\displaystyle 44+2	\displaystyle =	\displaystyle 46	Add 2 to 46
\displaystyle 46+2	\displaystyle =	\displaystyle 48	Add 2 to 46
\displaystyle 48+2	\displaystyle =	\displaystyle 50	Add 2 to 48

The complete pattern is: 40,\,42,\,44,\,46,\,48,\,50.

Idea summary

We can count on from a number by adding the same amount repeatedly to that number.

Make numbers

To find out the difference between two numbers, we can jump from our starting number to our target number, like we do in this video.

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Examples

Example 2

Find the missing number to equal the number 98.

89 + ⬚ = 98

Worked Solution

Create a strategy

Use a number line to count how many jumps are between the starting number and the target number.

Apply the idea

Locate where 89 is on a number line.

Jump to the right of 89 and count the number of spaces until we reach 98.

We have jumped 9 spaces to the right of 89. So: 89 + 9 = 98

20 + ⬚ = 98

Worked Solution

Create a strategy

Use a number line to count how many jumps are between the starting number and the target number.

Apply the idea

Locate where 20 is on a number line.

Jump to the right of 20 and count the number of spaces until we reach 98.

We have jumped 78 spaces to the right of 20. So:20 + 78 = 98

28 + ⬚ = 98

Worked Solution

Create a strategy

Use a number line to count how many jumps are between the starting number and the target number.

Apply the idea

Locate where 28 is on a number line.

Jump to the right of 28 and count the number of spaces until we reach 98.

We have jumped 70 spaces to the right of 28. So:28 + 70 = 98

Idea summary

To find how much we need to add to one number get to another number, we can plot both numbers on a number line and count the spaces between them.

Patterns in addition

Sometimes we can solve a problem, and then use that to find a pattern in addition or subtraction. Watch this video to see how.

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Examples

Example 3

113+20=133. Use this to find:

113 + 30 = ⬚

Worked Solution

Create a strategy

Use the given number sentence to find the pattern.

Apply the idea

Comparing the number sentences: 113 +20 = 133 and 113 + 30 = ⬚, we notice that they have the same first number 113. The second numbers 20 and 30 differ by 10. So we need to add 1 tens to 133.

Add the digits in each place value column.

	Hundreds	Tens	Units
	1	3	3
+		1	0
	1	4	3

113+30=143

113 + 40 = ⬚

Worked Solution

Create a strategy

Use the number sentence from the previous part to find a pattern.

Apply the idea

Comparing the number sentences: 113 +30 = 143 and 113 + 40 = ⬚, in the second number of each statement the number of tens differ by 1, so we need to add 1 ten to 143.

Add the digits in each place value column.

	Hundreds	Tens	Units
	1	4	3
+		1	0
	1	5	3

113+40=153

113 + 50 = ⬚

Worked Solution

Create a strategy

Use the number sentence from the previous part to find a pattern.

Apply the idea

Comparing the number sentences: 113 +40 = 153 and 113 + 50 = ⬚, in the second number of each statement the number of tens differ by 1, so we need to add 1 ten to 153.

Add the digits in each place value column.

	Hundreds	Tens	Units
	1	5	3
+		1	0
	1	6	3

113+50=163

Idea summary

If we notice a pattern in our problems, it can make it much easier to solve other problems. We can use place value to see what has changed and then focus on that in other problems.

Outcomes

ACMNA073

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

ACMNA076

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder

ACMNA083

Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction

2.06 Target numbers and patterns

Ideas

Are you ready?

Examples

Example 1

Make numbers

Examples

Example 2

Patterns in addition

Examples

Example 3

Outcomes

ACMNA073

ACMNA076

ACMNA083

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