Decimals and Place Value

Overview

This 60-minute lesson is designed for Year 6 pupils, focusing on multiplying and dividing decimals by 10, 100, and 1,000. It is aligned with the National Curriculum for England, specifically targeting the Mathematics Programme of Study for Number – Decimals (Year 6). The lesson utilises small-group activities to encourage active participation, deepen conceptual understanding, and build fluency.

National Curriculum Reference

Key Stage 2 Mathematics: Number - Decimals (Year 6)
Pupils should be taught to:

Multiply and divide numbers by 10, 100, and 1,000 giving answers up to three decimal places (DfE, 2014).

Learning Focus:

Understanding the effect of multiplying and dividing decimals by powers of 10 on place value.
Recognising the pattern of digits shifting left or right according to the power of 10.
Using visual and practical methods to reinforce understanding.

Learning Objectives

By the end of this lesson, pupils will be able to:

Multiply decimals by 10, 100, and 1,000 and understand how digits shift to the left accordingly.
Divide decimals by 10, 100, and 1,000 and understand how digits shift to the right accordingly.
Accurately calculate answers up to three decimal places.
Demonstrate understanding through practical, visual, and discussion activities.
Apply knowledge to real-life contexts, articulating reasoning clearly within small groups.

Resources Needed

Place value charts (large and individual) with decimal points
Whiteboards and markers
Number cards/decimal digit cards (digit 0-9)
Strips with the numbers 10, 100, 1,000 displayed for prompts
Pre-prepared worksheets with decimal problems
Mini whiteboards for group work
Base 10 decimal blocks or place value discs (optional for tactile support)
Stopwatch/timer for task management

Lesson Structure & Activities

Time (mins)	Activity	Purpose & Outcomes	Grouping
0–10	Introduction & Recap	Teacher-led recap of place value and decimals, illustrating how multiplying/dividing by 10, 100, 1,000 affects place value using charts and number lines.	Whole class
10–55	Five Small Group Activities	Small groups (4 pupils) rotate through each activity (10 min each). Teacher facilitates & supports understanding.	5 groups of 4 pupils each

Detailed Small Group Activities

Activity 1: Place Value Shift Sorting

Objective: Visualise how digits shift when decimals are multiplied or divided by 10, 100, 1,000.
Description:

Pupils are given a set of decimal numbers on cards (e.g., 3.46, 0.732).
Using place value charts, they will physically move digit cards left for multiplication and right for division by 10, 100, 1,000.
They record the new numbers and explain the shift pattern.
Assessment: Teacher questions groups on why and how digits move.

Activity 2: Decimal Multiplication/Division Relay

Objective: Improve fluency and speed of multiplying/dividing decimals by powers of 10.
Description:

Each group is given mini whiteboards.
Pupils take turns answering a multiplication or division problem by 10, 100, or 1,000 within a time limit (1 min per pupil).
Examples: 0.56 × 100; 7.025 ÷ 10.
Points are awarded for accuracy and speed.
Assessment: Monitor accuracy, give immediate feedback.

Activity 3: Interactive Number Line Estimation

Objective: Develop estimation skills and reinforce decimal scaling on a number line.
Description:

Pupils use a large classroom number line marked with decimals.
They estimate the result of multiplying/dividing decimals by 10, 100, 1,000 by “hopping” along the line physically or pointing to positions.
They record their estimated answers and then calculate the exact answer, comparing the two.
Assessment: Discuss differences between estimate and exact answer.

Activity 4: Real-Life Decimal Context Problem Solving

Objective: Apply multiplying/dividing decimals by powers of 10 in everyday contexts.
Description:

Pupils are presented with scenarios (e.g., converting currency units, measuring small lengths, or weights). Example: A rope is 0.75 metres long. What is its length if the measurement is in centimetres? (Multiply by 100)
Pupils discuss and solve the problems in the group, writing explanations for their answers.
Assessment: Review written explanations and solutions for concept application.

Activity 5: Decimal Puzzle Creation & Peer Teaching

Objective: Consolidate understanding by creating puzzles and teaching concepts.
Description:

Each group designs a short puzzle or riddle involving multiplying or dividing decimals by 10, 100 or 1,000. For example, “I am a decimal number. When I am divided by 100, the answer is 0.072. What number am I?”
Groups exchange puzzles with another group to solve and give feedback.
Assessment: Listen to group discussions and check puzzle solutions for conceptual correctness.

Plenary (5 mins)

Groups share one interesting fact or observation they found about multiplying/dividing decimals by powers of 10.
Teacher revisits the learning objectives and checks for understanding through targeted questioning.
Highlight common misconceptions observed and clarify.

Assessment & Differentiation

Formative assessment: Ongoing questioning and observation during activities.
Differentiation:
- Support pupils struggling with place value using manipulatives (like base 10 blocks).
- Challenge more able pupils with decimals involving more complex numbers and up to three decimal places.
Use mini-whiteboards for quick diagnostic checks after each activity.

Homework Extension (Optional)

Create 5 decimal problems involving multiplication or division by 10, 100, and 1,000 and explain the changes in place value.

Additional Notes

Encourage mathematical vocabulary use: decimal point, place value, multiply, divide, shift, powers of 10.
Promote collaboration and communication within groups to deepen conceptual understanding.
Move around groups, posing probing questions to challenge thinking and scaffold where necessary.

This lesson plan aligns precisely with the England National Curriculum Year 6 Number requirements, offering hands-on, varied, and ambitious activities to inspire both pupils and teachers.

Teaching Instructions