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Using Number Lines to Subtract Up to 100
This lesson shows how to use an open number line to subtract numbers up to 100. Students learn to place the starting number, jump backward by tens and then by ones, and land on the answer, building a visual, flexible strategy for two-digit subtraction.
Steps for Subtracting on a Number Line
Follow these steps any time you subtract two numbers up to 100 using an open number line.
- Write the larger number (the starting amount) at the right end of the line.
- Look at the number being subtracted and split it into tens and ones, for example 25 becomes 20 and 5.
- Jump backward by the tens part first, landing on a new point.
- Jump backward by the ones part from that new point.
- The number you land on after the final jump is the answer.
Worked Example: 72 Minus 25
Find \( 72 - 25 \) using an open number line. Since 25 splits into 20 and 5, start at 72 and jump back 20, then jump back 5.
The first jump of 20 takes you from 72 to 52. The second jump of 5 takes you from 52 to 47. So \( 72 - 25 = 47 \).
Choosing How to Split the Jumps
There is more than one way to break apart the number you are subtracting. Some students prefer jumping by tens first and ones second, as shown above. Others jump by ones first to reach a friendly number ending in zero, then finish with a big jump of tens. For example, subtracting 25 from 72 could also be done by jumping back 2 to reach 70, then jumping back 23. Both paths land on the same answer, 47, so pick whichever split feels easiest for the numbers in front of you.
This flexibility is one of the biggest advantages of an open number line over strictly counting to subtract up to 100 one step at a time. Instead of counting back 25 individual steps, you make only two or three larger jumps, which is faster and leaves less room for a counting mistake.
Second Example: 84 Minus 37
Try \( 84 - 37 \). Split 37 into 30 and 7. Starting at 84, jump back 30 to land on 54, then jump back 7 to land on 47. So \( 84 - 37 = 47 \).
Notice that jumping back a full ten always moves you the same distance no matter where you start, which is the same idea used when subtracting by 10s. Recognizing that pattern makes the tens jump on a number line almost automatic.
Why the Number Line Strategy Works
Subtraction on a number line works because subtracting a number is the same as moving that many spaces to the left. Splitting the amount you subtract into tens and ones does not change the total distance moved, it only breaks one long jump into two shorter, easier jumps. As long as the jumps add up to the correct total (in the example above, \( 20 + 5 = 25 \)), the landing point is guaranteed to be the correct answer.
This strategy connects directly to subtracting with digits up to 100, where the same tens-and-ones thinking is applied using written numbers instead of a picture. Practicing with the number line first helps build a strong mental picture of what is happening to the digits later on.
Common Mistakes to Avoid
- Jumping the wrong direction. Subtraction always moves left (backward) on the number line.
- Forgetting to check that the jumps add up to the full number being subtracted.
- Mixing up the starting number and the number being subtracted when placing the first point.
- Losing track of the landing point between jumps, especially with larger tens jumps.
A quick way to check your work is to add the number you subtracted back to your answer. If \( 47 + 25 = 72 \), then the subtraction \( 72 - 25 = 47 \) was done correctly.