Calculating with decimals – Grade 5 math lesson
Lesson 8 of 18 in the Grade 5 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 5 (ages 10–11) 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 5 (ages 10–11)
- 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: “How does an estimate help you put the decimal point in the right place?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Putting the point in the wrong place (0.3 × 4 = 12). Estimate first: 0.3 × 4 is about 1, so 12 cannot be right.
- Dividing 3 by 4 and getting 1.3. Write 3 as 3.00 and divide place by place.
Tip for home: Share a bill or a length of ribbon equally and work out each part together.
What your child will learn
Learning goal: multiply and divide decimals and change fractions to decimals.
Success looks like
- I can multiply decimals by whole numbers.
- I can divide decimals by whole numbers.
- I can change fractions to decimals.
Key words
- decimal place
- a place after the decimal point
- divide
- share into equal parts
- estimate
- a quick, sensible answer
- equivalent
- worth the same
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use money or a meter stick to act out decimal sums, such as sharing 2.40 between 4.
The big ideas (for the adult)
To multiply a decimal by a whole number, multiply as if there were no point, then put the point back: 0.3 × 4 is 3 × 4 = 12 tenths = 1.2.
To divide a decimal by a whole number, divide each place in turn and keep the point lined up.
A fraction is a division: 3/4 means 3 ÷ 4 = 0.75.
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 5 math lessons
- Order of operations
- Solving word problems
- Number patterns
- Place value: the value of each digit
- Decimals: tenths, hundredths and thousandths
- Multiplying and dividing by powers of 10
- Decimals and percentages
- Comparing, ordering and writing numbers
- Rounding decimals
- Adding and subtracting decimals
- Fractions of a whole number
- Adding and subtracting fractions with unlike denominators
- Multiplying fractions
- Converting measurement units
- Volume of rectangular prisms
- Classifying 2-D shapes
- Coordinates
Curriculum
Common Core State Standards 5.NF.B.3: “Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.