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CHAPTER 13: BUILDING STRATEGIES FOR FRACTION COMPUTATION (DIVISION…
CHAPTER 13: BUILDING STRATEGIES FOR FRACTION COMPUTATION
ADDITION AND SUBTRACTION
Contextual Examples and models
mix of models
area mocels
draw circles
length models
rods
rulers
number lines
Estimation and invented strategies
thinking tool
target answers
create own problems
Developing the algorithms
Like denominators
Unlike denominators
Make a common fraction
Fractions greater than one
Common errors
Adding both numerators and denominators
Failure to identify common denominators
Difficulty finding common multiples
Failing to estimate
Difficulty with mixed numebers
MULTIPLICATION
Contextual Examples and models
Multiply a fraction by the whole number
Example: Marvin ate 3 pounds of meat every day. HOw much meat did marvin eat in one week?
Murphy at 1/3 pounds of meat everyday. How much meat did murphy eat in one week?
Multiply a whole number by a fraction
EXAMPLE: There are 15 cars in Michael's toy collection. twow thirds of the cars are red. How many red cars does Michael have?
Fractions of fractions, without subdivision
EXAMPLE: you have 3/4 of a pizza left. If you give 1/3 of the leftover pizza to your brother, how much of a whole pizza will your brother get?
Fractions of Fractions: Subdividing the unit parts
When the pieces must be subdivided inot smaller unit parts, the problems become more challenging
Zach had 2/3 of the lawn left to cut. After lunch, he cut 3/4 of the grass he had left. How much of the whole lawn did zack cut after lunch?
Area model
DIVISION
Contextual exampls and models
Whole number divided by whole number
Fraction divided by a whole number (GRADE 5)
garden plots IE: Three gardeners are equally sharing 1/4 of an acre for their plots. What part of an acre is each gardeners plot?
Water bottles
Cheese sticks
Whole numbers divided by fractions
IE: Colin's smoothies shop has just bought a machine that blends 6 pints of smoothies for one batch. THeir Smoothie Cups hold 3/4 of a pint. How many smothies can be served from one batch?
Fractions divided by fractions
EX: Farmer Brown found that he had 2 1/4 gallons of liquid fertilizer concentrate. It take 3/4 gallon to make one tank of mixed fertilizer. How many tankfuls can he mix?
Developing the algorithms
the common-Denominator Algorithm
Invert and multiply algorithm