AC9M2A01: Additive patterns that grow and decrease

An additive pattern changes by adding or subtracting the same amount each time. That repeated amount is the constant change.

• Recognise whether a pattern is increasing or decreasing.
• Find the amount added or subtracted at each step.
• Describe a rule such as start at 4 and add 3 each time.
• Create the same pattern using numbers, objects, shapes or drawings.
• Use the rule to determine a missing or next element.
• Explain how a visual growing pattern connects to its number sequence.

Students should compare neighbouring terms rather than only looking at the numbers themselves. In 5, 8, 11, 14, …, each term is 3 more than the term before it, so the rule is add 3.

In 24, 20, 16, 12, …, each term is 4 less than the term before it, so the rule is subtract 4.

The same rule can be represented in different ways. A shape pattern that gains 2 objects each stage can be recorded as 3, 5, 7, 9, …

1. Build a pattern. Use counters, blocks or matchsticks to make 3, then 5, then 7 objects.
2. Ask what changed. Compare consecutive stages and identify that 2 objects were added each time.
3. Record the numbers. Write 3, 5, 7, 9 and connect each number to a stage of the model.
4. State the rule. Use complete language: “Start at 3 and add 2 each time.”
5. Reverse the thinking. Give a missing term and use the rule to work forwards or backwards.
6. Transfer the rule. Recreate the same number pattern using different materials or shapes.

Increasing pattern

6, 10, 14, 18, …

The constant change is +4, so the rule is start at 6 and add 4 each time. The next term is 22.

Decreasing pattern

35, 30, 25, 20, …

The rule is start at 35 and subtract 5 each time. The next term is 15.

Missing term

12, 15, __, 21, 24

The change is +3 each time. 15 + 3 = 18, so the missing number is 18.

Growing shape pattern

A model uses 3 sticks for stage 1, 5 sticks for stage 2 and 7 sticks for stage 3. The sequence is 3, 5, 7, … because 2 sticks are added each stage.

If every toy car has 4 wheels, the totals form a constant additive pattern.

The wheel totals increase by 4. Similar patterns can be found in windows, fence sections, tiles, seats or other repeated features.

Use a reliable, community-approved source and identify the specific Nation, People or community where the source does. Avoid presenting diverse First Nations knowledges and practices as one generic tradition. Follow local cultural and intellectual property protocols before inviting community participation or reproducing cultural material.

Key idea: An additive pattern changes by the same amount each step. Students need to identify and state the rule, not only find the next term.

Remember

• Identify constant change
• Continue patterns
• Find missing elements
• Create patterns
• Explain rules

Quick questions

• What is the rule for 8, 11, 14, 17?
• Find the missing term: 30, 25, __, 15.
• Create a pattern that increases by 4.
• Explain why 2, 4, 7, 9 is not constant.

If an answer is uncertain, return to the model and explain what each part represents before calculating or drawing a conclusion.

• Looking only at the final digit: compare whole terms, not just visible digit patterns.
• Changing the amount: 3, 5, 8, 10 is not a constant additive pattern because the changes are +2, +3, +2.
• Giving only “add” or “subtract”: require the amount too, such as “subtract 4 each time.”
• Guessing a missing term: verify the same rule on both sides of the gap.
• Disconnecting the model from the numbers: ask what physical part is added or removed at each stage.

• Support: build short patterns with counters and mark the added or removed objects in each stage.
• Core: move between material, picture, table and number-sequence representations.
• Extension: provide a rule and ask students to create two different visual patterns that follow it, or find a missing term before the starting term.

Content description: recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern.

• E1: create a pattern with materials, record the associated number sequence and describe a rule that can be reproduced with different materials.
• E2: identify additive patterns in the built environment and record them with diagrams or tables.
• E3: recognise the constant amount added or subtracted and use it to find missing elements.
• E4: use suitable digital tools to create patterns that increase or decrease by a constant amount and discuss the instructions used.
• E5: explore additive patterns on Country/Place and in First Nations Australians’ material culture using appropriate, locally authorised resources and representations (teaching context).

1. What is the rule for 7, 10, 13, 16, …?
2. Continue 40, 35, 30, ___, ___.
3. Find the missing number: 8, 12, ___, 20, 24.
4. Create a pattern that starts at 2 and adds 5 each time.
5. Explain why 4, 7, 11, 14 is not a constant additive pattern.
6. Draw a growing shape pattern whose number sequence is 2, 4, 6, 8.

When using a digital geometry or generative tool, the mathematical goal is still to describe the constant change clearly. Students can specify a starting stage and an instruction such as “add 2 squares to each new stage”, then check whether every stage follows that rule.

Teachers should review generated outputs before classroom use and ask students to verify the mathematics rather than accepting the output automatically.

Build and discuss a pattern first, use the static Teacher Slides for explicit instruction, then move to the worksheet and supported Practice. Use the Test when students can identify the constant change and justify missing terms without relying on visual guessing.

Curriculum equivalents for Recognise, describe and create additive patterns that increase or decrease...

Mapped skill: recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern

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

• AC9M2N04: Addition and subtraction strategies
• AC9M2N05: Equal groups, multiplication and division
• AC9M2A02: Addition facts to 20 and related subtraction facts
• AC9M2A03: Twos facts, doubling and halving