Tie

Raymond's solution is easier.

For students who have not done this question before, it would be helpful for them to work on understanding the pattern first, rather than to use the formula which they may not understand. One way to find the number of unshaded squares for Pattern 15: we can ask what numbers make up the total of white squares. 1 + 2 + 3 + 4 +...+ 13 + 14. How can we add up these numbers efficiently? We notice that we can pair up numbers to form 15 (1+14, 2+13, 3+14, ...7+8). Next question is how many groups of 15 can we get? Any other numbers not accounted for? No, so there are 7 groups of 15 = 7*15 = 105.

Another method if 'see' the pattern is by drawing rectangles 2 by 3, 3 by 4, 4 by 5, etc) using dots and halving the rectangle diagonally to realise that the number of dots on each half form a triangle, similar to the pattern in the question. That is why the formula for the number of dots is n(n+1)/2. One of the values of working this way is in the process to understand the pattern and come up with a rule rather than to use a formula that is not understood. Of course, after a few times of working on the same number, the student may be able to just apply the 'formula'. Even then, they should be able to explain how the 'formula' comes about.

Students who merely memorize the formula will not be able to apply it on all other questions, which is why showing them how the formula is derived is important. Even if they cannot recall the formula, by knowing how they can determine the pattern by way of derivation, they can still come up with the formula. I do not think educators worth their salt in this forum think that memorizing formulas is the way to go. That is why precisely the parent wishes to know how the formula came about.

Students nowadays can adapt a lot faster than we give them credit for. Maybe not all, but I have met my fair share of P5s and P6s who can understand this formula and apply it successfully. Since this formula comes in handy when they promote to secondary school, there is no harm teaching them how to use it now.

Number bonds suggested works in tightly with the formula, because the discerning students can see that 7x15 is the same as the formula (14 x 15)/2. So we are basically talking about the same animal except that the initial approach differs.

The semicircle has a diameter of 8 cm, so it's radius is 4 cm. The distance from AD to E is thus 4 cm. So the height of BCE is 10 - 4 = 6 cm. The area of triangle BCE is (8 x 6) /2 = 24 cm^2.

Why divided by 2?

1/2 base X height or BX H / 2

Micheal Lim...area of∆ is = half base x height... I draw the model if u want?

Yes pls.

Triangle BCE.. Base-8cm...Height-6cm Hope u understand Micheal Lim

Tks for the model

11@$0.20-$2.20 8@$0.50-$4.00 Total--$6.20 So the answer 11 twenty-cent coins

Total amount $6.20 3 twenty cent coins-$0.60 $6.20-$0.60= $5.60 20¢+50¢=70¢ $5.60/70¢= 8 coins 8 FiftyCentCoins+8TwentyCentCoins 8+3= 11(answer)

Yeo See Yeong...wow u are faster than me...LOL

U typed mah. I write faster. Haha.

Tks a lot

Brilliant job, Izam and Mister Yeo. Just want to show a slight variation here. Add three more 50-cent coins into the mix, so that the total value becomes $6.20 + $1.50 = $7.70 $7.70 ÷ ($0.20 + $0.50) = $7.70 ÷ $0.70 = 11

3. 11 cubes. Volume = 2×2×2×11 = 88sqcm. 4. Cube root of 64 is 4. So area is of any side is 4×4 = 16

Tks.

You are most welcomed!

Gear B is required to turn four rounds.

Xavier, is it because for every round that B completes, A will lag behind by 2 gear. So B needs to turn 4 rounds (2x4 =8 gears) for A to catch up?

Xavier Sng How do u get the answer four round？tks

my daughter answer is 24 round！ i am not sure

Good evening Winnie. Mister Yeo had pretty much explained it. For every round Gear A rotates, Gear B rotates 1 and 1/3 round. So when Gear A rotates three rounds, Gear B rotates 4/3 rounds x 3 = 4 rounds.

Thanks Mister Yeo and Xavier so much ！very detailed explained it ！ic now！

You are most welcomed Winnie. I didn't do much. Just guessing the logic based on Xavier's answer.

Glad to help, Winnie. Please don't sell yourself short, Mister Yeo. You are just too humble.