Expected level of development
Australian Curriculum Mathematics V9: AC9M2N04
Numeracy Progression: Additive strategies: P7, Number and place value: P5
At this level, students explore and test a range of computation strategies to solve additive situations – situations involving addition and subtraction. They use part-part-whole understanding to make sense of and represent problems involving one- and two-digit numbers. Students work toward making their own decisions about how to solve a given problem.
Assist students to discover and explore the use of doubles, near doubles and strategies involving partitioning. Provide opportunities for them to generate their own solutions to problems involving addition and subtraction and celebrate the diversity of solutions that emerge.
Use number talks regularly as a collaborative learning space where students make sense of and discuss each others’ strategies. Model curiosity around mistakes and help students see them as opportunities to learn. Give plenty of thinking time to solve problems.
Provide novel contexts, such as games and challenging tasks, to apply and consolidate skills learned. Story problems involving addition and subtraction can emerge as a result of recent classroom experiences, discussions or stories read. Include the use of stories and dances from different cultures that represent additive ideas.
There is an opportunity to connect learning about, and applying, addition and related subtraction facts to 20 (AC9M2A02). See the Year 2 Algebra topic: Patterns and number facts.
Teaching and learning summary:
- Explore addition and subtraction with materials, stories, role-play, games, collaborative conversations, challenging tasks and regular classroom talks.
- Ensure a playful culture of learning where mistakes and struggle are seen as valuable to learning.
- Include opportunities to solve worded problems in different ways.
- solve and model story problems involving addition and subtraction of numbers to 99
- mentally solve problems using strategies such as doubles, near doubles, bridging tens and partitioning
- provide an explanation of how a given solution does or doesn’t work to reach an accurate answer
- use various models to represent addition and subtraction (e.g. bar models, number lines and equations).
Some students may:
- think of the equals sign (=) as ‘here comes the answer’ instead of seeing it as a balance between equivalent statements. To address this, regularly present addition and subtraction problems in different ways. For example, 7 − 5 = ▢ can also be written as ▢ = 7 − 5 or 3 = 7 − ▢.
- not understand the commutative property of addition; that the order of the addends can be changed and it will not affect the answer, which they can draw on when solving additive problems. To address this, explicitly teach this idea using physical materials. Provide opportunities to explore, test and think about whether this property always works.
- not understand the associative property of addition; that it doesn’t matter which order you add numbers when adding three numbers or more. To address this, explicitly teach this idea, explaining how it is useful to make solving problems easier. In 3 + 6 + 7, for instance, adding the 3 and 7 to make 10, and then adding 6 to make 16 can be considered an easier path. Include a focus on these kinds of addition problems during regular classroom talks to support fluency with this idea.
- believe that adding zero (e.g. in 12 + 0) will result in a larger number because they have learnt that ‘adding makes numbers larger’. Similarly, when subtracting zero (e.g. in 12 − 0) they think the answer will be smaller than the minuend. To address this, provide repeated opportunities to explore problems that add and subtract zero.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
- We are learning to solve addition and subtraction problems.
Why are we learning about this?
- We use addition and subtraction in everyday life.
What to do
1. Play with numbers as they come up in the world around you. For example:
- 'I spot a number plate with the numbers 5, 4 and 8 on it. What would those numbers make added together? (5 + 4 + 8)'
- 'I spot the house number 39. I wonder: How many more is 50 than 39? What about 70? Or 100?'
2. Link addition and subtraction to everyday life. For example:
- Talk about situations involving addition and subtraction in storybooks.
- Discuss the scores in a game of sport and talk about the difference between scores. Work out how much the winning team has won by.
- Find opportunities to play with, sort and add up money.
- When shopping, or playing shops, talk about the total number of items in the basket. 'There are 8 apples, 6 bananas and 5 oranges. How many pieces of fruit altogether?'
- Talk about money calculations using whole dollars. 'The milk costs $3, the bread costs $3 and the bananas cost $4. So altogether, how much do we need to pay? If we pay with a $20 note, how much change will we get?'
3. Think about and discuss different ways of solving addition and subtraction. For example, to solve 17 + 6 you might decide to:
- count up from 17 using two jumps of 3 (17 … 20 … 23!)
- break the 6 up into 3 and 3 to ‘make a friendly 20’ (17 + 3 = 20; 20 + 3 = 23)
- start with the known doubles fact of 6 + 6 = 12; then add 11 more to get 23.
Don’t forget that mistakes are a normal part of learning to understand maths. Be curious about mistakes and see them as ways to help you learn. Take plenty of time to solve problems.
- use strategies such as ‘breaking numbers apart’, ‘using doubles’ and ‘using near doubles’ to help solve addition and subtraction problems
- solve addition problems involving one- and two-digit numbers and explain how I solved them
- solve subtraction problems involving one- and two-digit numbers and explain how I solved them.
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A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
Concrete, Representational, Abstract (CRA model)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.Go to resource
Culturally responsive pedagogy
Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.Go to resource
Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.Go to resource
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.Go to resource
It has been shown that good feedback can make a significant difference to a student’s future performance.Go to resource
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.Go to resource
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.Go to resource
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
Addition and subtraction: fact families, bonds and making ten
Use these activities to revisit foundational ideas before exploring and learning various strategies.Go to resource
Classroom talk prompts: Year 2 Number – addition and subtraction
Use this slidedeck to launch classroom talks that explore additive thinking.Go to resource
Stage 1 addition and subtraction
Use these activities to help make connections between counting, addition and subtraction strategies.Go to resource
Around the house
This game provides an authentic context for applying addition and subtraction to reach desired targets.Go to resource
This unit includes problems that invite the use of doubles and near doubles as a valuable strategy.Go to resource
Strike it out
This game is an authentic context for applying addition and subtraction. It also invites strategic thinking.Go to resource
Chapter 3: Using addition and subtraction
Use Chapter 3 Student Lesson Activity (LAB) pages 47 to 52 for magic square challenges and other contexts to apply addition and subtraction.Go to resource
Race to zero
Use this game to explore a novel number chart and to practise using place value and subtraction.Go to resource
Use this lesson to teach the problem-solving skill of generalising while exploring addition and subtraction.Go to resource
101 and bust!
Use this game as a meaningful context to apply knowledge of place value, addition and subtraction.Go to resource
By the end of Year 2, students solve addition and subtraction problems. They represent additive situations and choose and apply computation strategies to particular problems.
Assessment: Kangaroos and comparing bananas
Use these tasks to observe the strategies students use to solve and represent addition and subtraction problems.Go to resource
How would you solve this?
Use this open-ended task to gauge how students approach problems involving addition and subtraction.Go to resource