Part of the
Lesson
Introduction
10-20 sec
Connection
Stem
In this lesson you are
going to learn…by
doing/using…
In this lesson you will solve subtraction problems by finding the distance between two numbers
on a number line.
You know that…
You already know that when you subtract you are finding the difference. The difference between
two numbers is the distance between them.
You can see this on a number line.
7 – 4 can be represented as the space or distance between 4 and 7. If you count the distance
or the spaces between these two numbers you find that 7 – 4 = 3. The difference is a distance
of 3 units.
I’m going to explain this
idea by showing you…
You can use this same method to find the distance between larger numbers. Let’s say I want to
find the difference when I subtract 87 from 243.
I don’t need a number line, which is a good thing because a number line to 243 would probably
take up a few screens… I can actually create my own number line. All I need to do is draw a
straight line with arrows on either end, and mark my start point 87, and some distance after
mark my end point 243.
How does this help you find the difference? Well, let’s think about what we know. We know that
on number lines we count hops not marks. We also know that there are some friendly numbers
between 87 and 243. For example, 100 is a friendly number between 87 and 243. Let’s hop
from 87 to 100. Now, I need to think about how far I just hopped. If that is not something you
can figure out quickly, your first hop can be even smaller. I can hop 3 spaces from 87 to 90,
then 10 more to 100, so I just hopped a total of 13 spaces to get to 100. Let’s hop to another
friendly number, 200. That was an easy hop of 100 spaces. And, finally, from 200 to 243 we
know we just need to hop 43 spaces. Let’s look at the total distance we traveled. 13 + 100 +
43. Now I have an easy addition problem that I can rewrite vertically, or solve in my head. I
find that the distance between 87 and 243 is 156, so 243 – 87 = 156.
Let’s see how this works in
a problem…
Let’s see how this technique might help us solve a word problem. Nabisco produces 688 tons of
Oreos every day. It also produces 371 tons of Ritz crackers. How many more tons of Oreos are
produced each day?
This question is asking us, what is 688 – 371 = ?
I will start to solve this by drawing in my number line. I will make my first point as 371 and my
second point as 688.
Now, I will figure out what the first friendly number I can get to is. 371 + 9 is 380. 380 + 20 is
400. 400 + 200 is 600. 600 + 88 is 688, and we are there. Now let’s add our hops.
(Define Terms/ Building
on Prior Knowledge)
30-60 sec
Demonstration
1-3 minc
Application
1-2 min
Teachers Script
29 + 600 + 88 (line up vertically), or if you wanted to do this in your head you can make it
easier to add by adding one to 29 to make 30 and taking one away from 88 to make 87. 30 +
600 + 87. 630 + 80 is 710 + 7 = 717.
Conclusion
10-20 sec
So, now you know how
to…
by…
So, now you know how to solve subtraction problems by finding the distance between two
numbers on a number line.