N3C2TNp13

Answers to problem 13:  

1.   55

2.   17

Strategies may vary. For 37 + 18, some students might add the 10s first, then the ones, either in horizontal or vertical notations. Other students might add the ones then the tens. Still others might use a mental strategy of making 37 à 40 and making 18 à 15, then adding 40 + 15 to get 55.

For the subtraction problem, students may use the traditional algorithm, indicating a need to regroup the 35 to a 20 + 15 and then performing the subtraction…
15 – 8 = 7, 20 – 10 = 10, answer = 17. Some might say that 30 – 10 = 20,
5 – 8 = –3, so 20 – 3 = 17.

TEACHER NOTES:

“As students work with larger numbers, their strategies for computing play an important role in linking less formal knowledge with more sophisticated mathematical thinking. Research provides evidence that students will rely on their own computational strategies (Cobb et. al., 1991). Such inventions contribute to their mathematical development (Gravemeijer, 1994; Steffe, 1994). Moreover, students who used invented strategies before they learned standard algorithms demonstrated a better knowledge of base-ten concepts and could better extend their knowledge to a better knowledge of base-ten concepts and could better extend their knowledge to new situations, such as finding how much of $4.00 would be left after a purchase of $1.86 (Carpenter et al., 1998, p. 9). Thus, when students compute with strategies they invent or choose because they are meaningful, their learning tends to be robust—they are able to remember and apply their knowledge.” ¹⁰

[1] National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (pp. 85–86). Reston, VA: Author.