1. The final fractions problems in the final fractions unit in 5th grade Trailblazers, Math Trailblazers Student Guide Grade 5, p. 399:

Brandon made a cheese pizza. He put pepperoni on 1/2 of the pizza. He put onions on 3/4 of the half with pepperoni. Draw a picture showing the toppings on the pizza.

A. How much of the pizza has pepperoni and onions?

B. How much of the pizza has only cheese?

C. How much of the pizza has only pepperoni, but no onions?

A. Frank's guests ate 2/3 of a cake at his party. How much cake was left over?

B. The next day Frank ate 1/4 of the leftover cake. How much of the whole cake did he eat the day after the party?

2. From the final problems of the 5th grade Singapore Math fractions unit, Primary Mathematics 5A, p. 74.

Larry spent 1/2 of his money on a camera and another 1/8 on a radio. The camera cost $120 more than the radio. How much money did he have at first?

Mrs. Ricci had $480. She used 2/3 of it to buy an electronic fan. She also bought a tea set for $60. How much money did she had left?

3. Extra Credit:

A. Which problem set solicits higher level thinking as opposed to broadcasting the expected strategy?

B. Which problem set should true Constructivist Math Reformers prefer?

## Friday, April 24, 2009

### Math problems of the week: 5th grade Trailblazers vs. Singapore Math

Labels:
math,
Reform Math,
Singapore Math

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## 4 comments:

My 4th grader (who has just finished Singapore Math 4A) Did the Trailblazer problems in his head with no issue at all. In fact he was rather annoyed that I was asking him.

But I'm sure that he wouldn't get any credit for the answers since he didn't draw a picture.

Another rigged contest!

Quit using the actual books to compare the curriculum! Ask the professional educators which one is best LOL!

Um... the comic book? We wanna know how it went!! :]

The pizza and cake problems can be good problems: the question is when they come into the curriculum. Except that you should make the pizza rectangular. When you are trying to explain multiplication of fractions it is very helpful to use an area model. Thus 1/2 x 3/4 is the area of a rectangle of side 1/2 and 3/4 in some units. One starts with a unit square and makes a horizontal subdivision to produce one of the fractions and a vertical subdivision for the other. You end up naturally seeing why the denominator is the product of denominators and the numerator is the product of numerators.

I think this is much harder if you are subdividing circles. Since this is the last problem in the Trailblazers, I guess they are not using it to build up intuition for understanding the arithmetic, but as a crutch for doing the arithmetic.

The Singapore problems are very good. One underlying difficulty is that frankly the problems can be difficult for a lot of kids. The attitude you have to have in teaching someone with Singapore math is that, once you know you are teaching at the right level (does a given student need book 5 or 4?) is to emphasize the problem-solving strategies in reading and understanding the problems.

I worry that some people might think that Singapore Math is a panacea, that once you start using the right books the underlying difficulty of learning math will be finessed away. Not so.

Using Singapore as a benchmark (not a panacea) is correct. NCTM has not been honest with the public.

1. Half the families in Singapore speak a language other than English at home.

2. Singapore students are taught in English.

3. If you compare 'wordiness' - there are fewer words used in the Singapore curriculum and more diagrams used explain problems.

4. Singapore integrates geometry and algebra into their textbooks. US reform textbooks integrate soft subjects and require students have higher reading abilities than they actually do.

5. American students would be just as successful using Singapore as Singaporans.

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