AC9M4A01: Find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations

An equation states that two expressions have the same value. Solving means finding a value that preserves equality.

Learning routine: Read both sides → Identify the unknown’s role → Use a number relationship → Replace the box and check.

Success looks like

• I can find an unknown addend, starting amount, removed amount or result.
• I can explain why both sides of an equation have equal value, including when both sides show calculations.
• I can reorder and group addition, use a common difference, or use an inverse operation to calculate efficiently.
• I can show my reasoning with equal counters, a number line or a part-part-whole bar, then check the original equation.

equation

a statement that two expressions have equal value

expression

a number or calculation, such as 170 or 80 + 90

unknown

a value to find; a box marks its place in an equation

addend and sum

an addend is a part being added; the sum is the total

minuend and subtrahend

the minuend is the starting amount in a subtraction; the subtrahend is the amount removed

difference

the result of subtraction, also shown as the gap between two numbers

inverse operations

operations that undo each other; addition and subtraction connect the same whole and parts

commutative property of addition

changing the order of the addends preserves their sum

grouping addition

combining the same addends in a different grouping preserves their sum

The exact Australian Curriculum v9.0 content description and its four elaborations are listed below. The worked models and activities put each relationship into practice.

• Content description: find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations
• E1: demonstrating the commutative properties of addition using materials, diagrams and number lines; for example, using number lines to demonstrate that 5 + 2 = 2 + 5, demonstrating that 2 + 2 + 3 = 7 and 2 + 3 + 2 = 7 and 3 + 2 + 2 = 7
• E2: using balance scales and informal uniform units to create addition or subtraction number sentences showing equivalence, such as 7 + 8 = 6 + 9, and to find unknowns in equivalent number sentences, such as 6 + 8 = □ + 10
• E3: using relational thinking and knowledge of equivalent number sentences to explain whether equations involving addition or subtraction are true; for example, explaining that 27 − 14 = 17 − 4 is true and using a number line to show the common difference is 13
• E4: using part-part-whole diagrams or bar models to recognise and explain the inverse relationship between addition and subtraction, using this to make calculations easier; for example, solving 27 + □ = 63 using subtraction, □ = 63 − 27

Core idea: both sides of an equation must have the same value. Find the role of the unknown, choose a useful number relationship, then replace the box and check.

Important questions

• What does the equals sign mean? The expressions on its two sides have equal value. In 25 = 18 + 7, both sides are 25.
• Solve 348 + □ = 725. The missing part is 725 − 348 = 377. Check: 348 + 377 = 725.
• Solve □ − 286 = 439. The starting amount is 286 + 439 = 725. Check: 725 − 286 = 439.
• Solve 900 − □ = 347. The removed part is 900 − 347 = 553. Check: 900 − 553 = 347.
• Use grouping in 38 + □ + 62 = 145. 38 + 62 = 100, leaving 45 for the missing addend.
• Solve 125 + □ = 80 + 90. The known total is 170, so the missing addend is 45.
• Why is 27 − 14 = 17 − 4 true? Both endpoints decrease by 10, preserving the difference of 13.
• Why is 83 − □ = 83 solved by 0? The amount has not changed, so nothing was removed.

Quick exit check

1. Find the box in □ − 24 = 58. Explain its role.
2. Complete 47 + 26 = 50 + □ without first finding the entire sum.
3. Explain why 43 − 18 = 48 − 23 is true.

Expected responses: 82 is the starting whole because 24 + 58 = 82; the missing addend is 23 because increasing 47 by 3 requires decreasing 26 by 3; the last equation is true because both subtraction numbers increase by 5, preserving the difference of 25.

Support and extension

Support: start with whole numbers below 20 and real equal counters. Label whole and parts before recording an equation. Move the result to the other side and ask whether its meaning changes.

Extension within this code: give two different whole-number values that make □ + 18 = 18 + □ true when the same value fills both boxes. For example, 5 and 42 both work. Explain why any shared whole-number value works using the commutative property of addition.

Teach with the Topic Guide and Classroom View, then use Homework, Practice and Test. The worksheet asks for written working and models; Practice gives feedback, and Test checks independent application.

Teacher resource

Project the Classroom View and expand each section as you teach.

• “The equals sign tells me an answer comes next.” It states equal value. Read and compare the complete expressions on both sides.
• “Always subtract to find the box.” In □ − 35 = 62, the unknown is the starting whole, so add 35 + 62 = 97. In 97 − □ = 62, the unknown is the removed part, so calculate 97 − 62 = 35.
• “Subtraction can be reordered like addition.” The starting amount and removed amount have different roles. The commutative property of addition does not apply to subtraction.
• “Any change preserves an equation.” Check the relationship. For a constant difference, change both subtraction numbers by the same amount; for an unchanged sum, an increase in one addend must be balanced by an equal decrease in the other.
• “Finding a number finishes the work.” Put it into the original box and evaluate both sides. A check must keep the original operations and order.

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 Find unknown values in numerical equations involving addition and subtraction...

Mapped skill: find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations

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
• England National Curriculum
• New Zealand Curriculum
• NCERT textbooks

• AC9M4N01: Recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals
• AC9M4N02: Explain and use the properties of odd and even numbers
• AC9M4N03: Find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation
• AC9M4N04: Count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines
• AC9M4N05: Solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits
• AC9M4N06: Develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
• AC9M4N07: Choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions
• AC9M4N08: Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation