# Comparing Fractions

Description
This is a set of prompts consisting of purposely paired fractions to elicit the use of various strategies. The prompts may be used on different occasions depending on student readiness. Repeated practice and exploration in making comparisons between fractions will deepen student understanding. Encourage students to build models/representations and create contexts to support visualization of fractions, which in turn supports meaning-making.
Mathematics
Research shows that it is beneficial to spread fraction learning throughout the year and embed it in other strands. These prompts progress in complexity from comparisons of equivalent fractions, to examples that include same denominators, to comparisons of very close fractions with different numerators and denominators. Students are encouraged to develop a range of different strategies and to use them strategically, based on the situation.
Curriculum Connections
Students will:
• represent, compare and order fractional amounts using a variety of tools;
Instructional sequence
1. Partner students and introduce the task. Post the selected prompt (select from options to the right) on the black/whiteboard or interactive whiteboard, or distribute on a handout.
2. Provide students time to complete the task. Encourage them to use graph paper, rulers and manipulatives (concrete or virtual, such as the tools at mathies.ca).
3. Have students describe their thinking. Highlight different strategies by intentionally selecting students that solved the task in different ways. Have students identify the similarities and differences between the strategies.
 Prompt 1 Which is greater: 8 / 7 or 9 / 8 ? Show your thinking. Prompt 2Which is closer to 1 1 / 2 : 28 / 19 or 26 / 16 ? Prompt 3Which of these fractions is closer to 1 / 4 : 5 / 16 or 3 / 8 ? Prompt 4Which of these fractions is closer to 2 / 3 : 5 / 9 or 7 / 12 ? Prompt 5Which is greater: 2 / 5 or 5 / 7 ? Prompt 6If you are familiar with an Imperial tape measure, you will recognize these fractions. Place them in order on a number line. What pattern(s) do you notice? 3 / 4 , 3 / 8 , 1 / 2 , 9 / 16 , 1 / 4 , 1 / 8 , 13 / 16 , 5 / 8 , 7 / 8 , 5 / 16 , 1 / 16 , 1 Prompt 7Represent the fractions 7 / 5 and 5 / 3 using set, area and number line models. Use each to compare the two fractions. What is important to remember when making comparisons using each model?
Highlights of student thinking
Students may:
• construct accurate models to compare two or more fractions;
• rely on the algorithm for determining equivalent fractions;
• consider only the numerators or only the denominators;
• use benchmarks to make estimates for comparison;
• consider the size of the unit fractions (as indicated by the denominators);
• consider the proximity of the fraction to 1 by identifying the ‘missing piece’ (complement); and
• be purposeful about the strategy for comparison based on the fractions given.
Key questions