Topics
1. Number
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Australia
Year 6

1.04 Square and triangular numbers

Lesson
Practice
Lesson

Are you ready?

We've seen that  prime and composite numbers  are two types of numbers that can help us with calculations.

Examples

Example 1

The only factors a prime number has is 1 and itself.

Which of the following numbers are prime?

A
10
B
21
C
19
Worked Solution
Create a strategy

Write the factors of each option.

Apply the idea

Option A: 10 has the following factors:1,2,5,10

Option B: 21 has the following factors:1,3,7,21

Option C: 19 has the following factors:1,19

Among the choices, 19 is a prime number as its factors are 1 and itself. So, the correct answer is Option C.

Idea summary

  • Every whole number greater than 1 is either a prime number or a composite number

  • All even numbers greater than 2 are composite numbers

  • To be a prime number, a number can only have itself and 1 as factors

  • 0 and 1 are not prime or composite numbers

Square numbers

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Examples

Example 2

Write down the next square number after 16.

Worked Solution
Create a strategy

Find the 5th square number.

Apply the idea

16 is the 4th square number since 4\times 4=16.

To find the square number after 16, we need to find the 5th square number which is:5\times 5=25

25 is the next square number after 16.

Idea summary

If we multiply a number by itself, we make a square number. If we use dots to picture this as an array it will make a square shape.

Triangular numbers

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Examples

Example 3

Write down the next 3 triangular numbers.1,\,3,\,6,\,10,\,15,\,⬚,\,⬚,\,⬚

Worked Solution
Create a strategy

Add the the position of the number we are finding to the previous triangular number.

Apply the idea

To find the 6th triangular number we add 6 to the previous triangular number of 15:

\displaystyle 15+6\displaystyle =\displaystyle 21

To find the 7th triangular number we add 7 to the previous triangular number of 21:

\displaystyle 21+7\displaystyle =\displaystyle 28

To find the 8th triangular number we add 8 to the previous triangular number of 28:

\displaystyle 28+8\displaystyle =\displaystyle 36

Here is the complete list of triangular numbers:1,\,3,\,6,\,10,\,15,\,21,\,28,\,36

Idea summary

With triangular numbers, we add 1 more dot to each new row and create a triangle shape with dots.

Dot representations of 16 as a square number and 10 as a triangular number. Ask your teacher for more information.

Outcomes

AC9M6N02

identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations

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