Year Four - Making & Naming Number Patterns
Home - Making & Naming Number Patterns Map
About this Big Idea
In this Big Idea students explore number patterns and learn that this is an essential aspect of what mathematicians do. Students search for number patterns and investigate ways to illustrate and explain them.
Understanding Goals:
Students will understand:
- that mathematics is a search for patterns
- how exploring number patterns can lead to mathematical proofs
Background:
The emphasis in multiplication and division is on students developing mental strategies and using their own (informal) methods for recording their strategies. Comparing their own method of solution with the methods of other students will lead to the identification of efficient mental and written strategies. One problem may have several acceptable methods of solution. An inverse operation is an operation that reverses the effect of the original operation. Addition and subtraction are inverse operations; multiplication and division are inverse operations.
Core Content from the Syllabus:
Working Mathematically
Patterns & Algebra
- describe, continue and create number patterns
- model, describe and then record number patterns using diagrams, words or symbols
- ask questions about how number patterns have been created and how they can be continued (Communicating)
- create and continue a variety of number patterns that increase or decrease, and describe them in more than one way
- explore and describe number patterns resulting from performing multiplication
- find a higher term in a number pattern resulting from performing multiplication, given the first few terms
- describe how the next term in a number pattern is calculated
Language:
- pattern, goes up by, goes down by, even, odd, rows, digit, multiplication facts.
Connected to:
Mindset Mathematics Learning Activities
Visualise
Students begin their work with patterns by exploring the Fibonacci sequence and finding connections between numerical and visual representations of the pattern. - See page 74
Questions for reflection:
- What is the Fibonacci sequence? How does it work?
- How does the spiral represent the sequence?
- How can you predict what will come next using the sequence? Using the picture?
- How did the visual pattern help you understand the number sequence? How did the number sequence help you understand the visual pattern?
Play
Students extend their work with number patterns and visual patterns by making their own. We use the patterns students create to hold a pattern carnival in which kids engage with the patterns others create and try to identify and extend those patterns. - See page 83
Questions for reflection:
- How did you make your pattern? What was your process? What was challenging about making a pattern?
- What kind of patterns did you see? Are there patterns that are similar? How so? Which patterns were very different? Why?
- What comes next? How do you know?
- What is the rule for this pattern? How would we name it?
- What makes this pattern different? How would we describe those differences?
- When people came to your pattern, how did they figure it out? What did others notice in your pattern?
- What made your pattern interesting to you? To others? If you were to make another pattern, what would you do differently?
Investigate
Students will explore an unsolved mathematics conjecture, called the Collatz conjecture, related to a kind of number sequence. They will make number sequences using doubling and halving strategies, and develop visual diagrams to illustrate their number sequences. Students will use the visual diagrams to make their own conjectures about this fascinating problem. - See Page 88
- What do we seem to agree on? What evidence do we have as a class to support our ideas?
- What do we disagree on? What evidence have we found that seems to conflict? How can we resolve this? Do we need any additional evidence?
- How can we revise our conjectures into one class conjecture about hailstone sequences?
- Why do you think these number sequences are called hailstone sequences?
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
