Use Compensation to Subtract on a Number Line
π¦ Outfox the problem! If you need to subtract an annoying number like 39, it's much faster to subtract a massive 40 and give exactly 1 back to balance the scale.
Do this: Read the concept below, then try the quiz or activity.
Concept
Compensation subtraction is tricky, but it's the coolest mental math secret when numbers end in 8 or 9.
π― The "Steal Too Much and Give Back" Strategy: Example: 75 - 29 = ? Subtracting 29 is annoying. Let's pretend it is 30!
1. Steal Too Much: Start at 75 on the number line. Take a giant -30 leap backwards! * 75 - 30 = 45. 2. Wait, we stole too much! We were only supposed to subtract 29, but we subtracted 30. We took 1 too many! 3. Give 1 Back (Hop Forward): You hopped backward too far. Take 1 hop FORWARD on the number line to fix it. * 45 + 1 = 46. (We are HOPPING FORWARD because we gave 1 back!). So, 75 - 29 = 46.
Subtracting 30 (+1) is so much faster than writing down massive subtraction algorithms.
Try it
Steal too much, give 1 back!
Instructions: Jump backwards with a perfect "10", then hop exactly 1 space forward to fix the mistake!
Problem 1: 62 - 19 = ? * Pretend 19 is 20! * Jump backwards 20: 62 - 20 = ___ * Hop forward 1 to give it back: 42 + 1 = ___ * Answer: ___
Problem 2: 84 - 39 = ? * Pretend 39 is 40! * Jump backwards 40: 84 - 40 = ___ * Hop forward 1! ___ + 1 = ___ * Answer: ___
Problem 3: 56 - 29 = ? * Answer: ___
Problem 4: 91 - 58 = ? * (Hint: Pretend it's 60. Then hop forward 2!) * Answer: ___