Mathematics · 3rd Grade

Active learning ideas

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.

• Common Core State Standards
• CCSS.Math.Content.3.NBT.A.3

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• 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.

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.

What to look for

Provide students with the problem 5 x 30. Ask them to solve it and then write one sentence explaining how they used a basic fact (like 5 x 3) and place value to find the answer.

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

Activity 02

• 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.

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?'

What to look for

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

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

Activity 03

• 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.

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.

What to look for

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.'

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

• 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).

  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.

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Methods used in this brief

• Simulation Game
• Inquiry Circle
• Think-Pair-Share