Mathematics · Foundation

Active learning ideas

Counting On and Counting Back

Active counting strategies build strong early number sense because they shift students from rote recitation to purposeful movement along the number sequence. When children physically move forward or backward while saying each number, they connect quantity changes to spoken words, which strengthens their understanding of addition and subtraction as actions rather than abstract rules.

• ACARA Content Descriptions
• AC9M7N01

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

Activity 01

• Plan-Do-Review
• 25 min · Pairs

Pair Game: Dice Count On

Partners roll a die, start at a number card (e.g., 3), and count on by touching fingers or counters while saying numbers aloud. Switch roles after each turn, recording final numbers on a chart. Discuss who reached the highest.

If we start at 4 and count on two more, what number do we reach?

Facilitation Tip

During Dice Count On, pair students and have them take turns rolling a dot die and a numeral die to model counting on from the numeral die value.

What to look for

Present students with a number line from 0 to 10. Ask them to place a counter on the number 5. Then, instruct them to 'count on 3' and record the final number. Repeat with 'count back 2' from 8.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 30 min · Whole Class

Whole Class: Number Line March

Lay a giant number line on the floor. Call instructions like 'start at 5, count on 3' and have students march while chanting. Pause for thumbs up if correct, then try counting back from 8 by 2.

Can you count backwards from 10 to 1 using these number cards?

Facilitation Tip

For Number Line March, arrange students in a line and have them step or jump forward or backward while saying each number aloud to reinforce the movement of counting.

What to look for

Give each student a card with a simple addition or subtraction problem, like 'Start at 7, count on 2' or 'Start at 9, count back 3'. Ask them to write the answer and draw a picture showing the objects they counted.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 20 min · Small Groups

Small Group: Block Subtract

Groups get 10 blocks. One student builds a tower (e.g., 7 high), others count back as blocks are removed one by one, using a ten-frame mat. Rotate builder roles and compare results.

If I take away one block from this group of six, how many are left?

Facilitation Tip

In Block Subtract, provide each group with interlocking blocks so they can physically remove pieces and recount the remaining total.

What to look for

Ask students: 'Imagine you have 6 blocks and you give 2 blocks to a friend. How can you use counting back to find out how many blocks you have left? Explain your steps.'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 15 min · Individual

Individual: Finger Counting Cards

Provide cards with start numbers and add/subtract prompts. Students use fingers to count on or back, then circle the answer from three choices. Share one with a partner for verification.

If we start at 4 and count on two more, what number do we reach?

Facilitation Tip

When using Finger Counting Cards, ensure students touch each dot or numeral on the card as they say the counting sequence to connect visual and kinesthetic cues.

What to look for

Present students with a number line from 0 to 10. Ask them to place a counter on the number 5. Then, instruct them to 'count on 3' and record the final number. Repeat with 'count back 2' from 8.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Teachers should model counting on and back using think-alouds to show where to start and how to move. Avoid rushing to abstract symbols—students need repeated concrete experiences with manipulatives and number lines before transitioning to written equations. Research shows that students who practice these strategies with physical movements develop stronger mental number lines and more accurate recall of basic facts.

Successful learning looks like students starting from a given number and continuing their count without restarting, whether moving forward for addition or backward for subtraction. They should use tools like fingers, counters, or number lines to match movements to quantities and confidently explain the changes in amounts.

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Watch Out for These Misconceptions

• During Dice Count On, watch for students who restart their count from one each time they roll the dice rather than using the numeral die as the starting point.

  Remind students to say the numeral on the die first, then count on from that number as they touch each dot on the dot die, using partners to prompt the correct starting point.

• During Block Subtract, watch for students who recount the entire set of blocks after removing some instead of counting backward from the starting number.

  Have students place their blocks in a row and physically remove the specified amount while saying the numbers backward, then recount the remaining blocks to verify their count.

• During Number Line March, watch for students who believe counting back must always start from ten, even when the problem begins with a smaller number.

  Use number lines with varied starting points and have students practice counting back from different numbers to build flexibility in their backward counting paths.

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Methods used in this brief

• Plan-Do-Review