The Power of Place Value · Term 1

Patterns in the Number System

Identifying and describing sequences that increase or decrease by powers of ten, and other simple additive patterns.

About This Topic

Patterns in the number system allow students to see the predictable structure of mathematics. In Year 3, the focus is on sequences that increase or decrease by powers of ten, such as 10, 100, or 1,000. By identifying what stays the same and what changes as they count, students build the foundations for mental addition and subtraction. This topic links directly to AC9M3A01, where students describe and continue patterns.

Recognising these patterns helps students move away from counting by ones and towards more efficient strategies. In the Australian Curriculum, this also connects to understanding how our currency works and how we measure large distances. Students grasp this concept faster through structured discussion and peer explanation, where they can verbalise the 'rules' they discover in a sequence.

Learning Objectives

• Identify and describe number sequences that increase or decrease by multiples of 10, 100, or 1,000.
• Analyze what remains constant and what changes in number sequences when counting by hundreds or thousands.
• Predict the next number in a given sequence by explaining the additive pattern.
• Explain how understanding place value supports the continuation of number patterns.
• Compare and contrast patterns that increase by 10 with patterns that increase by 100.

Before You Start

Understanding Place Value to Thousands

Why: Students need a solid grasp of place value to identify what changes and what stays constant when counting by larger amounts.

Identifying Simple Additive Patterns

Why: Prior experience with patterns involving smaller numbers, like adding 1 or 2, prepares them for more complex patterns.

Key Vocabulary

Place Value	The value of a digit based on its position within a number, such as ones, tens, hundreds, or thousands.
Sequence	A set of numbers or objects that follow a specific order or rule.
Additive Pattern	A pattern where a constant number is added to get the next term in a sequence.
Multiple of Ten	A number that can be divided by 10 with no remainder, such as 10, 20, 30, 100, 200, etc.

Active Learning Ideas

Think-Pair-Share: Pattern Detectives

The teacher displays a sequence like 1,240, 1,340, 1,440. Students work in pairs to identify which digit is changing, by how much, and what the next three numbers will be before sharing their 'rule' with the class.

⏱ 15 min·Pairs

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Inquiry Circle: The Hundred Chart Mystery

Groups are given fragments of a 1,000-chart (e.g., a 3x3 grid starting at 450). They must use their knowledge of place value patterns to fill in the missing numbers in all directions (up, down, left, right).

⏱ 30 min·Small Groups

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Role Play: The Human Calculator

One student acts as the 'Input' and provides a starting number. Another acts as the 'Rule' (e.g., +100). A third student must quickly provide the 'Output'. Students rotate roles to practice different powers of ten.

⏱ 20 min·Small Groups

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Real-World Connections

Bank tellers count large sums of money by grouping bills into bundles of 10, 100, or 1,000, using place value patterns to quickly determine totals.

Construction workers use patterns when measuring materials for large projects, such as laying out fence posts every 10 meters or stacking bricks in layers of 100.

Watch Out for These Misconceptions

Common Misconception

Students may think that adding 100 only changes the hundreds digit, failing to regroup when they reach 900.

What to Teach Instead

Use a place value flip chart or digital counter to show what happens when 100 is added to 950. Peer modeling with MAB blocks helps students see the physical 'trade' that occurs when a place value column reaches ten.

Common Misconception

Difficulty identifying patterns that decrease, especially when crossing a place value threshold (e.g., 1,010 minus 20).

What to Teach Instead

Practice 'counting back' using a number line. Collaborative problem-solving where students have to 'undo' a pattern helps them see the relationship between increasing and decreasing sequences.

Assessment Ideas

Quick Check

Present students with a sequence like 345, 445, 545, ___. Ask them to write the next number and explain the pattern using the words 'add' and 'hundred'.

Discussion Prompt

Ask students: 'When we count by hundreds, like 200, 300, 400, what part of the number stays the same? What part changes? Why do you think this happens?'

Exit Ticket

Give each student a card with a starting number and a rule (e.g., Start at 7, add 10). Ask them to write the next three numbers in the sequence and circle the digit that changes each time.

Frequently Asked Questions

What patterns should Year 3 students recognise?

Students should be able to identify and continue sequences that increase or decrease by 10, 100, or 1,000. They should also start to notice patterns in the ones place when adding multiples of ten, and how the digits in higher place values remain constant unless a regrouping threshold is met.

How can active learning help students understand number patterns?

Active learning encourages students to look for the 'why' behind a pattern. By working in groups to solve puzzles or playing roles in a sequence, students are forced to articulate the rules they are following. This verbalisation helps move the pattern from a memorised sequence to a conceptual understanding of how our base-ten system functions.

How does this topic relate to real-world Australian contexts?

Patterns are everywhere, from the way house numbers are assigned on a street to the intervals of a bus timetable. In Australia, understanding patterns of 10 and 100 is essential for managing money ($1 and $10 notes) and measuring lengths in the metric system.

What is the best way to introduce decreasing patterns?

Start with a physical countdown or a game like 'Blast Off'. Use a number line to show the movement to the left. Comparing an increasing pattern with its decreasing 'opposite' helps students see that the same place value rules apply in both directions.