Comparing unit rates associated with ratios of fractions
- Slides: 38
Comparing unit rates associated with ratios of fractions
Solution 10 1
Solution 24 1
Try Assignment on page M 1 -66 thru 67 Steve baked 5 1/2 batches of cookies in one and one half hours. Vondra baked 3 1/3 batches of cookies in 11/12 hour. Which baker made cookies at a greater rate of batches per hour?
Activity Gulliver’s travel
Activity A photocopying machine can copy 12 papers per minute. Complete the table to show many copies can be made for the stated number of minutes. Minutes Number of copies 1 12 2 3 4
Direct Variation A connection between two units in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first.
Activity Riddle me this and riddle me that. Guess me this riddle or perhaps not. I am a word that starts with “P” all of the following words are apart of me. I have that number that remains the same, as long as equality of ratios are maintained. What word am I? Port Pro Portion Ratio
Proportionality Mrs. Grant Brooks Durham Bulls Math
Proportionality
Proportionality Recognizing proportionality worksheet. Check each table for proportionality, then in groups graph one of the questions for a gallery walk so that we can see what a proportional relationship does and does not look like. Claps to a minute. Create a table of your own that is proportional
Cartesian Plane
Ordered Pairs v Two numbers written in a certain order. Usually written in parentheses like this: (4, 5). v Can be used to show the position on a graph, where the "x" (horizontal) value is first, and the "y" (vertical) value is second. v Here the point (12, 5) is 12 units along, and 5 units up.
Cartesion Plane
Graphing equations We can graph equations on a Cartesian plane. This way of representing information pictorially. This consist of two number lines that are perpendicular (meet at right angle)to each other. The vertical line is called the “y axis” and the horizontal line is called the “x axis”
Lets look at these tables Decide which tables are proportional and which are not.
What is the constant that links both descriptions in the following table? A students can run 2 laps around the soccer field per minute. Complete the following table. Minutes Distance walked in metres 0 0 1 2 3 4
Lets Graph this table in groups A students can run 2 laps around the soccer field per minute. Complete the following table. Minutes Distance walked in metres 0 0 1 2 2 4 3 6 4 8
Constant of Proportionality The constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality. Based on the graph it will be y=2 x where k= 2 How can we make the equation equal to k?
Variable and Constant A variable is a letter or symbol used to represent a number. A constant is a value that doesn't change.
How can you know if a graph is proportional? What methods do you use to check for proportionality in tables? Describe the 3 characteristics of a proportional graph.
Solution Answer: linear (straight, not horizontal or vertical), passes through the origin, continuous
Equation for proportional graphs A graph that is proportional is usually arranged y as y=kx. Eg. Ordered pair (0, 0) x
What would be the equation for this graph? A graph that is proportional is usually arranged y as y=kx. Eg. Ordered pair (0, 0) x
Complete a table from this graph in groups. Give table a description. A graph that is proportional is usually arranged y as y=kx. Eg. Ordered pair (0, 0) x
I can determine if relationships represente in equations are proportional. complete the matching activity What relationships are there with the graph and the equations?
I can determine if relationships represented in words are proportional. Determine whether or not the following situations create proportional relationships. The growth of a plant Speed of a car A cell phone plan that has a $30 monthly fee and a $0. 40 charge for each M. . B of data Diameter of a given circle vs. the circle’s circumference Joe is a car salesman. He has a hourly rate of $6 plus 10% commission.
Solutions Determine whether or not the following situations create proportional relationships. Speed of a car (yes) A cell phone plan that has a $30 monthly fee and a $0. 40 charge for each M. B. of data ( no) Diameter of a given circle vs. the circle’s circumference (Yes) Joe is a car salesman. He has a hourly rate of $6 plus 10% commission. (No)
Summarizer Create your own example of a proportional relationship.
I can interpret the meaning of proportional relationships using the constant of proportionality. Constant of proportionality worksheet
summarizer A movie theater used Y=KX to calculate how much money they made selling 9 buckets of popcorn. They determined they made 45. 99 dollars. How much was it for each bucket? What does x represent? __________ y? __________ k? ____________ How do you know?
Constant Proportionality How far did the object go in : 30 minutes? 15 mins? 3 mins? 1 min?
Constant Proportionality Based on the graph Jon thinks that it would take 20 seed packets to get 2 plants. What is he doing wrong? What is the constant of proportionality for this graph? create a table based on the graph.
I can explain what the points (0, 0) and (1, r) mean on the graph of a proportional relationship, where r is the unit rate. Find the unit rate/ constant of proportionality and express it as an ordered pair
I can compare proportional relationships from a graph. Which graph has a higher rate of change? This graph shows 2 cars driving at a constant rate. Which car is going faster? The red or the green car? Why?
I can compare proportional relationships from a graph. If you could not see based on the shapes of the lines which had a higher state of change, what could you have done to compare the two cars?
summerizer Complete Proportionality in tables, equations and graphs activity write an equation to go with each table and graph. Discuss with their partner why they chose the equation. What each part represents. write a sentence in 10 words or less about what constant of proportionality is and how to determine it from a table equation or graph.
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