AC9M2N04: Addition and subtraction strategies

Students solve addition and subtraction problems by choosing strategies that make the numbers easier to work with. They connect concrete materials, bar models, number lines, hundreds charts and number sentences so the calculation always stays linked to the problem situation.

• Use part-part-whole reasoning to identify a whole and its parts.
• Represent a problem with a bar model and a number sentence.
• Use doubles, near doubles, bridging to 10 and bridging through tens.
• Partition two-digit numbers into tens and ones to calculate mentally.
• Use number lines, hundreds charts and informal jottings to keep track of steps.
• Recognise that adding zero leaves a number unchanged.
• Use the inverse relationship between addition and subtraction to check reasoning.

Part-part-whole models help students see how addition and subtraction are connected. If 24 and 13 are the parts, then 37 is the whole:

24 + 13 = 37, 13 + 24 = 37, 37 − 24 = 13 and 37 − 13 = 24.

Ask students to name the whole and the two parts before writing the number sentence. This prevents students from choosing an operation only because of a keyword.

Known doubles can be adjusted by one when the addends are close.

7 + 8 = 7 + 7 + 1 = 14 + 1 = 15.

Students should explain why this works: 8 has been partitioned into 7 and 1, so the total has not changed.

Split one addend so the first jump lands on a friendly ten.

7 + 8: split 8 into 3 and 5. Then 7 + 3 = 10 and 10 + 5 = 15.

47 + 6: split 6 into 3 and 3. Then 47 + 3 = 50 and 50 + 3 = 53.

For subtraction, bridge through a ten in the opposite direction; for example, 52 − 7 can be seen as 52 − 2 − 5.

Separate two-digit numbers into tens and ones, then recombine the partial results.

34 + 28: 30 + 20 = 50 and 4 + 8 = 12, so 50 + 12 = 62.

56 + 37: 50 + 30 = 80 and 6 + 7 = 13, so 80 + 13 = 93.

Students may jot down the partial amounts, but should still be able to explain where each number came from.

On a number line, make efficient jumps in tens and ones rather than counting every number.

To calculate 52 − 38, count up from 38: +2 to 40, then +12 to 52. The total increase is 14, so 52 − 38 = 14.

On a hundreds chart, moving down one row adds 10, moving up one row subtracts 10, moving right adds 1 and moving left subtracts 1.

For each problem, students should identify what is known, what is unknown and how the quantities are connected.

Example: Mia has 28 stickers and gets 16 more. A bar model shows 28 and 16 as two parts of an unknown whole. The matching number sentence is 28 + 16 = ?.

Example: A box held 45 pencils and 17 were used. The whole is 45, one part is 17 and the missing part is the number left. The number sentence is 45 − 17 = ?.

Zero ones do not change the amount. For example, 34 + 20 = 54 because 30 + 20 = 50 and 4 + 0 = 4.

Addition and subtraction can also check each other. If 63 − 27 = 36, then 36 + 27 should return to 63.

Use a reliable, community-approved source and identify the specific Nation, People or community where the source does. Avoid presenting diverse First Nations knowledges and practices as one generic tradition. Follow local cultural and intellectual property protocols before inviting community participation or reproducing cultural material.

Key idea: Addition can join parts or find a total. Subtraction can take away or find a missing part. Strategies help students work efficiently and explain their thinking.

Remember

• Represent with number sentences
• Use part–part–whole
• Add two-digit numbers
• Subtract two-digit numbers
• Explain strategies

Quick questions

• Solve 47 + 25 using partitioning.
• Write a number sentence for 63 minus 28.
• Use an inverse fact to check 82 − 35.
• Explain your strategy for 58 + 19.

If an answer is uncertain, return to the model and explain what each part represents before calculating or drawing a conclusion.

• Counting by ones when a larger jump is available: prompt students to look for tens, doubles or a friendly benchmark.
• Changing the value while partitioning: every split must recombine to the original number.
• Writing a number sentence that does not match the story: identify the whole and parts first.
• Forgetting the second part of a bridge: after reaching 10 or the next ten, the leftover amount still has to be added or subtracted.
• Ignoring place value: 4 ones + 8 ones makes 12 ones, which is 1 ten and 2 ones.
• Treating subtraction as only take-away: subtraction can also compare quantities or find a missing part/difference.

• Support: use counters, ten frames, base-ten blocks, open number lines and completed bar-model templates.
• Core: ask students to solve the same calculation with two strategies and choose the more efficient method.
• Extension: give missing-number equations such as 38 + □ = 65 or □ − 27 = 41 and ask students to justify their strategy.

Content description: add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies.

• E1: use associative thinking, partitioning, rearranging, regrouping, near doubles and bridging to 10.
• E2: use doubles, near doubles, part-part-whole knowledge, bridging tens and partitioning for two-digit calculations.
• E3: represent addition and subtraction problems with bar models and matching number sentences.
• E4: use mental strategies and informal written jottings, including recognising that adding zero leaves the number unchanged.
• E5: use physical or mental number lines and hundreds charts, moving in tens and ones.
• E6: use First Nations Australians’ stories and dances as a teaching context for balance and the connection between addition and subtraction.

1. Solve 8 + 9 using a near-double strategy.
2. Solve 46 + 7 by bridging to the next ten.
3. Solve 34 + 28 by partitioning tens and ones.
4. Use counting up to solve 61 − 48.
5. Draw a bar model for 27 + 16 = ?
6. Write the inverse check for 72 − 35 = 37.

Model one strategy at a time, then deliberately mix problem types so students must choose a suitable method rather than repeat the previous example. Use the Teacher Slides for explicit instruction, then move to the worksheet, Practice or Test depending on readiness.

Curriculum equivalents for Add and subtract one- and two-digit numbers, representing problems using...

Mapped skill: add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.

• Australian Curriculum Version 9.0
• Victorian Curriculum F–10
• NSW Curriculum

• AC9M2N01: Numbers to at least 1000
• AC9M2N02: Partition, regroup and rename numbers
• AC9M2N03: Halves, quarters and eighths
• AC9M2N05: Multiplication and division strategies
• AC9M2N06: Mathematical modelling and money problems