AC9M1N04_E1
Use drawings, physical and virtual materials and number combinations within 10 to add and subtract collections to 20.
About This Year 1 Maths Topic
Addition and subtraction within 20 develop from practical experiences with collections, pictures, number stories and familiar number relationships. Students need opportunities to represent each calculation before moving towards efficient mental strategies.
In this chapter, students use physical and virtual materials, drawings, ten-frames, number lines and Think Boards to represent addition and subtraction situations.
Students build on part-part-whole knowledge to 10 and develop strategies such as counting on, counting back, partitioning, making 10 and using known number bonds.
They recognise and use the plus sign, minus sign and equal sign, connect number sentences to story problems, and explain how their materials and representations match the mathematics.
These activities support the Australian Curriculum Version 9.0 content descriptor AC9M1N04 and its associated elaborations.
Australian Curriculum Alignment
AC9M1N04
Add and subtract numbers within 20 using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies.
AC9M1N04_E2
Add and subtract numbers within 20 using representations and strategies such as counting on, counting back, partitioning and part-part-whole knowledge to 10.
AC9M1N04_E3
Develop one-digit addition and subtraction strategies using part-part-whole relationships and subitising; for example, viewing 8 and 6 as 8 and 2 and 4.
AC9M1N04_E4
Represent addition and subtraction story problems within 20 using a Think Board. Recognise and use the plus, minus and equal signs and explain connections between the story, materials and number sentence.
AC9M1N04_E5
Create and perform addition and subtraction stories told through First Nations Australians’ dances, using respectful and appropriate sources and contexts.
Learning Intentions
Students will learn to:
- add numbers within 20;
- subtract numbers within 20;
- represent calculations using physical and virtual materials;
- use drawings and ten-frames to show number relationships;
- use counting-on and counting-back strategies;
- partition numbers to make calculations easier;
- use part-part-whole facts and number bonds to 10;
- use the plus, minus and equal signs correctly;
- represent story problems using a Think Board;
- explain how a strategy produces the answer.
Student Success Criteria
I can add numbers within 20.
I can subtract numbers within 20.
I can show a calculation with materials.
I can count on from the larger number.
I can count back to subtract.
I can partition a number to make 10.
I can use number bonds and part-part-whole facts.
I can use +, − and = correctly.
I can represent a story problem on a Think Board.
I can explain how I found my answer.
Key Vocabulary
addition
subtraction
add
subtract
plus
minus
equal
altogether
total
difference
left
count on
count back
partition
number bond
part-part-whole
strategy
Think Board
Teacher Guide
Recommended Materials
- counters, cubes, buttons or bottle caps;
- five-frames and ten-frames;
- part-part-whole mats;
- number bond templates;
- number lines and number tracks;
- dice and dominoes;
- number cards from 0 to 20;
- story problem picture cards;
- Think Board templates;
- mini whiteboards and markers;
- virtual manipulatives or digital ten-frames;
- safe props for role-play and movement stories.
Suggested Teaching Sequence
- Begin with practical joining and separating situations.
- Represent each situation using counters or other objects.
- Connect the materials to drawings and number sentences.
- Review part-part-whole combinations and number bonds to 10.
- Introduce counting on from the larger number.
- Introduce counting back for subtraction.
- Use partitioning to make 10 before adding the remaining part.
- Compare different strategies for the same calculation.
- Use Think Boards to represent story problems in several ways.
- Encourage students to explain and justify their chosen strategy.
Teacher Questions
- What is happening in the story?
- Are the quantities joining or separating?
- What is the starting number?
- Which number could you count on from?
- How many steps should you count back?
- Can you partition one number to make 10?
- Which number bond could help?
- How can you show the calculation with materials?
- What does the plus or minus sign tell us?
- What does the equal sign mean?
- Can you show the problem another way?
- Which strategy was most efficient, and why?
Common Misconceptions
Counting both collections from one instead of counting on
Ask students to identify the larger addend, hold that number in their head and count on only the smaller amount.
Counting the starting number as the first jump
Demonstrate that the first count or jump occurs after the starting number, not on it.
Confusing addition and subtraction signs
Connect each symbol to the action in the story: joining or adding more uses +, while taking away or finding a difference uses −.
Treating the equal sign as “the answer comes next”
Explain that the equal sign means both sides have the same value. Use balanced examples such as 7 + 3 = 6 + 4.
Partitioning a number but losing one of the parts
Record each part visibly and check that the parts recombine to make the original number.
Using a strategy without connecting it to the story
Ask students to explain what each number and symbol represents in the original context.
Year 1 Addition and Subtraction to 20 Activities
Activity 1: Add and Subtract with Collections
Give students two small collections to combine or one collection from which objects are removed.
Students model the action, draw what happened and record the matching number sentence.
Curriculum connection: AC9M1N04_E1
Activity 2: Ten-Frame Calculations
Represent additions and subtractions within 20 using two ten-frames and counters.
Ask students to use known combinations to 10 to determine the result efficiently.
Curriculum connection: AC9M1N04_E1
Activity 3: Counting-On Number Line
Place the larger addend on a number line and make one jump for each additional count.
Students record the jumps and explain why counting on is more efficient than starting at one.
Curriculum connection: AC9M1N04_E2
Activity 4: Counting-Back Challenge
Begin at the starting number and move backwards on a number line to represent subtraction.
Students check the answer using counters or a related addition fact.
Curriculum connection: AC9M1N04_E2
Activity 5: Make 10 to Add
Model a calculation such as 7 + 5 by partitioning 5 into 3 and 2. Combine 7 and 3 to make 10, then add the remaining 2.
Students practise the strategy with other calculations.
Curriculum connection: AC9M1N04_E2
Activity 6: Number Bonds and Subitising
Flash dot cards or ten-frame images briefly. Students identify the quantity and describe the parts they saw.
Use these relationships to solve one-digit additions and subtractions.
Curriculum connection: AC9M1N04_E3
Activity 7: Think Board Story Problems
Present a story problem within 20. Students represent it using materials, a drawing, a number sentence and a written or spoken explanation.
Compare how each representation shows the same mathematical relationship.
Curriculum connection: AC9M1N04_E4
Activity 8: Symbol Match
Give students story cards and number sentences. Students match each story to the correct plus or minus equation.
Ask them to explain what every number and symbol represents.
Curriculum connection: AC9M1N04_E4
Activity 9: Create a Movement Story
Students create a simple addition or subtraction story using movement, rhythm or dance actions.
When connecting the activity to First Nations Australians’ dances, use culturally appropriate, authoritative and community-approved teaching resources.
Curriculum connection: AC9M1N04_E5
Activity 10: Strategy Comparison
Solve the same calculation using materials, counting on, partitioning and a known number bond.
Students select the strategy they found most helpful and explain their choice.
Curriculum connection: AC9M1N04
Differentiation
Support
- begin with calculations within 10;
- use physical materials for every calculation;
- provide five-frames, ten-frames and number tracks;
- use one-step story problems with familiar contexts;
- practise number bonds to 5 before bonds to 10;
- highlight the starting number on number lines;
- provide partially completed Think Boards;
- use sentence starters and adult scribing;
- allow students to explain orally before recording.
Extension
- use calculations with missing numbers;
- compare two or more possible strategies;
- write related addition and subtraction facts;
- solve balanced equations with expressions on both sides;
- create original Think Board story problems;
- represent one calculation in several ways;
- explain why one strategy is more efficient;
- solve two-step contextual problems;
- extend calculations beyond 20 where appropriate.
Mathematical Sentence Starters
I started with _____.
I added _____ more.
I subtracted _____.
There are _____ altogether.
There are _____ left.
I counted on from _____.
I counted back _____ steps.
I partitioned _____ into _____ and _____.
I made 10 by _____.
The plus sign means _____.
The minus sign means _____.
Both sides are equal because _____.
This strategy helped me because _____.
Assessment Ideas
Observe whether the student can:
- add and subtract numbers within 20;
- represent calculations using materials and drawings;
- use counting-on and counting-back strategies;
- partition a number to make 10;
- apply part-part-whole knowledge and number bonds;
- recognise and use +, − and = correctly;
- represent a story problem using a Think Board;
- connect a number sentence to the original story;
- compare different calculation strategies;
- explain how the answer was found.
Quick Exit Ticket
- Show the calculation 8 + 6.
- Represent it using counters or a ten-frame.
- Use partitioning to make 10.
- Record and explain the answer.
Printable Teacher and Student Resources
Use the buttons below to open the available AC9M1N04 teaching materials and printable activities in a new browser tab.
Main Worksheets
Addition and Subtraction Strategies
Adding and Subtracting to 20 Activities
Addition and Subtraction with Materials
Addition Strategies Worksheets
Counting On, Counting Back and Partitioning
Part-Part-Whole Addition Strategies
Number Bonds and Subitising
Addition and Subtraction Story Problems
Think Board Word Problems
First Nations Addition and Subtraction Activities
First Nations Maths Story Problems
Resources open in a new tab. Browser PDF settings may affect whether a file opens in the browser or downloads.
Home Learning Ideas
Families can practise addition and subtraction using toys, buttons, pegs, socks, fruit, coins, building blocks or everyday household objects.
Create short number stories, represent them with objects and ask the child to choose and explain a calculation strategy.
Ask questions such as:
- What is the starting number?
- Are we adding or subtracting?
- Can you count on from the larger number?
- Can you count back to find the answer?
- Can you partition a number to make 10?
- Which number bond could help?
- What number sentence matches the story?
- Can you solve it another way?
- Which strategy was easiest, and why?