11 Math Problem Sums Every A* Student Knows

Problem sums, also known as Math word problems, has always been a challenge to many Primary school children and their parents. If you are having trouble solving these primary school Math problems, help is on its way!

In this Practicle Problem Sums Guide, we are going to identify 11 types of problem sums that often appear in primary school Math homework & school examinations.

Once you are able to master the Math concepts behind each of them, you’ll know how to solve problem sums regardless of the topic in a heartbeat.

1. Remainder Concept
2. Proportion Concept
3. Simultaneous Concept
4. Pattern Concept
5. Gap and Difference Concept
6. Equal Concept
7. Repeated Identity Concept
8. External Transfer (Unchanged Quantity) Concept
9. Internal Transfer (Unchanged Total) Concept
10. External Transfer (Same Difference) Concept
11. External Transfer (Changed Quantity) Concept

For the sake of simplicity, we’ve divided these concepts according to the primary school levels that they’ll first appear in.

Math questions that use the Remainder Concept are often problem sums that contain the word “remainder” or contain some kind of left-over. These questions deal with either whole numbers or fractions.

To solve these Math problem sums, use the Model Method (more specifically, part-whole models) or the Branching Method.

Here’s an example question:

Tommy the cat ate 4/9 of his food during breakfast. After eating 3/10 of the remainder and 58 g of food for lunch, he had 12 g of food left. What was the amount of food he had at first?

The Proportion concept forms the basis of most Math questions. However, they can be hard to solve for many students.

You will see that these problem sums will provide your child with the total quantity of the items, the proportion of one item to the other and a common characteristic between the items.

To solve them, apply the Grouping Method.

Here’s an example question:

Gary spent $1760 on some tables and chairs. He bought 20 more chairs than tables. If each table cost $77 and each chair cost $33, find the number of chairs he bought.

Simultaneous concept problem sums can vary in terms of difficulty. Although the concept is similar to simultaneous equations in Algebra in secondary school, the numbers that are used in such Math questions at the primary school level are usually more friendly.

In order to solve problem sums that compares different quantities of the same kinds of items, we’ll usually work with the relationship between the numbers or use the Model Method.

Here’s an example question:

Parker bought 3 pairs of sneakers and 5 t-shirts for $349. If 6 pairs of sneakers and 4 t-shirts cost $416, what is the cost of 1 pair of sneakers and 1 t-shirt?

Instead of problem sums, these Math questions can be thought of as puzzles. Depending on how good your spatial and temporal skills are, Math questions that uses the Pattern Concept can be the one of the easiest or most challenging ones to them.

The key to solving these questions is to link what you see in the puzzle to familiar numbers. There is no fixed way to solve such questions and there are usually more than one way of solving them.

Here’s an example question:

The pattern below is made up by arranging some tables and chairs. Study the pattern carefully and answer the questions below. How many chairs are there in Pattern 48?

The last type of Math problem sum question that we are going to look at involves the infamous Gap and Difference Concept (also known as the Excess and Shortage Concept).

These questions usually give us two scenarios that compares the quantities of two items and you’ll have too much of one item or too little of the item.

These Gap and Difference questions can be solved in three ways – the Model Method, the Units Method or purely through simple arithmetic.

Here’s an example question:

Mario wants to give out an equal number of blue shells to each friend. If he gives 10 blue shells to each friend, he will be short of 30 blue shells. If he gives 8 blue shells to each friend, he will be short of 6 blue shells. How many friends did he have?

The next kind of Math questions that we are going to look at are problem sums that use the Equal Concept. These Math problem sums will compare two fractions (sometimes expressed in percentages) of different items that represent equal amounts.

Solve such problem sums either by model drawing (using comparison models) or making the numerators the same.

Here’s an example question:

Thor and Hulk punched each other multiple times in the Contest of Champions battle. 3/4 of Thor’s punches were equal to 2/3 of Hulk’s punches. Both of them punched a total of 408 times. How many times did Thor punch the Hulk?

Like its name, the Repeated Identity Concept appears in word problems where there exist 2 or 3 items, with specific items sharing the same quantity.

To solve these Math questions, we’ll first need to identify the common quantity that is given in that particular problem sum. Once we spot that, we can then solve it using the Units Method.

Here’s an example question:

Doodles has 2/3 as many shiny cards as Ash. Ash has 1/5 as many shiny cards as Yugi. If the three of them have a total of 120 cards, how many shiny cards does Doodles have?

Now, let’s look at 4 different transfer type problem sums.

Understanding the main idea behind each Math concept is key to solving these problem sums naturally.

Such problem sums have two items involved and an event happening that results in a change in the quantity of one of the items while the other quantity remains the same.

Solving these questions can be done by either the Model Method or the Units Method if the number is not as friendly.

Here’s an example question:

There are 80 children at a swim club. 30% of them were boys. After a few boys left the club, the percentage of boys dropped to 20%. How many boys left the club?

Similar to what we discussed earlier on, these type of Math problem sums questions also involves two items and an event happening.

However, because the event usually refers to a transfer of a certain quantity of one item to the other, the quantity of each item changes. The only thing that remains constant is the total quantity of the two items.

We can either draw the model to solve this question or use the Units Method.

Here’s an example question:

The ratio of Tom’s allowance to Jerry’s allowance is 7:11. If Jerry gives Tom $84, they will have the same amount of money. How much do they have altogether?

Next, let’s look at Math problem sums that deals with the External Transfer Concept, also known as the Constant Difference Concept.

In these problem sums, the same quantity of each item will be added or subtracted from the two existing items that we have, Therefore, we’ll know for sure that the difference between the items will stay the same.

Once again, the Bar Model Method or the Units Method will come in handy when we are solving them.

Here’s an example question:

At first, Jay had $1144 while Samuel had $526. After they each spend an equal amount of money on some toys, Jay then had 4 times as much money as Samuel. How much did each boy spend?

The last type of transfer problem sums deals with the External transfer with changed quantity concept. This is one of the most difficult Math problem sums to master.

In these Math questions, the quantity of the two items given at the start and the end are different and it may be hard for children to visualise what is going on with the Model Method. Hence, solving them successfully usually requires using the Units and Parts method, which is a simplified form of Algebra using two variables.

Here’s an example question:

Snow had 40% as many apples as Sleepy at first. Snow bought another 8 apples and Sleepy ate 5 apples. Then, Snow had 80% as many apples as Sleepy. Find the number of apples Snow had at first.