Comparing and Ordering Fractions Activities
Supplies:
Class set of Page 6 sorting boards for students to use in pairs
Class set of Page 5 fractions for students to use in pairs (Give each pair one column
strip to cut apart and sort.)
Index cards, one per pair
Objective:
Students will use benchmark fractions to compare positive fractions.
Standards:
Grade 6 NS 1.0 Students compare and order positive and negative fractions,
decimals and mixed numbers.
6.NS.7.b Write, interpret, and explain statements of order for rational numbers in
real-world contexts.
Introduction Activity: Hand out sorting mats, index cards and simplified fraction.
“In pairs, you will sort these fractions into two or three categories on your sorting mat. You
choose how you want to separate them. Then, write down your categories on the index card and
turn it face down.”
1
1
verses less than , or fractions with an 8 in the
2
2
denominator verses fractions with different denominators.] Have students rotate to another table
to see if they can guess the how another group categorized their fractions. Share out some of the
categories chosen.
Possible student groupings: [greater than
“All of these categories work. Which one(s) would be helpful for comparing and ordering
1
1
1
fractions?” [greater than verses less than ] If no one uses the categories greater than and
2
2
2
1
less than , sort into those categories as a whole group.
2
Page 1 of 6
MCC@WCCUSD 11/13/12 I Do (Note-taking): Three methods for comparing fractions:
Method 1: Common Denominators
Method 2: Bar Models
6
3
?
7
5
6
7
>
3
5
5 6
3 7
•
?
•
5 7
5 7
30
35
>
21
35
Method 3: Benchmark Fractions
Close to 0
6
3
?
7
5
Close to
1
2
Close to 1
3
5
3
6
is a little more than one half and
is almost one,
5
7
6
7
∴
Page 2 of 6
6
3
>
7
5
MCC@WCCUSD 11/13/12 We Do (Note-taking): Order from least to greatest:
10 4 2 7
, , ,
7 5 9 15
Method 1: Common Denominators
10 45 450
•
=
7 45 315
4 63 252
•
=
5 63 315
2 35 70
•
=
9 35 315
7 21 147
•
=
15 21 315
Method 2: Bar Models
70 147 252 450
<
<
<
315 315 315 315
∴
2
7
<
<
9
15
4
10
<
5
7
10
7
∴
4
5
2
9
2
7
<
<
9
15
7
15
4
10
<
5
7
Method 3: Benchmark Fractions
“The first fraction,
“
10
, is bigger than one, so we can put it to the right of the Close to 1 section.”
7
4
1
is only away from 1, so which category should we use?” [Close to 1]
5
5
“Where should we put
2
?” [Close to 0] “Why?” [It’s only 2 out of 9 parts, or other responses]
9
“Where should we put
1
1
7
7
7
?” [Close to ] “Why?” [ is close to
, which is ]
2
2
15
15
14
Close to 0
Close to
7
15
2
9
∴ 92 < 157
1
2
<
Close to 1
4
5
10
7
4
10
<
5
7
Page 3 of 6
MCC@WCCUSD 11/13/12 You Do (Partner Activity): You and your partner will now use a sorting board to categorize your
1
fraction cards by benchmarks, Close to 0 , Close to and Close to 1 . Hand out sorting boards and
2
fraction cards.
Close to 0
2
9
Close to
1
5
3
8
1
2
Close to 1
5
8
1
2
3
4
2
3
1
4
5
6
We Do: “We can tell the order of most of these fractions just by looking at the benchmark categories. In the
Close to 0 group, how can we compare the three fractions?” [Common denominators, Bar models]
Common Denominators
Bar Models
1 36 36
•
=
5 36 180
2 20 40
•
=
9 20 180
1 45 45
•
=
4 45 180
∴
1
2
1
<
<
5
9
4
1
2
1
3
1
5
2
3
5
<
<
<
<
<
<
<
< < 4
5
9
4
8
2
8
3
4
6
You Do (Exit Ticket): Order from greatest to least:
decided the order.
5 2 6 9
Explain in writing how you
, , ,
11 7 5 10
Page 4 of 6
MCC@WCCUSD 11/13/12 4
FRACTION CARDS: One strip per group, cut into individual pieces
1
5
1
5
1
5
1
5
1
5
2
9
2
9
2
9
2
9
2
9
1
4
1
4
1
4
1
4
1
4
3
8
3
8
3
8
3
8
3
8
1
2
1
2
1
2
1
2
1
2
2
3
2
3
2
3
2
3
2
3
3
4
3
4
3
4
3
4
3
4
5
6
5
6
5
6
5
6
5
6
1
5
1
5
1
5
1
5
1
5
Page 5 of 6
MCC@WCCUSD 11/13/12 Page 6 of 6
MCC@WCCUSD 11/13/12