Free Printable Year 2 Additive Patterns Worksheets

About This Year 2 Maths Topic

In this Year 2 unit, children explore additive patterns that increase or decrease by the same amount each time.

An increasing additive pattern may be:

3, 5, 7, 9, 11

The rule is: start at 3 and add 2 each time.

A decreasing additive pattern may be:

20, 17, 14, 11, 8

The rule is: start at 20 and subtract 3 each time.

Children also create patterns with objects and shapes, record the matching number sequences, identify missing elements and explain the rule clearly enough for another person to reproduce the pattern.

These activities support Australian Curriculum Version 9.0 content descriptor AC9M2A01 and its associated elaborations.

The Big Idea for Parents

Children should learn to describe both:

• the starting element or starting number;
• the constant amount being added or subtracted.

For example, the sequence:

5, 9, 13, 17, 21

can be described as:

Start at 5 and add 4 each time.

Learning Intentions

Children will learn to:

• recognise additive patterns;
• distinguish increasing patterns from decreasing patterns;
• identify the starting element in a pattern;
• identify the constant amount being added;
• identify the constant amount being subtracted;
• continue number patterns;
• complete missing elements in sequences;
• create patterns using numbers, shapes and objects;
• connect growing object patterns to number sequences;
• describe pattern rules clearly;
• record patterns in tables and diagrams;
• find additive patterns in the built environment;
• use digital tools to generate patterns;
• write instructions that produce a constant pattern;
• represent environmental patterns using drawings and counters.

Student Success Criteria

Key Vocabulary

Teacher Guide for Parents

Teachers introduce additive patterns through physical materials and visual models before moving to number sequences and missing elements.

At home, follow this sequence: build it, count it, record it, describe it and extend it.

1. Begin with Physical Growing Patterns

Use counters, blocks, matchsticks, toothpicks or craft sticks to create a pattern that grows by the same amount each time.

For example, create connected triangles:

• 1 triangle uses 3 sticks;
• 2 connected triangles use 5 sticks;
• 3 connected triangles use 7 sticks;
• 4 connected triangles use 9 sticks.

The associated number sequence is:

3, 5, 7, 9

The rule is: start at 3 and add 2 each time.

2. Connect the Object Pattern to a Number Sequence

After building each stage, count the total number of materials used and write the result underneath.

Encourage your child to connect each number to a particular stage of the pattern.

3. Identify the Starting Number

The starting number is the first number shown in the sequence.

In:

4, 7, 10, 13, 16

the starting number is 4.

Children should include the starting number when describing the complete pattern rule.

4. Find the Constant Change

Compare each number with the number immediately before it.

For example:

6, 10, 14, 18, 22

Each number is 4 greater than the previous number, so the constant change is:

add 4.

5. Describe the Complete Pattern Rule

A complete rule should state:

• where the pattern starts;
• what is added or subtracted each time.

For:

12, 17, 22, 27, 32

the rule is:

Start at 12 and add 5 each time.

Saying only “add 5” describes the change but not the complete sequence.

6. Explore Decreasing Patterns

Use a collection of objects and remove the same number at each stage.

For example:

25, 21, 17, 13, 9

The rule is:

Start at 25 and subtract 4 each time.

Ask your child whether the numbers are becoming larger or smaller.

7. Complete Missing Elements

Begin with a sequence that contains one missing number:

7, 10, __, 16, 19

The rule is add 3, so the missing number is 13.

Encourage your child to check the pattern on both sides of the missing position.

8. Find Missing Elements at the Beginning

Missing numbers may appear at the beginning rather than in the middle.

For example:

__, 14, 18, 22, 26

Since the rule is add 4, work backwards by subtracting 4:

14 − 4 = 10

The missing number is 10.

9. Find Several Missing Elements

Once the child understands one missing element, use patterns with several gaps.

For example:

30, __, 24, __, 18

The constant rule is subtract 3:

30, 27, 24, 21, 18

10. Create Patterns with Different Materials

Ask your child to create one growing pattern with blocks and then describe it so another person can reproduce the same number sequence using counters.

This helps children understand that the mathematical rule stays the same even when the materials change.

11. Record Patterns in a Table

Tables help children connect the stage number with the total number of objects.

The number of wheels increases by 4 for every additional car.

12. Find Patterns in the Built Environment

Look for repeated quantities in buildings, vehicles and other constructed objects.

Examples include:

• windows in train carriages;
• wheels on cars;
• steps in repeated sections of a staircase;
• lights in rows;
• chairs arranged in equal sections;
• panels in a fence.

Ask your child to record the pattern using a drawing, number sequence or table.

13. Explore Train Carriage Window Patterns

Suppose each train carriage has 6 windows.

Record:

• 1 carriage has 6 windows;
• 2 carriages have 12 windows;
• 3 carriages have 18 windows;
• 4 carriages have 24 windows.

The number sequence is:

6, 12, 18, 24

The rule is: start at 6 and add 6 each time.

14. Compare Number Patterns with Shape Patterns

A shape pattern may grow by adding the same number of shapes at every stage.

For example:

• stage 1 has 2 squares;
• stage 2 has 5 squares;
• stage 3 has 8 squares;
• stage 4 has 11 squares.

The number sequence is:

2, 5, 8, 11

The visual arrangement may change, but the total increases by 3 each time.

15. Use Dynamic Geometric Software

A digital geometry tool can be used to copy, move and add shapes to create a growing pattern.

Ask your child to:

1. create the first stage;
2. add the same number of shapes for each new stage;
3. count and record the total at every stage;
4. describe the constant rule;
5. predict the next stage.

16. Create Patterns with a Generative AI Tool

Children may write instructions for a digital tool to generate a geometric pattern.

A simple instruction might be:

“Create four stages of a pattern. Start with 3 circles and add 2 circles at every new stage.”

After viewing the result, ask:

• Did the pattern follow the instruction?
• How many shapes are in each stage?
• Is the increase constant?
• How could the instruction be clearer?

17. Debug an Incorrect Digital Pattern

A digital result may not follow the intended rule.

For example:

3, 5, 8, 10

This is not a constant add-2 pattern because the change from 5 to 8 is 3.

Ask your child to identify the error and rewrite the instruction more precisely.

18. Explore Patterns on Country and Place

Children can observe repeated and additive arrangements in the environment on Country and Place.

These may be represented using:

• drawings;
• coloured counters;
• number sequences;
• tables;
• simple diagrams.

Use local or trusted First Nations educational resources when discussing cultural examples and keep the mathematical activity connected to its original context.

19. Check Whether a Sequence Is Truly Additive

Not every pattern is an additive pattern.

For example:

2, 4, 8, 16

does not increase by a constant added amount.

Ask your child to calculate or describe the change between each pair of terms. If the change is not constant, the sequence is not an additive pattern.

20. Predict Future Elements

Once the rule is known, children can use it to predict later elements.

For:

8, 13, 18, 23

the next two numbers are 28 and 33 because 5 is added each time.

Recommended Teaching Sequence at Home

1. Build a growing pattern with physical materials.
2. Count the objects in each stage.
3. Write the matching number sequence.
4. Identify the starting number.
5. Identify the constant change.
6. Describe the complete pattern rule.
7. Continue the pattern.
8. Find missing elements.
9. Create decreasing patterns.
10. Record patterns in tables and diagrams.
11. Find patterns in the built environment.
12. Create and evaluate digital patterns.
13. Explain how the pattern can be reproduced.

Common Misconceptions and How Parents Can Help

Simple Home Additive Pattern Activities

Questions Parents Can Ask

• What is the first number in the pattern?
• Is the pattern increasing or decreasing?
• What changes from one element to the next?
• How much is being added each time?
• How much is being subtracted each time?
• Is the change constant throughout the sequence?
• What is the complete pattern rule?
• What are the next three elements?
• What number belongs in the missing position?
• How can you check the missing number?
• Can you build the pattern with objects?
• Can you draw the pattern?
• What number sequence matches the shape pattern?
• Can you record the pattern in a table?
• Can someone reproduce the pattern from your instructions?
• Where can you see a similar pattern in the environment?
• Does the digital pattern follow the instruction?
• What needs to be corrected?
• Is this a repeating pattern or an additive pattern?
• How do you know?

Mathematical Sentence Starters

Supporting Different Learners at Home

Children Who Need More Support

• begin with physical counters or blocks;
• use small starting numbers;
• begin with add 1, add 2 or add 5 patterns;
• use number lines to show constant jumps;
• highlight the new objects added at each stage;
• show only one missing element at first;
• place the missing element near the end of the pattern;
• provide the starting number or constant rule;
• use tables with partially completed entries;
• allow oral explanations before written rules.

Children Ready for Extension

• use larger starting numbers;
• create patterns with larger constant changes;
• complete patterns with several missing elements;
• find missing elements at the beginning of sequences;
• compare two patterns with the same constant change;
• create several visual patterns for the same number sequence;
• identify an error in an almost-correct pattern;
• write instructions for another learner or digital tool;
• represent one pattern with materials, a table and a diagram;
• explain why a sequence is not additive.

Quick Parent Check

Use these questions to check whether your child understands the main ideas.

1. Continue the pattern: 4, 7, 10, 13, _____, _____.
2. Describe the complete rule for: 9, 14, 19, 24.
3. Complete the pattern: 20, 17, _____, 11, _____.
4. Create an increasing pattern using counters.
5. Write the number sequence represented by the counter pattern.
6. Create a decreasing pattern that subtracts 4 each time.
7. Record a car-wheel pattern in a table.
8. Explain how another person could reproduce your pattern.
9. Identify whether a digital pattern follows a constant rule.
10. Explain the difference between a repeating pattern and an additive pattern.

A child shows secure understanding when they can identify the constant change, continue and complete a sequence, create a matching visual pattern and communicate the complete rule.

Quick Exit Ticket

1. Complete: 6, 10, 14, _____, _____.
2. Describe the complete pattern rule.
3. Create a decreasing pattern with five elements.

Printable Teacher, Parent and Student Resources

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Home Learning Summary

Additive pattern understanding grows when children build, record and explain patterns using several representations.

Use this simple routine:

1. identify the starting element;
2. compare consecutive elements;
3. find the constant amount added or subtracted;
4. describe the complete pattern rule;
5. continue or complete the sequence;
6. represent the pattern with objects, shapes or a table;
7. explain how another person could reproduce it.

Related Foundation, Year 1 and Year 2 Maths Topics

Children who need additional support can revisit these earlier counting and pattern topics.