Decimals and percentages – Grade 5 math lesson
Lesson 7 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: “Which is bigger, 0.6 or 55%? How do you know?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Thinking 0.125 is bigger than 0.5 because it has more digits. Line up the decimal points and compare the tenths first.
- Writing 5% as 0.5. Per cent is out of 100: 5% is 5 hundredths, 0.05.
Tip for home: Spot percentages in shops and on food labels, and say them as decimals.
What your child will learn
Learning goal: use thousandths, convert decimals to fractions and understand per cent.
Success looks like
- I can read and write thousandths.
- I can change between decimals, fractions and percentages.
- I can solve simple percentage problems.
Key words
- thousandth
- one of 1,000 equal parts
- percent
- out of 100 (%)
- decimal
- a number with a decimal point
- simplify
- write a fraction with smaller numbers
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Make a fraction, decimal and percentage matching game with cards such as 1/2, 0.5 and 50%.
The big ideas (for the adult)
Thousandths are one more place after the point: 0.007 is 7 thousandths.
Per cent means "out of 100", so 35% is 35 hundredths, or 0.35.
To change a decimal to a fraction, read its place value: 0.4 is 4 tenths, which simplifies to 2 fifths.
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
- Calculating with decimals
- 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.5.a: “Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.”
Common Core State Standards 5.NF.B.5.b: “Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.