Addition & Subtraction Activities for Primary Schools

Addition & Subtraction — The Foundations of Number

Addition and subtraction are the first formal operations students encounter in primary mathematics, and fluency with these operations underpins everything that follows. Multiplication is built on repeated addition. Division is built on repeated subtraction. Algebraic thinking, measurement, and data interpretation all depend on students being able to add and subtract confidently and flexibly.

In the Australian Curriculum v9, addition and subtraction sit within the Number strand and are developed progressively from Foundation through Year 6. The curriculum emphasises not just procedural fluency — getting the right answer — but also the ability to choose and apply appropriate strategies, reason about number relationships, and solve problems in context.

The best addition and subtraction activities help students build a rich repertoire of mental strategies before moving to formal written methods. When students understand why addition and subtraction work — not just how to do them — they develop the flexible number sense that supports all future maths learning. Browse the teacher-created resources below to find worksheets, games, and hands-on activities for your year level.

The Australian Curriculum v9 develops addition and subtraction progressively across the primary years. Here is what students are expected to learn at each stage.

Foundation

Foundation students explore the concepts of combining and separating small collections. They use concrete materials to model situations where objects are added to or taken away from a group, and begin to use the language of addition ("and", "more", "altogether") and subtraction ("take away", "less", "how many left"). Counting on from a given number is introduced as an early addition strategy.

Year 1

In Year 1, students work with addition and subtraction within 20. They represent problems using number sentences (e.g., 8 + 5 = 13) and develop strategies including counting on, counting back, and using doubles. Students begin to understand the relationship between addition and subtraction — that one operation undoes the other — and use this to check their answers.

Year 2

Year 2 extends addition and subtraction to numbers within 100. Students are introduced to regrouping (trading ten ones for one ten) and apply mental strategies such as bridging through 10, using known facts, and the split strategy. They solve one-step and two-step word problems and represent their thinking with number lines and part-part-whole models.

Year 3

By Year 3, students add and subtract with three-digit numbers. Mental strategies become more sophisticated, including compensation (rounding and adjusting) and the jump strategy on empty number lines. Students begin to use formal written methods (vertical algorithms) alongside mental strategies, and learn to choose the most efficient method for a given problem.

Year 4

Year 4 students work with multi-digit addition and subtraction, including numbers in the thousands. Formal written algorithms are consolidated, and students develop fluency with regrouping across multiple place value columns. Problem solving involves multi-step tasks in real-world contexts — money, measurement, and data interpretation.

Year 5 & Year 6

In the upper primary years, students apply addition and subtraction fluently to larger whole numbers and extend these operations to decimals. They solve complex multi-step problems, estimate to check reasonableness, and apply their skills across all areas of the curriculum — fractions, measurement, statistics, and financial contexts.

One of the most important shifts in modern maths teaching is the emphasis on mental strategies before written algorithms. Students who develop a toolkit of flexible mental strategies understand numbers more deeply and can choose the most efficient approach for any problem. Here are the key strategies to teach, roughly in the order they are typically introduced.

Counting On and Counting Back

The most basic addition and subtraction strategy. Students start at the larger number and count forward (for addition) or backward (for subtraction). For example, 8 + 3: start at 8, count on three — 9, 10, 11. This is typically the first strategy Foundation and Year 1 students learn and is effective for adding or subtracting 1, 2, or 3.

Number Bonds (Friends of 10)

Number bonds are pairs of numbers that combine to make a target number, most commonly 10. Knowing that 7 + 3 = 10, 6 + 4 = 10, and so on gives students anchor points for mental computation. For example, to solve 7 + 5, a student who knows 7 + 3 = 10 can think "7 + 3 = 10, plus 2 more = 12." Number bonds are typically introduced in Year 1 and practised extensively in Year 2.

Doubles and Near Doubles

Students learn doubles facts (3 + 3, 5 + 5, 8 + 8) as anchor facts, then use them to solve near doubles. For example, 6 + 7 = 6 + 6 + 1 = 13. Doubles are among the easiest facts for students to memorise and provide a useful starting point for many calculations. This strategy is introduced in Year 1 and reinforced in Year 2.

Bridging Through 10 (Make to 10)

This strategy uses 10 as a stepping stone. To solve 8 + 6, a student thinks: "8 + 2 = 10, then 10 + 4 = 14." Bridging through 10 relies on solid number bonds knowledge and is one of the most powerful mental strategies for addition and subtraction within 20. It is typically introduced in late Year 1 or Year 2.

Split Strategy (Partitioning)

The split strategy involves partitioning both numbers into place value parts and adding or subtracting each part separately. For example, 47 + 36: split into 40 + 30 = 70 and 7 + 6 = 13, then 70 + 13 = 83. This strategy works well for two-digit addition without regrouping and is introduced in Year 2.

Jump Strategy (Number Line)

The jump strategy uses a mental or drawn number line. To solve 48 + 35, a student starts at 48, jumps +30 to 78, then +5 to 83. For subtraction, students jump backwards. This strategy is particularly effective for problems that involve crossing a tens boundary and is commonly taught in Year 2 and Year 3.

Compensation (Round and Adjust)

Compensation involves rounding one number to make the calculation easier, then adjusting the answer. For example, 67 + 29: think "67 + 30 = 97, then subtract 1 = 96." This strategy is efficient for numbers close to a multiple of 10 and is typically introduced in Year 3 or Year 4.

Formal Written Algorithms (Vertical Addition and Subtraction)

The traditional column method — lining up numbers by place value and working from right to left, regrouping as needed. Written algorithms are powerful for multi-digit calculations but should be introduced only after students have a strong foundation of mental strategies and place value understanding. The Australian Curriculum introduces formal written methods from Year 3, with consolidation in Year 4. For detailed content descriptors and elaborations, see the NSW Education Standards Authority (NESA) mathematics syllabus.

Fluency with addition and subtraction facts — being able to recall basic facts quickly and accurately — is essential for freeing up working memory for more complex problem solving. But fluency is built through understanding first, then practice. These eight hands-on activities develop both understanding and speed.

1. Ten Frames

Ten frames are rectangular grids with two rows of five spaces. Students place counters on the frame to represent numbers, making it easy to see how numbers relate to 5 and 10. For addition, students fill one frame and see how many more are needed to make 10, then count the extras. Ten frames build powerful visual images of number bonds and bridging through 10.

2. Number Bonds Rainbow

Students draw a rainbow arc connecting pairs of numbers that make a target number (e.g., for 10: connect 1 and 9, 2 and 8, 3 and 7, and so on). This visual representation helps students see all the bond pairs at once and recognise the symmetrical pattern. Display completed rainbows in the classroom as a reference tool.

3. Dice Games

Simple dice games provide repeated, motivating practice. Roll two dice and add the numbers. Roll three dice and find the total. Roll two dice, make a two-digit number, and subtract from 100. The variety is endless, and the element of chance keeps students engaged. Dice games work well for early finishers, warm-ups, and maths centres.

4. Domino Addition

Dominoes are a ready-made addition resource. Students pick a domino, add the two sides together, and record the number sentence. For differentiation, use double-six dominoes for simpler facts or double-nine dominoes for more challenging ones. Students can also sort dominoes by their total, reinforcing the idea that different combinations can make the same sum.

5. Number Line Jumps

Give students a blank or partially labelled number line and ask them to show their addition or subtraction as jumps. For 48 + 25, a student might draw a jump of +20 from 48 to 68, then a jump of +5 from 68 to 73. Number line jumps make the jump strategy visible and help students develop mental imagery of how numbers move along the number line.

6. Part-Part-Whole Mats

A part-part-whole mat is a simple diagram with two "part" sections and one "whole" section. Students place counters in the parts and combine them to find the whole (addition), or start with the whole and work out a missing part (subtraction). This model explicitly connects addition and subtraction as inverse operations.

7. Fact Family Triangles

A fact family triangle has three numbers — two addends and a sum — arranged at the three corners. Students use the triangle to write all four related facts (e.g., 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5, 8 − 5 = 3). Fact family triangles reinforce the inverse relationship and help students see that knowing one fact gives them three more for free.

8. Card Games (Make 10, Close to 100)

Playing cards (with picture cards removed) are a versatile maths resource. In "Make 10," students turn over cards and find pairs that make 10. In "Close to 100," students draw cards, make two-digit numbers, and add them, trying to get as close to 100 as possible without going over. Card games combine strategy with facts practice.