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Subtracting by Jumping Up to 100

This lesson teaches the jump strategy for subtracting numbers up to 100. Students learn to break a subtraction problem into jumps of tens and ones, either jumping back from the larger number or jumping up from the smaller number, to reach the answer efficiently using landmark numbers like multiples of ten.

What Does It Mean to Subtract by Jumping?

Counting backward one number at a time works for small subtraction problems, but it gets slow and error prone once the numbers get closer to 100. The jump strategy solves this by breaking a subtraction problem into a few bigger, friendlier moves along an imagined number line. Instead of moving one space at a time, you jump by tens, and then clean up the leftover ones. This builds directly on skills from using number lines to subtract up to 100 and pairs well with subtracting by 10s, since landing on a multiple of ten is what makes each jump easy to do in your head.

There are two common ways to use the jump strategy for subtraction: jumping back from the larger number, and jumping up from the smaller number. Both give the same correct answer, so it helps to know both and choose whichever feels more natural for a given problem.

Jumping Up to Find a Difference

When two numbers are fairly close together, it is often easier to start at the smaller number and jump up to the larger number, keeping track of how big each jump is. The total distance jumped is the answer to the subtraction.

Consider \( 63 - 28 \). Start at 28 and jump up to a nearby landmark number, then jump up again toward 63.

Jump from 28 up to 30. That is a jump of 2.
Jump from 30 up to 60. That is a jump of 30.
Jump from 60 up to 63. That is a jump of 3.

Now add up all three jumps: \( 2 + 30 + 3 = 35 \). So \( 63 - 28 = 35 \).

The jump strategy for 63 minus 28: jumping up in three friendly steps from 28 to 63.

Notice that every jump landed on a number that was easy to work with, either a multiple of ten or the final target. That is the whole point of the strategy: choosing jump sizes that make the mental math simple.

Jumping Back by Tens and Ones

The jump strategy also works in reverse, moving backward from the larger number. This models the idea of subtraction as taking away, which connects to what you practiced in counting to subtract up to 100, except now the jumps are bigger and faster.

Consider \( 82 - 45 \). Break 45 into a tens part and a ones part, then jump back in two stages.

Jump back 40 from 82: \( 82 - 40 = 42 \).
Jump back the remaining 5 from 42: \( 42 - 5 = 37 \).

So \( 82 - 45 = 37 \). Some students prefer to split the second jump even further, for example jumping back 2 to land on the friendly number 40, then jumping back the last 3, but the total distance jumped never changes.

Why Jump to Landmark Numbers?

Landmark numbers, especially multiples of ten, are easy anchor points because adding or subtracting a multiple of ten only changes the tens digit. That is why so many jump strategies deliberately steer through a number like 30, 40, 60, or 80 on the way to the answer. Once a jump lands on a landmark number, the next jump is almost always simpler to picture and calculate.

This same idea shows up when you compare place value pieces directly, as in subtracting with place value models up to 100, and when you line up digits in subtracting with digits up to 100. The jump strategy is really a mental shortcut for the same tens-and-ones thinking behind those methods.

Checking Your Answer

Because subtraction and addition undo each other, you can always check a jump strategy answer by adding the difference back to the smaller number. For \( 63 - 28 = 35 \), check with \( 28 + 35 \). If that sum equals 63, the subtraction is correct. This habit is worth building alongside your recall of basic subtraction facts up to 100, since knowing facts quickly makes each jump even faster to plan and check.

Practice Tip

When a new subtraction problem comes up, ask yourself: are the two numbers close together, or far apart? If they are close, jumping up is often quicker. If they are far apart, jumping back in tens and then ones usually works well. Sketching a quick number line, or even just picturing one, helps keep the jumps organized until the strategy becomes automatic.

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