Constant increases/decreases | Year 2

01 / LEARN

Understand the idea.

Compare neighbours

A constant step makes the same change between neighbouring numbers. In $12, 17, 22, 27$ , each jump adds five. Check every jump shown before continuing; a rule that fits only the first pair may not fit the rest.

A pattern can go backwards

A pattern can decrease as well as increase. In $60, 50, 40, 30$ , each next number is ten smaller. Describe both the size and direction of the jump: adding ten and subtracting ten lead to different next numbers.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

An increasing pattern

Continue 14, 17, 20, 23 with two more numbers.

Worked solution

1
Check the change between the given numbers.
$\begin{array}{c} 14 + 3 = 17 \\ 17 + 3 = 20 \\ 20 + 3 = 23 \end{array}$
Every shown jump adds three, so continue using that same step.
2
Find the first new number.
$23 + 3 = 26$
Add three to the last number shown.
3
Find the second new number.
$26 + 3 = 29$
Use the same step again, starting from the new number twenty-six.

Answer

26, 29

EXAMPLE 02

A decreasing pattern

Continue 45, 40, 35 with two more numbers.

Worked solution

1
Check the backward step.
$45 - 5 = 40, 40 - 5 = 35$
Both shown jumps subtract five.
2
Continue one step.
$35 - 5 = 30$
The pattern keeps decreasing by five.
3
Continue a second step.
$30 - 5 = 25$
Another equal backward jump gives the second new number.

Answer

30, 25

03 / YOUR TURN

Try it yourself.

Check your understanding

What is the next number: 22, 24, 26, 28?

Show answer & reasoning

The jumps $22$ to $24$ , $24$ to $26$ and $26$ to $28$ all add two. Continue once more: $28 + 2 = 30$ .

Keep practising

6 worksheet questions

Open worksheet Worked solutions

Read the questions online

Write the next two numbers: $3, 6, 9, 12$ .
Write the next two numbers: $40, 35, 30$ .
What is the step in $16, 26, 36, 46$ ?
What is the step in $18, 16, 14, 12$ ?
Continue $90, 80, 70$ with one more number.
Is $5, 10, 15, 21$ an add-5 pattern all the way? Explain.

Read the worked solutions

Write the next two numbers: $3, 6, 9, 12$ .
Add 3 twice.
$15, 18$
Write the next two numbers: $40, 35, 30$ .
Subtract 5 twice.
$25, 20$
What is the step in $16, 26, 36, 46$ ?
$26 - 16 = 10$ , and the later steps match.
Add 10.
What is the step in $18, 16, 14, 12$ ?
Each number is 2 smaller.
Subtract 2.
Continue $90, 80, 70$ with one more number.
$70 - 10 = 60$ .
60
Is $5, 10, 15, 21$ an add-5 pattern all the way? Explain.
$15 + 5$ would be 20, not 21.
No. The final step adds 6.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Constant increases/decreases; describing rules; missing terms; shape/number patterns.

Official curriculum source ↗

In this lesson

Understand the idea.

Compare neighbours

A pattern can go backwards

See the method in action.

An increasing pattern

Check the change between the given numbers.

Find the first new number.

Find the second new number.

A decreasing pattern

Check the backward step.

Continue one step.

Continue a second step.

Try it yourself.

Check your understanding

Keep practising