Instructional Sequence for Addition and Subtraction of Fractions

Concepts
Fractional numbers must be added with consideration of their part values
Fractional numbers must be subtracted with consideration of their part values.

Prior knowledge
Understand fractional values
Can represent fractional values with models, pictures, and symbols... (pictures of pies, pizza, candy bars, blocks, cuisenaire rods, grid paper, number line, folded paper, rulers, geoboard, money...)
Different kinds of addition and subtraction problems with whole numbers (
separate, part-part-whole, join, compare or equalize)
Fraction as equal parts of a whole or group
Changing whole numbers into fractions 2/2, 3/3, 4/1...

Background information
Common denominators are not necessary.
Story problems - reference numbers with actual objects or experiences

Sequence ideas
For all of the activities students can estimate answers to land marks such as near 1, 1/2, or 1...

Create problems with the same syntax as the different types of
additon and subtraction of whole numbers (Join, separate, part-part-whole, compare or equalize.) Example - Join with missing end or result unknown. Sandra ate 1/4 of a pie and Jimmy ate 1/4. How much was eaten all together?] Have students represent the problems with models, pictures, words (written and oral), act out, symbols...

Problems with mixed numbers and common denominators.

Move to problems with different denominators by doing problems similar to using measuring cups and pour 1/2 cup colored water into a measuring cup with a 1/4 cup oil and ask how much together. Discuss with models, pictures... and use problems from all groups of the different types of addition and subtraction of whole numbers.

Introduce multiples and ratio table for students to use to find common multiples

Problems with mixed numbers and fractions with common and uncommon denominators.