Mathematics · Year 4 · Place Value and the Power of Ten · Autumn Term

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

Students will practice counting forwards and backwards in multiples, identifying patterns.

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

About This Topic

Year 4 students count forwards and backwards in multiples of 6, 7, 9, 25, and 1000, with emphasis on spotting patterns. Multiples of 9 show a digit sum of 9, such as 18 (1+8=9) or 27 (2+7=9). Multiples of 25 cycle through endings of 00, 25, 50, 75, while 1000s highlight place value shifts. Backwards sequences, like from 300 in 25s (300, 275, 250), build fluency and prediction skills.

This topic anchors the place value and power of ten unit, connecting to number sequences and mental strategies. Students analyse patterns in 9s, predict terms like the next three backwards from 300 in 25s (225, 200, 175), and distinguish 6s (all even) from 7s. These activities develop number sense for later multiplication and division.

Active learning excels with this topic through physical and collaborative tasks. Students jump multiples on playground grids or chain-count in teams, making patterns kinesthetic and social. Such approaches reveal misconceptions quickly via peer explanations and cement sequences through repetition and joy.

Key Questions

1. Analyze the patterns that emerge when counting in multiples of 9.
2. Predict the next three numbers in a sequence counting backwards in 25s from 300.
3. Differentiate between counting in multiples of 6 and counting in multiples of 7.

Learning Objectives

• Calculate the next three numbers when counting forwards in multiples of 6, 7, 9, 25, or 1000 from a given starting number.
• Analyze the digit sum pattern for multiples of 9 up to 100.
• Predict the next three numbers when counting backwards in multiples of 25 from a given three-digit number.
• Compare and contrast the characteristics of sequences generated by counting in multiples of 6 versus multiples of 7.
• Identify the repeating pattern of the last two digits when counting in multiples of 25.

Before You Start

Counting Forwards and Backwards in Steps

Why: Students need to be able to count on and back in consistent steps (like 1s, 2s, 5s, 10s) before tackling larger or less common multiples.

Introduction to Multiples

Why: Understanding what a multiple is, and having some familiarity with basic multiplication facts, is essential for this topic.

Key Vocabulary

multiple	A number that can be divided by another number without a remainder. For example, 18 is a multiple of 6 because 18 divided by 6 is 3.
sequence	A set of numbers that follow a specific rule or pattern. Counting in multiples creates a number sequence.
digit sum	The sum of the individual digits of a number. For example, the digit sum of 27 is 2 + 7 = 9.
place value	The value of a digit based on its position within a number, such as ones, tens, hundreds, or thousands.

Watch Out for These Misconceptions

Common Misconception

Multiples of 9 do not always sum to 9 in digits.

What to Teach Instead

Show examples like 36 (3+6=9) and 45 (4+5=9); students test with calculators then discuss. Group sorting cards reveals the rule consistently, building confidence through hands-on verification.

Common Misconception

Backwards counting in 25s skips numbers irregularly from 300.

What to Teach Instead

Model on number lines: 300, 275, 250. Relay games where teams call aloud correct errors in real time. Physical subtraction with base-10 blocks clarifies borrowing across places.

Common Misconception

Multiples of 6 and 7 overlap frequently.

What to Teach Instead

List both on Venn diagrams; pairs highlight unique traits like 6s even, 7s odd pattern. Collaborative hunts on hundred charts spot differences quickly through shared pointing and talk.

Active Learning Ideas

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.

30 min·Pairs

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.

25 min·Small Groups

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.

20 min·Whole Class

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.

15 min·Pairs

Real-World Connections

• Supermarket pricing often uses multiples. For instance, a 'buy 3 for £6' deal means each item costs £2, a multiple of 2. Calculating the total cost for multiple packs involves counting in multiples.
• Event ticketing or seating arrangements might use multiples. A concert hall might have 25 seats per row, so knowing the total number of seats in 10 rows requires counting in multiples of 25.

Assessment Ideas

Quick Check

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.

Discussion Prompt

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?'

Exit Ticket

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.

Frequently Asked Questions

year 4 patterns in multiples of 9

Focus on digit sum rule: digits always add to 9 or a multiple of 9. Start with concrete examples like counting beads in groups of 9, then abstract to numbers. Use hundred squares shaded for 9s to visualise repeats every 10. Practice forwards and backwards to reinforce, linking to divisibility tests for efficiency.

counting backwards in 25s from 300 year 4

Sequence is 300, 275, 250, 225, 200. Teach by partitioning 25 as 20+5 for mental subtraction. Number lines or abacuses help visualise jumps. Games like relays build speed; predict next three to check understanding of place value changes.

active learning activities for year 4 multiples counting

Kinesthetic tasks like hopscotch for 6s/7s or human number lines for 1000s make sequences physical. Small group card sorts for 9s patterns spark discussion. Relays for backwards 25s add competition. These methods engage movement and talk, helping students internalise patterns faster than worksheets alone.

differentiate multiples of 6 and 7 year 4

6s are even and link to 2s/3s tables; 7s follow no simple parity. Use overlapping lists: 6,7,12,14,18,21. Colour-code on grids to compare gaps. Pairs quiz each other on next terms, reinforcing distinctions through active recall and explanation.