Operations with integers – Grade 7 math lesson

Lesson 4 of 21 in the Grade 7 math course

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

A complete 45-minute lesson for grade 7 (ages 12–13) 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 7 (ages 12–13)
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 subtracting a negative number make the answer bigger?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Using the multiplying sign rule for adding (−3 + −4 = 7). Adding two negatives moves further left: −7.
Thinking 4 − (−2) = 2. Taking away a debt makes you richer: 4 + 2 = 6.

Tip for home: Talk about money owed and paid back, or floors above and below ground in a lift.

What your child will learn

Learning goal: add, subtract, multiply and divide with negative numbers.

Success looks like

I can add and subtract negative numbers.
I can multiply and divide negative numbers.
I can solve problems with negatives.

Key words

negative number: a number less than zero
integer: a whole number, positive or negative
sign: the + or − in front of a number
product: the answer to a multiplication

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Use two colors of counters as positives and negatives; a pair of one of each makes zero.

The big ideas (for the adult)

Adding a negative number is the same as subtracting: 5 + (−3) = 2. Subtracting a negative is the same as adding: 5 − (−3) = 8.

When multiplying or dividing, two signs the same give a positive answer; two different signs give a negative answer.

Use a number line for adding and subtracting, and the sign rules for multiplying and dividing.

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

Grade 7 Math: Rational Numbers Practice TestGraded instantly

All Grade 7 math lessons and tests · Math Department

Curriculum

Common Core State Standards 7.NS.A.1.d: “Apply properties of operations as strategies to add and subtract rational numbers.”

Common Core State Standards 7.NS.A.2.c: “Apply properties of operations as strategies to multiply and divide rational numbers.”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.