Thursday, July 24, 2008

Math problems of the week: grade 2 Trailblazers vs. Singapore Math

1. From the fractions unit in the grade 2 Math Trailblazers Student Guide Book Two:

Banana Split

After buying a banana at a local fruit store, Jess and Bess started squabbling about who would get more.

"Let's cut it in half," said the first to the other.
"We'll each have two pieces and none for our brother."

"Hold on one minute!" the second one cried.
"I think we'll get more if we further divide.

Halves means two pieces. In fourths, there are four.
If we split the fruit that way, we're bound to get more!"

"But if fourths are good, then eighths must be great!"
So, they both got four pieces which each of them ate.

Do Jess and Bess understand fractions? Explain. You may wish to draw a picture to help explain your thinking.

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2. From the fractions unit in the grade 2 Singapore Math Primary Mathematics 2B:

Sam ate 5/8 of a pizza. How much was left over?

Mrs. Smith made 2 cakes that were exactly the same size.
She cut Cake A into fourths and Cake B into sixths.
(a) Which cake had more slices?
(b) Which cake had larger slices?

Paula had 3 pairs of shoes.
She has a pair of blue sneakers, a pair of brown dress shoes and a pair of brown sandals.
What fraction of her shoes are brown?

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Extra Credit:

For each set, estimate the ratio of language arts skills to math skills required to answer the questions.

Estimate the fraction of high functioning children with autism who are able to handle the Trailblazers problems vs. the Singapore problems without special help.

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