Unit 3: Fractions and Decimals

Section 9: Adding and subtracting fractions


Warning! This week looks short.  It does have less different stuff in it than last week's assignments did.  It is an illusion that this is easier.  It's not.  This topic usually takes a full week, because, after doing all this in 1-2 days, people like you usually turn in stuff, and they have missed half of the important ideas.  Then I have to stop the class and redo everything, and make everyone in the class redo everything.  I will do that to you, if you miss stuff the first time around.  Watch and read carefully, think about details, and don't get lulled into a false sense of security because it seems easy.


Writing word problems

A fraction of something: multiplication and recognizing wholes
 How to specify a fractional amount for an addition or subtraction word problem
Subtraction word problems revisited
Analyzing word problems "of" and other things that might go wrong.  An analyzed exampleWord problems to analyze
Assignment 38: Write addition and subtraction of fractions word problems . (Warning--if you mess up your subtraction word problems, I will insist that you redo them until you get them right) July 22
Quiz: Analyzing fraction addition and subtraction word problems. (In D2L quizzes) July 22


Adding and subtracting with materials:

Watch: Examples of how to explain adding and subtracting fractions with different denominators
Adding with fraction circles
Subtracting with fraction circles
Assignment: July 24
Assn 39: Adding and subtracting with fraction circles
Instructions for explanation videos about fractions

Adding and subtracting with array pictures or materials

Addition and subtraction with drawn or folded squares showing fractions
Addition and subtraction with rectangles on grid paper showing fractions
Read: My written example of how to explain adding fractions with different denominators
Assn 40:  Record a detailed description of how to add fractions using an array diagram, paying special attention to how the array is formed, and how the equivalent fractions are deduced using multiplication from the array (3/8 + 4/5). July 24
I recommend that you wait until you have feedback on your addition explanation, before doing Assn 41.  If you make errors that I want you to correct in assn 55, I will want you to correct them in your assignment 56 before I look at it.
Assn 41: Then, do the same thing for a subtraction .of fractions problem (7/8 - 2/3). July 26
Instructions for explanation videos about fractions


Adding and subtracting fractions numerically:

with and without a least common denominator

Watch: 3 levels of abstraction in numerical fraction work
Examples with addition
Examples with subtraction
Assn 42: Choose a fraction addition or subtraction problem where the least common denominator is smaller than the denominator that you get by multiplying the two denominators, and where neither denominator is a multiple of the other (for example, 4 is a multiple of 2, so you can't use halves and fourths), and show how compute the sum or difference in all 3 ways I showed. (Pencil and paper work is sufficient--carefully show all steps in your work). July 26