EvaEdu

🔴 Fraction Model Problem (Primary 6)

At first. Mrs. Ang had twice as many red beads as yellow beads. She used two-thirds of her yellow beads and some of her red beads to make necklaces. In the end, three out of five of the remaining beads were red. What fraction of her red beads did Mrs. Ang use?

🟪 🟪 🟪
red yellow

🟦🟦🟦 🟦🟦🟦 🟦🟦🟦
red yellow

In the end, 3 red beads for every 2 yellow beads left

------------------------left--------------------------------
🟧🟧🟧🟧🟧🟧 🟧🟧🟧🟧🟧🟧 🟧🟧
---------------all minus unknown "x"-------------------

12🟧-x 3 3🟧
--------- = --- = ---- so x=9🟧
14🟧-x 5 5🟧

What fraction of her red beads did Mrs. Ang use?

9 3
-- = --
12 4

In this solution we have used "Dynamic model updating" — start with base quantities and adjust units step-by-step as each condition is given. Then compare what’s left to what’s expected using block equivalence.

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📘 P6 Question (Rephrased):

A roll of tape has a repeated pattern of stars and hearts.
Mabel cuts off a piece of the tape. In that piece, there are 135 stars.
Find the possible number of hearts on that piece of tape.

🔍 Step-by-Step Working:

1️⃣ Observe the Pattern
From the image, the repeating pattern is:

⭐ ⭐ ❤️ ⭐ ❤️

👉 In one complete pattern, there are:

⭐ Stars = 3

❤️ Hearts = 2

2️⃣ Work Out How Many Full Sets
135 stars ÷ 3 stars per set = 45 full sets

3️⃣ Find Number of Hearts
Each set has 2 hearts

So, 45 sets × 2 hearts = 90 hearts

🎯 Final Answer:
Mabel’s piece of tape has 90 hearts.

🧠 Notes for Students:

Always look carefully at the unit pattern

Count how many stars and hearts appear in one set

Use division to find number of sets.

Then multiply to find total hearts.

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P5 question:

Mei and Wendy have 140 sweets altogether. 1/2 of Wendy's sweets is equal to 2/3 of Mei' sweets.

👉How many sweets does Mei have?

Here, I used the ASSUMPTION METHOD.

They start with a total of 140, Mei + Wendy = 140 sweets
From the clue given (1/2 of Wendy's sweets is equal to 2/3 of Mei's sweets). Wendy has more.

So instead of assuming 70+70 for both of them, I assume 80+60.

The test it out: 1/2 of 80=40 =2/3 of 60.

So, the answer is: Mei has 60 sweets.

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Question:

At a class party, a total of 40 pupils were given some Jellybeans.
Each boy received 5 Jellybeans, and each girl received 2 Jellybeans.
If the boys received 25 more jellybeans than the girls, how many
boys and how many girls are there?
The total number of jellybeans is unknown. This is a PRIMARY 5 QUESTION. Is it to be resolved using the Assumption method?

This Primary 5 question can be solved using the Assumption Method, which is a common Singapore Maths heuristic strategy.

Given:

Total pupils = 40

Each boy gets 5 jellybeans; Each girl gets 2 jellybeans

Boys received 25 more jellybeans than girls.

✅ Step-by-Step (Assumption Method):
1️⃣ Assume all 40 pupils are girls
Each girl gets 2 jellybeans ⇒
➡️ Total = 40 × 2 = 80 jellybeans

2️⃣ Now, replace one girl with one boy
Difference in jellybeans:

Boy gets 5, girl gets 2 ⇒ boy gets 3 more than a girl

So each time we swap a girl with a boy, total jellybeans increases by 3.

3️⃣ We want the boys to get 25 more jellybeans than the girls
That means total jellybeans needs to increase by 25

➡️ How many swaps needed?
25 ÷ 3 = 8 R1 → Not whole number

But we need exact match. Let's try trial and error:

Try 5 boys:
Boys: 5 × 5 = 25

Girls: 35 × 2 = 70
➡️ Difference = 25 − 70 = −45 ❌ too little

Try 10 boys:
Boys: 10 × 5 = 50

Girls: 30 × 2 = 60
➡️ Difference = 50 − 60 = −10 ❌ too little

Try 15 boys:
Boys: 15 × 5 = 75

Girls: 25 × 2 = 50
➡️ Difference = 75 − 50 = +25 ✅ Correct!

🎯 Final Answer:
15 boys

25 girls

Here's a challenge for P3's stepping up toP4:

Mrs. Lim had 265 fewer buttons than Mr. Q.
Mrs. Lim sold 199 buttons, and Mr. Qi sold 50 buttons.
In the end, Mr. Qi had four times as many buttons as Mrs. Lim.
How many buttons did Mrs. Lim have in the end?

One solution:

Step-by-Step Model Drawing Approach (P4-friendly)

Let’s use blocks to represent Mrs. Lim's remaining buttons as 1 unit.
Then, Mr. Qi’s remaining buttons = 4 units.

Let’s work backwards:

1. Let 1 unit = Mrs. Lim’s final number of buttons
→ Mr. Qi’s final = 4 units
→ Difference in final amounts = 3 units

2. Find how many more buttons Mr. Qi had in the end
Since he sold fewer buttons than Mrs. Lim (only 50 vs 199), he ended up with more.

Start-of-difference = 265
Sold difference = 199 – 50 = 149 more sold by Mrs Lim

So, Mr Qi had 265 + 149 = 414 more at the end
That means:

3 units=414⇒1 unit=414÷3=138

✅ Mrs. Lim’s final number of buttons = 138

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Here’s a challenge for P3s stepping up to P4!

🟣 Amy had 48 stickers. She gave the same number of stickers to each of her 3 friends and had 6 left.

❓How many stickers did each friend receive?

🧠 Encourage your child to solve it using model drawing or
guess-and-check!

🔍 Let’s break it down visually:

One way to work it out:


🟧🟧🟧+ 6 = 48

Number of stickers given to her friends:
➡️ 48 – 6 = 42

An equal number of stickers was given to each friend
So each friend got :

➡️ So each friend got = 14 stickers

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🎁 P6 Problem Solving: Mr Lee & Mr Yeo’s Children’s Day Gifts
💡 A practical example of applying Singapore Math models and algebra to solve real-world problems.

Content:

Both Mr. Lee and Mr. Yeo spent $74.80 on identical gifts.
Mr. Yeo received 6 more gifts than Mr. Lee because of a 15% discount coupon.

Question:

Mr. Lee and Mr. Yeo bought identical children's day gifts for their students. Each of them spent
'$74.80. Mr. Yeo got 6 more gifts than Mr. Lee because he has a coupon that gives him a 15%
discount.
(a) What was the price of each gift without the discount?
(b) How many gifts did Mr. Yeo get?

🧠 Our thoughts:

You can approach this through algebra:

You can start by assuming price = P

You can set up:

74.80/P = Lee’s quantity
and 74.80/0.85𝑃=Yeo’s quantity

Then you can equate the difference to 6:

74.80/0.85𝑃−74.80/𝑃=6

Solved algebraically → P = $2.20

You will find that

Mr Lee was given : 74.80 ÷ 2.20 = 34 gifts

Mr Yeo was given : 34 + 6 = 40 gifts ✅

In Singapore Maths Model Approach, we compare the number of blocks using price, quantity and adjusting for the discount rate.

..🟧🟧🟧
..🟧🟧🟧+6

74.80/ 85% of P - 74.80/100%of P = 6 where P is undiscounted price

Multiply by P

74.80/ 85% - 74.80/100% = 6P

74.80 x100/85 - 74.80 x100/100 =6P

2.20=P (Undiscounted Price)

74.80/2.20=34 (Number of gift obtained by Mr. Lee.

88=6P

so P= $2.20 and

number of gifts obtained by Mr. Lee was 74.80/2.20=34

Parents and Students Welcome! 💖 hope this helped clarify Singapore Math comparison models!

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Question:

In a sewing factory, 5 seamstresses can sew 10 dresses in 10 hours on average.
How long will 50 seamstresses in the factory take to sew 50 dresses on average?

Our thoughts:

✅ Step-by-Step Thinking with Blocks
🧠 Step 1: Understand the base rate
From the problem:

5 seamstresses → 10 dresses in 10 hours
So, 1 seamstress → 2 dresses in 10 hours

🟧🟧 = 2 dresses (by 1 seamstress in 10 hours)

🔍 Step 2: What's the task now?

We want to sew 50 dresses.

Since 1 seamstress can do 2 dresses in 10 hours,

✅ 25 seamstresses will take 10 hours to sew 50 dresses.

🟧🟧 x 25 = 50 dresses (25 seamstresses needed)

But the factory has 50 seamstresses — that’s double the manpower.

📏 Step 3: Use Comparison Model

👩👩‍🦰👩‍🦰👩‍🦰 👩‍🦰work done by 25 workers in 10 hours
👩👩‍🦰👩‍🦰👩‍🦰 👩‍🦰👩👩‍🦰👩‍🦰👩‍🦰 👩‍🦰= same work can now be split between 50 workers
Each unit is done twice as fast, so the time is halved.

⏱️ Final Answer:
🧮 50 seamstresses can sew 50 dresses in 5 hours.

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Problem: Four girls shared the cost of a book equally. When calculating the amount of each share, one of the girls made an error by dividing the book's price by 3 instead of 4. Each girl paid $5 more than her Share. What was the cost of the book?

ProsperiSupportHub enjoys this question.

Equal Sharing with Comparison; Two-Step Mixed Operation Model (because there's interpretation + comparison)

Level: Primary 4?

🧠 Block Model Solution (Child-friendly Visual)

✅ Step 1: Represent the problem using a model

🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦
(Book = 12 units, shared equally by 4 )

→ Each girl pays 3 🟦

✅ Step 2: Represent the Mistake

Same book price wrongly divided among 3 girls:

🟦🟦🟦🟦 🟦🟦🟦🟦 🟦🟦🟦🟦 = 16 🟦 total

(Each girl pays 4 🟦 instead of 3 🟦)

✅ Step 3: Comparison

Each girl overpaid:
4 🟦 − 3 🟦 = 1 🟦

Since 4 girls each overpaid by 1 unit,

4 units = $20 → 1 unit = $5

✅ Step 4: Final Answer

Total cost of the book = 12 🟦 × $5 = $60

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🔹 Question:

Equal Grouping Model

A total of 24 apples were packed equally into 6 baskets.
How many apples were packed in each basket?

For student's working, see image.

📦 Model Type: Equal Grouping Model

➡️ Equal groups model:

|🟦4 | 🟦 4 | 🟦 4| 🟦4 | 🟦 4 | 🟦 4|

Correct Model Type
🟦 Equal Grouping Model — ✔
You interpreted the total of 24 apples as being divided equally into baskets.

Accurate Visual Representation
▫ One box labelled "24 Apples"
▫ Split into 6 equal boxes, each with “4” — ✔
▫ Visually balanced and labelled (1–6 baskets)

Logical Working Strategy
✔ Explored possible groupings:
"If 1 apple… then 6, 2 apples… then 12, 3 apples… then 18…"

Shows trial-and-error reasoning with eventual correct match:
"4 apples in each basket → 24 total" — ✔

Correct Computation
🧮 24 ÷ 6 = 4 (though not stated algebraically, the logic shows mastery)

Clear Final Statement
"4 apples were packed in each basket" — ✔
✅ Complete and correctly labelled with units

❗ Common Student Errors
🔴 Writing "4" with no sentence or context
🔴 Mixing up part and whole (e.g., saying 6 apples in total)
🔴 Incorrect division: adding or subtracting rather than distributing
🔴 Inconsistent group sizes (unequal or boxes not matching the model)

🍎 How do we help Primary 3 students understand division without memorizing formulas?
Through Equal Grouping Models, they see the math happen:

24 apples

6 baskets

Neatly grouped

Instead of guessing, students explore, reflect, and arrive at the answer:
“4 apples were packed in each basket.”

✅ They don’t just divide.
🔁 They understand division as equal sharing.

📘 This is how our model-based Primary 3 course builds lasting math confidence.

Question:

Lily has 3 baskets. Each basket contains 6 mangoes.
How many mangoes does Lily have in total?

For student's working, see image.

📦 Model Type: Equal Grouping Model
🟦 6 Mangoes | 🟦 6 Mangoes | 🟦 6 Mangoes

🧮 Equation:
6 + 6 + 6 = 18 ✅
(Also acceptable: 6 × 3 = 18)

✅ Final Statement:
"Lily has a total of 18 mangoes."

🔹 Correct Model Type

Equal Groups — ✔

Lily has 3 equal groups of mangoes.
Each group contains **6 mangoes**.

🔹 Accurate Layout

Each box shows one group:

🟦 6 Mangoes | 🟦 6 Mangoes | 🟦 6 Mangoes — ✔

Clearly labelled and visually balanced.

🔹 Correct Equation

6 + 6 + 6 = 18— ✔
(Also acceptable: 6 × 3 = 18)

🔹 Final Statement

"Lily has a total of 18 mangoes." — ✔
✔ Clear ✔ Complete ✔ Mathematically correct.

❗ Common Student Errors (for Parent Awareness)

❌ Using addition model instead of multiplication:
Students might draw unequal boxes or skip grouping.
❌ Omitting units** (e.g., forgetting to write “mangoes”).
❌ Inconsistent number of groups: e.g., drawing 4 boxes but adding 3 values.
❌ Incomplete final answer: Writing “18” without explaining *what* it means.

Singapore Math- Model Drawing for Problem Solving at Primary 3.

💭 How do we teach 8-year-olds to master multiplication without memorizing times tables blindly?

In our Primary 3 course, we train students to visualize multiplication through neat, logical model drawings like this:

Lily has 3 groups of 6 mangoes.

She has a total of 18 mangoes.

> 💯 Prosperi Math Support Hub, our students don't just get the right answer — they understand why.