Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.9

Lesson 8.48.4 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write inequalities to represent real-world situations, explain what each part stands for, and build one for a situation I have not seen before.

Why This Matters This is your challenge small group for Lesson 8.4. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
InequalitySpanish: Desigualdad A math sentence that compares two sides with <, >, ≤, or ≥. x ≥ 18
Greater thanSpanish: Mayor que The > sign, showing one number is bigger. 8 > 3 — eight is larger than three
Less thanSpanish: Menor que The < sign, showing one number is smaller. 2 < 7 — two is smaller than seven
At least / At mostSpanish: Al menos / A lo más 'At least' means ≥. 'At most' means ≤. 'At least 10 players' → p ≥ 10 (could be 10, 11, 12, ...); 'At most 5 tries' → t ≤ 5 (could be 5, 4, 3, ...)
VariableSpanish: Variable A letter that stands for a number that is unknown or can change. the x in x ≥ 18
No more thanSpanish: No más de A phrase meaning less than or equal to (≤). “No more than 8 people” means people ≤ 8.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A van can carry at most 8 riders. Write an inequality for r, the riders.

  1. Key words: “at most.” Is 8 allowed? Yes.
  2. “At most” means less than or equal to: r ≤ 8.
  3. Test: 8 works, 5 works, 9 does not.

Answer: r ≤ 8

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Clue: "A bag holds fewer than 10 items." Write an inequality for the number of items n.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The phrase tells me the symbol is .
  • My inequality is because .
  • The value (is / is not) a solution because .
  • This inequality has many solutions because .

Word bank inequalityat leastat mostmore thanless thangreater thansymbolconstraintvariablesolutionboundaryrange

Watch out!A common mistake

A common mistake in Write Inequalities is using a strict symbol (> or <) for a phrase that actually includes the boundary value. For 'the suspect is at least 18 years old,' students often write a > 18 instead of the correct a ≥ 18

Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.9

Lesson 8.48.4 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write inequalities to represent real-world situations, explain what each part stands for, and build one for a situation I have not seen before.

Why This Matters This is your challenge small group for Lesson 8.4. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    ScorePass?
    70?
    69?
    Test each score.

    To pass a test, a student must score no less than 70. Write an inequality for a passing score s.

    1. 1Is a score of 70 a pass? Is 69?
    2. 2Which symbol do we use?
    3. 3Write the inequality.
    Final answer:
  2. 2Complete each step, then write the final answer.
    LengthAllowed?
    22 in.?
    23 in.?
    Test each length.

    A carry-on bag must not be longer than 22 inches. Write an inequality for the length l. Then explain the symbol.

    1. 1Is a 22-inch bag allowed? Is a 23-inch bag?
    2. 2Which symbol do we use?
    3. 3Why is l < 22 wrong for this rule?
    Final answer:
  3. 3Complete each step, then write the final answer.

    An elevator can carry a maximum of 1,500 pounds. Which symbol goes in the box: w ☐ 1,500?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Players need a minimum of 3 hours of practice each week. Which symbol goes in the box: h ☐ 3?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    Pia earns $8 per hour. She wants to earn more than $100. Which symbol goes in the box: 8h ☐ 100?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Clue: "The suspect is not taller than 70 inches." Which symbol goes in the box for the height h: h ☐ 70?

    Show your work
    Final answer:

Explain your thinkingSome phrases sound like the opposite symbol, like "no less than." How do you test a phrase to choose the right symbol?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help