Thursday, December 3, 2009

Math problems of the week: 6th grade Connected Math vs. Singapore Math

1. The final fractions calculations problems in 6th grade Connected Mathematics 2, Bits and Pieces I: Understanding Fractions, Decimals, and Percents, p. 52:

Extensions:

For exercises 55-60, find an estimate if you cannot find an exact answer. You may find that drawing a number line, a hundredths grid, or some other diagram is useful in solving the problem. Explain your reasoning.

55. What is 1/4 of 12?

56. What is 2/9 of 18?

57. What is 1/4 of 3?

58. What is 3/4 of 8?

59. What is 2/9 of 3?

60. What is 3/4 of 3?

2. The final fractions calculations problems in 6th grade Singapore Math Primary Mathematics 6B Workbook, p. 13:

Find the value of each of the following:

(a) 1/2 + 1/2 × 1/4 - 3/8

(b) 2/5 × (5 - 3) ÷ 7/10

(c) 2/3 ÷ 4 × 3/4

(d) 2 ÷ (1/2 + 1/4) × 3/8

(e) (1 - 3/8) ÷ (1/2 + 1/3)

(f) 1/6 + 5/6 ÷ 5/6 - 2/3

3. Extra Credit

Which problem set involves more mathematical "extensions"?

Find an estimate if you cannot find an exact answer. You may find that drawing a number line, a hundredths grid, or some other diagram is useful in answering this question. Explain your reasoning.

1 comment:

JuliaD said...

When I was a kid, all they did was teach us algorithms (or what I thought were "tricks") to finding answers to math problems. We were just supposed to memorize the steps, but they never explained why the steps worked. I think where we've gone wrong with all these visuals and explanations (number lines, hundredths grid, etc.) is that we are encouraging students to use them *instead* of memorization, when we should be using them only help students understand why the quick algorithms work. As an adult, I absolutely use the memorized "math facts" and algorithms that were drilled into me, and I could not function without them. But I also like that I now know why they work.

If I see one more GED student try to add 1-digit numbers by drawing a bunch of dots (in the middle of a multi-step algrebra problem), I'm going to scream.