Unit 4
The Coordinate Plane
The Coordinate Plane
Notebook:
Reminder: The coordinate plane is a set of two (or more) number lines that intersect at their zero points.
A ratio is a comparison of two numbers.
Using this coordinate system we can compare two different values and get a picture of the comparison.
A ratio is a comparison of two numbers.
Using this coordinate system we can compare two different values and get a picture of the comparison.
How many cents do you have if you have one quarter?
What if you have two quarters?
What if you have three?
Previously, we have used a ratio table to display this comparison. Now let's make a graph.
How many cents would you have if you had 640 quarters? How many dollars is that?
...
I really like this word problem that came out of New York:
Let's break this problem down.
First: " A publishing company is looking for new employees to type novels that will soon be published."
Second: " The publishing company wants to find someone who can type at least 45 words per minute."
Third: " Dominique discovered she can type at a constant rate of 704 words in 16 minutes."
Fourth: a question:
"Does Dominique type at a fast enough rate to qualify for the job? Explain why or why not."
I really hope she does qualify for the job. Dominique seems like a good person with a lot of ambition. She's a discoverer, you know.
Mr. Welky, on the other hand, is a stickler for the rules. He knows that faster typing means more books in a short amount of time. And more books means more reading. And more reading makes smarter people.
He points to the clearly marked advertisement: AT LEAST 45 WORDS PER MINUTE. He kind of looks mad. He isn't, he just has a face that looks mad sometimes. He's actually very nice.
I really hope Dominique gets the job. Does Dominique get the job??
Classwork & Homework:
California Standards:
CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
CCSS.Math.Content.6.RP.A.3.a
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
CCSS.Math.Content.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
CCSS.Math.Content.6.RP.A.3.a
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
CCSS.Math.Content.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.