💡 Lesson Overview
This lesson builds conceptual foundations for fractions as fair division. Students work in teams to share a LEGO® model fairly between 2 and 4 people, checking fairness by counting bricks — not by size or shape.
The focus of this lesson is:
- understanding that sharing fairly means giving the same amount
- dividing a LEGO model into two and four fair shares
- comparing and testing different splitting strategies
- explaining fairness using precise math language
- using multiple representations of fair sharing
- collaborating to solve an open-ended problem
- supports purposeful decision-making when choosing a model
🧠 Key Concept (Brickit Fractions Definition):
Equal shares do not need to look the same. Fair sharing means each person receives the same number of bricks.
We do not use "size" or abstract geometric measurements in Grades 1–2.
Designed for Grades 1–2, with extensions for Grade 3. Aligned with Common Core (1.G.A.3, 2.G.A.3), Cambridge Primary (Stage 1–2), and IB PYP.
Part of the Brickit approach — transforming existing LEGO® bricks into meaningful learning.
🎯 Today's Goal for Students
👩🏫 What to tell your students at the start of the lesson:
"Today we are learning about fair sharing. We will share our bricks equally between 2 people and 4 people. Fair sharing means everyone gets the same number of bricks."
💡 This simple statement helps students understand the purpose of the lesson and makes their actions more meaningful and focused.
🎯 Learning Goals
Fair Sharing
Understand that sharing fairly means giving the same amount
Divide a LEGO model into two and four fair shares
Problem Solving
Compare and test different splitting strategies
Adjust shares to make them fair
Mathematical Language
Explain fairness using precise math language
Use terms: fair, equal, share, whole, part
Representation
Use multiple representations of fair sharing
Draw fair shares and explain strategies
Reasoning
Explain why sharing is fair or unfair
Compare strategies and justify choices
Collaboration
Work cooperatively to solve an open-ended problem
Share reasoning with partners
🧠 Skills Developed
| Domain | Focus in this Lesson |
|---|---|
| Mathematics | Fair sharing, equal division, fractions foundation |
| Problem Solving | Testing strategies, adjusting shares, comparing approaches |
| Cognitive Skills | Reasoning about fairness, justifying decisions |
| Communication | Using fraction vocabulary, explaining strategies |
| Collaboration | Working as a team to solve sharing problems |
| Representation | Drawing fair shares, describing strategies |
🧰 Teacher Preparation
Materials per team (typically 2–4 students; up to 5–6 if needed)
200–400 mixed LEGO® bricks
1 device with Brickit App for Schools
Printed Student Recording Sheet (1 per student)
Teacher Observation Checklist
Environment
Tables arranged so bricks can be spread for scanning
Space between groups for easy teacher movement
Before the lesson
Pre-scan one sample pile to check lighting and camera distance
Prepare teacher prompts (see below)
- "How would you check if this sharing is fair?"
- "Can there be more than one fair answer?"
- "Do equal shares have to look the same?"
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
Every Brickit Math lesson begins with: Sort → Scan → Choose → Build.
This routine:
- reduces frustration by organising the pile
- helps students understand what pieces they have
- allows them to make meaningful choices
- builds motivation and ownership
- creates a concrete model that becomes the foundation for mathematical thinking
- strengthens problem solving when substitutions are needed
- supports tactile and visual learners
- aligns with inquiry-based mathematics (Common Core, PYP, Cambridge)
Building is not optional: it is the engine that drives mathematical exploration in this lesson.
📄 Student Recording Sheet
Print this worksheet for each student or group:
Fair Sharing Challenge – Lesson 2.2
Name: __________________ Date: ____________
Fair Share: 2 People
My whole has ______ bricks.
Person A gets ______ bricks.
Person B gets ______ bricks.
This is fair because ____________________________.
(Draw both shares.)
Fair Share: 4 People
Each person gets ______ bricks.
All parts are equal because _______________________.
(Draw 4 shares.)
My Strategy:
I made my sharing fair by _________________________.
Something I discovered today: ________________
📘 Lesson Flow
🧺 Sort the Pile
Duration: 5–8 minutes
👩🏫 Instructions
"Sort your bricks by an attribute. Today we will explore what makes sharing fair. We check fairness by counting bricks, not by shape."
"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
- If you see a sorting strategy you like, try it
👩🏫 Teacher Focus
- Reinforce: Sorting helps us organise for fair sharing
- Remind: Fairness is about amount, not appearance
- Accept any reasonable sorting strategy
🟦 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."
"Choose a model. This will be your whole that we share."
"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
- can be shared fairly (even numbers work best)
👧👦 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.
🧱 Build the Whole
Duration: 5 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
"Now build your chosen model. This will be your whole."
"How many bricks does your whole have? Choose a counting strategy that helps you stay accurate."
"Write this number on your Recording Sheet."
👧👦 What You Need to Do
- Build the chosen model collaboratively
- Count total bricks in the model
- Choose a counting strategy (ones, groups of 2, groups of 5)
- Record the total on Recording Sheet
👩🏫 Teacher Focus
- Ensure accurate counting
- Reinforce: This is the "whole"
- Observe counting strategies used
🟠 Important Teacher Note
If the number of bricks does not split easily (for example, 11 cannot become 2 equal shares), students may:
- add or remove a brick
- or choose a different whole
This supports conceptual understanding of even vs. uneven totals.
🟦 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 count seems wrong: "Try counting again using a different method."
- 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.
🔍 Fair Share: 2 People
Duration: 10–12 minutes
👩🏫 Instructions
"Work in teams to split your whole model fairly between two people. Each person should get the same number of bricks."
"Equal shares contain the same number of bricks. Shapes may differ — fairness is about amount, not shape."
"You may take apart the model, rebuild two new structures, or use loose bricks to adjust balance."
👧👦 What You Need to Do
- Split the whole model fairly between two people
- You may: take apart the model, rebuild two new structures, use loose bricks to adjust balance
- Count bricks in each share
- Adjust until both shares have the same number of bricks
- Record brick counts
- Explain strategies
👩🏫 Teacher Focus
- Ask: "How many bricks are in each share?"
- Ask: "How do you know this is fair?"
- Ask: "What did you change to make it fair?"
- Ask: "Do these two parts look different? Is that OK?"
- Reinforce: Fairness is about amount, not shape
🟦 Teacher Tip
Fairness is about amount, not shape. Students may create shares that look different but have the same number of bricks — this is correct.
🔁 If students struggle…
- If shares are unequal: "Count bricks in each share. Do they match?"
- If students focus on shape: "Fairness is about number of bricks, not shape. Count the bricks."
- If total is odd: "Try adding or removing 1 brick to make an even number."
🔍 Fair Share: 4 People
Duration: 10–12 minutes
👩🏫 Instructions
"Now try splitting the same whole fairly among 4 people. Make 4 groups, count bricks in each group, and adjust until all 4 match."
"Optional: rebuild small models for each person."
"When we share the same whole with more people, each person gets fewer bricks."
👧👦 What You Need to Do
- Create 4 groups from the whole
- Count bricks in each group
- Adjust until all 4 groups have the same number of bricks
- Optional: rebuild small models for each person
- Record brick counts
👩🏫 Teacher Focus
- Ask: "How many bricks does each person get?"
- Ask: "Is this fair? How do you know?"
- Ask: "What changed when we shared with more people?"
- Reinforce: More people = fewer bricks per person
🟦 Teacher Tip
More people means fewer bricks per person. Students will notice that sharing with 4 people gives each person fewer bricks than sharing with 2 people — this is the key concept.
🔁 If students struggle…
- If groups are unequal: "Count bricks in each group. Do they all match?"
- If students can't make 4 groups: "Start with just 2 groups, then split each into 2 more."
- If total doesn't divide evenly: "Try adding or removing bricks to make a number that divides by 4."
⚖️ Strategies & Reasoning
Duration: 5 minutes
👩🏫 Instructions
"Discuss with your team:"
- "Which sharing strategy was easiest?"
- "Which was harder — 2 people or 4 people?"
- "Why do some totals share easily while others don't?"
"Use full sentences: 'This is fair because…', 'We checked fairness by counting…', 'We changed our model by…'"
👧👦 What You Need to Do
- Discuss sharing strategies with your team
- Compare strategies for 2 people vs. 4 people
- Explain why some totals share easily
- Use full sentences to explain reasoning
👩🏫 Teacher Focus
- Encourage full sentences
- Reinforce: Fairness is checked by counting
- Celebrate clear explanations
🟦 Teacher Tip
Discussion builds understanding. Students see that different strategies can work, and that even numbers share more easily than odd numbers.
🔁 If students struggle…
- If explanation is unclear: "Tell me: how did you check fairness? Did you count the bricks?"
- If students can't compare: "Which was easier — sharing with 2 people or 4 people? Why?"
💭 Reflection & Recording
Duration: 5 minutes
👩🏫 Instructions
"Complete your Recording Sheet with all your work."
"What strategy helped you share fairly today?"
"Did you try a new strategy or learn from someone else?"
👧👦 What You Need to Do
- Write brick totals on Recording Sheet
- Explain fairness
- Draw your shares
- Describe your strategy
- Reflect on sharing strategies you used
👩🏫 Teacher Focus
- Collect evidence of learning through Recording Sheets
- Use observation checklist: counts correctly, equal shares verified, reasoning clear, collaboration effective
- Take photos of models if helpful
- Quick interviews: "Tell me about your fair shares."
🟦 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 brick totals and shares — make sure everything is recorded."
- If reflection is unclear: "Tell me: how did you make fair shares?"
🧩 Differentiation
Emerging Learners (Grade 1)
- Start with only 2-person sharing
- Use loose bricks to practice equal groups
- Teacher simplifies whole to 8–10 bricks
Developing Learners (Grade 2)
- Complete 2 and 4 person sharing
- Explain fairness in sentences
- Compare strategies
Advanced Learners (Grade 2–3)
- Find multiple fair solutions
- Explore "Can I share 12 bricks among 3 people?"
- Compare fair vs. unfair shares and explain why
🧮 Teacher Observation Checklist
Use during circulation.
| Skill | Evidence | Check |
|---|---|---|
| Identifies whole | Counts the bricks accurately | ☐ |
| Shares fairly | Creates equal shares (by brick amount) | ☐ |
| Explains fairness | Uses reasoning, not shapes | ☐ |
| Compares strategies | Describes multiple approaches | ☐ |
| Representation | Draws fair shares | ☐ |
| Collaboration | Works as part of a team | ☐ |
🌿 Extension Ideas
Make an Unfair Share
Make an unfair share, then fix it
Pattern Exploration
Share 16 bricks among 2, 4, 8 people — what patterns do you see?
Real-Life Stories
Build a real-life fair sharing story (e.g., cookies, apples, building materials)
Odd Numbers
Explore what happens when totals are odd (9, 11, 13)
📚 Curriculum Alignment
| Framework | Standards |
|---|---|
| Common Core (US) | 1.G.A.3 — partition into 2 and 4 equal shares; 2.G.A.3 — describe equal shares; MP1, MP2, MP3 — problem solving, reasoning, explanation |
| Cambridge Primary (Stage 1–2) | M2.3 — equal shares, fair sharing |
| IB PYP Mathematics | "Mathematics is a tool for making decisions (fairness)." "Inquiry through hands-on modelling." |