Friday, June 25, 2010

Math problems of the week: 4th grade Trailblazers vs. Singapore Math

I. The last four decimals problems in the "Using Decimals" chapter of the 4th grade Math Trailblazers Student Guide, p. 286:

["/" stands for tenths; "." stands for hundredths]

4. Jessie and Roberto were playing Hundredths, Hundredths, Hundredths. Roberto made the following number.

///// . . . . 

Write the common fraction and the decimal fraction for Roberto's number.

5. When it was Jessie's turn, she wanted to make 6.48. Use base-ten shorthand to show Jessie's number.

6. Roberto wanted to build the number 9.06. Use base-ten shorthand to show what [base-ten] pieces he should use.

7. Jessie wrote nine and six hundredths like this: 9.6. Explain why this is incorrect.

II. The last four decimals problems in "The Four Operations of Decimals" chapter of the 4th Grade Singapore Math Primary Mathematics 4B, pp. 75-76:

4. Gwen and Susan bought the box of crackers and the tub of ice cream. They shared the cost equally. How much did each girl pay? [picture of cracker box, labeled $3.15; picture of ice cream tub, labeled $4.65]

5. Angela bought 5 kg of grapes. She gave the cashier $50 and received $18.75 change. Find the cost of 1 kg of grapes.

6. The total weight of 5 blocks of butter and a bag of flour is 2.7 lb. If the weight of the bag of flour is 1.2 lb, find the weight of each block of butter.

7. A painter mixed 10.5 liters of white paint with 15.5 liters of red paint. He poured the mixture equally into 4 cans. How much paint was there in each can?

III. Extra Credit

Comparing the mathematical demands of the two problem sets, discuss whether "base 10 shorthand" offers Trailblazers students a shortcut through decimals.

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