Mathematics · Year 1

Active learning ideas

Counting to 20: Forward and Backward

Active learning builds deep understanding of counting by engaging students in hands-on, pattern-seeking tasks. This topic requires students to move beyond rote memorization and see the predictable structure behind our number system, which only happens when they interact with materials in meaningful ways.

• ACARA Content Descriptions
• AC9M1N01

• 15–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Pattern Detectives

Set up three stations where students find patterns: one with a 100s chart and transparent counters, one with physical base-ten blocks, and one with a digital number line. Students move in small groups to identify what happens to the 'ones' column as they move down the chart.

Explain the pattern when counting forwards from 1 to 20.

Facilitation Tip

During Pattern Detectives, circulate and ask students to verbalize the pattern they see, such as 'The ones digit is always the same in this row.'

What to look for

Show students a number line from 1 to 20. Ask: 'What number comes next?' after pointing to a number. Then ask: 'What number comes before?' after pointing to another number. Record correct responses.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Mystery of Zero

Show students a sequence of numbers with a missing zero and ask what would happen if zero disappeared from our world. Students discuss in pairs how we would write '10' or '100' without it, then share their theories with the class.

Differentiate the process of counting backwards from 20 to 1.

Facilitation Tip

During The Mystery of Zero, pause pairs to ask, 'Why does zero feel different when counting backward from 10?'

What to look for

Give each student a card with a number between 5 and 15. Ask them to write the number that comes directly after it and the number that comes directly before it on the back of the card.

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

Activity 03

• Inquiry Circle
• 30 min · Whole Class

Inquiry Circle: Giant Number Line

Clear a space and have students work together to place number cards from 0 to 100 in the correct order across the room. They must justify where a number like 45 goes by looking at the numbers already placed (44 and 46).

Analyze the importance of knowing number order for everyday tasks.

Facilitation Tip

During Giant Number Line, have students physically step forward and backward to reinforce the direction of counting.

What to look for

Ask students: 'Imagine you are counting the cars in a parking lot. Would you count forwards or backwards? Why?' Then ask: 'If you were counting down the minutes until recess, would you count forwards or backwards? Explain your choice.'

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

A few notes on teaching this unit

Focus on the transition points at 10 and 20, using visual and physical models to build number sense. Avoid teaching counting as isolated facts; instead, emphasize the predictable pattern in the ones digit. Research shows that students who understand these transitions develop stronger mental computation skills and fewer errors in later grades.

Students will confidently count forward and backward within 20, explain the repeating pattern in the ones place, and correctly identify numbers before and after any given number up to 20. They will also verbalize why the pattern continues beyond 10 or 100.

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Watch Out for These Misconceptions

• During Pattern Detectives, watch for students who stop counting after reaching 10 or 100, treating these as final numbers rather than transition points.

  Have students use the 100s chart to trace the pattern from 10 to 11, then from 20 to 21, asking them to identify the repeating ones digit and explain why the pattern continues.

• During Collaborative Investigation, watch for students who confuse 'teen' numbers like 13 and 31, reversing the tens and ones digits.

  Ask students to physically build each number using bundles of ten sticks and loose ones, then compare the two numbers side by side to feel the difference between one ten and three ones versus three tens and one one.

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Methods used in this brief

• Stations Rotation
• Think-Pair-Share
• Inquiry Circle