Today in class students worked together to determine the relationship, an equation, between data given in a scenario (concert tickets and prices).
Answers to HW: 1.a. The car travels 65 miles in 1 hour; the car is traveling 65 miles per hour; 65 miles per hour is the constant of proportionality. b. The car travels 97.5 miles in 1.5 hours. c. It take the car 2/5 of an hour, or 0.4 hours, or 24 minutes to travel 26 miles. 2.a. w = 17b or b = 1/17 w b. 867 fluid ounces because 17 times 51 = 867 c. 3 bottles because 51/17 = 3 3. x = 1.61y and y = 1/1.61 x OR y = 0.62x 4.a. number of quarters number of toonies 1 1/8 16 2 20 2.5 24 3 b. 1/8 means that one eighth of a toonie equals one quarter 5. The scale factor down the first table is times 3/2, down the second table is times 2, and down the third table is times 3. The unit rate, or constant of proportionality, is 1:5 for the first table, 1:1/4 for the second table, and 1:3/5 for the third table x | y x | y x | y 2 | 10 12 | 3 5 | 3 3 | 15 20 | 5 10 | 6 7 | 35 40 | 10 30 | 18 1 | 5 1 | 1/4 1 | 3/5
0 Comments
Today in class students learned about two constants of proportionality - a coefficient and its reciprocal - that relate data in a table to each other. A unit rate is an example of a constant of proportionality.
Answers to HW: 1.a. meters kilometers 1,000 1 3,500 3.5 500 0.5 75 0.075 1 0.001 x 0.001x b. y = 0.001x 2.w = 28b and b = 1/28w 3.a. $0.80 per meter b. 1.25 meters or 5/4 meters or 1 1/4 meters Today in class students clarified some of our math vocabulary thus far, and worked out writing an equation to represent the proportions in a table of data.
Answers to HW: 1. square meters of ceiling number of tiles 1 10.75 10 107.5 9 100 a 10.75a 2. 1.6 hours because 1/500(800) = 1.6 3.a. constant of proportionality is 4 and P = 4s b. constant of proportionality is 3.14 and C = 3.14d 4. Yes; 12 inches per foot and 5,280 feet per mile, so there's 63,360 inches per mile and 1,267,200 inches in 20 miles. Today in class students took the Unit 2 Pre-diagnostic Test (not for a grade). They received their new Unit 2 workbooks, and determined some of the big ideas we will be learning about next. Hopefully those students who needed to finish the Unit 1 test did so today. We had a sub today while I was a county mandated math training.
Today in class students took the Unit 1 Unit Test. A few students will finish this tomorrow.
Today in class students reviewed using scale, scale factors, and converting units. Test tomorrow
Today in class students learned about using units in scaled drawings. I gave everyone a sheet of unit conversions to refer to, and these should now be in your math folder. We know that in order to scale a figure larger, we multiply by a number greater than 1. In order to revert back to the original size, we multiply by the reciprocal of that number.
Answers to HW: 1. E would work best. A, B, and D will not fit on the page, and C or F are a bit small 2. The scale is 1 inch = 9 feet 3. A and D 4. 36 square units. Use the scale factor squared times the original area. The scale factor is 2 and 2 x 2 = 4 and 4 x the original area of 9 = 36 5. a. $12.50 because $1.25 x 10 = $12.50 b. $25 because 1.25 x 20 = 25 c. $62.50 because 1.25 x 50 = 62.5 6. a. number of batches cups of water cups of detergent 1 6 1 2 12 2 3 18 3 4 24 4 b. 8 48 8 You could use the unit rate of 6 cups of water per batch x 8 batches, or you could double the amount used for 4 batches to find the answer. Today in class students learned about using one given scale to create another, and then used their scale drawing to find area, using 1/2 base x height, OR multiplying the scale factor squared times the original area. If you didn't try that in class, you absolutely should tonight! Oh, and if you haven't checked the google classroom lately, your classmates are posting helpful videos about scale and scale factors...
Answers to HW: 1a. Because the scale drawing is 10 cm long and 5 cm wide, the actual pool is 10 m long and 5 m wide. b. It will be smaller because it will take fewer cm to represent the actual width and length of the pool. c. Your pool should be about 1/2 the size of the given scale drawing; 5 cm long, and 2.5 cm wide. 2. The larger map has the scale of 1 inch to 500 feet. It takes twice the number of units on this map to represent the same distance as the other scaled map. Think about 1 inch = 1000 feet vs. 1 inch = only 500 feet, so 2 inches represents 1000 feet here. 3. Han is not correct. Every square inch represents a 12x12 square or 144 square feet in the restaurant. Actual area = 8,640 square feet. 4. 186 5. angle DEF angle EFD segment DF segment ED Today in class students learned how to create a scale, not just recognize a scale factor. A scale must have units, and often has two different units, e.g. centimeters and meters, so that you can convert the scale copy to the original, or vice versa.
Answers to HW: 1.a. 1 inch to 6 inches b. 18 inches 2.a. Your flag should be 3 cm long and 2 cm tall. The yellow rectangle is 1 cm tall and the red and blue rectangles are each 0.5 cm tall. b. Your flag should be 12 cm long and 8 cm tall. The yellow rectangle is 4 cm tall and the red and blue rectangles are each 2 cm tall. 3.a. 4 b. 1/4 c. 16 d. 1/9 e. 4/9 f. 9/16 4.a. C, D, E, and H have the same scale factor for both length and width, and the corresponding angles are the same. b. Check your rectangle with your classmates tomorrow, Today in class students learned the differences between scale drawings and non scaled drawings. There are benefits and drawbacks to either. Scaled drawings include details inside the figure that are also drawn to scale, not just the perimeter.
Answers to HW: 1a. 46 feet b. 12 feet c. 9 meters 2. 30 feet long and 55 feet wide 3. a. about 800 ft by 500 ft b. 1 inch might represent 300 ft 4. a. 16 times larger (72/4.5 = 16) b. 4 c. 12 units |
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
October 2018
Categories |