Lesson 2 — building the concept
Multiplication as scaling, not repeated addition
This distinction matters for fractions, ratios, and algebra. Work at your own pace — no one else can see where you are.
How would you explain 3 × 5 to a student — and does your explanation still work for 3 × ½?
Repeated addition model
5 + 5 + 5 = 15 ✓ Works for whole numbers. But what does "add ½, three times" look like?
Scaling model
3 × ½ = a quantity ½ as large. Scaling works for all numbers — fractions, decimals, and beyond.
Common Core defines multiplication as scaling — this is why your Grade 4 students need this model. Repeated addition breaks down the moment fractions arrive.
A student says: "I can't multiply by ½ because you can't add something half a time." Which response opens up their thinking?
Cohort — Ontario Grade 4
9 teachers · Facilitated by Assata Moore
Upcoming · Thursday Apr 3, 2026
Monthly cohort meeting #4
- Sharing: where are you with multiplicative reasoning?
- Deep dive: connecting multiplication to fraction division
- Student work: what did you see in your classrooms?
- Next month's focus: fraction operations
Discussion threads
LC
Lisa Cortez
2h ago
3
Has anyone else's students confused multiplication with addition when they see 3 × ½? I tried the scaling explanation from lesson 2 and one student got it immediately — others still looked blank.
7 repliesModule 3 · Lesson 2
DP
David Park
Yesterday
The area model really clicked for me this week. I never understood why 23 × 47 works the way it does — decomposing into partial products makes so much more sense than how I was taught.
4 repliesModule 2 · Area models
AM
Assata Moore · Facilitator
3 days ago
📌 Pinned: Before our Apr 3 meeting, try this with your class — ask students "what does × mean?" and bring back what you hear. No wrong answers expected, just curious observation.
Pinned by facilitator12 seen
YB
Yuki Brennan
4 days ago
Uploaded student responses to the fraction task — the AI feedback was really useful. Sharing here in case others want to compare with their class results.
2 repliesStudent work attached
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Recent uploads
Fraction worksheet — March 20
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Multiplication exit tickets — Mar 14
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Area model task — Mar 5
Analyzing…
AI analysis — student work
Fraction worksheet · Mar 20 · Grade 4 · 8 students
Task: "Show what 3 × ½ means in two ways"
3 × ½ = ½ + ½ + ½ = 3/2 = 1½ ✓
Drawing: three circles each labelled "½"
→ (student drew 3 whole circles, each labelled "½" as a name, not a quantity)
Student note: "You just count the halves and add them"
Student computed correctly using repeated addition but the visual model reveals a deeper gap: ½ is treated as a label, not as a quantity that can be scaled.
What this student understands
- Can compute 3 × ½ correctly using repeated addition procedure
- Understands ½ + ½ + ½ = 3/2 and can convert to a mixed number
- Comfortable with fraction notation and arithmetic rules
Key misconception identified
The visual drawing reveals a whole-number image of multiplication — the student sees × as counting whole objects, not as scaling a quantity. This is a common Grade 4 pattern directly connected to limited exposure to the scaling model. The student can follow the rule but cannot yet represent ½ as something that gets stretched or shrunk.
Suggested next instructional moves
1
Use a number line: start at 0, scale by ½ to land at ½, repeat twice more. This builds the scaling image without abandoning the correct answer the student already has.
→ Module 3, Lesson 3: Number line representations
2
Ask: "If a ribbon is 1 m long and I cut it to ½ its size, how long is it? Now cut that to ½ again — what's happening?" Then connect this chain of halvings to multiplication.
→ Module 3, Lesson 4: Contextual scaling problems
3
Bring this student's work (anonymised) to your Apr 3 cohort meeting — 3 other teachers have seen the same pattern and it's on the agenda.
→ Cohort meeting Apr 3 — fraction misconceptions thread
Your reflection
Does this match what you observed in class? Did other students show similar or different approaches?
Platform flagged to your coach
The AI noticed you've been on Step 3 of Lesson 2 for 3 sessions, and that 5 of 8 students showed a whole-number multiplication image. Assata has been notified and reached out below.
Assata Moore · 9:14 AM
Hi Maria — I saw the platform flagged your lesson progress and your student work upload. That's not a bad sign at all. This concept genuinely trips up teachers because it conflicts with how most of us were taught. How are you feeling about it?
📎 Ma (1999) — Chapter 3 on multiplicative structures
You · 10:02 AM
Honestly a bit embarrassed that I'm stuck on something that seems so basic. I can do the computation but I'm not sure I could explain WHY scaling is different to a student.
Sent
Assata Moore · 10:18 AM
Please don't be embarrassed — the system didn't prepare you for this. I didn't fully understand multiplicative reasoning until I was 12 years into teaching. The fact that you're naming the gap is already the hardest step. Let's make it the centrepiece of our Apr 3 meeting.
Assata Moore · 10:19 AM
Also — I saw your March 20 upload. Five of 8 students with a whole-number multiplication image is actually a really useful dataset. Would you be willing to share it (anonymised) with the cohort? It perfectly illustrates what several of us have been noticing.
You · 10:35 AM
Yes — happy to share. That actually makes me feel better. At least I can see it clearly now even if I'm still working through the why.
Sent