Mathematics · Year 3 · Multiplication, Division, and Scaling · Spring Term

Multiplying by 10 and 100

Students explore the effect of multiplying whole numbers by 10 and 100, understanding place value shifts.

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

About This Topic

Multiplying by 10 and 100 focuses on how place value shifts when whole numbers are scaled. Year 3 students discover that multiplying by 10 moves each digit one place left and adds a zero in the units column. Multiplying by 100 moves digits two places left and adds two zeros. They answer key questions like explaining digit changes, comparing the two multiplications, and predicting products such as 45 x 100 equals 4500.

This topic sits within the KS2 Mathematics standards for multiplication and division, part of the Spring Term unit on Multiplication, Division, and Scaling. It builds fluency with multiples of 10 and 100, links to earlier place value work, and sets up scaling in fractions and measures. Students apply it to contexts like doubling recipes or counting in larger steps, fostering number sense.

Active learning suits this topic perfectly because visual and tactile methods make shifts concrete. Base-10 blocks let students manipulate units into tens and hundreds, while number lines show jumps clearly. Partner games build quick recall through repetition, turning rules into patterns students own.

Key Questions

1. Explain what happens to the digits of a number when it is multiplied by 10.
2. Compare multiplying by 10 to multiplying by 100.
3. Predict the product of any number multiplied by 100.

Learning Objectives

• Calculate the product of any whole number up to 100 when multiplied by 10.
• Calculate the product of any whole number up to 100 when multiplied by 100.
• Explain the effect of multiplying a two-digit number by 10 on the position of its digits.
• Explain the effect of multiplying a two-digit number by 100 on the position of its digits.
• Compare the digit shifts when multiplying by 10 versus multiplying by 100.

Before You Start

Understanding Place Value (Up to Hundreds)

Why: Students need to understand the value of digits in the ones, tens, and hundreds places to grasp how they shift.

Basic Multiplication Facts

Why: Students must be able to perform single-digit multiplication to build upon for multiplying by 10 and 100.

Key Vocabulary

Place Value	The value of a digit based on its position within a number, such as ones, tens, or hundreds.
Multiply by 10	When a whole number is multiplied by 10, each digit shifts one place to the left, and a zero is added in the ones place.
Multiply by 100	When a whole number is multiplied by 100, each digit shifts two places to the left, and two zeros are added in the ones and tens places.
Digit Shift	The movement of a digit to a different place value column (e.g., from ones to tens) when a number is multiplied or divided.

Watch Out for These Misconceptions

Common Misconception

Multiplying by 10 adds one zero but keeps digits in the same columns.

What to Teach Instead

Place value charts with arrows show the leftward shift clearly. Hands-on work with base-10 blocks helps students see units become tens physically, correcting the static view through manipulation and peer explanation.

Common Misconception

Multiplying by 100 is the same as by 10 done twice.

What to Teach Instead

Direct comparison activities reveal the single two-place shift versus two one-place shifts, avoiding double work. Number line jumps demonstrate the larger leap at once, building accurate mental images via movement.

Common Misconception

Numbers ending in zero like 20 x 10 become 200, but 25 x 10 drops the 5.

What to Teach Instead

Emphasize all digits shift fully. Partner prediction games with counters reinforce that no digits vanish, as students build and count the full amount together.

Active Learning Ideas

Manipulatives: Base-10 Shifts

Give pairs base-10 blocks and place value charts. Students build a two-digit number like 23, then multiply by 10 by regrouping 10 units into a ten rod, recording the new number. Repeat for 100, exchanging into flats. Discuss patterns observed.

35 min·Pairs

Number Line Jumps: Scaling Paths

Draw large number lines on the floor with chalk or tape. Students start at a number like 12, jump forward in steps of that number to show x10 (120), then x100 (1200). Pairs take turns leading jumps and predicting landings.

25 min·Small Groups

Scaling Shop: Bulk Buys

Set up a role-play shop with price cards like 5p per item. In small groups, students calculate costs for 10 times or 100 times the quantity, using jottings or counters. Share strategies with the class.

40 min·Small Groups

Prediction Relay: Digit Dash

Divide class into teams. Call a number; first student writes it, passes to next who multiplies by 10, then 100 down the line. Correct predictions score points; review errors together.

20 min·Whole Class

Real-World Connections

• A shopkeeper calculating the total cost of 10 identical items priced at £25 each would multiply 25 by 10 to find the total is £250.
• When planning a school trip for 100 students, if each ticket costs £3, the organiser calculates the total cost by multiplying 3 by 100, resulting in £300.

Assessment Ideas

Quick Check

Present students with a multiplication problem, such as 34 x 10. Ask them to write the answer and then draw an arrow showing where the digit '3' moved and explain why.

Exit Ticket

Give students two problems: 45 x 10 and 45 x 100. Ask them to write the answers and then write one sentence comparing what happened to the digits in each case.

Discussion Prompt

Ask students: 'Imagine you have 7 apples. How many apples would you have if you multiplied that amount by 10? Now, what if you multiplied by 100? How is multiplying by 100 different from multiplying by 10?'

Frequently Asked Questions

What happens to digits when multiplying by 10?

Each digit shifts one place to the left, and a zero appears in the units place. For example, 34 becomes 340. Students use place value grids to track this pattern, connecting it to how tens become hundreds, building confidence in larger numbers.

How do you compare multiplying by 10 and by 100?

Multiplying by 10 shifts digits one place left; by 100 shifts two places. Visual aids like arrowed charts or base-10 models highlight the double shift for 100. Activities encourage students to generate examples and spot the zero count difference.

How can active learning help students master multiplying by 10 and 100?

Active approaches like base-10 manipulatives and floor number lines make abstract shifts tangible. Students physically regroup blocks or jump distances, internalizing patterns through touch and motion. Games add collaboration and speed, ensuring retention beyond rote memorization, with immediate feedback from peers.

What real-life examples illustrate multiplying by 100?

Scaling recipes, like 3 ingredients for 100 people becomes 300, or money packs of 100 pennies making pounds. Shop role-plays let students calculate bulk costs, linking maths to everyday decisions and reinforcing place value in context.