Multiplication and Division of Whole Numbers

1. Divide multiples of powers of ten by multiples of ten (e.g., $$2,400\div60$$). (Note: they will only encounter examples in which the computation involved is a basic fact, i.e., they will not encounter a problem such as $$4,500\div70$$.) 
2. Look for patterns in division of multiples of powers of ten (MP.8).
3. Estimate products by rounding values to their largest place value. (Note: they will only see problems in which rounding to the largest place value results in a quotient that is easy to compute once the values are rounded to their largest place value, e.g., $$402\div19\rightarrow 400\div 20 = 20$$.) 

• Throughout Lessons 11—19, students see and make use of structure (MP.7) and attend to precision (MP.6) as they decompose numbers into sums of multiples of base-ten units to divide them. 

• In the book Teaching Student-Centered Mathematics, Grades 3-5, vol.1, John A. Van de Walle writes, “Language plays an enormous role in thinking conceptually about the standard division algorithm. More adults are accustomed to the “goes into” language that is hard to let go. For the problem $${583\div4}$$, here is some suggested language:

  • I want to share 5 hundreds, 8 tens, and 3 ones among these 4 sets. There are enough hundreds for each set to get 1 hundred. That leaves 1 hundred that I can’t share. 
  • I’ll trade the remaining hundred for 10 tens. That gives me a total of 18 tens. I can give each set 4 tens and have 2 tens left over. Two tens are not enough to go around the 4 sets. 
  • I can trade the 2 tens for 20 ones and put those with the 3 ones I already had. That makes a total of 23 ones. I can give 5 ones to each of the four sets. That leaves me with 3 ones as a remainder. In all, I gave each group 1 hundred, 4 tens, and 5 ones, with 3 ones left over.”

(Van de Walle, Teaching Student-Centered Mathematics, Grades 3—5, vol. 2, p. 191).

• Problem Set

• Problem Set Answer Key