Primary 4 Mathematics: Modeling topic (14x questions from year 2018 SA1/SA2 papers)

Singapore MOE is very proud of their mathematics modeling, which I do not understand why. The modeling can be solved by algebra sometimes. I also heard many good primary school students in mathematics meet difficulties in secondary school as they could not understand the algebra logic. That is very dangerous. I think they probably did too many modeling questions in primary school until their brain cannot switch or comprehend the simple algebra. I teach both concepts to my boy. Don’t worry, it will not confuse them. 

He is going to finish all 32x test papers of Primary 4 (left 3x more papers). I hand-picked 14x nice modeling questions from the year 2018 SA1/SA2 test questions that he had completed. He got about 70% right. These 14x questions are very good questions for Primary 4 students. If you can get them all correct, your standard is, surely and definitely in the range of 95%-100%.

You probably wonder why I only show the modeling questions of Primary 4 but not other topics. It is simply because other topics are all very easy. My boy can easily get 95% right for other topics. Hence I believe most students will get all correct too except the modeling questions.

The 14x modeling questions below represent the difficulty/ standard of Primary 4 only. It should get tougher and trickier in Primary 5 and 6.

Here is a quick glance of 14x answers sheet. :)

 

Nan Hua Primary School 2018 SA1 Mathematics, question 43.

Question 43: Abel has $180 more than Bob. Calvin has twice as much as Abel. The three children have a total amount of $1,140. How much does Bob have?

The construction of the model is rather simple. You need to make sure to include $180 at Calvin model too. With the right distribution of $180 (total 3 blocks), you minus those $180 blocks from the total amount of $1,140 then it is easy to find out the per unit block value.

Nan Yang Primary School 2018 SA1 Mathematics, question 33 & 40.

Question 33: Sam jogged once every week. The distance that he jogged in a particular week was twice the distance that he jogged in the previous week. He jogged 700 m in the second week. What was the total distance that Sam jogged in the first 4 weeks?

This question is to test your English comprehension too. You need to understand what it really meant by a particular week was twice the distance in the previous week. Since the question is asking for the first 4 weeks, you need to construct the modeling continuously for 1^st , 2^nd, 3^rd and 4^th. 700 meter is a hint for you to find out the per block value of 350, and you have total 15 block (units).

Question 40: Alison and Benny have 3,753 beads altogether. Alison and Charles have 6,389 beads altogether. The number of beads Charles has is three times that of Benny.

(a) How many beads does Benny have?

(b) How many beads does Alison have? 

3 primary schools had come out with such similar questions. You will see the other 2 similar questions below. This is a classical “algebra” question. The difference between 6,389 and 3,753 will remove Alison’s amount and do take note Benny has 1 unit and Charles has 3 units, so it ends up 2 units remaining after the above subtraction. With this, you easily find the value of 1 unit and you can find Charles and Alison amount easily. This is algebra question. I also show the simple representation of algebra method, just for reference. It tells the whole story behind the modeling subtraction above.

 

Catholic High Primary School 2018 SA1 Mathematics, question 30 & 31.

Question 30: Eric had 208 more marbles than Rachel. After Rachel gave 59 marbles to Eric. Eric now has 2 times as many marbles as Rachel. How many marbles did Rachel have at first

This is a short modeling question. You must know after Rachel gave 59 marbles to Eric, you can also immediately identify the block value of 59 at Eric model at both sides. With that, you can find the unit value and don’t forget to add back the value of 59 as the question is asking the marbles Rachel has at first.

Question 31: Francis and George had a total of $670. After Francis gave George $150, they had an equal amount of money. How much money did George have at first?

This is another short modeling question. Read the question carefully and assign the 150 at the right block, you need to remember to assign 150 at Francis model too and you shall get the answer easily. The per unit value just happen to be the money George has at first.

Maha Bodhi Primary School 2018 SA1 Mathematics, question 41.

Question 41: Clara and Alicia collected 1289 stamps. Alicia and Bernice collected 634 stamps. Clara collected 6 times as many stamps as Bernice. How many stamps did Alicia collect?

This is the second “algebra” question I mentioned. They just twist the question here and made the model to be 6 times instead. With the same method mentioned, you can find the per unit value easily with the subtraction of 1289 and 634 which is equal to 5 units.

CHIJ Nicholas Girls’ School 2018 SA1 Mathematics, question 33.

Question 33: Walter had 279 more ice cream sticks than Zack. Zack gave 68 ice cream sticks to Walter. How many more ice cream sticks did Walter have than Zack?

This is another short and sweet modeling question. As you assign 68 from Zack to Walter, do assign 2 blocks at Walter side. That is the catch. You don’t have to find the unit value. The answer is already shown after you complete the model information neatly.

 

Henry Park Primary School 2018 SA2 Mathematics, question 38

Question 38: Jamie has 1,120 stamps and Macy has 340 stamps. How many stamps must Jamie give to Macy so that Macy will have 160 more stamps than Jamie?

This question is quite confusing. I prefer to draw out the before and after models to keep myself alert. You know the total number never change but the end-result will make Macy to have 160 more. So, minus 160 from the total amount of 1460, that is to find out the per block value easily, which is what Jamie left. With initial amount of 1,120, you can find how many she had given out.

 

Raffles Girls’ Primary School 2018 SA2 Mathematics, question 43.

Question 43: Lynette had 93 pencils and pens. After giving away ¾ of her pens and 28 pencils, she had an equal number of pencils and pens left. How many pencils did she have at first.

This question is evil. You must understand how to construct the model correctly. The critical information is she had an equal number of pencils and pens left. This equal number is one block. The question told you she gave away ¾ , so left ¼ and this 1 block is ¼ . So total 4 blocks. You can’t draw the right size of the block for 28 pencils, you just simply assign a 28 value like I did above. Minus 28 from 93, that’s the value of 5 blocks. Then, you can proceed to find the answer.

Methodist Girls’ School 2018 SA2 Mathematics, question 43.

Question 43: Andy had $2 more than Samy. After Andy spent $6.50, Samy had 3 times as much money as Andy.

(a) How much money did Andy have left?

(b) What was the total amount the 2 boys had at first?

This is also a tricky question. When Andy spent $6.50, you need to remember to minus the $2 that he had more than Samy, that will give you $4.50. With the block formation, you realized this $4.50 is actually a 2-blocks value. Then, you can proceed to find per block value. As the question is asking for total amount of the 2 boys had at first, you need to find each boy value first.

Catholic High School 2018 SA2 Mathematics, question 38.

Question 38: Eight years ago, Alan was 4 times as old as Geetha. Their total age now is 46 years. How old was Geetha eight years ago?

Not really a modeling question but more like a Math Olympia question. Total age is 46 years, 8 years ago, you need to remember to minus 8 years x 2 person = 16 years. That will give you the value for the total block of 5, then you can find the per block value easily.

 

Rosyth School 2018 SA2 Mathematics, question 40, 41 & 42.

Question 40: Both Alice and Julia had the same amount of money at first. After Julia spent $15.50 and Alice spent $3.50, Alice had 5 times the amount of money Julia had. How much money did Julia have at first?

Rosyth school is amazing. I found out this school always have unique questions by her own. This modeling question can be misleading. You need to remember only after Alice spent $3.50, then she had 5 times the amount of money Julia had. So, do remember to minus this $3.50 from $15.50, that is the value for 4 units. This is the crucial part.

 

Question 41: At a party, there were three times as many girls as boys. Each girl was given two balloons and each boy was given three balloons.

(a) How many balloons did 3 girls and 1 boy have?

(b) Given that a total of 135 balloons were given out, how many girls were there?

What a weird and confusing question. The first part is easy, 3 girls and 1 boy will have 9 balloons. I think they purposely ask this simple question in part (a) to help you to construct the model in part (b) with the same pattern, which is three times as many girls as boys. From the information each girl was given 2 balloons and each boy was given 3 balloons, you can sub divide the blocks into the block of “balloons”. It is like constructing model in the model. Confused? 135 balloons divided by 9 = 15, that’s balloon value, multiply by 6 blocks (of balloons), you get 90 balloons. Since each girl was given 2 balloons, there are 45 girls.

 

Question 42: Judy and Ben had a total of 115 stickers. Ben and Eugene had a total of 160 stickers. Eugene had 4 times as many stickers as Judy. How many stickers did Ben have?

This is the 3^rd algebra question I mentioned earlier. Rosyth school has the weirdest model questions in their test paper. This question needs no guidance by now. Subtraction of 115 from 160 gives you 3 units. The rest is simple. 

By now, you should enjoy modeling questions and be expert in it, do remember, this is Primary 4 standard. I spent a good 180 minutes preparing all these. How many questions you get it right? 😊