CH03-08 lesson

Writing Inequalities Learning Activity

A focused Grade 6 learning session for Writing Inequalities using visual models, worked examples, strategy guidance, and a short mastery check.

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15
minutes
6
lesson parts
11
practice items
Learning goal

Students will build Grade 6 mastery of writing inequalities using models, equations, and test-style reasoning.

Student goal: I can solve problems involving writing inequalities.

Helpful first: Solving One-Step Equations
concept

Learn the Idea

Writing Inequalities means choosing a model, naming what each number means, and explaining the strategy.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.
visual model

See the Math

Visual Model 1

Question: You can practice your instrument for more than \(30\) minutes but must stop before \(60\) minutes. If \(t\) is the time in minutes, which two inequalities best describe this?

InequalityMeaning
\(t>30\)more than \(30\) min
\(t<60\)less than \(60\) min
  • A. \(t<30\) and \(t<60\)
  • B. \(t>30\) and \(t>60\)
  • C. \(t>30\) and \(t<60\)
  • D. \(t\leq30\) and \(t\geq60\)

Why it works: "More than \(30\)" is \(t>30\). "Stop before \(60\)" is \(t<60\). Together: \(t>30\) and \(t<60\).

Answer: \(t>30\) and \(t<60\)

worked example

Follow a Worked Example

Example 1

Question: Which inequality is shown by the graph above?

Example 1

  • A. \(2\leq x<6\)
  • B. \(2
  • C. \(2
  • D. \(2\leq x\leq6\)
  1. The filled circle at \(2\) means "equals \(2\)" (\(\geq\)).
  2. The open circle at \(6\) means "not including \(6\)" (\(<\)).
  3. Together: \(2\leq x<6\).

Answer: \(2\leq x<6\)

Example 2

Question: Based on the number line above, which inequality is represented?

Example 2

  • A. \(0
  • B. \(0\leq x<5\)
  • C. \(0
  • D. \(0\leq x\leq5\)
  1. The open circle at \(0\) means "not including \(0\)" (\(>\)).
  2. The filled circle at \(5\) means "including \(5\)" (\(\leq\)).
  3. Together: \(0<x\leq5\).

Answer: \(0

real world

Connect It to a Real Situation

Problem 1

Question: A roller coaster requires riders to be at least \(48\) inches tall. Which inequality describes the height \(h\) (in inches) needed to ride?

  • A. \(h<48\)
  • B. \(h>48\)
  • C. \(h\leq48\)
  • D. \(h\geq48\)

Why it works: "At least \(48\)" means \(48\) or more, which is written as \(h\geq48\).

Answer: \(h\geq48\)

strategy

Avoid Mistakes and Choose a Strategy

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.
  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.
summary

Remember the Key Idea

Writing Inequalities becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G6-C03-T08-Q001 About 1 min

A roller coaster requires riders to be at least \(48\) inches tall. Which inequality describes the height \(h\) (in inches) needed to ride?

  1. A \(h<48\)
  2. B \(h>48\)
  3. C \(h\leq48\)
  4. D \(h\geq48\)
Check answer and explanation

Answer D: \(h\geq48\)

"At least \(48\)" means \(48\) or more, which is written as \(h\geq48\).

G6-C03-T08-Q002 About 1 min

The speed limit on the highway is no more than \(65\) miles per hour. Which inequality represents the allowed speed \(s\)?

  1. A \(s>65\)
  2. B \(s\leq65\)
  3. C \(s\geq65\)
  4. D \(s=65\)
Check answer and explanation

Answer B: \(s\leq65\)

"No more than" means at most \(65\), which allows \(65\) and anything less: \(s\leq65\).

guided

1 question
G6-C03-T08-Q003 About 1 min

A swimming pool must have a temperature greater than \(78\) degrees Fahrenheit. Which inequality matches this requirement for temperature \(t\)?

  1. A \(t\leq78\)
  2. B \(t=78\)
  3. C \(t>78\)
  4. D \(t<78\)
Check answer and explanation

Answer C: \(t>78\)

"Greater than" means strictly more, not equal: \(t>78\). This excludes \(78\) itself.

practice

5 questions
G6-C03-T08-Q004 About 1 min

To qualify for a school club, you must have no less than a \(3.0\) grade point average. Which inequality describes the minimum GPA \(g\)?

  1. A \(g<3.0\)
  2. B \(g>3.0\)
  3. C \(g\leq3.0\)
  4. D \(g\geq3.0\)
Check answer and explanation

Answer D: \(g\geq3.0\)

"No less than \(3.0\)" means \(3.0\) or more: \(g\geq3.0\).

G6-C03-T08-Q005 About 1 min

A discount applies when you spend less than \($50\). If \(d\) represents the amount you spend, which inequality is correct?

  1. A \(d<50\)
  2. B \(d\leq50\)
  3. C \(d>50\)
  4. D \(d\geq50\)
Check answer and explanation

Answer A: \(d<50\)

"Less than \($50\)" means strictly below \(50\): \(d<50\).

G6-C03-T08-Q006 About 1 min

Which phrase best describes the inequality \(x\geq12\)?

  1. A Less than \(12\)
  2. B Greater than \(12\)
  3. C No more than \(12\)
  4. D At least \(12\)
Check answer and explanation

Answer D: At least \(12\)

\(x\geq12\) means \(x\) can equal \(12\) or be larger, which matches "at least \(12\)."

G6-C03-T08-Q007 About 1 min

The weight of a piece of luggage must not exceed \(50\) pounds. Which inequality best represents this, where \(w\) is the weight?

  1. A \(w>50\)
  2. B \(w\leq50\)
  3. C \(w<50\)
  4. D \(w\geq50\)
Check answer and explanation

Answer B: \(w\leq50\)

"Must not exceed" means at most \(50\): \(w\leq50\).

G6-C03-T08-Q008 About 1 min

Which inequality corresponds to "\(x\) is less than or equal to \(-3\)"?

  1. A \(x\geq-3\)
  2. B \(x<-3\)
  3. C \(x\leq-3\)
  4. D \(x>-3\)
Check answer and explanation

Answer C: \(x\leq-3\)

"Less than or equal to" uses the \(\leq\) symbol: \(x\leq-3\).

exit

3 questions
G6-C03-T08-Q009 About 1 min

You need to save more than \($200\) for a new computer. If \(s\) is the amount you save, which inequality represents this?

  1. A \(s<200\)
  2. B \(s=200\)
  3. C \(s\leq200\)
  4. D \(s>200\)
Check answer and explanation

Answer D: \(s>200\)

"More than \(200\)" means strictly greater: \(s>200\).

G6-C03-T08-Q010 About 1 min

A recipe calls for no more than \(\frac{1}{2}\) cup of salt. Which inequality represents the amount \(a\) of salt that can be used?

  1. A \(a<\frac{1}{2}\)
  2. B \(a\geq\frac{1}{2}\)
  3. C \(a\leq\frac{1}{2}\)
  4. D \(a>\frac{1}{2}\)
Check answer and explanation

Answer C: \(a\leq\frac{1}{2}\)

"No more than" means at most: \(a\leq\frac{1}{2}\).

G6-C03-T08-Q011 About 1 min

Your age must be at least \(13\) years old to join the club. Which inequality best fits, where \(y\) is your age?

  1. A \(y<13\)
  2. B \(y\leq13\)
  3. C \(y>13\)
  4. D \(y\geq13\)
Check answer and explanation

Answer D: \(y\geq13\)

"At least \(13\)" allows \(13\) and everything above: \(y\geq13\).

Keep the learning path connected
Previous skillSolving One-Step Equations Recommended nextGraphing Inequalities on a Number Line Same strandExponents and Order of Operations Same strandTranslating Words into Expressions
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