Inequalities – Grade 9 math lesson

Lesson 8 of 17 in the Grade 9 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 9 (ages 14–15) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.

Time: 45 minutes + 20 min homework
Grade: Grade 9 (ages 14–15)
You need: Paper, a pencil and this page
Graded: Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.

Read what your child will learn and the big ideas together.
Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
Finish with the exit ticket and the talk question: “Why does the sign turn round when you divide by a negative?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Forgetting to turn the sign when dividing by a negative. Test a number: −2x > 6 means x < −3.
Using a filled circle for <. Filled means equal is allowed: ≤ or ≥.

Tip for home: Talk about age or height limits as inequalities.

What your child will learn

Learning goal: solve inequalities and show them on a number line.

Success looks like

I can show inequalities on a number line.
I can solve inequalities.
I can list integers that satisfy an inequality.

Key words

inequality: a statement using <, >, ≤ or ≥
integer: a whole number
solution set: all the values that work
number line: a line showing the solutions

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Show inequalities with string on a number line laid on the floor.

The big ideas (for the adult)

An inequality says one side is bigger or smaller: x > 3 means any number greater than 3.

On a number line, an open circle means not included (< or >); a filled circle means included (≤ or ≥).

Solve like an equation, but if you multiply or divide by a negative number, turn the inequality sign round.

The lesson, step by step

45 minutes in 5 parts
Part	Time	How it is checked
Starter: quick recall	5 min	Graded by Classfern
Teaching input	10 min	Not assessed, self-checked
Worked examples and guided practice	9 min	Not assessed, graded by Classfern
Independent practice	15 min	Graded by Classfern
Closure and exit ticket	6 min	Graded by Classfern, self-checked

Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.

More practice

Algebra 1: Linear Equations and Inequalities Practice TestGraded instantly

All Grade 9 math lessons and tests · Math Department

More Grade 9 math lessons

Curriculum

Common Core State Standards HSA.REI.B.3: “Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.”

Common Core State Standards HSA.REI.D.12: “Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.”

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