Comparing Parts to Wholes

Transcription

1 Comparing Parts to Wholes A ratio is a comparison. Some ratios compare part of a collection of things to the total number of things in the collection. For example, the statement 1 out of 6 students in the class is absent compares the number of students absent to the total number of students in the class. Another way to express this ratio is to say, For every 6 students enrolled in the class, 1 student is absent or 1 6 of the students in the class are absent. If you know the total number of students in the class, you can use this ratio to find the number of students who are absent. For example, if there are 12 students in the class, then 1 6 of 12, or 2 of the students are absent. If there are 18 students in the class, then 1 6 of 18, or 3 students are absent. If you know the number of students who are absent, you can also use this ratio to find the total number of students in the class. For example, if 5 students are absent, there must be a total of 6 º 5, or 30 students in the class. Use the Square Tiles from Math Journal 2, Activity Sheet 7 to model and solve the following ratio problems. 1. Place 28 tiles on your desk so that 3 out of 4 tiles are white and the rest are shaded. How many tiles are white? How many tiles are shaded? Draw your tile model. 2. Place 30 tiles on your desk so that 4 out of 5 tiles are white and the rest are shaded. How many tiles are white? How many tiles are shaded? 3. Place 7 shaded tiles on your desk. Add some tiles so that 1 out of 3 tiles is shaded and the rest are white. How many tiles are there in all? Draw your tile model. 4. Place 25 white tiles on your desk. Add some tiles so that 5 out of 8 tiles are white and the rest are shaded. How many tiles are there in all? 408

2 Ratio Number Stories Use your tiles to model and solve the number stories below. 1. Take 32 tiles. If 6 out of 8 are white, how many are white? 2. Take 15 tiles. If 6 out of 9 are white, how many are white? 3. Place 24 tiles on your desk so that 8 are white and the rest are shaded. One out of tiles is white. 4. Place 18 tiles on your desk so that 12 are white and the rest are shaded. out of 3 tiles are white. 5. It rained 2 out of 5 days in the month of April. On how many days did it rain that month? 6. For every 4 times John was at bat, he got 1 hit. If he got 7 hits, how many times did he bat? 7. There are 20 students in Mrs. Kahlid s fifth-grade class. Two out of 8 students have no brothers or sisters. How many students have no brothers or sisters? 8. Rema eats 2 eggs twice a week. How many eggs will she eat in the month of February? How many weeks will it take her to eat 32 eggs? 9. David took a survey of people s favorite flavors of ice cream. Of the people he surveyed, 2 out of 5 said that they like fudge swirl best, 1 out of 8 chose vanilla, 3 out of 10 chose maple walnut, and the rest chose another flavor. a. If 16 people said fudge swirl is their favorite flavor, how many people took part in David s survey? b. If 80 people participated in David s survey, how many preferred a flavor that is not fudge swirl, vanilla, or maple walnut? 409

3 Calculating Choices 1. The ice-cream shop has 3 flavors of ice cream and 5 different toppings. a. Use the Multiplication Counting Principle to calculate the total number of choices for one flavor of ice cream and one topping. b. Draw a tree diagram to show the possible combinations. 2. U.S. radio station call letters must start with W or K as in WNIB or KYFM. a. How many choices are there for the first letter? The second letter? The third letter? The last letter? b. How many different 4-letter combinations are possible? c. Would you use a tree diagram to solve this problem? Explain why or why not. 3. There are 4 number cards: 1, 2, 3, and 4. a. Calculate the total number of possible combinations for two cards if you mix the cards, draw one card without looking, replace the drawn card, remix the cards, and draw one card again. b. Calculate the total number of possible combinations for cards if you mix the cards, draw one card without looking and put it aside, remix the cards, and draw one card again. 410

4 Math Boxes 1. Divide mentally. a a. A rectangle has an area of 8 cm 2. Draw and label the sides of the rectangle. b. 389 / 6 c. 729 / 8 d e b. What is the perimeter of the rectangle you ve drawn? Multiply. Use the partial-products algorithm. 4. a. Draw a circle with a radius of 2.5 centimeters. a. 26 b c b. What is the area of this circle to the nearest centimeter? Area π radius 2 About (unit)

5 Square Tiles Activity Sheet 7