Operations with multi-digit decimals – Grade 6 math lesson
Lesson 12 of 26 in the Grade 6 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 6 (ages 11–12) 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 6 (ages 11–12)
- 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 4.8 ÷ 0.6 give the same answer as 48 ÷ 6?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Lining up the last digits instead of the decimal points. Line the points up first.
- Dividing 4.8 by 0.6 and getting 0.8. Make the divisor a whole number by multiplying both by 10.
Tip for home: Work out unit prices or shares of a bill with decimals together.
What your child will learn
Learning goal: add, subtract, multiply and divide whole numbers and decimals with written methods.
Success looks like
- I can add and subtract decimals.
- I can multiply decimals.
- I can divide by a decimal.
Key words
- decimal place
- a place after the decimal point
- product
- the answer to a multiplication
- quotient
- the answer to a division
- estimate
- a quick check using rounded numbers
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Estimate first, then calculate exactly; compare the two answers.
The big ideas (for the adult)
For adding and subtracting decimals, line up the decimal points and fill empty places with zeros.
To multiply decimals, multiply without the points, then count the decimal places in the question: 0.3 × 0.12 has three, so 36 becomes 0.036.
To divide by a decimal, multiply both numbers by 10, 100… until you divide by a whole number: 4.8 ÷ 0.6 = 48 ÷ 6 = 8.
The lesson, step by step
| 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
More Grade 6 math lessons
- Solving word problems
- Fractions, decimals and percentages
- Ratios
- One quantity as a fraction or percentage of another
- Percent
- Proportional relationships
- Rates and unit rates
- Unit prices and best buys
- Converting units
- Negative numbers and temperature
- Integers and absolute value
- Operations with fractions
- Greatest common factor and least common multiple
- Square and cube numbers
- Writing expressions
- Evaluating expressions
- Simplifying expressions
- Solving equations
- Inequalities
- Writing equations for situations
- 3-D shapes and nets
- Coordinates
- Volume and surface area
- Mean, median and mode
- Box plots and interquartile range
Curriculum
Common Core State Standards 6.NS.B.3: “Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.”
Common Core State Standards 6.NS.B.2: “Fluently divide multi-digit numbers using the standard algorithm.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.