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.

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 examplewriting an inequality for a constraint

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

A club trip requires each member to save at least $45. Write an inequality for the amounts that work.

  1. Name the variable: let s = the dollars a member saves.
  2. Find the key phrase: 'at least' means the amount can equal 45 or be more.
  3. That phrase matches the symbol ≥, so write s ≥ 45.
  4. Test values: 45 works and 52 works, but 39 falls below the limit.

Answer: s ≥ 45, so any amount of 45 dollars or more is a solution.

Now you trySame steps, your turn

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

A team must win at least 7 games to reach the playoffs. Write an inequality for the wins.

  1. Name the variable: let w = .
  2. The phrase 'at least' means w can be equal to or it.
  3. Write the inequality: w 7
  4. Test: is 6 a solution? Is 11 a solution?
Answer:inequality for the number of wins

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 outA 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 — this wrongly excludes 18 itself, even though 'at least 18' means 18 counts as a match. The same error happens in reverse with 'at most': for 'the getaway bag holds at most 12 items,' students write n < 12 instead of n ≤ 12. Always ask: does the key phrase include the number ('at least,' 'at most,' 'no more than,' 'no fewer than' → use ≥ or ≤) or exclude it ('more than,' 'fewer than' → use > or <)?

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.

  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.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help