One of the foundational concepts in grades 3-5 is an understanding of fractions – some of the questions we investigate with students are:
What is a fraction? What makes a fraction a fraction?
How can we order and compare fractions?
When do we use fractions in our daily life?
What different ways can we represent fractions?
What are equivalent fractions?
In our BC mathematics curriculum, the big idea for grade 3 that we guide students to understand by the end of the school year is that “fractions are a type of number that can represent quantities” – this is a significant concept. I often have discussions with older students who have the conception that fractions have something to do with shapes/geometry, possibly because of the models used in school to represent fractional numbers (think circles/pies/pizzas or rectangles/chocolate bars). An intentional focus is to provide opportunities for students to see and represent fractional amounts using different models – area/region, set and linear. In grade 4, students learn about the relationship between fractional and decimal numbers and in grade 5, consolidate their understanding of fractions by working with equivalent fractions. During these investigations, students may begin to see relationships and connections to whole number operations when working with fractions and decimals. We want students to be able to think flexibly with fractions and decimals, just as they do with whole numbers and think about composing and decomposing, benchmark numbers, etc as they consider addition, subtraction, multiplication and division.
This term I have been thinking a lot about fractions with students and teachers. I visited two classes at Homma and a class at Wowk and hosted classes at The Studio at Grauer to investigate fractions including a grade 4 class from Woodward, the grades 3&4 class from Grauer and the Richmond School Program students from Blundell.
The following are some images sharing our investigations. As you scroll through the images, consider:
What do you notice? What do you wonder?
What instructional routines and structures have we used to support students in their understanding of fractions?
What different materials have been provided to create opportunities to think about fractions?
What conceptions do students reveal in their representations of fractions? What might you ask students? How does this information guide where we go next?