Unit 3: Fractions
Section 9: Adding and subtracting fractions
Goals:
- Recognize word problems that include multiplication
- Write word problems for addition
- Write word problems for subtraction.
- Add and subtract with materials
- Add and subtract with square or rectangle diagrams
- Add and subtract with least common denominators
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, students in an in-person will turn in assignments, and I will discover
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
Adding and subtracting with materials:
Watch: Examples of how to explain
adding and subtracting fractions with different denominators
Assignment:
Adding and subtracting with array pictures or materials
Read: My
written
example of how to explain adding fractions with different
denominators
Assignment:
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).
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 40, I will want you to correct them in your assignment 41 before I look at it.
Assn 41: Then, do the same thing for a subtraction .of fractions
problem (7/8 -
2/3).
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
Assignment:
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 (so you if you multiplied the denominators to find a common denominator, you would need to simplify at the end),
- neither denominator is a multiple of the other (for example, 6 is a multiple of 2, so you can't use halves and sixths)
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