Mathematics · Year 4 · Patterns and Algebra · Term 4

Investigating Decreasing Number Patterns

Identifying and describing patterns involving subtraction and division, and predicting next terms.

• ACARA Content Descriptions
• AC9M4A01

About This Topic

Decreasing number patterns involve sequences where terms reduce through repeated subtraction or division. Year 4 students identify rules like subtract 3 or divide by 2, describe patterns such as 50, 45, 40, 35 or 48, 24, 12, 6, and predict next terms. This aligns with AC9M4A01 by developing skills to recognise, explain, and create patterns, building on prior work with increasing sequences.

Students compare decreasing patterns to increasing ones, noting how rules generate change over time. These activities strengthen algebraic thinking, number sense, and problem-solving, preparing for more complex functions. Real-world links include money savings decreasing by fixed amounts or cell division halving quantities, making patterns relevant.

Active learning benefits this topic because students use manipulatives like counters or number lines to physically subtract or halve groups, testing rules collaboratively. Games and pattern hunts turn prediction into engaging challenges, helping students internalise abstract concepts through trial, error, and peer feedback.

Key Questions

1. Compare increasing and decreasing number patterns.
2. Explain how to find the rule for a decreasing pattern.
3. Design a decreasing number pattern that follows a specific rule.

Learning Objectives

• Compare the rules of increasing and decreasing number patterns.
• Explain the process for finding the subtraction or division rule in a decreasing number pattern.
• Calculate the next three terms in a decreasing number pattern given its rule.
• Design a decreasing number pattern with a specific subtraction or division rule.
• Analyze a given decreasing number pattern to identify its rule.

Before You Start

Identifying Increasing Number Patterns

Why: Students need to be familiar with identifying rules involving addition and multiplication before they can effectively compare and contrast them with subtraction and division.

Basic Subtraction Facts

Why: A strong foundation in subtraction is necessary for students to accurately apply subtraction rules within number patterns.

Basic Division Facts

Why: Students require proficiency with division facts to correctly identify and apply division rules in decreasing patterns.

Key Vocabulary

Decreasing Pattern	A sequence of numbers where each term is smaller than the previous term. This is achieved through repeated subtraction or division.
Rule	The specific mathematical operation (subtract a number or divide by a number) that is consistently applied to get from one term to the next in a pattern.
Term	Each individual number within a number sequence or pattern.
Predict	To use the identified rule of a pattern to determine what the subsequent numbers in the sequence will be.

Watch Out for These Misconceptions

Common Misconception

All decreasing patterns subtract the same amount each time.

What to Teach Instead

Many patterns use division, like halving, which changes the decrease size. Active group creation tasks let students test rules with counters, comparing subtraction and division visually to spot differences.

Common Misconception

The rule is always subtract 1 or divide by 10.

What to Teach Instead

Rules vary, such as subtract 4 or divide by 3. Prediction games with mixed sequences encourage peer checks, helping students articulate flexible rules through discussion.

Common Misconception

Patterns stop making sense after a few terms.

What to Teach Instead

Rules apply indefinitely. Extended relay activities push predictions further, building confidence as students verify with manipulatives and see consistency.

Active Learning Ideas

Stations Rotation: Pattern Rule Stations

Prepare four stations with sequences: subtract constant, subtract multiples, divide by 2, divide by 3. Groups rotate every 10 minutes, identify rules, predict three more terms, and explain on worksheets. Debrief as a class.

45 min·Small Groups

Pairs Challenge: Create and Predict

Partners choose a starting number and rule, like subtract 7 or halve. They generate 8 terms, swap papers, predict next two terms, and verify rules together. Extend by drawing number lines.

25 min·Pairs

Whole Class: Pattern Relay Race

Divide class into teams. Project a decreasing sequence; first student writes next term on board, tags next teammate. Correct rule earns points. Discuss errors immediately.

30 min·Whole Class

Individual: Manipulative Halving

Each student uses 64 counters, halves piles repeatedly, records pattern. Predict terms without counters, then check by recounting.

20 min·Individual

Real-World Connections

• A baker might decrease the number of cookies they bake each day to manage inventory, starting with 100 cookies on Monday and decreasing by 15 each day. Students can calculate how many cookies are left by Friday.
• A savings account balance can decrease as money is withdrawn. If a person starts with $500 and withdraws $50 each week, students can determine the balance after a certain number of weeks.
• In a game, a player might start with a certain number of lives and lose a set number each round, or their score might be halved after each incorrect answer. This involves identifying the decreasing pattern to strategize.

Assessment Ideas

Quick Check

Present students with two patterns: one increasing (e.g., 5, 10, 15) and one decreasing (e.g., 50, 45, 40). Ask: 'Which pattern is decreasing? How do you know? What is the rule for the decreasing pattern?'

Exit Ticket

Provide each student with a card showing a decreasing pattern, such as 72, 36, 18. Ask them to write down the rule for the pattern and calculate the next two terms. Collect these to gauge understanding of rule identification and prediction.

Discussion Prompt

Pose the question: 'Imagine you have 60 marbles and you want to share them equally among friends, but you want to see how many marbles each friend gets if you keep halving the group. What would the pattern look like? What is the rule?' Facilitate a class discussion on their findings.

Frequently Asked Questions

What are decreasing number patterns in Year 4 Australian Curriculum?

Decreasing patterns reduce through subtraction or division, per AC9M4A01. Examples: 100, 90, 80 (subtract 10) or 81, 27, 9 (divide by 3). Students identify rules, predict terms, and compare to increasing patterns, fostering algebraic reasoning for real applications like budgeting.

How do you find the rule for a decreasing pattern?

Subtract consecutive terms to check constant difference, or divide for ratio. For 36, 24, 16, subtract gives 12 then 8, so not constant; divide by 1.5 each time. Practice with tables helps students test operations systematically before predicting.

How can active learning help students with decreasing number patterns?

Active methods like counter halving or relay predictions make rules tangible. Students manipulate objects to see decreases, collaborate to verify, and play games for repetition. This counters passivity, boosts engagement, and solidifies understanding through hands-on trial and peer teaching, aligning with inquiry-based maths.

What activities teach predicting decreasing patterns?

Use stations for rule practice, pair swaps for creation, or relays for speed. Manipulatives visualise changes. These build prediction skills by linking concrete actions to abstract rules, with debriefs addressing errors and extending to design tasks.