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Year Three - Understanding 12

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About this Big Idea

In this Big Idea students develop a deep understanding of what fraction is and why a fraction is best seen as a relationship between the numerator and denominator that creates one number.

"I have found in my teaching and work with students that the most important idea for students when learning fractions is the idea of a relationship. I teach students that what is special about a fraction is that the numerator relates to the denominator and that we do not know anything about the fraction without knowing what that relationship is." (Boaler, Munson & Williams. 2018 p149)

Understanding Goals:

Students will understand:


In Stage 2 Fractions and Decimals 1, fractions with denominators of 2, 3, 4, 5 and 8 are studied. Denominators of 6, 10 and 100 are introduced in Stage 2 Fractions and Decimals 2. Fractions are used in different ways: to describe equal parts of a whole; to describe equal parts of a collection of objects; to denote numbers (eg 12 is midway between 0 and 1 on the number line); and as operators related to division (eg dividing a number in half).

Core Content from the Syllabus:

Working Mathematically

Fractions & Decimals


Connected to:

Mindset Mathematics Learning Activities


Students build a deep and flexible understanding of (Communicating, Problem Solving) 12 and whole by trying to spy 12 in a complex geometric image. - See page 151

Questions for reflection:



Students play with finding half of numbers using the Number Visuals Sheet and looking for patterns connecting 12 to even and odd, doubling, and equal groups. - See page 160

Questions for reflection:



Students connect previous work with half of shapes and half of numbers to find half of the area of different sizes of squares. Students generate multiple ways to partition squares in half, justify those as half, and look for patterns. - See page 171

Questions for reflection:

Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012



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