I chose ___ because ___ .
4. 8

   Back to the modelHow do you decide whether a word problem needs an equation or an inequality?

   I use an equation when the problem says ___, but I use an inequality when the problem says ___ because ___.

Use the words

Fill each blank with a word from the bank.

• A drawing, equation, or diagram that represents a situation is a ___.
• A math sentence with an equal sign is an ___.
• A math sentence that compares values with <, >, ≤, or ≥ is an ___.
• Checking whether an answer makes sense for the problem is checking 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: A common mistake in Equations and Inequalities Problem Solving is matching the wrong model to a key phrase.
2. 10

   Say moreWhat was your plan to solve this problem, and how did you check that your answer was reasonable?

   My plan was to ___, and I knew to ___ because ___.
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 8.6. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: 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

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 8.6Quick check — you've got this: Solve and describe the graph: x + 5 < 11

   1. Ax < 6; open circle at 6, shade left
   2. Bx ≤ 6; closed circle at 6, shade left
   3. Cx > 6; open circle at 6, shade right
   4. Dx < 16; open circle at 16, shade left
3. 14

   From Lesson 8.6How is s ≥ 27 graphed?

   1. AClosed circle at 27, shaded to the right
   2. BOpen circle at 27, shaded to the right
   3. CClosed circle at 27, shaded to the left
   4. DOpen circle at 27, shaded to the left

Be honest — this tells your teacher what to do next