Questions: Mental Math Strategies for Two-Digit Addition

Question 1

Which mental math strategy makes 48 + 25 easiest to solve in your head?

• A. Decompose both numbers: 40+20=60, 8+5=13, 60+13=73 (three separate steps)
• B. Make a ten: give 2 from 25 to 48 to get 50+23=73 (one clean step once 50 is reached)
• C. Count on from 48 one at a time, 25 times
• D. Write it down — two-digit addition is too hard to do mentally

Answer: (B)

48 is only 2 away from 50, a round ten. By borrowing 2 from 25 to reach 50, the problem becomes 50+23=73, which requires almost no mental effort. Decomposing into tens and ones also gives the right answer but requires three steps (add tens, add ones, combine), which is more to hold in memory. The make-a-ten strategy exploits the proximity of 48 to a round number — recognizing that opportunity is the key skill.

Question 2

A teacher instructs a student to always use the 'decompose into tens and ones' strategy for every two-digit addition problem. The student applies it to 50 + 37: (50+30=80, 7+0=7, 80+7=87). What is wrong with this approach?

• A. The student got the wrong answer — 50+37 is not 87
• B. The strategy gives the right answer, but it unnecessarily breaks down a problem that can be seen directly — 50+37 doesn't need decomposing
• C. The strategy can only be used when both numbers have nonzero tens digits
• D. Nothing is wrong — the decompose strategy should always be used for consistency

Answer: (B)

50+37 is mentally immediate: 50 plus 37 more is 87. Decomposing it (50+30=80, then 80+7=87) gives the right answer but adds two unnecessary steps. The insight is that mental math is about choosing the path of least mental effort for each specific problem. Rigidly applying one strategy regardless of the numbers treats mental math like a written algorithm — which defeats the purpose. A student who always decomposes knows a procedure; a student who picks the right tool for each problem has genuine mental math flexibility.

Question 3

The goal of mental math is to find the one correct strategy and usually use it, regardless of the specific numbers in the problem.

• T. True
• F. False

Answer: False

Mental math is fundamentally about flexibility — choosing the strategy that makes a particular problem easiest given its specific numbers. Different strategies suit different problems: 'make a ten' is best when a number is close to a round ten (like 48); 'decompose' is best when both numbers need to be split (like 34+28); direct addition is best when one number is already a round ten (like 50+37). Applying one strategy rigidly misses the point.

Question 4

The 'make a ten' strategy works by adjusting one number to the nearest round ten, then compensating with the remaining amount from the other number.

• T. True
• F. False

Answer: True

For example, with 34+28: 28 needs 2 more to reach 30. Take 2 from 34, giving 32+30=62. The total stays the same because you moved 2 from one addend to the other without changing the sum. This works because addition is flexible in how you partition numbers. The strategy is especially effective when one number is close to a round ten (like 28 being close to 30, or 48 close to 50).

Question 5

A student knows the 'decompose into tens and ones' strategy but uses it for every problem, even when other strategies would be faster. What is this student missing about mental math?

Model answer: Mental math is not just about computing correctly — it's about choosing the most efficient path for each problem. A student who rigidly applies one strategy is treating mental math like a written algorithm, where you follow the same steps every time regardless of the numbers. The real skill is noticing which features of a problem suggest a shortcut: Is one number near a round ten? (make a ten). Are both numbers easy to split? (decompose). Is one number already a round ten? (direct addition). Flexibility — recognizing which tool fits which problem — is what separates a student who knows procedures from one who has genuine number sense.

The deeper lesson is that strategies are tools, not rules. A hammer is great for nails but not for screws. Similarly, 'make a ten' is great when a number is close to 10 but wasteful when it isn't. Developing the judgment to match strategy to problem is what makes mental math genuinely fast and fluid.