Multiplying by Multiples of Ten

Active learning works for multiplying by multiples of ten because it turns an abstract concept into a concrete experience. Students see how place value shifts when they handle physical or visual models, which builds lasting understanding beyond memorized tricks. This hands-on approach reduces errors from rote procedures and builds confidence in mental math.

• 3rd Grade
• Mathematics
• 3 activities
• 15 min–30 min

Learning Objectives

1. Calculate the product of a one-digit whole number and a multiple of 10 using place value strategies.
2. Explain how multiplying by 10, 20, or 30 relates to basic multiplication facts and place value.
3. Justify why understanding the base ten system is crucial for multiplying by multiples of ten.
4. Compare the results of multiplying a one-digit number by a multiple of 10 with multiplying it by the base fact.
5. Demonstrate the associative property of multiplication when solving problems like 3 x 40.

Simulation Game

⏱ 20 min·Whole Class

Simulation Game: The Place Value Shift

Students stand on a large place value mat holding digit cards. When the teacher says 'multiply by 10,' the students must all move one place to the left while a new student fills the ones place with a zero.

Prepare & details

Predict what happens to the value of a digit when it shifts one place to the left.

Facilitation Tip: During the Place Value Shift, have students physically move digit cards to see the shift when multiplying by 10, 20, or 30.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Inquiry Circle

⏱ 30 min·Small Groups

Inquiry Circle: The Tens Factory

Groups are given 'orders' for items in multiples of ten (e.g., 6 boxes of 30 markers). They must use base-ten rods to build the total and then write the corresponding multiplication sentence using basic facts.

Prepare & details

Explain how to use basic facts to solve larger multiplication problems.

Facilitation Tip: In The Tens Factory, circulate and ask guiding questions like, 'How many tens are in 50? How does that help you solve 3 x 50?'

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: Fact Power

Show a basic fact like 5 x 4. Ask students to brainstorm how many related problems they can solve using multiples of ten (5 x 40, 50 x 4, etc.) and explain the pattern they see.

Prepare & details

Justify why it is important to understand the base ten system when multiplying.

Facilitation Tip: For Fact Power, listen closely to pairs’ discussions to identify who is still relying on the 'adding zero' shortcut.

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

Teach this topic by emphasizing the base-ten system over shortcuts. Use place value tools consistently so students see multiplication as repeated grouping of tens. Avoid rushing to the 'add a zero' rule, as it won’t serve students later with decimals or larger numbers. Research shows that visual and hands-on experiences lead to deeper understanding than verbal explanations alone.

What to Expect

Successful learning looks like students explaining place value shifts instead of just adding zeros. They should connect basic facts to larger multiples of ten and justify their reasoning using tools or discussions. By the end of the activities, students should solve problems mentally and explain their process clearly.

Watch Out for These Misconceptions

Common Misconception

During the Place Value Shift, watch for students who mechanically 'add a zero' without understanding the shift in place value.

What to Teach Instead

Ask students to explain why they moved the digit card to the tens place and how that relates to multiplying by ten. Use the slider to show the physical movement of digits.

Common Misconception

During The Tens Factory, watch for students who multiply the tens digit but forget the value of the zero (e.g., 3 x 40 = 12).

What to Teach Instead

Have students use base-ten blocks to build 40 three times. Ask them to count the total and explain why 12 is unreasonable compared to the model.

Assessment Ideas

Exit Ticket

After The Place Value Shift, provide the problem 5 x 30. Ask students to solve it and write one sentence explaining how they used a basic fact (like 5 x 3) and place value to find the answer.

Quick Check

During The Tens Factory, write '7 x 40' on the board. Ask students to show their answer using whiteboards or fingers. Then ask: 'What basic fact did you use? How did you know to add the zero?'

Discussion Prompt

After Fact Power, pose the question: 'Imagine you have 6 groups of 50 stickers. How can you figure out the total number of stickers without counting each one? Explain your strategy using the idea of place value.'

Extensions & Scaffolding

• Challenge: Provide problems like 7 x 400, asking students to explain their strategy using place value language and tools.
• Scaffolding: Give students a place value chart and counters to model 2 x 30 before moving to abstract problems.
• Deeper exploration: Ask students to create their own word problem involving multiples of ten and trade with a partner to solve.

Key Vocabulary

Multiple of Ten	A number that can be divided by 10 with no remainder, such as 10, 20, 30, and so on.
Place Value	The value of a digit based on its position within a number, such as ones, tens, or hundreds.
Base Ten System	Our number system, which uses ten digits (0-9) and is organized by powers of ten.
Associative Property of Multiplication	The property that states that the way factors are grouped in a multiplication problem does not change the product, for example, (a x b) x c = a x (b x c).