Year Four - Seeing Patterns Inside Numbers
Home - Seeing Patterns Map
About this Big Idea
In this Big Idea students explore patterns within and between numbers and investigate powerful visualisations which bring these to life. Students conclude this investigation by exploring the concept of number flexibility.
Understanding Goals:
Students will understand:
- that mathematics is a search for patterns
- how exploring patterns in and between numbers can lead to enhanced number sense and confidence with number
Background:
Students use mental strategies to recall multiplication facts up to 10 × 10 and related division facts. They use informal written strategies for multiplication and division of two-digit numbers by one-digit numbers. They record, describe and complete number patterns. Linking multiplication and division is an important understanding for students in Stage 2. They should come to realise that division 'undoes' multiplication and multiplication 'undoes' division.
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
- describe how the next term in a number pattern is calculated
Multiplication & Division
- uses mental and informal written strategies for multiplication and division
- find 'multiples' for a given whole number, eg the multiples of 4 are 4, 8, 12, 16
- relate multiplication facts to their inverse division facts
- determine 'factors' for a given whole number, eg the factors of 12 are 1, 2, 3, 4, 6, 12
Language:
- pattern, goes up by, goes down by, even, odd, rows, digit, multiplication facts.
Connected to:
Mindset Mathematics Learning Activities
Visualise
In this activity, students work with the number visual page to explore the patterns that they can see inside of numbers. In this activity, we open the door to understanding factors, multiples, and primes, as well as other number patterns. - See page 26
Questions for reflection:
- What patterns do different numbers share?
- What are you wondering now about these numbers?
- What are you wondering about the numbers we haven't looked at yet?
- What do you think is the most interesting number on this page? Why?
Play
Students play a game using the number visuals to further explore the idea of factors. Pairs of students each try to claim four squares in a row on a number game board, while thinking both visually and numerically. - See page 33
Questions for reflection:
- How did you decide what numbers a picture might represent?
- How did you then choose which of those numbers you would mark?
- What made the game hard? Did you make any mistakes? What did you learn from those mistakes?
- Which numbers were easiest to capture? Which were hardest? Why do you think that is?
- How would you make an easy game board? A very chalenging game board?
Investigate
In this activity, we extend the work students have been doing with the number visuals and focus on the importance of factors for making numbers useful and flexible. Making equal groups is a central idea for number flexibility and is a different way of decomposing numbers than students may often use. - See Page 41
Questions for reflection:
- If you wanted to find an inflexible number, how would you do it?
- If you wanted to find a very flexible number, how would you do it?
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
