Friday, May 14, 2010

Math problems of the week: 7th grade Connected Math vs. 1920s Math

I. From Hamilton's Essentials of Arithmetic, Higher Grades (published in 1919), final problem set (for 7th grade) involving fractions, p. 154:

Make out sales slips for the following purchases in this form:

[A model sales slip including fields for Quantity, Article, Amount, Total, and Change Due]

1. Edith Mason bought 2 ¼ yd. lace @ 32 ¢; 2 5/8 yd. edging at 7 ¢; 1 ¼ yd. chiffon @ $2.50. Amount received, $5.00.

2. Cora Wise bought ½ doz. lienen towels @ $6.75; ¾ doz. linen napkins @ $5.94; 1 ½ doz. kitchen towels @ $2.95. Amount received, $13.

3. Ruth Wade bought 5 ¼ yd. serge @ $2.35; 4 7/8 yd. wool Jersey cloth @ $2.75. Amount received, $30.

4. Alice Miner bought 1 chiffon blouse @ $5.95; 5 5/8 yd. ribbon @ 29 ¢; 2 ¼ yd. braid @ 19 ¢. Amount received, $10.

5. Clara Hold bought ½ doz pencils @ $.3; 1 box writing paper @ $.59; ¼ gross pens @ $1.0; ½ doz pads @ $1.15; 1 founatin pen for $2.75. Amount received, $5.

6. Emma Stone bought 3/8 yd. damask @ 225; ¼ doz. napkins @ $5.90. Amount received, $3.

7. Maud Smith bought 13 /8 yd. cretonne @ 45 ¢; 12 3/8 pd. ribbon @ 12 ½ ¢; 6 5/8 yd. braid @ 19 ¢; 7 ¼ yd. lace @ 17 ¢; 2 5/8 yd. edging @ 9 ¢. Amount received, $15.


II. From Bits and Pieces 2, Using Fractions Operations booklet, final problem set, p. 64:

Unit Review

Use Your Understanding: Fraction Operations

1. The Scoop Shop sells many types of nuts. Jayne asks for this mix:

½ pound peanuts
½ pound almonds
1/6 pound hazelnuts
¾ pound cashews
¼ pound pecans

a. Nuts cost $5.00 per pound. What is Jayne’s bill?

b. What fraction of the mix does each kind of nut represent?

c. Diego does not like cashews, so he asks for Jayne’s mix without the cashews. What is his bill?

d. Kali is making small bowls of nuts for a party. Each bowl uses ¼ cup of nuts. Kalli has 3 3/8 cup of nuts. How many bowls can she make?

2. Shaquille likes dried fruit. He wants a mix of peaches cherries, pineapple chunks, an apple rings. The following chart shows how much The Scoop Shop has of each fruit and how much of each fruit Shaquille orders.

The Scoop Shop’s Stock: 1 ¼ pounds dried peaches.
Shaquille’s Order: ½ of the stock
The Scoop Shop’s Stock: 4/5 pound dried cherries
Shaquille’s Order: ½ of the stock
The Scoop Shop’s Stock: ¾ pound dired pineaaple chunks
Shaquille’s Order: 2/3 of the stock
The Scoop Shop’s Stock: 2 ¼ pounds dried apple rings
Shaquille’s Order: 3/5 of the stock

a. How many pounds of dried fruit does Shazuille order?

b. Dried fruit costs $5.00 per pound. What is Shaquille’s bill?

Explain Your Reasoning

When you use mathematical calculations to solve a problem or make a decision, it is important to be able to support each step in your reasoning.

3. What operations did you use to find the cost of the nuts in Jayne’s mix?

4. How did you find the fraction of the mix for each kind of nut?

5. 4 ÷ 1/3 = 12 and 4 ÷ 2/3 = 6. Why is the second answer half of the first?

6. Use the following problems to show the steps involved in algorithms for adding, subtracting, multiplying, and dividing fractions. Be prepared to explain your reasoning.
a. 5/6 + ¼
b. ¾ - 2/3
c. 2/5 × 3/8
d. 3/8 ÷ 3/4

III. Extra Credit

What is Diego's bill?

1 comment:

Barry Garelick said...

The problems in the old arithmetic book are quite good and require multiplication of fractions in order to arrive at the sub-costs. There are similar type problems in Singapore's unit on fractions.