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.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 8.4–8.7: 8.4 Write and Represent Inequalities, 8.5 Understand Inequalities and Their Solutions, 8.6 Solve and Graph Inequalities, 8.7 Equations and Inequalities Problem Solving. Work one example from each lesson, then prove you're caught up in the mixed practice.

Start hereWords for this lesson

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

Word	What it means	Example
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.
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.

Clue: "The suspect is at least 18 years old." Write an inequality for the age a.

Find the key words: at least 18 → 18 or more
Pick the symbol and write the inequality: a ≥ 18
a ≥ 18
Graph t ≥ 2 on a number line.
Draw the circle at the boundary number: ≥ → closed circle at 2
Shade the side that works: t ≥ 2 → shade right
Closed circle at 2. Shade to the right.
Solve x + 3 > 53. Then graph the solution.
Subtract 3 from both sides: 53 − 3 = 50 → x > 50
Draw an open circle at 50: > → open circle
Shade to the right: x > 50 → shade right
x > 50. Open circle at 50, shaded to the right.
A total divided equally among 4 people gave each person $85. Find the total.
Write an equation for the exact total: t ÷ 4 = 85
Multiply both sides by 4: t = 85 × 4 = 340
The total was $340.

Now you trySame steps, your turn

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

A class has more than 20 students. Which symbol goes in the box: s ☐ 20?

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 InequalityGreater thanLess thanAt least / At mostVariableNo more thanequationinequalityequalat leastat mostmore than

Watch out!A 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.

1Complete each step, then write the final answer.

You must be at least 13 to see a movie. Which symbol goes in the box for the age a: a ☐ 13?
Show your work
Hint "At least 13" means 13 or more. Is 13 included?
Final answer:
2Complete each step, then write the final answer.

A pencil box holds fewer than 24 pencils. Which symbol goes in the box: p ☐ 24?
Show your work
Hint "Fewer than 24" means less than 24. Is 24 included?
Final answer:
3Complete each step, then write the final answer.

Graph x ≥ 14. Which circle do you draw at 14: open or closed?
Show your work
Hint Does ≥ include 14? Is 14 ≥ 14 true?
Final answer:
4Complete each step, then write the final answer.

Graph x < 11. Which way do you shade from 11: left or right?
Show your work
Hint Numbers less than 11 are on which side of 11?
Final answer:
5Complete each step, then write the final answer.

Solve x + 4 > 11. What is the boundary number?
Show your work
Hint 4 is added to x. Subtract 4 from both sides.
Final answer:
6Complete each step, then write the final answer.

Solve x − 3 ≤ 9. What is the boundary number?
Show your work
Hint 3 is subtracted from x. Add 3 to both sides.
Final answer:
7Complete each step, then write the final answer.

A total divided equally among 2 people gave each person $35. What was the total?
Show your work
Hint Write t ÷ 2 = 35. Multiply both sides by 2.
Final answer:
8Complete each step, then write the final answer.

A cup holds at most 8 ounces. It has 5 ounces of juice. How many more ounces can you add at most?
Show your work
Hint "At most" is a limit. Write 5 + j ≤ 8.
Final answer:

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 ___.

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