- Mixed, improper and proper fractions should be interspersed throughout fractions teaching and learning so that the students build flexibility with these early.
- "Models" include linear, area, volume, and set representations.
Operations With Fractions:
Addition and subtraction
Op DAdd and subtract fractions with friendly but unlike denominators (e.g., 2 and 30) using models and symbols
Op BUse models to compose and decompose fractions with like denominators as a form of adding and subtracting fractions
- The most appropriate models for multiplication and division of fractions are number lines and rectangular area models (array models).
- Mixed, improper and proper fractions should be interspersed throughout fractions teaching and learning.
- Students will use their understanding of the inverse relationship between multiplication and division to solve tasks. This may mean that they solve division questions using multiplication.
- Prior to commencing learning about multiplication and division of fractions, students should have a solid understanding of:
- the multiple meanings of multiplication and division with whole numbers;
- unit fractions;
- number lines and area models for representing, comparing and adding/subtracting fractions.
OPERATIONS WITH FRACTIONS: MULTIPLICATION AND DIVISION
OP FUse models to recognize that any fraction is a multiple of its unit fraction (e.g., 3/4 is 3 × 1/4)
OP-HUse models to decompose fractions using unit fractions as a form of division (e.g., How many 1/4 in 7/4?)
OP JDivide a fraction by a like-denominator unit fraction using models and symbols (e.g., 3/8 ÷ 1/8)
OP KDivide a fraction by a like-denominator fraction with a whole number result (e.g., 9/4 ÷ 3/4 = 3)
OP LMultiply fractions where the numerator of one is the denominator of the other using models (e.g., 4/5 × 1/4)
OP MDivide a fraction by a smaller friendly denominator fraction with a whole number result (e.g., 6/4 ÷ 3/8 = 4)
OP ODivide a fraction by a like-denominator fraction with a whole number remainder (e.g., 10/4 ÷ 3/4 = 3 1/3)
OP PDivide a fraction by an unlike-denominator fraction with a non-whole number remainder (e.g., a remainder of 3/8 ÷ 1/2 = 3/4)
Created by Dr. Cathy Bruce, Tara Flynn, and Shelley Yearley.
Fractions Learning Pathways are inspired by Dr. Jere Confrey's work, based on international and Ontario classroom research, and informed by feedback from classroom teachers and student thinking.
The purpose of this interactive planning tool for teaching fractions is to provide educators with a research informed framework. It includes a range of field-tested tasks (grades 3-10) that have proven to be effective in Ontario schools. The collection of tasks follows a logical sequence that can be modified and/or adjusted to fit teacher and student needs. Video and photos are also included to bring the learning to life. This interactive planning tool also includes one page summaries of key fractions math ideas as well as anticipation guides that feature Ontario students’ thinking.