Expectations:

B2.5 add and subtract fractions with like denominators, in various contexts

Key Concepts:

• When working with fractions as parts of a whole, the fractions are compared to the same whole.

• Fractions can be compared spatially by using models to represent the fractions. If an area model is chosen, then the areas that the fractions represent are compared. If a linear model is chosen, then the lengths that the fractions represent are compared.

• If two fractions have the same denominator then the numerators can be compared. In this case the numerator with the greater value is the greater fraction because the number of parts considered is greater (e.g., 23 >13)

• If two fractions have the same numerators, then the denominators can be compared. In this case the denominator with the greater value is the smaller fraction because the size of each partition of the whole is smaller (e.g., 56 <53)

• Fractions can be compared by using the benchmark of "half"and considering each fraction relative to it. For example, 56 is greater than 38 because 56 is greater than one half and 38 is less than one half.

• Fractions can be ordered in ascending order- least to greatest- or in descending order- greatest to least.

Note: The choice of model used to compare fractions may be influenced by the context of the problem. For example: a linear model may be chosen when the problem is dealing with comparing things involving length, like lengths of a ribbon or distances. An area model may be chosen when the problem is dealing with comparing the area of two-dimensional shapes, like a garden or a flag.

Learning Goals Success Criteria

Prior to this lesson: Students need to have a worked with Cuisenaire/relational rods and understand what tenths are and how they are modelled with Cuisenaire/relational rods.

Source: http://www.edugains.ca/newsite/DigitalPapers/FractionsLearningPathway/OperationsWithFractions-C-traingame.html

1. Place many relational rods of different lengths in paper bags, and distribute these to pairs of students, along with a recording chart BLM 1

2. Before beginning the task, ask students to select an orange rod and 5 red rods. Prompt them to discuss with an elbow partner how they can express a single red rod.

Key questions

• What did you use first –improper fraction notation or mixed fraction notation?

• Which was easier and why?

• If you start with an improper fraction, what could you do to change it to a mixed fraction?

• Most of your number sentences involved repeated addition. Is there another way those number sentences could be written?