Counting in Multiples of 6, 7, 9, 25, 1000Activities & Teaching Strategies
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.
Learning Objectives
- 1Calculate the next three numbers when counting forwards in multiples of 6, 7, 9, 25, or 1000 from a given starting number.
- 2Analyze the digit sum pattern for multiples of 9 up to 100.
- 3Predict the next three numbers when counting backwards in multiples of 25 from a given three-digit number.
- 4Compare and contrast the characteristics of sequences generated by counting in multiples of 6 versus multiples of 7.
- 5Identify the repeating pattern of the last two digits when counting in multiples of 25.
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Outdoor: 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.
Prepare & details
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.
Setup: Charts posted on walls with space for groups to stand
Materials: Large chart paper (one per prompt), Markers (different color per group), Timer
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.
Prepare & details
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.
Setup: Charts posted on walls with space for groups to stand
Materials: Large chart paper (one per prompt), Markers (different color per group), Timer
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.
Prepare & details
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.
Setup: Charts posted on walls with space for groups to stand
Materials: Large chart paper (one per prompt), Markers (different color per group), Timer
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.
Prepare & details
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.
Setup: Charts posted on walls with space for groups to stand
Materials: Large chart paper (one per prompt), Markers (different color per group), Timer
Teaching This Topic
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.
What to Expect
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.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring 9s Digit Sum Hunt, watch for students who assume all multiples of 9 have a single-digit sum of exactly 9.
What to Teach Instead
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.
Common MisconceptionDuring Outdoor Multiples Hopscotch, watch for students who skip or repeat numbers when counting backwards in 25s.
What to Teach Instead
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.
Common MisconceptionDuring Pattern Prediction Race, watch for pairs who confuse multiples of 6 and 7 due to overlapping results.
What to Teach Instead
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.
Assessment Ideas
After Outdoor Multiples Hopscotch, write the number 450 on the board. Ask students to write the next three numbers when counting forwards in 25s and the next three when counting backwards. Collect answers and review aloud to correct errors in real time.
During Whole Class 1000s Power Chain, present two sequences: 9, 18, 27, 36 and 7, 14, 21, 28. Ask students to explain the rule for each and identify which sequence’s numbers always have digits adding to 9. Listen for explanations that mention digit sums or even/odd patterns.
After Small Groups 9s Digit Sum Hunt, give each student a card starting at 1000 and counting in 7s. Ask them to write the next two numbers and, on the back, note one pattern they observed while counting.
Extensions & Scaffolding
- Challenge: Give students a blank 12x12 grid and ask them to highlight all multiples of 6 and 7. Then have them color the overlap and write a rule for the combined pattern.
- Scaffolding: Provide a partially filled 100 chart for multiples of 9 with every third multiple missing; students fill gaps and check digit sums.
- Deeper exploration: Ask students to research how multiples of 25 appear in real-world contexts like money (quarters) or time (25-minute intervals) and present one example with a poster.
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. |
Suggested Methodologies
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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