The Ultimate Guide To Primary 3 Mathematics

Contents:

1. Overview
2. Numbers
   1. Whole Numbers
   2. Addition & Subtraction
   3. Multiplication
   4. Division
   5. Solving Mathematical Operations Word Problems
   6. Fractions
   7. Money
3. Measurement and Geometry
   1. Length, Mass, and Volume
   2. Time
   3. Lines
   4. Angles
   5. Perimeter
   6. Area
4. Graphs
   1. Bar Charts
5. Conclusion

Overview

With the rigorous Mathematics syllabus in Primary Schools, it is no doubt that Primary 3 is a key milestone for students in their transition to the Primary School Leaving Examinations (PSLE).

In Primary 1 and 2, students are taught foundational mathematical concepts such as the multiplication table, basic mathematical operations, and fundamental measurement techniques. However, it is only in Primary 3 where students make a jump to applying these basic concepts to problem solving questions, encountering more complex topics such as area calculations and fractions.

As such, we will not only cover the key content in the Primary 3 Mathematics syllabus, but also some step-by-step guide to solving basic questions, preparing students for the examinations.

Numbers

Whole Numbers

Number Notation

With the uncountable range of numbers in the real world, students in Primary 3 take a step forward in this aspect by learning about larger numbers, up till the thousands. At this stage, students learn about numbers in the ones, tens, hundreds, and thousands place.

1 2 3 4

In the number above:

• The number ‘1’ is in the thousands place.
• The number ‘2’ is in the hundreds place.
• The number ‘3’ is in the tens place.
• The number ‘4’ is in the ones place.

 

Number Value

Apart from that, students are also expected to understand the value of each number notation. With an understanding of the value of each number notation, students would then be able to gain perspective into the value of numbers and compare between them.

Each number notation can be ordered as such:

Largest                                      Smallest

Thousands   Hundreds   Tens   Ones

1 2 3 4

In the number above:

• The number ‘1’ is in the thousands place and it has a value of 1000 (one thousand).
• The number ‘2’ is in the hundreds place and it has a value of 200 (two hundred).
• The number ‘3’ is in the tens place and it has a value of 30 (thirty).
• The number ‘4’ is in the ones place and it has a value of 4 (four).

Put together, we can read the number above as one thousand, two hundred and thirty-four.

Number Patterns

While there is a huge range of number patterns available which can be tested during the examinations, we will only be covering the commonly encountered number patterns in this guide. Ultimately, students can hone their sense of mathematical perception through constant practice, allowing them to easily identify number patterns.

Addition of Similar Terms:

• (Addition of 1) – 1, 2, 3, 4, 5, 6, …
• (Addition of 2) – 1, 3, 5, 7, 9, … or 2, 4, 6, 8, 10, …
• (Addition of 5) – 5, 10, 15, 20, 25, …

Addition of Consecutive Terms:

• (Addition of 1, 2, 3, 4, 5, …) – 1, 2, 4, 7, 11, …
• (Addition of 2, 4, 6, 8, 10, …) – 1, 3, 7, 13, 21, … or 2, 4, 8, 14, 22, …

Subtraction of Similar Terms:

• (Subtraction of 1) – 10, 9, 8, 7, 6, ….
• (Subtraction of 2) – 10, 8, 6, 4, 2, … or 9, 7, 5, 3, 1, …

Subtraction of Consecutive Terms:

• (Subtraction of 5, 4, 3, 2, 1, …) – 11, 7, 4, 2, 1, …
• (Subtraction of 10, 8, 6, 4, 2, …) – 22, 14, 8, 4, 2, … or 21, 13, 7, 3, 1, …

Multiplication of Similar Terms:

• (Multiplication of 2) – 2, 4, 8, 16, 32, …
• (Multiplication of 3) – 3, 9, 27, …

Division of Similar Terms:

• (Division of 2) – 16, 8, 4, 2, …
• (Division of 3) – 27, 9, 3, …

Combination of Operations:

(Multiplication of 2, followed by Addition of 1) – 1, 3, 7, 15, 31, …

Addition & Subtraction

Comparison to Earlier Levels of Mathematical Operations

In earlier levels of Primary School Mathematics, students were only required to add and subtract 3-digit numbers, up to the hundreds place. However, in Primary 3 Mathematics, students are required to now handle the 2 basic mathematical operations with 4-digit numbers.

It is important to note that in adding or subtracting 4-digit numbers, the workings are completely identical, only with the new addition of a number in the thousands place.

Example of Workings for 4-digit Addition

Example of Workings for 4-digit Subtraction

Multiplication

Multiplication Tables

Prior to Primary 3, students were only taught up to the ‘5’ multiplication table. However, the Primary 3 Mathematics syllabus requires students to understand and have the remaining multiplication tables at their fingertips.

6 x 1	6		7 x 1	7		8 x 1	8		9 x 1	9
6 x 2	12		7 x 2	14		8 x 2	16		9 x 2	18
6 x 3	18		7 x 3	21		8 x 3	24		9 x 3	27
6 x 4	24		7 x 4	28		8 x 4	32		9 x 4	36
6 x 5	30		7 x 5	35		8 x 5	40		9 x 5	45
6 x 6	36		7 x 6	42		8 x 6	48		9 x 6	54
6 x 7	42		7 x 7	49		8 x 7	56		9 x 7	63
6 x 8	48		7 x 8	56		8 x 8	64		9 x 8	72
6 x 9	54		7 x 9	63		8 x 9	72		9 x 9	81
6 x 10	60		7 x 10	70		8 x 10	80		9 x 10	90

 

Example of Workings for 3-digit Multiplication

In the Primary 3 Mathematics syllabus, students are also required to learn how to conduct multiplications for a 3-digit number by any 1-digit number. It is important to note that in multiplying 3-digit numbers, the workings are completely identical with that of 2-digit numbers, only with the new addition of a number in the hundreds place.

Division

Division Tables

The underlying concept behind division can be seen as the reverse of multiplications. As such, while Primary 3 students are required to now divide numbers by 6, 7, 8, and 9, students can simply refer to the multiplication table above to do so. For example, dividing 56 by 8 would then give us 7.

Example of Workings for 3-digit Division

In the Primary 3 Mathematics syllabus, students are also required to learn how to conduct divisions for a 3-digit number by any 1-digit number. It is important to note that in dividing 3-digit numbers, the workings are completely identical with that of 2-digit numbers, only with the new addition of a number in the hundreds place.

Students are also now required to deal with remainders, which can be seen as the leftovers to the division. Take for example, dividing 123 cookies by 4 students. This would give us a quotient of 30 and a remainder of 3 (workings shown below). This means that each student would get 30 cookies, and after distributing the cookies evenly among the 4 students, there would be a leftover of 3 cookies.

Solving Mathematical Operations Word Problems

While some questions may seem difficult on first look, these word problems are often solvable. In this step-by-step guide, we will cover the basic steps towards solving basic word problems.

Step 1: Read

It is always important to read the question sentence by sentence.

Step 2: Draw

As you read from the front to the back, draw out a model based on your understanding of the question, and add or remove parts to or from the model depending on the question.

Step 3: Analyse

Once you have drawn your model, go back to the question and analyse what is required. In other words, find out what the question is asking for. Is it the total number of chocolates? Is it the number of chocolates one particular student has at the end? Or is it the number of chocolates one particular student had in the beginning?

Step 4: Identify

Using your model and your knowledge of mathematical operations, identify if the question requires you to use addition, subtraction, multiplication, division, or a combination of mathematical operations.

Step 5: Use

Breakdown your model into units if possible and use your mathematical operations to solve for what is required by the question!

Fractions

Simplifying Fractions

Simplifying fractions requires basic knowledge of division. To simplify a fraction, we need to divide the numerator (the top of the fraction) and the denominator (the bottom of the fraction) by the same number.

For example:

Another term to take note of when simplifying fractions would be ‘simplest form’. When a question asks for a fraction to be found in its simplest form, we always simplify our fraction until it cannot be simplified further. This means that we only stop simplifying our fraction, when we are sure that both the numerator and denominator cannot be divided by the same number anymore.

Equivalent Fractions

Equivalent fractions refer to fractions who have the same value but are expressed differently. For them to have the same value, they would need to have the same simplest form expression. Fractions with the same simplest form expression can thus be said to be equivalent fractions.

For example:

Addition and Subtraction of Fractions

While we can easily add and subtract whole numbers, these mathematical operations become slightly more complex when it comes to fractions. Just like whole numbers, we can also add and subtract fractions. However, there are a few key steps that we would have to take note of!

Step 1: Making the denominator the same

To make the denominator the same, we would have to multiply the denominator of the 1st fraction by the denominator of the 2nd fraction, and vice-versa. We also have to take note that when multiplying the denominators of both fractions, we must not forget to multiply the numerator by the same number that we did for the denominator.

Step 2: Adding / Subtracting the numerators

Once we have multiplied both numerators and denominators, the next step would be to just add or subtract the numerators only! It is important to note that we should not be adding or subtracting the denominators together!

Step 3: Simplifying

More often than not, questions would require us to always simplify our answers. Even if the question did not specify for us to simplify our final answer, it is always good practice to do so as well.

Fraction Size

With different fractions representing different sizes of a whole, it is important to know which fractions are larger than others, and which are smaller than the rest. To do so, a key tip would be to make the denominators of all fractions equal. Once we have done so, simply comparing the size of the numerators would allow us to determine which fractions are larger or smaller than others.

For example:

Money

Denominations of Money

In the Primary 3 Mathematics syllabus, students are required to add and subtract money involving decimals. As such, we will first talk about what constitutes decimals in this topic of money.

In local currency (Singapore dollars), we are always looking at dollars ($) and cents (¢). Each dollar is known to be made up of 100 cents, and each cent is known to make up 0.01 dollars (also written as $0.01).

100¢ = $1 and 1¢ = $0.01

We should also note that where the Singapore dollar is concerned, there are only 2 decimal places to the currency. This means that even if we have 10 cents, we should also remember to write the 2nd zero ($0.10).

Addition and Subtraction of Money in Decimals

To add and subtract money with decimals, we ought to treat it like any other addition or subtraction involving decimals.

For example:

$1.23 + $4.56 = ?

Quick Tip: When we add and subtract money involving decimals, it would be advised to always leave the 2 decimal places there even if the value does not involve it!

For example:

$4 + $3.60 = ?

Measurement and Geometry

Length, Mass, and Volume

Length

Length refers to how long an object is, or how far is the distance between points. Primary 3 students are expected to be able to grasp the understanding of unit conversions, from kilometres (km) to metres (m) then to centimetres (cm), and vice-versa.

For example:

6.5 km = 6.5 x 1000 = 6500 m

3.7 m = 3.7 x 100 = 370 cm

37 cm = 37 100 = 0.37 m

841 m = 841 1000 = 0.841 km

Mass

Mass is an indication of how heavy an object or a person is and is often measured in either grams (g) or kilograms (kg). Just like length, students need to know how to convert between the two mass units, from kilograms to grams and vice-versa.

Quick Tip: Conversion between kilograms and grams is just like the conversion between kilometres and metres!

For example:

64.8 kg = 64.8 x 1000 = 6480 g

913 g = 913 1000 = 0.913 kg

Volume

Volume is a measure of the amount of space occupied by an object and is measured using millilitres (ml) or litres (L). Similarly, Primary 3 students need to be able to convert between the two volume units, from millilitres to litres and vice-versa.

Quick Tip: Conversion between litres and millilitres is just like the conversion between kilometres and metres as well!

For example:

33.2 L = 33.2 x 1000 = 3320 ml

94 ml = 94 1000 = 0.094 L

Time

Time is an integral part of everyone’s lives, and it all begins at Primary 3 where students learn how to tell the time up to the minute, calculate time, as well as convert time.

Telling Time

Whenever we look at a clock or a watch, there are always 2 arrows pointing outwards from the centre. These 2 hands are known as the hour hand (the shorter arrow hand) and the minute hand (the longer arrow hand).

Quick Tip: If the hour hand is pointing in between hours, it is the earlier hour of the two.

Time can be written in 2 ways:

1. Worded Description

• If the minute hand is pointed to ‘12’ (the beginning of a new hour), we describe the time using ____ o’clock.
• If the minute hand is pointed to ‘3’ (15 minutes into the hour), we describe the time using quarter past ____.
• If the minute hand is pointed to ‘6’ (30 minutes into the hour), we describe the time using half past ____.
• If the minute hand is pointed to ‘9’ (45 minutes into the hour, and 15 minutes to the new hour begins), we describe the time using quarter to ____.

Likewise, the above rules can also be used when the minute hand is pointed to other numbers. However, instead of using the words ‘quarter’ and ‘half’, we would describe the minutes in its own value. The hour would then be described as its own number.

For example:

The time in the clock above can be written as ten past one.

Minute Hand Pointing to Number _____	Worded Description
1	Five past ____
2	Ten past ____
3	Quarter past ____
4	Twenty past ____
5	Twenty-five past ____
6	Half past ____
7	Twenty-five to ____
8	Twenty to ____
9	Quarter to ____
10	Ten to ____
11	Five to ____
12	____ o’clock

 

2. Digital Description

The digital description of time is made up of numbers as well. However, its presentation is slightly different. The hour can be just written as its own number.

• The minute can just be written as its own number after the hour but separated by a decimal.
• Depending on the hour of the day, if it is after 12 midnight but before 12 noon, the units used would be ‘a.m.’. If it is after 12 noon but before 12 midnight, the units used would be ‘p.m.’.

Quick Tip: It is important to note that 12 noon is considered to be ‘p.m.’ while 12 midnight is considered to be ‘a.m.’.

For example:

The time in the clock above can be written as 1.10 a.m. or 1.10 p.m. depending on the time of the day.

Time Conversion

While the concept behind hours and minutes may seem complex and confusing for most students, it is important to note that they are alike in representing time, just different magnitudes of it (just like metres and kilometres). However, the conversion from minutes to hours and vice-versa is slightly different compared to that of length, mass and volume which was covered earlier.

For example:

1 hour 34 minutes = 60 minutes + 34 minutes = 94 minutes

70 minutes = 60 minutes + 10 minutes = 1 hour 10 minutes

Lines

Types of Lines

There are 2 main types of lines to take note of, and they are: Perpendicular Lines and Parallel Lines

Perpendicular Lines are lines which lie across each other at a right angle (otherwise known as a 90° angle). More about angles will be gone through in the next section. These perpendicular lines can also be said to form sharp and perfect square corners.

Parallel Lines are lines which are always the same distance apart and will never meet no matter how far they extend. Parallel lines can also be identified when they have arrows across them (as seen in the figure below).

Orientation of Lines

Some keywords to note when dealing with lines at the Primary 3 level would include horizontal, vertical, and diagonal.

Horizontal: Horizontal lines are lines which lie parallel to the plane. Another way to put it would be that these lines are parallel to the bottom of your paper.

Vertical: Vertical lines are lines which lie perpendicular to the plane. Another way to put it would be that these lines are perpendicular to the bottom of your paper.

Quick Tip: It is always true that horizontal lines and vertical lines are perpendicular to each other!

Angles

There are 3 types of angles that primary school students should take note of. They are acute angles, obtuse angles, and right angles. Note that the unit for angles is ° which is read as degrees. For example, 80° will be read as 80 degrees.

Acute Angles

Acute angles are angles which do not exceed 90°. In other words, they come together to form corners which are narrower than a right angle. For an angle to be considered acute, it has to have an angle of between 0° to 90° (but not including both 0° and 90° themselves).

Source

Obtuse Angles

On the contrary, obtuse angles are angles exceeding 90°. They come together to form corners which are wider than a right angle. For an angle to be considered obtuse, it has to have an angle of between 90° to 180° (but not including both 90° and 180° themselves).

Quick Tip: Note that a 180° angle simply means a flat line!

Source

Right Angles

As mentioned earlier, right angles are angles which measure up to exactly 90°. They form perfect square corners and are said to be perpendicular as well. Unlike the drawings above which use arcs to represent the angle, right angles make use of tiny squares.

Source

Perimeter

Perimeter can be described as the total length of the boundary of an object. For Primary 3 students, you will need to know how to determine the perimeter of squares, rectangles, and other rectilinear figures. It is also important to note that the perimeter of a figure is a measure of length, hence it will take on the same units we covered in length (centimetres, metres, and kilometres).

For any general object, the perimeter can be found by simply taking the sum of the sides which form the figure’s boundary. However, there are some special rules which can be applied to common shapes such as squares and rectangles.

Squares

Squares are made up of 4 equal sides, each perpendicular to the 2 sides beside it.

While the perimeter can be found by adding up all 4 sides, another way to determine the perimeter would be to take the length of 1 side and multiply it by 4.

Rectangles

Like squares, each side of a rectangle is also perpendicular to the 2 sides beside it. However, rectangles do not have 4 equal sides. Instead, they have 2 pairs of equal sides known as the length (the longer side) and the breadth (the shorter side).

While the perimeter can be found by adding up all 4 sides, another way to determine the perimeter would be to add the multiplication of both the length and breadth by 2.

Quick Tip: A square is always a rectangle, but a rectangle may not always be a square!

Rectilinear Figures

Each rectilinear figure may be unique, and students may be taken aback when seeing it for the first time. As such, students may wish to follow the steps below to help break down each rectilinear figure into something more familiar before solving it.

Step 1:

Split the entire rectilinear figure into basic shapes (squares and rectangles) at the edges and the corners. Do not split them in the middle of edges!

Step 2:

Determine the length of each outer boundary. Those dotted lines which you have drawn do not need to be found, they are only for breaking down the figure for easier visualisation!

Step 3:

Add up all the outer lengths to find the perimeter!

Area

Area is known as the quantity of space taken up by a figure. In Primary 3 Mathematics, we are only concerned with 2-dimensional (2D) figures. It is important to note that as area is a measure of space, it also takes on the square units of length (square centimetres, square metres, and square kilometres).

The area of a figure is then found by multiplying its 2 adjacent sides, otherwise known as the length and breadth.

Square Units of Length

The square units of length can be represented as square centimetres, square metres, and square kilometres. To represent these units in writing, we simply write the unit of the length, followed by a superscript (smaller wording at the top right-hand corner) of the number ‘2’.

• Square Centimetres: cm2
• Square Metres: m2
• Square Kilometres: km2
• Squares & Rectangles

To find the area of squares and rectangles, students would simply need to multiply the length of the figure by its breadth.

Rectilinear Figures

Just like the perimeter of a rectilinear figure, we can also follow the same steps to determine the area of the entire figure.

Step 1:

Split the entire rectilinear figure into basic shapes (squares and rectangles) at the edges and the corners. Do not split them in the middle of edges!

Step 2:

Determine the area of each sub-figure (each square and rectangle within the rectilinear figure).

Step 3:

Add up all the areas of the sub-figures to determine the total area of the entire figure!

Graphs

Bar Charts

Bar Charts are constructed to be intuitive and there is often a common set of questions targeting bar charts. The bar chart is made up of 2 axes, the horizontal axis (which is often the categories involved), and the vertical axis (which is often the quantity).

Read off the category and the corresponding quantity, and that is the quantity for that particular category.

For example:

From the above bar chart, we can identify that there are 5 cats, 2 dogs, 4 rabbits, 12 hamsters, and 9 terrapins at the pet store.

Using these numbers, students would then be able to solve almost all the questions that can be asked regarding a bar chart.

Commonly asked questions can include:

• Individual Category: How many cats are there at the pet store? Answer: 5 cats
• Sum of All Categories: How many pets are there in total? Answer: 32 pets
• Addition/Subtraction: How many more hamsters are there to dogs? Answer: 10
• Multiplication/Division: The number of hamsters outweigh the number of dogs by how many times? Answer: 6 times

Conclusion

With that, we have covered nearly all the main topics in the Primary 3 Mathematics syllabus, and we hope that this ultimate guide has been of use to you! With all the quick tips and step-by-step guides, we hope that you would be able to apply them to solving mathematical problems in class and during the examinations.

Ultimately, Mathematics always boils down to practice, practice, and practice. After all, practice makes perfect. Do engage yourself in more practice questions and try to apply what you have learnt from this quick guide. Do not be afraid to make mistakes! Learn from your mistakes, never give up, and all the best in your studies!