💡 Lesson Overview
This lesson introduces a foundational mathematical skill: composing and decomposing numbers in different ways.
Students will:
- build a Brickit model
- count the total number of bricks in the model
- break that total into different combinations
- explore flexible thinking about numbers
- represent compositions with equations
- compare strategies between groups
- supports purposeful decision-making when choosing a model
🔹 New conceptual note: "Mathematicians show the same number in many ways. These are called multiple representations — different forms that share the same total."
This prepares children for place value, addition strategies, and early algebraic reasoning.
Aligned with Common Core (1.OA.C.6), Cambridge Primary Stage 1–2, IB PYP.
🎯 Today's Goal for Students
👩🏫 What to tell your students at the start of the lesson:
"Today we are learning that the same number can be made in different ways. We will find different ways to make the same total using our bricks."
💡 This simple statement helps students understand the purpose of the lesson and makes their actions more meaningful and focused.
🎯 Learning Goals
Number Sense
Count total bricks accurately
Represent the same total in multiple ways
Operations
Create addition equations showing different compositions (e.g., 9 = 5+4 = 3+3+3)
Reasoning
Explain why different equations make the same total
Compare strategies between groups
Communication
Use vocabulary: total, part, compose, decompose, equation, attribute, representation
Problem Solving
Adjust compositions using groups, colours, or shapes
🧠 Skills Developed
| Domain | Focus in this Lesson |
|---|---|
| Mathematics | composing & decomposing numbers; multiple representations |
| Reasoning | explaining equivalence of equations |
| Data Organisation | structuring totals into parts |
| Communication | describing equations & parts using mathematical vocabulary |
| Collaboration | discussing and recording compositions |
| Problem Solving | adjusting compositions using available attributes |
🧰 Teacher Preparation
Materials per team (typically 2–4 students; up to 5–6 if needed)
200–300 LEGO® bricks
1 device with Brickit App for Schools
Student Recording Sheet – Number Compositions
Teacher Observation Checklist
Mini whiteboards
Before class
Write examples on the board: 8 = 4 + 4, 8 = 5 + 3, 8 = 2 + 2 + 2 + 2
Add this teacher explanation: "These are multiple representations of 8 — different ways of showing the same total."
This lesson also supports strategy awareness — children observe how others sort, count, and group materials and may choose strategies that work for them.
This lesson encourages purposeful model choice — students learn to select a model that interests them and is appropriate for the time available.
📝 Teacher Notes — Why We Build First
A real model gives students a tangible total.
Multiple compositions become meaningful when they connect to something physical.
📄 Student Recording Sheet
Print this worksheet for each student or group:
Lesson 1.5 – Number Compositions
Name: _____________________ Date: _______________
1. Total number of bricks: ______
2. Ways I composed this number:
1. ______ + ______ = ______
2. ______ + ______ + ______ = ______
3. ______ groups of ______ = ______ (optional)
3. The attribute I used to create parts:
☐ colour ☐ shape ☐ size ☐ layer ☐ other: __________
4. Explain:
"These equations all make the same total because they are different representations of the same number."
5. Draw your compositions:
📘 Lesson Flow
🧺 Sort the Pile
Duration: 5–8 minutes
👩🏫 Instructions
"Sort your bricks by an attribute. This will help you choose parts when composing your number."
"If you choose colour, put similar shades together — all blues in one group, all yellows in another. No need for exact shade matching."
"You can sort by colour families, shape, height, or number of studs. Choose what makes sense to you."
"Do not aim for perfect sorting. If bricks are connected, leave them together."
👧👦 What You Need to Do
- Sort by chosen attribute (colour families, shape, height, or studs)
- Do not aim for perfect sorting
- Organise for easy access during composition activities
- If you see a sorting strategy you like, try it
👩🏫 Teacher Focus
- Reinforce: Sorting is mathematical thinking — grouping, comparing, organising
- Accept any reasonable sorting strategy
- Notice which students organise for easy access
🟦 Teacher Tip
Sorting is a warm-up, not a requirement. It helps organise materials and activates attention. Connected bricks can stay together. Multi-colour bricks can go in mixed groups or by dominant colour — both choices are fine.
🔁 If students struggle…
- Remind: "Similar colours go together — no need for exact matching."
- If bricks are hard to separate: "Leave them together — that's fine."
- If a student is stuck: "Try sorting by shape instead."
📝 Teacher Notes
- Sorting is not required for the Brickit scan and does not need to be exact.
- If some bricks are tightly connected, leave them together — perfection is not required.
- If a brick has more than one colour (windows, wheels), place it in a mixed-colour group or choose the dominant colour. Either choice is acceptable.
- Sorting helps children notice attributes, organise materials, and prepare for counting. Its purpose is cognitive activation, not correctness.
- Children may use different sorting strategies. Encourage noticing how others work and trying new strategies. Strategies are optional — accuracy in counting is the goal.
📷 Scan & Choose a Model
Duration: 5–8 minutes
👩🏫 Instructions
"Spread your bricks into one flat layer — one brick thick. This helps Brickit see everything."
"Now scan with the Brickit App. Look at the models it suggests."
"Pick a model you want to count and decompose. We'll explore multiple ways to represent the same total."
"Choose a model your team likes, can build, and can build quickly — about 5–7 minutes."
"Brickit recognises shape and size, not colour. You can use any colours you have. Substitutions are correct and encouraged."
📋 Model Selection Rule
A model is "just right" if:
- students LIKE it
- they CAN build it (not too many tiny parts)
- they can build it QUICKLY (5–7 minutes)
- approx. 8–15 bricks (if visible in app)
- simple shape, no rare bricks
- substitutions are expected
👧👦 What You Need to Do
- Spread bricks on a flat surface (one layer thick)
- Scan with the Brickit App
- Look at suggested models
- Choose a model that feels "just right"
👩🏫 Teacher Focus
- Ensure each team makes their own choice
- Reinforce: Every choice is valid
- If your Brickit shows piece-count, guide toward 8–15 bricks
🟦 Teacher Tip
Children choose by interest first. Guide gently toward models they can build in 5–7 minutes: one clear object, few tiny pieces, visually simple.
🔁 If students struggle to choose…
- Remind the three rules: LIKE it, CAN build it, QUICK to build
- Help find a simpler model if current choice is too complex
- Say: "If it feels 'just right', that's perfect."
⚠️ If students struggle to build
- Switch to a simpler model
- Freeze the build "as is" and move to math
- Move to math even if model is unfinished — the goal is mathematical reasoning, not perfect building
📝 Teacher Notes
- The colour of the suggested Brickit model does not matter. Children may build using any available colours.
- If a piece is missing, students should choose a similar size/shape — this is correct problem-solving.
- If your Brickit version shows piece-count, aim for 8–15 bricks. If not, guide using visual simplicity.
- Sorting and rebuilding do not need to be perfect. The goal is mathematical reasoning, not precision.
🧱 Building the Model
Duration: 8–10 minutes
👩🏫 Instructions
"Now build your chosen model. Work together."
"If a piece is missing, find a similar one — same size or shape. That's correct problem-solving."
"As you build, notice which attributes help you see natural parts — colours, shapes, or sizes."
👧👦 What You Need to Do
- Build collaboratively
- Help each other find pieces
- Notice which colours or shapes repeat
- Substitute missing pieces with similar shapes/sizes
👩🏫 Teacher Focus
- Ask: "Which attribute helps you see natural parts in your model?"
- Ask: "Which colours or shapes repeat?"
- Observe problem-solving strategies
- Support teams that struggle with substitutions
🟦 Teacher Tip
Substitutions are correct and encouraged. If a team can't find the exact piece, they should use a similar one. This is mathematical problem-solving, not a building test.
🔁 If students struggle…
- If building takes too long: "Freeze your model as is and move to counting."
- If many pieces are missing: "Use similar pieces — that's fine."
- If team is stuck: "Ask another team for help finding pieces."
📝 Teacher Notes
- Brickit recognises shape and size, not colour. Substitutions are expected and correct.
- The model does not need to match the instructions exactly. Approximate matches are fine.
- If building is taking too long, it's acceptable to move to the math part with an incomplete model.
🔍 Mathematical Exploration — Counting & Identifying the Total
Duration: 7 minutes
🧠 Strategy Awareness
You may count in different ways (ones, groups of 2, groups of 5). Notice how others work and try new strategies. Strategies are optional; accuracy is the goal.
👩🏫 Instructions
"Count the total bricks in your model. Choose a counting strategy that helps you stay accurate."
"Write the total on your Recording Sheet."
"This total can be shown in many ways. Mathematicians call this multiple representations."
👧👦 What You Need to Do
- Count the total bricks in the model
- Choose a counting strategy (ones, groups of 2, groups of 5)
- Write the total
👩🏫 Teacher Focus
- Observe counting strategies used
- Support students who need to recount
- Reinforce: One number can be shown in many ways
🟦 Teacher Tip
Children may count in different ways. Encourage noticing how others count and choosing the strategy that helps them stay accurate. Strategies are optional — students choose what works for them.
🔁 If students struggle…
- If count seems wrong: "Try counting again using a different method."
- If students skip bricks: "Point to each brick as you count."
- If team is stuck: "Try counting by groups of 2 or 5."
🔍 Mathematical Exploration — Creating Number Compositions
Duration: 10 minutes
👩🏫 Instructions
"Now create different compositions by grouping bricks using attributes."
"You can group by colour, shape, size, or layers. Each grouping shows the same total in a different way."
"These are different representations of the same total."
👧👦 What You Need to Do
- Create compositions by grouping bricks using attributes
- By colour:
4 blue + 5 red = 9 - By shape:
3 tall + 6 flat = 9 - By size/layers:
2 base + 7 top = 9 - Equal groups (optional):
3 groups of 3 = 9 - Write equations on Recording Sheet
👩🏫 Teacher Focus
- Show examples on the board
- Highlight: Different representations of the same total
- Support students who need to start with just one attribute
- Celebrate multiple representations
🟦 Teacher Tip
Multiple representations build number sense. Students see that 4 + 5, 3 + 6, and 2 + 7 all equal 9 — the same total shown in different ways.
🔁 If students struggle…
- If composition is unclear: "Start with just one attribute — try grouping by colour first."
- If students forget total: "Check your total — all compositions should equal the same number."
- If format is hard: "Show me: number + number = total."
⚖️ Comparison & Reasoning
Duration: 5–7 minutes
👩🏫 Instructions
Your teacher will compare two groups' equations on the board and ask:
- "What attribute did each group use?"
- "How do these representations show the same total?"
- "Which representation is clearest in your model?"
"Explain your reasoning in full sentences."
👧👦 What You Need to Do
- Compare your compositions with other teams
- Explain which attribute you used
- Articulate how different representations show the same total
- Answer comparison questions in full sentences
👩🏫 Teacher Focus
- Highlight that different attributes can create different compositions
- Reinforce: All representations equal the same total
- Celebrate clear explanations
🟦 Teacher Tip
Comparison builds understanding of equivalence. Students see that 4 + 5 and 3 + 6 both equal 9 — different ways to show the same number.
🔁 If students struggle…
- If explanation is unclear: "Tell me: which attribute did you use? How does it show the same total?"
- If students can't compare: "Look at the equations — do they both equal the same number?"
💭 Reflection & Recording
Duration: 5 minutes
👩🏫 Instructions
"Complete your Recording Sheet with all your work."
"What strategy helped you create different compositions today?"
"Did you try a new strategy or learn from someone else?"
"Use the word 'representations' in your explanation."
👧👦 What You Need to Do
- Record total on Recording Sheet
- Record compositions (by colour, shape, size, etc.)
- Write explanation using the word "representations"
- Draw your model
- Reflect on composition strategies you used
👩🏫 Teacher Focus
- Collect evidence of learning through Recording Sheets
- Check understanding of "representations"
- Take photos of models if helpful
- Quick interviews: "Tell me about your compositions."
🟦 Teacher Tip
Reflection builds metacognition. Students think about their own thinking and learn from others' strategies.
🔁 If students struggle…
- If Recording Sheet is incomplete: "Check your total and compositions — make sure everything is recorded."
- If reflection is unclear: "Tell me: which attribute did you use to create compositions?"
🧩 Differentiation
Emerging (Grade 1)
- Make 1–2 compositions
- Use 2-part equations
Developing (Grade 2)
- Create multiple representations
- Include 3-part equations
Advanced (Grade 2–3)
- Compare representations
- Create equal-group decompositions
🧮 Assessment Tools
Use during circulation.
| Skill | Observable Behaviour | Check |
|---|---|---|
| Total identification | Counts accurately | ☐ |
| Composition | Creates ≥2 correct representations | ☐ |
| Reasoning | Explains equivalence | ☐ |
| Vocabulary | Uses "compose", "total", "attribute", "representations" | ☐ |
| Collaboration | Works cooperatively | ☐ |
| Creativity | Chooses flexible attributes | ☐ |
Success indicators:
Student understands "same total, different representations"
Student can create at least 2 compositions
Student uses correct math vocabulary
🌿 Extensions & Challenges
Change the Attribute
Compose the number using a different attribute
Unknown Part
If 12 = 4 + __, what is missing?
Representation Swap
Exchange representations with another group and explain why both are correct
Rebuild Challenge
Rebuild a new model with the same total but different internal parts
📚 Curriculum Alignment
| Framework | Standards |
|---|---|
| Common Core (US) | 1.OA.C.6 — Compose/decompose numbers; 1.OA.B — Understand addition structure; MP2 — Reason about representations |
| Cambridge Primary (Stage 1–2) | N1–N2: part-whole composition; N2.2: relational understanding |
| IB PYP Mathematics | "Numbers can be represented in different ways." "Representations help us describe relationships." |