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Number Pattern
ELPSA Lesson Plan (Printable)
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Number Pattern — ELPSA Lesson Plan

This lesson uses the Number Pattern tool to help students see collecting like terms as a multiplicative structure rather than a memorised algebra procedure. Students begin with repeated products such as 3 × 7 + 2 × 7 + 5 × 7, notice the common factor, and generalise that it is more efficient to add the number of equal groups first, then multiply by the repeated factor. The reveal feature supports students to visually identify the like groups before moving to symbolic generalisation.

Duration: 50–70 min
Focus: repeated products → collecting like terms
Tools: Teacher Explore, Student Quiz, Worksheet Creator

Learning intention LI

  • Recognise repeated products with a common factor.
  • Interpret collecting like terms as combining the number of equal groups.
  • See collecting like terms as a multiplicative shortcut, not just an additive rule.
  • Generalise from numeric repeated products to algebraic expressions.

Success criteria SC

  • I can explain why 3 × 7 + 2 × 7 + 5 × 7 can be rewritten as 10 × 7.
  • I can identify the repeated factor in an expression.
  • I can describe collecting like terms as combining the number of groups first.
  • I can apply the same structure to algebraic examples such as 3x + 2x + 5x.
Teacher tool shortcuts and flow Keyboard
Enter reveal answer   •   Space new question
Suggested sequence: Number Pattern first for repeated products and structure, then open Collecting Like Terms from the Tools menu as the next visual step toward algebra.

Materials & setup Prep

  • Project the Number Pattern teacher tool.
  • Mini whiteboards, markers and erasers.
  • Optional student devices for the Student Quiz.
  • Optional printed practice from the Worksheet Creator.
Suggested opening examples: 3 × 7 + 2 × 7 + 5 × 7, then change the common factor to 8, 9, 12, etc. Later vary the total number of groups: 5, 11, 14, and so on.

Teacher settings and what they mean Tool guide

Core settings
  • Total — sets the total of the coefficients once collected. For example, if total = 10, the coefficients might be 3, 2 and 5.
  • Number of terms — sets how many separate addends appear before collection, such as 2 terms, 3 terms, 4 terms or 5 terms.
  • Randomise total — changes the total automatically with each new question.
  • Randomise Number of Terms — changes the number of addends automatically with each new question.
Visual and algebra settings
  • Reveal groups — colour-codes the repeated factor so students can visually notice the like groups.
  • Algebraic examples — changes the repeated factor from a number to a variable or variable pair, such as x or ab.
  • This allows the lesson to move from number structure to algebraic structure without changing the core reasoning.
Teaching purpose: these settings help vary the surface features while preserving the same underlying structure — add the coefficients first, then multiply by the common factor.

E Experience — launch with repeated products (10–15 min)

Teacher actions Do
  • Write on the board: 3 × 7 + 2 × 7 + 5 × 7.
  • Ask students to solve it individually on mini whiteboards.
  • Invite multiple methods, including direct calculation and grouping thinking.
  • Change all 7s to 8s, then 9s, then 12s while keeping the coefficients the same.
  • Ask students what stays the same and what changes.
Notice & Wonder prompts Ask
  • “What do you notice about each term?”
  • “What is repeated?”
  • “What changes when I swap 7 for 8?”
  • “Is there a quicker way than doing each multiplication separately?”
  • “Why might this be the same as 10 lots of 7?”
Teacher talk moves Moves
  • Revoice: “So you’re saying there are ten equal groups of 7 altogether?”
  • Press for structure: “Where do you see the 10 in the expression?”
  • Compare methods: “Which method would still work if I changed every 7 to 38?”
  • Generalise early: “What part are we really adding?”
Bridge statement: “Today we are looking for a smarter way to see expressions with the same factor repeated — not as lots of separate calculations, but as a multiplicative pattern.”

L Language — build the vocabulary and meaning (10 min)

Key terms
  • Common factor — the repeated factor that appears in each term.
  • Coefficient — the number of groups of the common factor.
  • Like terms — terms with the same variable part or same repeated factor.
  • Collecting like terms — combining the number of equal groups.
  • Equivalent expression — a different-looking expression with the same value.
Mini-whiteboard language practice
  • “The common factor is ___.”
  • “The coefficients are ___, ___ and ___.”
  • “This expression is really ___ groups of ___.”
  • “A shorter equivalent expression is ___.”
Keep returning to “groups of” language so students hear the multiplicative structure.

P Pictorial — use the Number Pattern tool to expose structure (15–20 min)

Teacher explore sequence
  1. Open the Number Pattern tool.
  2. Set a fixed Total, such as 10.
  3. Use 3 terms, then 4 terms, then 5 terms.
  4. Keep the repeated factor numeric at first.
  5. Turn on Reveal groups so the repeated factor is highlighted in colour.
What students should notice
  • The coloured part stays the same in every term.
  • The coefficients are what combine.
  • The tool is showing repeated equal groups, not unrelated addends.
  • The expression can be compressed into one multiplication statement.
Suggested teacher prompts during pictorial phase
  • “What part is the same each time?”
  • “What part is changing?”
  • “If the total coefficient is 11, what single multiplication could replace the whole expression?”
  • “Why does colouring the repeated factor help?”
  • “How is this more useful than saying ‘you can add apples and apples’?”
The reveal is not just a hint — it is the visual bridge showing that like terms are really equal groups of the same thing.

S Symbolic — generalise the rule (10–20 min)

Teacher-led modelling
  • Start with 3 × 7 + 2 × 7 + 5 × 7.
  • Rewrite as (3 + 2 + 5) × 7.
  • Simplify to 10 × 7.
  • Repeat with another common factor, such as 8 or 38.
  • Ask students to explain why the method still works.
Student symbolic practice
  • Write the collected version of a generated expression.
  • Explain in words what has been added first.
  • State the total number of groups and the common factor.
  • Compare a long method and a collected method.
Transition to algebra
  • Turn on Algebraic examples.
  • Show expressions such as 3x + 2x + 5x or 4ab + 3ab + 2ab.
  • Ask: “What has changed? What has stayed the same?”
  • Emphasise that the same reasoning from the numeric examples still applies.
Generalisation: we are not adding the variables — we are adding the number of equal groups of that variable expression.

Next visual step — move to algebra tool Progression

What to do next
  • While still in the Number Pattern tool, open the Tools menu.
  • Click Collecting Like Terms.
  • Use that tool as the next visual step once students understand the repeated-product structure.
Why this progression matters
  • Number Pattern builds the idea through repeated multiplication.
  • Collecting Like Terms then shifts students into more formal algebraic notation.
  • This helps students see algebra as a continuation of structure, not a separate topic with new arbitrary rules.
Suggested teacher line: “Now that we can see repeated groups in number form, let’s move to Collecting Like Terms and see the exact same idea in algebra.”

A Application — practice and transfer (15–30+ min)

Practice options using your tools
  • Student Quiz for independent practice with the same structure.
  • Worksheet Creator for printed fluency and consolidation.
  • Use level Sweet when students still need the support of revealed groups.
The Sweet level is especially useful because the revealed groups keep the multiplicative structure visible during practice.
Transfer prompts
  • “Which is quicker: 8 × 23 + 3 × 23 or 11 × 23? Why?”
  • “How does this idea help with 6x + 5x + 2x?”
  • “What would the collected form of 4ab + 7ab be?”
  • “Create your own expression with a total coefficient of 14.”
Challenge tasks
  • Make three different expressions that all simplify to 12x.
  • Create one numeric and one algebraic example with the same structure.
  • Explain why 3x + 2y cannot be collected in the same way.
  • Write an expression that has 5 terms but simplifies to 11ab.
OpenMiddle NRICH Collecting Like Terms

Assessment for learning AFL

Checks during the lesson
  • Mini-whiteboard “show me” responses after each variation.
  • Ask students to identify the common factor and coefficient total.
  • Listen for explanations using “groups of” language.
  • Check whether students generalise beyond a single numeric example.
Exit ticket
  • Simplify: 4 × 9 + 3 × 9 + 2 × 9.
  • Explain why your method is efficient.
  • Simplify: 5x + 6x.
  • Write one sentence explaining what collecting like terms really means.

Differentiation Support / Extend

Support
  • Keep the common factor numeric first.
  • Use smaller totals such as 5, 6, 7 or 8.
  • Leave Reveal groups on.
  • Use 2 or 3 terms before increasing complexity.
Extension
  • Use larger totals and more terms.
  • Turn on Algebraic examples.
  • Use two-letter factors such as ab.
  • Ask students to compare efficient collection with full expansion-style calculation.

Teacher notes Notes

  • Keep the focus on structure, not just answer getting.
  • Use repeated variation to help students notice what changes and what stays invariant.
  • Avoid reducing this to “same letters can be added” too early; instead foreground equal groups.
  • The progression from Number Pattern to Collecting Like Terms helps algebra feel sensible and connected.
Key caution: students may still default to order-of-operations calculation. Keep pressing the question, “What is the smarter structure here?”
This resource and more can be found at www.millsmathstools.au
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