we are going to look at the 2019 PSLE Math Question on Patterns which many Singaporean primary school kids got stuck at. grade 7 math worksheets philippines

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Let’s take a look at this Math question together! At once glance,
you’ll be able to tell that it’s a pattern question because of the figure numbers and shapes that you see.

This Math question is divided into 3 parts. In the first part, we are supposed to fill in the missing blanks in the table,
so looks like we are supposed to find the number of white triangles and the number of grey triangles for figure 5.

In the second part of the question, we need to find the total number of grey and white triangles in Figure 250.
And finally, the last part of this PSLE Math question, part c,
we see something new. We are asked to find the percentage of greytriangles in Figure 250. Now, let’s put these questions aside forawhile and concentrate on the figures.grade 7 math worksheets philippines

If you had seen our previous video on solving Pattern questions,
you would have known that the #1 rule of solving any question that deals with Pattern is to look at the shapes,
numbers and relationships. grade 7 math worksheets philippines
So first of all, let’s see what shapes we have. Looks like we have triangles of the same size stacking up and there seems to be 2 kinds of triangles here, grade 7 maths worksheets with answers

the white ones and the grey ones. The colours of the triangles appear to taketurns in each row.
We have a white triangle in row one, followed by grey triangles in row 2,
and then the white triangles appear again in row 3 and so on.
That’s it for the colours. Now let’s look at the numbers we have and see what relationship we can find.
What are we given?

We have the figure number,
the number of white triangles, the number of grey triangles and the total number of triangles for each figure.
Let’s think about how these numbers arerelated to one another, grade 7 math worksheets philippines
ok? The easiest relationship that we can find will be the relationship between the figure number and the total number of triangles. Looking at these numbers 1, 4, 9, 16, you should be able to tell that they are square numbers.

And how are the square numbers related tothe figure numbers?
We can see that in order to get the totalnumber of triangles in any figure,
what we need to do is to square the figure number. In other words,
to multiply the figure number by the figure number.
So instead of drawing each figure one by one, we’ve discovered a shortcut!
Well done! Then what about the white triangles and grey triangles? grade 7 math worksheets philippines

Let’s try to see what’s the differencebetween them.
Do you notice anything strange when wetry to subtract the numbers? It looks like the number of grey triangles is always more than the number of white triangles in the even figures and the number of white triangles is always more than the number of grey triangles in the odd numbers. grade 7 math worksheets philippines
Well, that’s something interesting. Anyway, let’s subtract the smaller number from the bigger number to find the difference in the number of white and grey triangles. grade 7 maths worksheets with answers

Hmm…it appears that the difference in thenumber of white and grey triangles turns out to be the same as…
the figure number! This means that as long as we have the figure number,
we’ll always be able to find the difference in the number of white and greytriangles for that particular figure.

That’s another great discovery! Then, what about the individual number of white triangle and the grey triangles in each figure?
How do we go about finding them?
Well, here’s the trick to this 2019 PSLEMath question and it is built upon the comparison model that you have learnt before.
If you know the total of 2 items and the difference between them,
are you able to work out the number of items with the smaller quantity?
Let’s focus on this idea for the time being and after understanding this important concept, you’ll be able to learn the secret behindunlocking this 2019 PSLE Math question, grade 7 math worksheets philippines
alright? What we are going to do now is to draw a simple comparison model to help you see better.grade 7 math worksheets deped

We are going to draw a rectangular box to represent the item that has the smaller number.
And then, we are going to draw a longer rectangular box to represent another item with the bigger number.

What do we do if we want to find the smaller number? We’ll subtract the difference from the total.
This gives us 2 equal parts. And to find the value of one of these parts,
we’ll divide what we have by 2! Did you figure this out? If you did,
great job! Now let’s apply what we have learnt to thisPSLE pattern question. We’ll draw the same comparison model asbefore, but this time round,

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instead of item 1 and item 2, we are comparing the number of white triangles and the number of grey triangles.
Let’s pick a random figure as an example. We’ll use figure 2 here.
Let’s think about what we know.
We know the total number of white and grey triangles in figure 2 is 4, correct?

And we also know that the difference in the number of white triangles and grey triangles is same as the figure number which happens to be 2.
How do we go about finding the smaller number?
Well, we’ll subtract the difference of 2, from the total which is 4.
This gives us 2 and what we are going to do next is to divide this number by 2. And that’s how we know that we have 1 white triangle. Following so far?
In order to find the number of grey triangles, what do we do? grade 7 math worksheets philippines
We’ll simply take the total number of triangles and subtract the number of white triangles from it.
So 4 – 1 gives us 3 grey triangles which is exactly what we have in this table. So far so good? Now that we have understood the pattern better,
we are ready to solve the question. Let’s look at part a.
To find the number of white triangle in figure 5, let’s think of whether there should be more white triangles or more grey triangles. Looking at the odd columns, we can tell that the number of white triangles is always more than the grey ones.

So this means that the smaller number will refer to the grey triangles.
For Figure 5, notice that the total numberof triangles we are given is 25?
and the figure number is 5. Let’s make use of these numbers to work out the number of grey triangles first.
Do you remember how to do that? We are looking at figure number 5,
so the difference between the white and grey triangles must be 5.
To find the smaller number, we’ll subtract the difference from the total, and that’s why we’ll take 25 – 5.
And after doing that, we’ll divide the answer by 2. This gives us an answer of 10 for the number of grey triangles. grade 7 maths worksheets with answers

Once we have the number of grey triangles, finding the number of white triangles for figure 5 should be easy.
All we need to do is to subtract this number from the total number of triangles in Figure 5. So 25 – 10 gives us an answer of 15 white triangles. Understand so far?

Now let’s move on to part b. How do we go about finding the total numberof grey and white triangles in Figure 250?
This should be simple.
Remember that the total number of grey and white triangles in any figure can be found by multiplying the figure number by the figure number?
So in order to solve this, we’ll simply take the figure number of 250 x the figure number of 250. Did you get a total of 62 500 grey and white triangles? Well, if you did,
great job! That’s a lot of triangles! And finally, let’s solve part c. grade 7 math worksheets philippines

In order to find that answer,
we’ll need to know a few things.
We’ll first need to know the number of grey triangles and then we’ll also need to know the total number of triangles.
After knowing these numbers, we are going to express them as a fraction and multiply it by 100% to change it into a percentage. grade 7 maths worksheets with answers

The first step to finding the number of greytriangles in Figure 250 is to determine whether we are supposed to look for the bigger no.
or the smaller no.
Since we know that 250 is an even number, let’s look at the even columns again. What do you notice?
The number of grey triangles is more thanthe number of white triangles for the even columns, correct? grade 7 math worksheets philippines

So we know that the number that we are looking for must be the bigger number. The total number of triangles for figure 250 is 62 500,
the difference in the number of white triangles and the number of grey triangles is the figure number which happens to be 250. So let’s work backwards.

62500 – 250 gives us 62250 and when we divide this by 2,
we’ll get 31125. Now this is the smaller number.
To find the bigger number, we’ll subtract what we have from the total number of triangles. 62500 – 31125 gives us 31 375.
Before you get too excited, this is not the final answer! To find the percentage of grey triangles in Figure 250,