Unit 1 End of Module Assessment Study Guide: Module 1 vocabulary: Unit Rate: y x. How many y per each x. Proportional relationship: Has a constant unit rate. Constant of proportionality: Unit rate for a proportional relationship. Y divided by x Coordinate: Point on a graph (x,y) (x over, y up and down) Independent Variable (x) part that stands alone Dependent Variable (y) part that changes as a result of the IV Table X is the left column Y is the right column K = constant of proportionality or y/ x Graph X axis is independent variable Y axis is dependent variable Equation K x = y y x k = y k x y K = x y x = K Equivalent Ratios Scale Factor (aka unit rate) is the constant of proportionality for a scale drawing x = independent variable y = the original picture K = scale factor to find K = y x to find x = y K equation y= Kx Scale Drawing When we draw something bigger or smaller than the original object the relationship is proportional Enlargement - make larger Reduction - make smaller
Things to know (example problems) Make a table or graph given ratios or a description of a situation. (Lesson 4 PS 2) Tell from a table or graph if a relationship is proportional and be able to explain why. (Lesson 3 PS #1-3, Lesson 5 PS #1) Understand what coordinates on a graph represent in terms of a situation. (Lesson 8 Example 2a) Be able to use a unit rate or constant of proportionality to solve problems, including those examples -Cost per pound = money pound -Miles per hour, be able to calculate the miles involving fractions. (Lesson 12) -multiplication and division of frictions - change mixed fractions to improper fractions 2 ' ->( ' - change improper fractions to mixed fractions 9 -> 4 ' ' Write equivalent ratios. (Lesson 1, PS #2) Two or more fractions that have the same value. Ex., (), *) ' )) +) Calculate unit rate. (Lesson 1, PS #1) Unit rate Determine which is the better buy. (Lesson 1, Exercise 1) Calculate constant of proportionality from a situation, a graph, or a table. (Lesson 7, Lesson 8) Yes Straight line graph Graph starts at (0,0) origin No Not a straight line No Graph does not start at the origin Write an equation for a situation using the constant of proportionality. (Lesson 8, Lesson 9)
Equation K x = y x k = y y K = x y x = K k y x Be able to determine scale factor, including when you have different units. (Problem Set 17, including #1,2) Be able to use scale factor to determine new lengths based on original or original based on new. (Problem set 18) Original = x Scale Factor = k Scale drawing (new) = y K = y divided by x K = new divided by scale factor Be able to calculate area based on a scale drawing. (lesson 19) Example, if the length of a small rectangle is 3 inches and the width is 4inches, what is it for the new rectangle that has a scale factor 1 in: 5 in Original area = 3 x 4 =12 3 x 5 = 15 length of new rectangle 4 x 5 = 20 width of new rectangle 15 x 20 = 300 inches 2 is area of new rectangle Note: you cannot just multiply the original area times the scale factor Note: you can multiply the original area times the (scale factor) 2 Calculate the new or original price after a markup or discount (Lesson 14) Find the sale price of a pair of shoes that is 30$ marked ¼ off Sale price = original price x,, -, or original price x *,
Sample Questions: 1 a) A turtle walks 1 4 mile in a half hour. What is the rate he walks per hour? Ø, ' Then Keep 1 st fraction, change to x, and flip the 2 nd fraction Ø ', x ' Ø ' miles per half hour 1 b) Write an equation that represents the relationship between the number of miles (m) and the numbers of hour (h) y= k x X = hour Y = miles K = ' m = ' h m = ' h = x, ' ', =, check 1 c) How long will it take to walk 2 miles? Ø m = ' h Ø 2 x 2 = ' x ' h Ø 4 = h Four hours 2 a) A blueprint has the scale 1 cm = 7 m. What is the scale factor? Ø 1 cm = new Ø 7 m = original Ø note: you must convert cm to meters
o 1 cm = 700 cm Ø scale factor = >?@ = ABCDCA>EF G)) 2b) If the picture is 10 cm x 15 cm. What are the dimensions of the actual shape in meters? Ø 1 cm = 7 m 15 cm 15 x 7 = 105 m 10 cm 10 x 7= 70 m 2c) The blueprint has an area of 8 cm 2. What is the area of the actual shape in m 2? Ø 1 cm = 7 m 4 cm 4 x 7 = 28 m A = 8 2 cm 2 x 7 = 14 m cm2 A = 28 x 14 = 392 m 2
3) An object is normally $81. It is on sale for 1 off. What is its sale price? 3 81 27 27 27 Ø 81 27= $54 Ø 3x = 81 Ø *K * =L * Ø x = 27 4a) Girls send 7 texts for every 5 texts a boy sells. Make a chart and a graph. Is it proportional? Boys Girls 5 7 10 14 15 21 20 28 25 35 30 42 Yes the relationship is proportional The unit rate is the same throughout The graph is a straight line The graph is starting at (0, 0) 4b ) What is this situation (0,0) on the graph? When girls sent 0 text messages the boys sent 0 messages