Download Subtracting Fractions - a possible progression

Subtracting Fractions…..A Possible Progression
Background Knowledge –
What do I already know about ½, ¼ and 1/8s? 1/10 and 1/5s? 1/3 and 1/6s? Prove it (using
manipulatives such as the fraction strips/tiles, number lines, etc.)
What does subtraction mean/represent? For example….10-8 = ? What is the difference between 8 and
10? Can you prove this on a number line?
Can the same strategy apply to subtracting fractions? (If it is a strong strategy, it will be useful for a wide
range of numbers systems) Can you find the difference between two fractions on a number line?
Column #1 – knowledge of whole numbers and unit fractions
1–¼
1-½
1 - 1/10
1 – 1/3
1 – 1/8
1 – 1/6
Question – what do already know about partners that make a whole? OR what is the difference
between ¼ and 1 on a number line? The difference/space between these two numbers is ¾…
0
1/4
1
Column #2 – extend to non “ unit fractions”
1 – 2/2
1–¾
1 – 2/8
1 – 3/5
1 – 4/10
1 – 5/6
1 – 2/3
Question – what do I already know about partners that make a whole? OR what is the difference
between 3/5 and 1 on a number line? The difference/space between these two numbers is 2/5…..
Column #3 – partners to a whole (using missing pieces)
1-
=¾
1-
= 5/8
1-
= 2/5
1-
= 6/10 1 -
= 1/3
1-
= 4/9
Question – What do I already know about ¾ and a whole that might help me?
Column #4 – similar fractions (with a common denominator)
¾-¼
7/8 – 2/8
2/2 – ½
8/10 – 3/10
4/5 – 1/5
2/3 – 1/3
5/6–4/6
Question – What is the difference between 3/10 and 8/10 on a number line? The difference/space
between these two numbers is 5/10….
Column #5 – mixed numbers (with common denominators)
1½-½
1¼-¾
1 5/10 – 6/10
1 2/8 – 4/8
1 1/3 – 2/3
1 2/5 – 4/5
Question – What is the difference between 2/3 and 1 1/3 on a number line? If I start at 2/3, I will need a
jump of 1/3 to get to “1” and then I need 1/3 more to get to 1 1/3, therefore the difference/space
between these two numbers is 2/3…..
0
2/3
1
1 1/3
2
Column #6 – related fractions
½-¼
¾-½
¼ - 1/8
6/8 – ½
9/10 – 1/5
4/5 – 1/10
2/3-1/6
Question – What do I “already know” about these fractions to be able to work with them in this
context? For example, in order to find the difference between 1/8 and ¼, I will rely on the fact that I
already know that ¼ is the same as 2/8, therefore, the difference between 1/8 and 2/8 is 1/8….
Column #7 – mixed numbers
1¼-½
2 1/8 – 1 ½
1 1/10 – 1/5
1 2/5 – 2/10
1 2/3 – 1/6
2 5/6 – 1/3
Question – What is the difference between 1 ½ and 2 1/8? If I start at 1 ½, I will need to make a jump of
½ to get to the whole number “2”, then I will need to make another jump of 1/8 to get to 2 1/8, so my
answer is ½ + 1/8 = 5/8…..
Column #8 – more difficult….
1 1/3 – 1/5
Question – What is the difference between 1/5 and 1 1/3? If I start at 1/5, I will need to jump 4/5 to get
to “1” and then I will need to jump 1/3 to get to 1 1/3 – therefore, my answer must be 4/5 + 1/3….
February 2016 (revised)