Mathematics · Grade 2

Active learning ideas

Representing Numbers in Different Ways

Active learning works well for this topic because students need to physically manipulate quantities to understand how digits represent different place values. Representing numbers in standard, expanded, and word forms becomes clearer when students build, match, and discuss numbers with their hands and voices. These kinesthetic and social activities make abstract concepts concrete and memorable for second graders.

• Ontario Curriculum Expectations
• 2.NBT.A.3

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Base-10 Build: Triple Forms

Draw a number card up to 200. Use base-10 blocks to model hundreds, tens, and ones. Record the number in standard, expanded, and word forms on a sheet, then explain to a partner.

What does the number 135 look like in expanded form?

Facilitation Tip

During Base-10 Build, model how to align blocks precisely so students see that ten ones make one ten and ten tens make one hundred.

What to look for

Present students with a number in standard form, for example, 163. Ask them to write it in expanded form and word form on a whiteboard or paper. Observe their ability to correctly represent the value of each digit.

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

Activity 02

• Think-Pair-Share
• 30 min · Small Groups

Matching Cards: Number Sets

Prepare cards showing numbers up to 200 in standard, expanded, and word forms. Students in small groups match three cards representing the same number. Discuss matches and sort into categories.

How do you write the number 148 in words?

Facilitation Tip

For Matching Cards, circulate and listen for students reading numbers aloud to catch word form errors like ‘one four eight’ before they become habits.

What to look for

Give each student a card with a number in either word form or expanded form (e.g., 'one hundred forty-two' or '100 + 40 + 2'). Ask them to write the number in the other two forms (standard and the remaining one). Collect these to gauge individual understanding.

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

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Dice Roll: Form Challenge

Roll three dice for hundreds, tens, ones (hundreds max 2). Write the number in all three forms. Pairs compare rolls and check each other's work using place value charts.

Can you show the same number up to 200 in three different ways?

Facilitation Tip

When running Dice Roll, remind students to record all three forms immediately after rolling to avoid skipping steps due to excitement.

What to look for

Pose the question: 'If you have the number 185, how can you show it in three different ways? Explain why each way represents the same amount.' Listen for students' explanations connecting digits to their values across the different forms.

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

Activity 04

• Think-Pair-Share
• 35 min · Small Groups

Class Number Hunt: Representations

Post numbers around room up to 200. Whole class hunts in teams, records each in three forms on clipboards. Share findings on a group chart.

What does the number 135 look like in expanded form?

Facilitation Tip

In Class Number Hunt, pair students with mixed abilities so they can discuss and correct each other’s representations on the spot.

What to look for

Present students with a number in standard form, for example, 163. Ask them to write it in expanded form and word form on a whiteboard or paper. Observe their ability to correctly represent the value of each digit.

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

A few notes on teaching this unit

Teachers approach this topic by starting with concrete manipulatives before moving to abstract symbols. Research suggests students need repeated practice building and breaking apart numbers, not just filling out worksheets. Avoid rushing to symbols—let students verbalize the value of each digit in multiple forms. Use peer teaching because explaining to others strengthens individual understanding. Avoid worksheets that only require circling answers; require students to construct representations and explain their thinking aloud.

Successful learning looks like students confidently switching between number forms without hesitation, explaining why 157 is the same as 100 + 50 + 7 or one hundred fifty-seven. Students should also justify their answers by pointing to the hundreds, tens, and ones in their representations. Clear connections between forms show deep understanding of place value.

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Watch Out for These Misconceptions

• During Base-10 Build, watch for students writing 1 + 3 + 5 for 135.

  Stop students immediately and ask them to build 135 with blocks. Guide them to bundle ones into tens and tens into hundreds, then write each group’s value: 100, 30, and 5. Have them read their expanded form aloud while pointing to each bundle.

• During Matching Cards, listen for students saying ‘one four eight’ for 148.

  Pull out a number chart and have the student find 148. Point to each digit while saying its place value: ‘one hundred, four tens, eight ones.’ Then have the student read it together aloud three times before matching cards. Ask another student to model correct pronunciation.

• During Dice Roll, observe students ignoring the zero in numbers like 105.

  Prompt students to build 105 with blocks and ask why there are no ten sticks. Have them write 100 + 0 + 5 in expanded form and say, ‘The zero means no tens, but it holds the tens place.’ Repeat this for 203 to reinforce the pattern.

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Methods used in this brief

• Think-Pair-Share