Friday, March 13, 2009

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

1. From "Bit and Pieces II" unit of the 6th grade Connected Mathematics curriculum (Bits and Pieces, II. p. 48):

Problem 4.4

Work with your group to develop at least one algorithm for adding fractions and at least one algorithm for subtracting fractions. You might want to look back over the first three problems in this investigation and discuss how each person in your group thought about them. Look for ideas that you think will help you develop algorithms for adding and subtracting fractions that always work, even with mixed numbers

Test your algorithms on a few problems, such as these:

5/8 + 7/8 3/5+5/3 3 3/4 + 7 2/9
3/4 - 1/8 5 4/6 - 2 1/3 5/6 - 1/4

If necessary, make adjustments to your algorithms until you think they will work all the time. Write up a final version of each algorithm. Make sure they are neat and precise so others can follow them.

Problem 4.4 Follow-Up

1. Exchange your addition algorithm with that of another group. Test the other group's plan. Write a paragraph explaining how your algorithm and the other group's algorithm are alike and how they are different.
2. Exchange your subtraction algorithm with that of another group (a different group from the group you exchanged with in part 1). Test the other group's plan. Write a paragraph explaining how your algorithm and the other group's algorithm are alike and how they are different.

2. From the "Fractions" unit of the 6th grade Singapore Math curriculum (Primary Mathematics 6B, p. 14):

Exercise 7

1. A shopkeeper had 150 lb of rice. He sold 2/5 of it and packed the remainder equally into 5 bags. Find the weight of the rice in each bag.

2. Peter had 400 stamps. 5/8 of them are U.S. stamps and the rest are Canadian stamps. He gave 1/5 of the U.S. stamps to his friend. How many stamps did he have left?

3. Kyle gave 2/7 of his money to his wife and spent 3/5 of the remainder. If he had $300 left, how much money did he have at first?

4. 2/3 of the beads in a box are red, 1/4 are yellow and the rest are blue. There are 42 more red beads than blue beads. How many beads are there altogether?

3. Extra Credit

Work with a group and write a paragraph about (1) which problem set involves more higher level thinking, and (2) which one is more irritating. Then exchange your answer to the first question with one group and and your answer to the second question with another group, and write two paragraphs explaining how your answers are alike and how they are different.

1 comment:

bky said...

When the curriculum has students invent algorithms for basic mathematical operations, to me the message is this: none of this really matters -- that's why we're letting 10-year olds make the decisions.

What if you teach them how to add fractions and build it up by: (1) giving a good foundation of what a/b means (b partitions of [0,1], count up a of them), (2) using that foundation to show, very common sensibly at this point, how to add fractions with like denominators, then (3) give a good foundation for understanding equivalent representation of fractions (e.g. why 2/3 = 4/6), and then (4) very naturally lead to the general algorithm for adding fractions with different denominators ...? (that sentence started out as a question) Then the message is that adding fractions is so important (and the students are so important) that we want the kids to really be able to do it and understand how it works.