Expected level of development
Australian Curriculum Mathematics V9: AC9M1N04
Numeracy Progression: Additive strategies: P6, Number and place value: P3
At this level, students build upon the foundations of additive thinking. They draw upon part-part-whole understanding of numbers to 10 as they explore addition and subtraction within 20.
Use physical and virtual materials (such as leaves, pebbles, twigs, counters and blocks) to model addition and subtraction problems involving collections up to 10, then 20. Include tens frames and number lines as useful tools when modelling additive situations.
Make it clear that there can be multiple ways to solve a given problem. Encourage students to choose solution paths that make the most sense to them and have them provide explanations about how a particular solution works. Model curiosity around mistakes and help students see them as opportunities to learn. Give plenty of thinking time to solve problems.
Help students understand and connect key language to mathematical symbols. For instance, ‘three more than five is eight’ can be described and written as ‘3 and 5 is 8’ and ‘8 is 3 and 5’. It can also be written as 3 + 5 is 8 and 5 + 3 is 8 as well as 3 + 5 = 8 and 8 = 5 + 3. Be explicit about the job of the equals sign (=) which is there to tell us that the quantities on either side of it are the same; they are equal. Include interactions with equations such as 4 + 3 = 2 + 5.
Provide novel contexts, such as games and challenging tasks, to apply and consolidate addition and subtraction. Story problems involving addition and subtraction can emerge as a result of recent classroom experiences, discussions or stories read. Be sure to include stories, dance and games from different cultures that involve additive situations.
Teaching and learning summary:
- Explore addition and subtraction with materials, stories, role-play, games, 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.
- model and describe addition and subtraction in different ways using part-part-whole knowledge
- solve and model story problems involving addition and subtraction of numbers to 20
- choose reliable strategies to solve addition and subtraction, for example, they use counting-up and counting-down along with known number facts to support computation
- recognise and use the + and − symbols and the equals sign (=) to represent addition and subtraction.
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 and 2 = 7 − ▢.
- not understand the commutative property in addition; that the order of the addends can be changed and it will not affect the answer and so draw on this when solving additive problems. To address this, use physical materials to model the property and provide opportunities to explore, test and think about whether this property always works.
- not understand the associative property in addition; that it doesn’t matter which order you add numbers when adding three numbers or more. To address this, explicitly teach this idea and how useful it is 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.
- think that adding zero (e.g. 5 + 0) will result in a larger number because they have learned that ‘adding makes numbers larger’. Similarly, when subtracting zero (e.g. 5 − 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:
When engaged in creative play, notice situations involving addition and subtraction. Model curiosity and pose questions such as:
- You’ve some green blocks there and some red blocks. How many of each? How many blocks altogether?
- There are 4 wheels on the truck and another 4 wheels on the car. How many wheels altogether? How do you know for sure?
- How many gumnuts have you there? What if I took these two, how many would be left?
Read storybooks and discuss situations involving addition and subtraction. Model curiosity and pose questions such as:
- There are 5 lemons here … and 2 more lemons here. How many altogether?
- Dog is joined by his friends. How many animals are there now?
- Oh, the goat just ate another apple! There were 5 apples. How many are left now?
Link addition and subtraction to everyday situations. For example:
- Provide opportunities to play with, sort and add up money.
- When shopping, or when playing shops, talk about the total number of items in the basket. For example: There are 4 apples, 5 bananas and 2 oranges. How many pieces of fruit altogether?
- When drawing pictures, notice and describe additive aspects such as the number of legs on two dogs (4 and 4) and the number of legs on the person (2) makes a total of 10 legs.
- When making money calculations use whole dollars. For example: The milk costs $3 and the bread costs $3. So altogether, how much do we need to pay? If we pay with a $10 note, how much change will we get?
Play games involving additive thinking. For example:
- Play Concentration (also known as Memory) where two sets of cards are numbered 0 to 10. In this variation, the aim is to collect the most pairs of cards as possible that make 10.
Think about and discuss different ways of solving addition and subtraction. For example, To solve 7 + 6 you might decide to:
- Count up from 7, 6 times (...8, 9, 10, 11, 12, 13)
- Break the 6 up into 3 and 3 to ‘make a friendly 10’: 7 + 3 = 10; 10 + 3 = 13
- Start with a known doubles fact of 6 + 6 = 12. Then add 1 more to get 13.
Know that mistakes are a normal part of building mathematical understanding. Be curious about mistakes and see them as opportunities to learn. Take plenty of time to solve problems.
- use language like ‘____ and _____ makes _____’ and ‘____ plus ____ equals’ to describe addition
- use language like ‘_____ take away ______ leaves’ and ‘____ minus ____ equals’ to describe subtraction
- use strategies such as ‘counting up’, ‘breaking numbers apart’ and ‘using known facts’ to help solve addition and subtraction problems.
Please note: This site contains links to websites not controlled by the Australian Government or ESA. More information here.
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
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.
Put them together
Use these language-based activities to understand commutativity by exploring addition problems.Resource details
Classroom Talk Prompts – Year 1 Number_Addition and Subtraction
Use this slide deck to launch classroom talks that explore additive thinking.Resource details
Addition and subtraction (within 10)
Use these activities to develop strategies with problems involving numbers to 10.Resource details
Dot Card Talk 1
Use this visual lesson to connect addition and subtraction to numbers when thinking of them in terms of parts.Resource details
Eggs in a basket
This task presents an open-ended problem without an obvious answer. Solutions emerge through reasoning, and trial and error.Resource details
Addition and subtraction (within 20)
Use these activities to develop strategies with problems involving numbers to 20.Resource details
Heads and feet
This activity presents an open-ended problem without an obvious answer. Solutions emerge through reasoning, and trial and error.Resource details
Number round up
These puzzles provide an authentic context for using trial and error, and the reasoning required when working on tricky problems.Resource details
By the end of Year 1, students can/should be able to solve problems involving the addition and subtraction of numbers to 20.
Use this diagnostic interview to gauge students’ number knowledge.Resource details
Assessment task: How many? Representing sharing and grouping
Use this task to assess students’ knowledge and use of additive thinking.Resource details
Mathematics Year 1: ACARA
Refer to Year 1 work sample 6, Number: I dropped my counters. Students are given a handful of counters and use drawings and numbers to represent their thinking.Resource details