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.

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.

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).

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.

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.

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.

• Australian Curriculum Version 9.0
• Victorian Curriculum F–10
• NSW Curriculum

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