Multiplying by 10 and 100

Active learning helps Year 3 students grasp multiplying by 10 and 100 because it turns abstract place-value shifts into visible, tactile experiences. When students move base-10 blocks or jump along number lines, they see digits slide left and zeros appear, building lasting mental models instead of memorizing rules.

• Year 3
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

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

Think-Pair-Share

⏱ 35 min·Pairs

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.

Prepare & details

Explain what happens to the digits of a number when it is multiplied by 10.

Facilitation Tip: During Base-10 Shifts, have students record each digit’s movement on a place-value chart before moving the blocks to connect the physical action to the written change.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Think-Pair-Share

⏱ 25 min·Small Groups

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.

Prepare & details

Compare multiplying by 10 to multiplying by 100.

Facilitation Tip: For Scaling Shop, model how to round prices to the nearest ten or hundred before multiplying so students focus on the scaling rather than complex calculations.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Think-Pair-Share

⏱ 40 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.

Prepare & details

Predict the product of any number multiplied by 100.

Facilitation Tip: In Prediction Relay, require students to write their predicted product and digit shifts before the next team checks their work, reinforcing accountability and reflection.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Think-Pair-Share

⏱ 20 min·Whole Class

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.

Prepare & details

Explain what happens to the digits of a number when it is multiplied by 10.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Experienced teachers begin with concrete manipulatives like base-10 blocks to show the physical shift, then transition to semi-concrete number lines and grid paper to bridge to abstract symbols. Avoid rushing to the rule; instead, ask students to verbalize what they see happening to the digits. Research shows that movement-based activities, like number line jumps, strengthen spatial understanding of multiplication as scaling, which supports later work with decimals and percentages.

What to Expect

Students will confidently explain how multiplying by 10 or 100 shifts digits left and adds zeros, and they will compare the two operations with clear reasoning. They will use manipulatives and number lines to justify their answers and correct peers’ misconceptions during group work.

Watch Out for These Misconceptions

Common Misconception

During Base-10 Shifts, watch for students who add zeros without shifting digits or who keep digits in the same columns.

What to Teach Instead

Have students place a single counter on their place-value chart, multiply by 10, and move the counter as a group while tracing its path with an arrow. Ask them to record the new position and explain why the digit moved left before adding zeros.

Common Misconception

During Number Line Jumps, watch for students who think multiplying by 100 is the same as multiplying by 10 twice.

What to Teach Instead

Ask students to draw two separate jumps on the same number line: one labeled “x 10” that moves one place, and one labeled “x 100” that moves two places. Discuss the difference in distance and ask them to write a sentence comparing the two jumps.

Common Misconception

During Scaling Shop, watch for students who believe multiplying 25 by 10 drops the 5 because the answer ends in zero.

What to Teach Instead

Give pairs a set of 10p coins and ask them to build 25 x 10 by arranging the coins into stacks of ten. Have them count aloud to confirm that all digits remain and the total value matches, not just the final zero.

Assessment Ideas

Quick Check

After Base-10 Shifts, present students with 34 x 10 and ask them to write the answer, draw an arrow showing where the digit ‘3’ moved, and explain why it moved one place left on a mini whiteboard.

Exit Ticket

After Number Line Jumps, give students 45 x 10 and 45 x 100. Ask them to write the answers and one sentence comparing how the digits shifted in each case, using the language of place-value movement.

Discussion Prompt

During Prediction Relay, 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?’ Listen for mentions of digit shifts and zero placement.

Extensions & Scaffolding

• Challenge students to create three different multiplication problems (e.g., 12 x 10, 12 x 100, 12 x 1000) and compare the patterns in their products.
• Scaffolding: Provide pre-labeled place-value charts and counters so students can focus on the digit movement without constructing the model themselves.
• Deeper exploration: Introduce a real-world scenario where students must decide whether to multiply by 10 or 100 to solve a bulk-buying problem, justifying their choice with calculations and explanations.

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.