Mathematics · Year 1

Active learning ideas

Partitioning Numbers to 100

Active learning builds concrete understanding of abstract place value concepts. When Year 1 students touch, move, and visualize tens and ones, they connect symbolic numbers to their real quantity. Partitioning becomes meaningful when students physically separate blocks or arrange counters, turning abstract '47' into tangible forty plus seven.

• ACARA Content Descriptions
• AC9M1N02

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

Activity 01

• Placemat Activity
• 30 min · Small Groups

Manipulative Build: Tens and Ones Blocks

Provide base-10 blocks. Students build a two-digit number called by the teacher, like 47, then repartition it into different tens and ones combinations, such as 30 + 17. Record each partition on a chart and discuss why they work. Share one favourite with the class.

Analyze how partitioning a number helps us understand its value.

Facilitation Tip

During Manipulative Build, circulate and ask students to verbalize how four tens rods equal forty before adding seven ones to make forty-seven.

What to look for

Present students with a two-digit number, such as 52. Ask them to write down two different ways to partition this number using tens and ones. For example, 50 + 2 or 40 + 12.

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

Activity 02

• Placemat Activity
• 25 min · Pairs

Tens Frame Partition: Visual Decompose

Give dry-erase tens frames and counters. Students represent a number like 63, then repartition by moving counters to show 50 + 13 or 40 + 23. Draw the frames and label equations. Pairs compare and explain their partitions.

Design multiple ways to partition the number 47.

Facilitation Tip

In Tens Frame Partition, model how to slide groups of ten counters to the top frame before counting ones, emphasizing the visual shift from scattered to structured.

What to look for

Give each student a card with a number like 38. Ask them to draw base-ten blocks to represent the number and then write two equations showing different ways to partition it. For instance, 30 + 8 and 20 + 18.

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

Activity 03

• Placemat Activity
• 20 min · Pairs

Roll and Partition Game: Dice Challenge

Pairs roll two dice: one for tens (multiply by 10), one for ones, to make a number like 40 + 5. Repartition three ways and record. Switch roles and check partner's work against place value rules.

Explain the relationship between place value and partitioning numbers.

Facilitation Tip

For Roll and Partition Game, demonstrate rolling the dice and immediately grouping the ones into tens to prevent counting all as separate units.

What to look for

Ask students to explain why partitioning the number 63 into 60 + 3 is helpful for understanding its value. Prompt them to compare this to another partition, like 50 + 13, and discuss which one shows the tens and ones most clearly.

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

Activity 04

• Placemat Activity
• 35 min · Individual

Bundling Sticks: Real-World Partition

Use sticks bundled in tens and loose ones. Students bundle 56 sticks into different partitions, like four bundles and 16 loose. Photograph or draw results, then write number sentences. Whole class votes on most creative partition.

Analyze how partitioning a number helps us understand its value.

Facilitation Tip

Use Bundling Sticks to show how ten single sticks become one bundle, then ask students to recount the total to prove bundling doesn’t change the value.

What to look for

Present students with a two-digit number, such as 52. Ask them to write down two different ways to partition this number using tens and ones. For example, 50 + 2 or 40 + 12.

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

A few notes on teaching this unit

Start with concrete manipulatives before moving to symbols. Research shows that students need 6-8 experiences with base-ten materials before abstract notation makes sense. Avoid rushing to worksheets; let students discover that 47 is always forty-seven, no matter how it’s split. Use partner talk to encourage explanations, as verbalizing reasoning strengthens understanding. Watch for students who count all objects one-by-one rather than grouping tens first, and redirect them to the tens frames or blocks.

Students will confidently break two-digit numbers into tens and ones in multiple ways. They will explain how different partitions represent the same value and use manipulatives to verify their thinking. By the end of the activities, they should see partitioning as a tool for understanding numbers, not just an exercise.

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Watch Out for These Misconceptions

• During Manipulative Build, watch for students who count four tens and seven ones as forty-seven separate units instead of recognizing that four tens equals forty.

  Prompt students to push the four tens rods together and say 'four tens make forty,' then add seven ones. Ask them to recount the total by groups of ten first.

• During Roll and Partition Game, watch for students who believe there is only one correct way to partition a number.

  After their turn, ask, 'Can you show another way to split this number?' Use the dice results to model flexibility, such as 35 as 30 + 5 or 20 + 15.

• During Bundling Sticks, watch for students who think bundling changes the number's value, believing 17 bundled as 10 + 7 is now 'more' than 17 loose sticks.

  Have students recount the total sticks after bundling and ask, 'Is it still 17?' Use the bundling process to emphasize that bundling is just organizing, not altering quantity.

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Methods used in this brief

• Placemat Activity