💡 Lesson Overview
This is one of the key lessons in the entire unit, because here children meaningfully understand the fundamental principle of fractions: when you cut the same whole into more equal parts, each part becomes smaller.
In the LEGO format, this works perfectly because children see and touch the difference between halves, thirds, and quarters. They build their own shares and compare them using brick counts.
The focus of this lesson is:
- comparing the sizes of halves, thirds, and quarters
- explaining that more equal parts → smaller share
- using brick-count to justify comparisons
- building and representing halves, thirds, and quarters
- connecting model-based fractions to early abstract understanding
- understand that comparisons may show differences or equality
- supports purposeful decision-making when choosing a model
🧠 Core Concept (Brickit Fractions Definition):
Fraction size depends on how many equal shares the same whole is divided into. More shares = fewer bricks per share.
Equal shares are defined by same number of bricks. Shapes may differ. We avoid the word "size" in an abstract geometric sense — everything tied to brick amount.
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 that when you cut the same whole into more equal parts, each part becomes smaller. We will compare halves, thirds, and quarters to see this."
💡 This simple statement helps students understand the purpose of the lesson and makes their actions more meaningful and focused.
🎯 Learning Goals
Fraction Comparison
Compare the sizes of halves, thirds, and quarters
Explain that more equal parts → smaller share
Justification
Use brick-count to justify comparisons
Explain reasoning using clear math language
Building & Representation
Build and represent halves, thirds, and quarters
Use multiple representations (models, drawings, words)
Conceptual Understanding
Connect model-based fractions to early abstract understanding
Understand the fundamental principle: more parts = smaller share
Mathematical Language
Use terms: half, third, quarter, bigger, smaller, more, fewer
Explain comparisons in complete sentences
Problem Solving
Adjust models when totals don't divide evenly
Find solutions for different partitioning strategies
🧠 Skills Developed
| Domain | Focus in this Lesson |
|---|---|
| Mathematics | Fraction comparison, halves/thirds/quarters, fundamental fraction principle |
| Problem Solving | Adjusting models, comparing strategies, finding patterns |
| Cognitive Skills | Reasoning about relationships, pattern recognition, generalization |
| Communication | Using fraction vocabulary, explaining comparisons |
| Collaboration | Working as a team to build and compare shares |
| Representation | Building models, drawing fractions, describing relationships |
🧰 Teacher Preparation
Materials per team (typically 2–4 students; up to 5–6 if needed)
250–400 mixed LEGO® bricks
1 device with Brickit App for Schools
Printed Student Recording Sheet (1 per student)
Teacher Observation Checklist
Optional: colour cards (½, ⅓, ¼ symbols)
Environment
Tables arranged so bricks can be spread for scanning
Space between groups for easy teacher movement
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:
Comparing Fraction Sizes – Lesson 2.4
Name: __________________ Date: ____________
My Whole Has: ______ bricks
My Shares:
One half = ______ bricks
One third = ______ bricks
One quarter = ______ bricks
My Comparison:
The biggest share is __________ because __________.
The smallest share is __________ because __________.
My Rule:
When we make more equal parts, each part ___________________.
My Drawings:
(half – third – quarter)
📘 Lesson Flow
🧺 Sort the Pile
Duration: 5–8 minutes
👩🏫 Instructions
"Sort your bricks by an attribute. Today we compare how big each share is when we divide a whole into 2, 3, or 4 equal parts. We will use the number of bricks to check fairness."
"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 comparison
- 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
Before scanning:
Spread all bricks into one flat layer (1 brick thick). Avoid tall piles. Flat surfaces improve Brickit recognition.
Teacher prompt:
"Scan with Brickit. Look at the models Brickit suggests. Choose a model."
How to choose a model:
- Choose a model you LIKE.
- Choose a model you CAN build (not too many tiny parts).
- Choose a model you can build QUICKLY (about 5 minutes).
If it feels "just right", that is the perfect choice.
Key explanation:
- Brickit recognises shapes, not colours
- Substitutions are welcome
- The colour of the suggested Brickit model does not matter. Children may build the model using any available colours.
Student actions:
- Spread bricks on a flat surface (one layer thick)
- Scan with the Brickit App
- Choose a model (12–18 bricks recommended)
🟠 Teacher Note:
If the chosen model has a tricky total (not divisible by 2, 3, or 4), students may add or remove 1–2 bricks or choose a different model.
Goal: the whole must be split into halves, thirds, and quarters.
Teacher Note — Choosing a Model:
Children choose models by interest first. Guide them gently to select a model they can build in 5–7 minutes: one clear object, few tiny pieces, visually simple. If a model is too complex, help the group find a "just-right" choice that supports the mathematical goals of the lesson.
If students struggle to choose, remind them of the three rules: LIKE it, CAN build it, QUICK to build.
🧱 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."
"Is this number easy to divide into 2, 3, and 4 equal parts?"
"Write your number on your Recording Sheet."
"Equal shares are checked by counting bricks."
👧👦 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
- Ask: "How many bricks does your whole have?"
- Ask: "Is this number easy to divide into 2, 3, and 4 equal parts?"
- Reinforce: Equal shares are checked by counting bricks
- Observe counting strategies used
🟦 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.
🔍 Make Halves
Duration: 5–6 minutes
👩🏫 Instructions
"Split your whole into 2 equal shares. Count bricks in each share. Adjust as needed."
👧👦 What You Need to Do
- Split the whole into 2 equal shares
- Count bricks in each share
- Adjust to ensure equality
- Record your halves on Recording Sheet
👩🏫 Teacher Focus
- Ask: "How many bricks are in each half?"
- Ask: "How did you check fairness?"
- Reinforce: Fairness is checked by counting bricks
🟦 Teacher Tip
Fairness is about amount, not shape. Students may create halves 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."
🔍 Make Thirds
Duration: 8 minutes
👩🏫 Instructions
"Now split the whole into 3 equal shares. Count bricks. Adjust."
"How is this different from halves?"
"Optional: rebuild shares into simple mini-models."
👧👦 What You Need to Do
- Split the whole into 3 equal shares
- Count bricks in each share
- Adjust to ensure equality
- Optional: rebuild shares into simple mini-models
- Record your thirds on Recording Sheet
- Compare to halves
👩🏫 Teacher Focus
- Ask: "Does each third have the same number of bricks?"
- Ask: "How is this different from halves?"
- Reinforce: Thirds have fewer bricks than halves
🟦 Teacher Tip
More parts means fewer bricks per part. Students will notice that thirds have fewer bricks than halves — 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 3 groups: "Start with just 2 groups, then split each into more."
- If total doesn't divide evenly: "Try adding or removing 1–2 bricks to make a number divisible by 3."
🔍 Make Quarters
Duration: 8 minutes
👩🏫 Instructions
"Now split the whole into 4 equal shares. Adjust to equal brick numbers."
👧👦 What You Need to Do
- Split whole into 4 equal shares
- Count bricks in each share
- Adjust to ensure equality
- Record your quarters on Recording Sheet
- Compare to halves and thirds
👩🏫 Teacher Focus
- Ask: "Is each quarter equal by brick count?"
- Ask: "Do all four shares look the same or different?"
- Reinforce: Quarters have the fewest bricks
🟦 Teacher Tip
More parts means fewer bricks per part. Students will notice that quarters have fewer bricks than both halves and thirds — 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 1–2 bricks to make a number divisible by 4."
⚖️ Compare Sizes
Duration: 5 minutes
👩🏫 Instructions
"Lay out your shares: half – third – quarter"
Answer these questions:
- "Which share has more bricks?"
- "Which share has fewer bricks?"
- "Why is the quarter smaller than the half?"
- "Why are thirds bigger than quarters?"
"The more equal parts we make, the fewer bricks each part has."
"This is the conceptual heart of fractions."
👧👦 What You Need to Do
- Lay out shares: half – third – quarter
- Compare sizes using brick counts
- Explain which share has more/fewer bricks and why
- Articulate the general rule
👩🏫 Teacher Focus
- Reinforce: The more equal parts we make, the fewer bricks each part has
- Celebrate clear explanations
- Support students who need help articulating reasoning
🟦 Teacher Tip
This is the conceptual heart of fractions. Students see that 1/2 > 1/3 > 1/4 because halves have more bricks than thirds, and thirds have more bricks than quarters.
🔁 If students struggle…
- If explanation is unclear: "Tell me: how many bricks in one half? How many in one quarter? Which is bigger?"
- If students can't compare: "Look at your Recording Sheet — compare the numbers."
💭 Reflection & Recording
Duration: 5 minutes
👩🏫 Instructions
"Complete your Recording Sheet with all your work."
"What strategy helped you compare shares today?"
"Did you try a new strategy or learn from someone else?"
👧👦 What You Need to Do
- Write number of bricks in each share
- Write which is biggest/smallest, or are they equal
- Write your general rule
- Draw shares
- Reflect on comparison strategies you used
👩🏫 Teacher Focus
- Check for: correct brick counts, correct comparisons, correct reasoning, understanding of the rule
- Collect evidence of learning through Recording Sheets
- Take photos of models if helpful
- Quick interviews: "Tell me about your comparison."
🟦 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 counts and comparisons — make sure everything is recorded."
- If reflection is unclear: "Tell me: which share has the most bricks? Which has the fewest?"
🧩 Differentiation
Emerging Learners (Grade 1)
- Compare only halves vs. quarters
- Use simple wholes like 12 bricks
- Focus on counting and basic comparison
Developing Learners (Grade 2)
- Compare all three (½, ⅓, ¼)
- Draw models
- Explain the rule in their own words
Advanced Learners (Grade 2–3)
- Test with multiple wholes
- Create a "fraction wall" with real bricks
- Compare sixths and eighths for curiosity
🧮 Teacher Observation Checklist
Use during circulation.
| Skill | Evidence | Check |
|---|---|---|
| Partitioning | Creates halves, thirds, quarters | ☐ |
| Fairness | Shares equal by brick count | ☐ |
| Comparison | Correctly identifies biggest/smallest share | ☐ |
| Reasoning | Uses verbal explanation to justify | ☐ |
| Representation | Draws halves/thirds/quarters | ☐ |
| Generalization | States rule about "more parts → smaller share" | ☐ |
🌿 Extension Ideas
Fraction Tower
Build a fraction tower from largest share to smallest
Different Wholes
Compare two different wholes → "Do halves of different wholes match?"
Story Problems
Story problems (pizza, cookies, building materials)
📚 Curriculum Alignment
| Framework | Standards |
|---|---|
| Common Core (US) | 1.G.A.3 — identify halves, fourths; 2.G.A.3 — partition into equal shares; describe shares; MP2, MP3 — reasoning and explanation |
| Cambridge Primary (Stage 1–2) | M2.3 — equal parts, comparison of partitioning |
| IB PYP Mathematics | "Understanding systems and relationships." "Inquiry through hands-on modeling." |