122 ◆ Modeling Thinking
Double Open Number Line
The double number line is a great model for comparing two different
things. For example, Sue had 15 apples and Josie had 4 more than she did. How
many did Josie have?
Students draw a line and then plot one part of the comparison on
the top and the other part of the comparison on the bottom (see
Figure 7.25).
Figure 7.260 1(^2) ⁄ 5 =
(^1) ⁄ 10 2 ⁄ 10 3 ⁄ 10 4 ⁄ 10 5 ⁄ 10 6 ⁄ 10 7 ⁄ 10 8 ⁄ 10 9 ⁄ 10
(^4) ⁄ 10
Sue
Josie +4 19
15
Figure 7.25
Double Number Line for Fraction Problems
Sue walked^3 ⁄ 10 of a mile in the morning. In the afternoon she walked^2 ⁄ 5 of a mile.
How far did she walk altogether? Using a double number line students would
first think of a common denominator. Then they would plot one of the
numbers. In this case, we can use tenths as our common denominator and
plot^3 ⁄ 10. We know that^2 ⁄ 5 is equivalent to^4 ⁄ 10 so we just hop on. So we
know that^3 ⁄ 10 +^4 ⁄ 10 =^7 ⁄ 10 (see Figure^ 7.26).
Let’s look at another problem. Let’s say Joe ran^2 ⁄ 6 of a mile in the morn-
ing and 2 ⁄ 3 of a mile in the afternoon. How far did he run altogether? We know
that^2 ⁄ 3 is equivalent to^4 ⁄ 6 so we just count on. We get^6 ⁄ 6 , or 1 whole mile
(see Figure 7.27).