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

Lesson 8.78.4–8.7 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 8.4–8.7 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Write InequalitiesSpanish: Escribir desigualdades Represent a range of possible values with <, >, ≤, or ≥. You must be at least 12 years old: a ≥ 12.
InequalitySpanish: Desigualdad A math sentence that compares two sides with <, >, ≤, or ≥. x > 5 means x can be 6, 7, 8, ... — any number greater than 5
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. In x > 5, the letter x stands for any number greater than 5.

How it worksWorked example

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

Lesson 8.4 — Write and Represent Inequalities: 'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <.

  1. Lesson 8.5 — Understand Inequalities and Their Solutions: Closed circle for ≤ or ≥ (included), open circle for < or > (not included); shade right for greater, left for less.
  2. Lesson 8.6 — Solve and Graph Inequalities: Solve with inverse operations, then graph the solution set: open circle for < or >, closed for ≤ or ≥.
  3. Lesson 8.7 — Equations and Inequalities Problem Solving: 'Equals' or 'exactly' points to an equation (=); 'at least, at most, more than, fewer than' points to an inequality.

Now you trySame steps, your turn

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

From 8.4: Clue: 'A bag holds fewer than 10 items.' What does 'fewer than' mean?

Answer:

Say it and write itSentence starters

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

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

Word bank Write InequalitiesInequalityGreater thanLess thanAt least / At mostVariableequationinequalityequalat leastat mostmore than

Watch outA common mistake

A common mistake in Equations and Inequalities Problem Solving is matching the wrong model to a key phrase. For 'the getaway car held no more than 6 bags,' students often write the equation b = 6 instead of the inequality b ≤ 6, because they see one number and assume it must be exact. The same mistake happens in reverse: for 'the reward split equally among 5 people gave each $40,' students sometimes write the inequality 5p ≥ 40 instead of the equation 5p = 40, because 'split equally' sounds like it could mean a range. Before you submit, ask: does this phrase give one exact value (equation, =) or a limit/range (inequality, <, >, ≤, ≥)?

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

Lesson 8.78.4–8.7 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 8.4–8.7 by using each lesson's big idea in mixed practice.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 8.4) Which inequality represents: 'The temperature is less than 40 degrees'?

    1. At < 40
    2. Bt > 40
    3. Ct ≤ 40
    4. Dt = 40

    Hint Find the comparison phrase: 'less than 40 degrees'. Does 40 itself count, or only temperatures below it?

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 8.4) Which inequality represents: 'You must be at least 48 inches tall to ride'?

    1. Ah ≥ 48
    2. Bh > 48
    3. Ch < 48
    4. Dh ≤ 48

    Hint 'At least 48' — ask yourself: can a rider who is EXACTLY 48 inches tall ride? That decides whether 48 is included.

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 8.5) Which graph represents x < 5?

    1. AOpen circle at 5, shaded left
    2. BClosed circle at 5, shaded left
    3. COpen circle at 5, shaded right
    4. DClosed circle at 5, shaded right

    Hint Every inequality graph asks two questions: is 5 itself a solution (circle type), and which side holds the solutions (shading)?

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 8.5) Which graph represents x ≥ 3?

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

    Hint Check the symbol: ≥ has the 'or equal' bar. What does that bar mean for the circle at 3?

    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 8.6) Solve: x + 6 > 14

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

    Hint Solve it like an equation: x has 6 added to it. The > symbol just rides along.

    Show your work

Explain your thinkingHow do you decide whether a word problem needs an equation or an inequality?

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

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