Mathematics · Year 4

Active learning ideas

Counting in Multiples of 6, 7, 9, 25, 1000

Active learning transforms abstract counting into tangible movement and discussion, helping students internalize patterns they might otherwise miss when working only on paper. For multiples like 9 and 25, physical and visual experiences make invisible rules—like digit sums or place-value shifts—visible and memorable.

• National Curriculum Attainment Targets
• NC.MA.4.N.4

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

Activity 01

• Outdoor Investigation Session
• 30 min · Pairs

Outdoor Investigation Session: Multiples Hopscotch

Draw chalk grids on the playground with starting numbers for multiples of 6 or 7. Students hop forward or backward, calling the next multiple aloud. Pairs compete to complete sequences first, then switch to 25s from a high number like 300.

Analyze the patterns that emerge when counting in multiples of 9.

Facilitation Tip

During Multiples Hopscotch, position larger multiples like 25 or 1000 closer together to highlight step size differences.

What to look for

Write the number 450 on the board. Ask students to write down the next three numbers if counting forwards in multiples of 25. Then, ask them to write the next three numbers if counting backwards in multiples of 25 from 450.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 02

• Carousel Brainstorm
• 25 min · Small Groups

Small Groups: 9s Digit Sum Hunt

Provide cards with numbers; groups sort multiples of 9 and check digit sums. Discuss patterns like why 81 (8+1=9) fits. Extend to backwards counting from 99, predicting and verifying.

Predict the next three numbers in a sequence counting backwards in 25s from 300.

Facilitation Tip

In the 9s Digit Sum Hunt, provide digital calculators so students can test sums immediately and avoid miscounting digits.

What to look for

Present two sequences: 9, 18, 27, 36 and 7, 14, 21, 28. Ask students: 'What is the rule for each sequence? How are the patterns different? Which sequence has numbers whose digits always add up to 9?'

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 03

• Carousel Brainstorm
• 20 min · Whole Class

Whole Class: 1000s Power Chain

Students stand in a circle and count forwards in 1000s from 2000, passing a beanbag. Reverse direction for backwards. Pause to predict next terms and link to place value charts on the board.

Differentiate between counting in multiples of 6 and counting in multiples of 7.

Facilitation Tip

For the 1000s Power Chain, use place-value counters to physically model the shift from thousands to hundreds when subtracting 1000.

What to look for

Give each student a card with a starting number and a multiple (e.g., Start at 1000, count in 7s). Ask them to write the next two numbers in the sequence. On the back, ask them to write one thing they noticed about counting in that specific multiple.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 04

• Carousel Brainstorm
• 15 min · Pairs

Pairs: Pattern Prediction Race

Pairs race to extend sequences like backwards 25s from 300 or forwards 9s from 72. Use mini whiteboards to show work. Share and justify predictions with the class.

Analyze the patterns that emerge when counting in multiples of 9.

Facilitation Tip

During Pattern Prediction Race, require pairs to justify each prediction aloud before moving on to slow impulsive guessing.

What to look for

Write the number 450 on the board. Ask students to write down the next three numbers if counting forwards in multiples of 25. Then, ask them to write the next three numbers if counting backwards in multiples of 25 from 450.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with the familiar—like counting in 10s or 5s—before introducing less intuitive multiples such as 7 or 9. Use choral counting and echo counting to build rhythm and reduce cognitive load for struggling learners. Avoid rushing through patterns; give students time to verbalize what they notice, even if their language is rough at first. Research shows that articulating patterns aloud strengthens internalization more than silent repetition.

Students will confidently count forwards and backwards in multiples, recognize repeating patterns, and explain their thinking using precise language. They will use tools like number lines, Venn diagrams, and digit-sum checks to support their reasoning.

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Watch Out for These Misconceptions

• During 9s Digit Sum Hunt, watch for students who assume all multiples of 9 have a single-digit sum of exactly 9.

  Prompt students to test numbers like 36 and 45 with calculators, then sort digit-sum cards into ‘sums to 9’ and ‘other’ groups. When inconsistencies appear, have them revisit their sums and correct errors together.

• During Outdoor Multiples Hopscotch, watch for students who skip or repeat numbers when counting backwards in 25s.

  Have students trace their steps on a number line drawn on the ground while calling out each number aloud. If a student hesitates, pause the game and re-model the sequence with base-10 blocks to show the borrowing step.

• During Pattern Prediction Race, watch for pairs who confuse multiples of 6 and 7 due to overlapping results.

  Provide Venn diagram sheets and colored pens. Ask pairs to list traits of each multiple first (6 is even, 7 alternates odd and even), then place numbers in the correct sections, discussing overlaps only after clear distinctions are made.

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Methods used in this brief

• Outdoor Investigation Session
• Carousel Brainstorm