Mathematics · Year 5 · Additive and Multiplicative Structures · Autumn Term

Division by 10, 100, 1000

Students will divide whole numbers and decimals by 10, 100, and 1000.

• National Curriculum Attainment Targets
• KS2: Mathematics - Multiplication and Division

About This Topic

Division by 10, 100, and 1000 requires students to shift digits right on a place value chart, making numbers smaller each time. In Year 5, they start with whole numbers like 450 divided by 10 equals 45, then tackle decimals such as 3.6 divided by 100 equals 0.036. They compare this to multiplication: dividing by 100 reverses multiplying by 100. Students justify the one-place-right shift for each factor of 10 and construct examples showing decimals become smaller, like 2.4 divided by 1000 equals 0.0024.

This topic fits the Autumn term unit on additive and multiplicative structures, reinforcing place value for all decimal operations under KS2 Mathematics standards. It builds reasoning skills as students explain patterns and effects, preparing for more complex calculations and proportional reasoning.

Active learning suits this topic perfectly. Manipulatives like base-10 blocks let students physically regroup and shift values, while real-world tasks with money or measurements make shifts meaningful. Group discussions uncover errors quickly, and games build fluency without rote drill, helping every student grasp the logic deeply.

Key Questions

1. Compare the effect of multiplying by 100 with dividing by 100 on a number.
2. Justify why dividing by 10 moves digits one place to the right.
3. Construct an example where dividing a decimal by 100 results in a smaller decimal.

Learning Objectives

• Calculate the result of dividing whole numbers and decimals by 10, 100, and 1000.
• Explain the pattern of digit movement on a place value chart when dividing by powers of 10.
• Compare the effect of dividing a number by 100 to multiplying it by 100.
• Construct examples demonstrating how dividing decimals by 10, 100, or 1000 changes their value.

Before You Start

Place Value of Whole Numbers

Why: Students need a strong understanding of place value for whole numbers to comprehend how digits shift and change value when divided.

Place Value of Decimals

Why: Understanding the value of digits to the right of the decimal point is essential for accurately dividing decimals by 10, 100, and 1000.

Multiplication by 10, 100, 1000

Why: Familiarity with the inverse operation, multiplication by powers of 10, helps students understand the reciprocal relationship and the direction of digit movement.

Key Vocabulary

Place Value	The value of a digit based on its position within a number, determining its magnitude (e.g., the '5' in 500 is worth 500, while the '5' in 50 is worth 50).
Decimal Point	A symbol used to separate the whole number part of a number from its fractional part. Its position dictates the value of the digits that follow.
Digit Shift	The movement of a digit to a different position on a place value chart, which changes its value. Dividing by 10, 100, or 1000 causes digits to shift to the right.
Powers of 10	Numbers that can be expressed as 10 multiplied by itself a certain number of times (e.g., 10, 100, 1000). Dividing by these numbers follows predictable patterns.

Watch Out for These Misconceptions

Common Misconception

Dividing by 10 moves digits left, like multiplication.

What to Teach Instead

Shifts go right for division, as values decrease. Hands-on place value charts let students model 420 divided by 10 as 42, seeing the pattern visually. Pair talks help them compare and correct their initial ideas.

Common Misconception

Any decimal divided by 100 gives a whole number.

What to Teach Instead

Results stay decimals but smaller, like 5.5 divided by 100 equals 0.055. Manipulative money tasks show this clearly, as groups divide amounts and realise fractions persist. Group verification builds accurate mental models.

Common Misconception

Dividing large numbers by 1000 always rounds up.

What to Teach Instead

Exact shifts preserve value without rounding unless specified. Relay games with base-10 blocks demonstrate precise regrouping, and class discussions reveal why precision matters in real contexts.

Active Learning Ideas

Place Value Shift Relay: Division Dash

Prepare large place value charts. In pairs, one student calls a number and divisor (10, 100, or 1000), the other shifts digits right on the chart. Switch roles after five problems, then pairs justify one shift to the class.

25 min·Pairs

Money Division Stations: Budget Challenges

Set up stations with scenarios like dividing £500 by 100 for per-person shares. Small groups use play money to model divisions, record results, and create their own problems. Rotate stations and share one insight per group.

40 min·Small Groups

Decimal Roll and Divide: Game Boards

Students roll dice for decimals (e.g., 4.2) and divide by 10, 100, or 1000 cards drawn. In pairs, they plot answers on number lines, discuss patterns, and race to fill boards first while checking work.

30 min·Pairs

Whole Class Pattern Hunt: Multiples Match

Project numbers. Whole class chorally divides by 10s, tracking digit shifts on personal whiteboards. Vote on predictions for decimals, then reveal and discuss why shifts work the same way.

20 min·Whole Class

Real-World Connections

• Financial analysts use division by 10, 100, and 1000 when converting large sums of money between currencies or when calculating percentage changes in stock values. For example, converting $5,400 to hundreds of dollars results in $54.
• Engineers and scientists frequently divide measurements by powers of 10. A scientist measuring a substance in millimeters might divide by 1000 to express the quantity in meters, such as converting 0.025 meters to 25 millimeters.

Assessment Ideas

Quick Check

Present students with three problems: 780 ÷ 10, 4.5 ÷ 100, and 12,300 ÷ 1000. Ask them to write the answer and draw an arrow on a place value chart to show the digit movement for each calculation.

Discussion Prompt

Ask students: 'If you divide a number by 100, what happens to the digits? Now, what happens if you multiply the same number by 100? How are these actions related?' Encourage them to use examples to explain their reasoning.

Exit Ticket

Give each student a card with a decimal, for example, 6.7. Ask them to write two division problems using this number: one dividing by 10 and one dividing by 100. They should then write the answers and explain how the decimal point moved in each case.

Frequently Asked Questions

How do I teach Year 5 students to divide decimals by 100?

Start with place value charts: show 4.5 divided by 100 by shifting digits right twice to 0.045. Use money examples, like £4.50 shared among 100 people equals 4.5p each. Practise with worksheets progressing from wholes to decimals, and have students create examples to justify patterns. This builds confidence step by step.

What is the effect of dividing by 100 compared to multiplying by 100?

Dividing by 100 makes a number 100 times smaller, inverse to multiplication which enlarges it 100 times. For instance, 500 times 100 is 50,000; divided by 100 is 5. Students explore this with scales or maps, drawing to compare, which cements the relationship through visual scaling.

How can active learning help students master division by powers of 10?

Active methods like manipulatives and games turn abstract shifts into concrete actions. Base-10 blocks let students physically move units to tenths or hundredths during division. Collaborative relays and stations encourage explanation, spotting errors early. Real-world links, such as resizing recipes by dividing ingredients by 10, make it relevant and memorable, boosting retention over worksheets alone.

Why do digits move right when dividing by 10?

Each division by 10 reduces place value by one position, so 350 divided by 10 becomes 35.0, shifting right. Students justify this with arrow cards or charts showing thousands to hundreds. Group challenges to invent examples reinforce the rule, linking it to the structure of our base-10 system.