Primary 4 Mathematics: Seeing Patterns (6x questions including 1x 2019 PSLE question)

 

 

“Pattern, pattern, pattern.” Can you see it?

By far, this is the most controversial mathematics question appeared in year 2019 PSLE. It is shown below too.
Some primary 4 students have encountered such question in the school test. Among the 12 famous schools, “seeing pattern through figures” question appeared only 5 times out of total 24 test papers. The schools are:

(1)Nanyang Primary School (SA1 test)

(2)Tao Nan Primary School (SA1 & SA2 test) appeared twice!

(3)Henry Park Primary School (SA2 test)

(4)Catholic High School (SA2 test)

The above 4 primary schools have early exposure with such topic to be quizzed.

Nanyang Primary School 2018 SA1 Mathematics, question 42.

 

Part (a) is easy. The pattern is obvious. 4, 6, 8, 10. You need to find the pattern carefully for the number of matchsticks, 12, 19, 26, etc. It has the pattern of (number of triangles x 3 + n). Alternatively, you can draw the figure 4 to find out the answer easily.

Part (b) is straightforward. Just add 2 continuously. That’s one easy pattern.
You should apply formula above to find part (c) answer. You do not want to draw the figures all the way to "figure 9". That’s not the intention of the test. Knowing figure 9 will have 20 triangles, you can know matchsticks quantities with the formula of (number of triangles x 3 + n), which is ( 20 x 3 + 8 ) = 68.
List down the pattern neatly. I prefer to list down the information in vertical style.

Tao Nan School 2018 SA1 Mathematics, question 10.

Part (a) is easy. We can see the pattern is +2, +3, +4, +5, … etc.

How to find 66 dots? You can continue to do the addition +6, +7, +8, +9, +10, etc. until 66 is reached. Figure 11 (+11) is the answer.
I do not know the easier way.

Henry Park 2018 SA2 Mathematics, question 43.

 

 

Part (a) is easy. It has the pattern of +2, +2, +2, +2, etc. to reach the answer of 11.

To find out the answer for part (b), you need to find the pattern of figure number and number of buttons, which is (number of buttons -2). If you have the total buttons of 129, the answer is 129-2 =127.
To search the answer for part (c) , you then need to see the pattern of figure number and the number of sticks, which is (figure number x 2 + 1), hence the number of sticks at figure 17 would be 17x2+1 = 35.

p/s: typo at the image above 4-2=2 . :)

Catholic High School 2018 SA2 Mathematics, question 45.

 

Part (a) is too easy! The number of rectangles = figure number. Figure 10 has 10 rectangles!

Part (b) is a good question. The pattern is, +4, +4, +4, +4, etc.
As you know figure 1 has 6 circles, that’s the first starting point that you add 4. In order to find 98 circles, you need to minus 6 from 98 first, then divide it by 4.
The tricky part is here. You need to remember to +1 to get the answer of 24.
Why?
This is the famous “tree distance” question.
2 trees form a distance.
The distance here is four (“+4 “) and your 2 trees are figure 1 and 2.
You have a total distance of 92. You need to divide the total distance by 4 and remember to add 1 back due to the principle of 2 trees form a distance. Remember this!

Tao Nan 2018 SA2 Mathematics, question 18.

 

Part (a) is simple. You count the squares from the figures to obtain 13 and 17.

You continue to draw figure 4 at part (b) by adding one square each at east, south, north and west. Simple!
For the part (c), you shall find the pattern of +4, +4, +4, +4, etc. .
This is the same “tree distance” question again.
You know the figure 1 (starting point) has 9 squares. Minus 9 from 93 to get 84. That’s your “distance”. Divide by 4 to get 21 “trees”. Do remember to add 1 to get the answer of 22 “trees”, which is figure 22.
2 trees form a distance theory. I call it. : )
These “pattern” questions are primary 4 level only.
I believe such question will appear again in primary 5 and 6 SA1/SA2 test.
Let’s take a look at the controversial mathematics question in year 2019 PSLE. It is crowned as the toughest question.

 

 

Primary 4 student shall get the part (a) and (b) right, 2 marks are given here freely.

To find the number of white and grey triangles at figure 5, you just need to draw it out and have a good look at it. The pattern is clear. For figure 5, there is no addition for the grey triangles, so the number will stay at 10. The addition row is white triangles and it will have 9 additional white triangles added, so the answer is 16+9 = 25.
Pause a while and see the pattern of the triangle.
It has a pattern of 1, 3, 5, 7, 9, 11, 13, 15, etc..
White triangle has the pattern of 1, 5, 9, 13, etc., pattern of (+4).
Grey triangle has the pattern of 3, 7, 11, 15, etc., pattern of (+4) as well.
The part (b) asks for the total number of grey and white triangles for figure 250. Of course, we now must create an additional column of total triangle of white and grey. From the table, you can see the total triangle has the pattern of “figure number x figure number”. That is one easy pattern you shall observe. To find the answer of figure 250, it is just 250x250=62500. Simple! 2 marks free!

Part (c) is tough. I agree.

It is almost impossible to see the pattern if you do not extend the table. The interest here is to find the total number of grey triangles.
So, you draw out only the grey triangle table, which contain figure 2, 4, 6, 8, 10, etc.
You should see the pattern of total triangle to be +7, +11, +15, +19, etc..
Now, how to find the pattern to reach figure 250 and that also correspond to the total triangle number? This is the toughest part.
Here is the trick.
Just write down what you have in mind first, then try to observe if there is any pattern we can conclude.

3 is like 3 x 1 = 3
10 is like 10x 1 = 10 , or 5x 2 = 10.
21 is surely 3x 7 = 21.
36 is like 6 x 6= 36, 4x9 = 36.
55 is nothing but just 11x5 = 55.

Once you pen down all your thoughts, you should see a pattern of 1, 2, 3, 4, 5, etc..
That’s one good pattern! Re-arrange them and you shall get 1x3, 2x5, 3x7, 4x9, 5x11.
The question asks for grey triangle at figure 250. We know the first pattern is figure number divided by 2, which is 250/2 =125.
We then find the second pattern, which is x3, x5, x7, x9, x11, that’s simply add the “figure number+1”, which is 250+1 = 251.
To reach the answer, you multiply 125x251=31375.
What an evil question!
To find the percentage, simply divide 31375 by 62500 x 100% =50.2%.
3 marks here. You shall present your procedures clearly here. Although you might not reach the right answer, you could still be given 1 point or 2 out of 3. Do not leave it blank, try your best!
There are many such pattern questions on the Internet. You can always download various test papers to have more practices.
Practice makes perfect!
p/s: image above for percentage calculation, missing "x100%".