AC9M2A02: Recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts

Students move from counting to recalling and deriving addition facts efficiently. They use ten-frames, counters and part-part-whole diagrams to explain why a strategy works before practising until the facts can be recalled.

• Recall doubles and combinations that make 10.
• Derive near doubles by adjusting a known double by one.
• Bridge through 10 by partitioning one addend.
• Rearrange parts without changing the total.
• Use one addition fact to state two related subtraction facts.
• Record partitions systematically and explain how the list is complete.

Addend means a number being added; the sum is the total. A part-part-whole model shows two parts joined to make one whole. A ten-frame makes combinations to 10 visible.

If the parts are 8 and 7 and the whole is 15, the fact family is 8 + 7 = 15, 7 + 8 = 15, 15 − 8 = 7 and 15 − 7 = 8.

1. Secure anchors: build doubles and combinations to 10 with counters or ten-frames.
2. Near doubles: use 7 + 7 = 14 to derive 7 + 8 = 15 because one addend is one greater.
3. Bridge through 10: for 8 + 7, partition 7 into 2 and 5; then 8 + 2 = 10 and 10 + 5 = 15.
4. Connect subtraction: cover one part of a part-part-whole model to derive 15 − 7 = 8 and 15 − 8 = 7.
5. Build fluency: mix facts so students choose a strategy instead of repeating the previous procedure.

Teacher language: “Which known fact can help? What part will make 10? What stayed the same when you rearranged the parts?”

Ask students to find every way to split 10 between two groups. Record 10 = 10 + 0, 9 + 1, 8 + 2, …, 0 + 10. Changing one part down by one while the other goes up by one proves no partition has been skipped. Discuss which pairs are reversals.

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

• Content description: recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts
• E1: using ten-frames or materials such as connecting cubes to develop and record addition and subtraction strategies including doubles, near doubles, counting on, combinations to 10 and bridging to 10, explaining patterns and connections noticed within the facts
• E2: partitioning and rearranging collections to practice and develop fluency with addition and subtraction facts to 20 leading to the recall of these facts; for example, partitioning using materials and part-part-whole diagrams to develop subtraction facts related to addition facts, such as 8 + 7 = 15 therefore, 15\space - \space7 = 8 and 15 \space- \space8 = 7
• E3: using partitioning to develop and record facts systematically; for example, “How many ways can 10 birds be spread among 2 trees?”, 10 = 10 + 0, 10 = 9 + 1, 10 = 8 + 2, 10 = 7 + 3, …; explaining how they know they have found all possible partitions

Key idea: Addition facts to 20 support fast calculation. Related subtraction facts use the same whole and parts.

Remember

• Recall addition facts
• Use doubles
• Use make ten
• Write related subtraction
• Apply facts

Quick questions

• Write a fact family for 7, 8 and 15.
• Use make ten to solve 9 + 5.
• What addition fact helps with 16 − 7?
• Why is 15 − 8 not the same as 8 − 15?

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

Read the topic guide and use the teacher slide for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.

• Counting every item: prompt with “Which double or make-10 fact can help?”
• Losing part of an addend: after splitting 7 into 2 and 5, check that 2 + 5 still equals 7.
• Subtracting in the wrong direction: identify the whole first; subtraction starts with the whole.
• Writing unrelated equations: keep the same two parts and whole in all four equations.
• Repeating or missing partitions: change each part by one in opposite directions and mark the endpoints.

1. Use a near double to solve 6 + 7. Expected: 6 + 6 + 1 = 13.
2. Bridge through 10 to solve 9 + 8. Expected: 9 + 1 + 7 = 17.
3. Write the related subtraction facts for 8 + 7 = 15. Expected: 15 − 8 = 7 and 15 − 7 = 8.
4. List all unordered pairs that make 10 and explain why none are missing. Evidence: a systematic sequence from 0 + 10 to 5 + 5.

Mastery means recalling familiar facts, deriving an unfamiliar fact efficiently, explaining the partition used and keeping the same parts and whole across the fact family.

• Support: use two-colour counters, ten-frames and part-part-whole templates; keep totals within 10 before moving to 20.
• Core: solve mixed addition facts to 20, name the strategy and derive both related subtraction facts.
• Extend: find all partitions of a chosen whole to 20 and justify that the list is complete, without introducing formal algebra.

This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.

Curriculum equivalents for Recall and demonstrate proficiency with addition facts to 20; extend...

Mapped skill: recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts

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
• Common Core State Standards
• Next Generation Science Standards
• England National Curriculum
• New Zealand Curriculum
• NCERT textbooks

• AC9M2N01: Recognise, represent and order numbers to at least 1000 using physical and virtual materials, numerals and number lines
• AC9M2N02: Partition, rearrange, regroup and rename two- and three-digit numbers using standard and non-standard groupings; recognise the role of a zero digit in place value notation
• AC9M2N03: Recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving
• AC9M2N04: 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
• AC9M2N05: Multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies
• AC9M2N06: Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation
• AC9M2A01: Recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern
• AC9M2A03: Recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving