WHAT THEY NEED TO KNOW
Students tackle the Pythagorean theorem, bringing their math to a higher level of algebraic reasoning and knowledge of the properties of operations. With their understanding of unit rates and proportional relationships, they connect these concepts to points on a line and ultimately use them to solve linear equations.
In English, students will read major works of fiction and non-fiction from all over the world and different time periods, seeking to understand, evaluate and analyze the works. Writing may include stories, essays, reports, and “persuasive papers.”
MATH
Expressions and Equations
* Understand the connections between proportional relationships, lines, and linear equations
* Use linear equations to graph proportional relationships, interpreting the unit rate as the slope of the graph
* Know and apply the properties of integer exponents (positive numbers, negative numbers, or 0) to write equivalent expressions (such as 42•43 = 45)
(
)
Problem: Two cars are traveling from point A to point B. Their speeds are represented on a graph and in a table. Which car is traveling faster?
Solution: Even though car #1 starts out ahead by 4 miles, students identify the rate of change — or slope — of the equations presented in the table and graph as equal (55 miles per hour), meaning that both cars are traveling at the same speed.
Functions
* Understand that a function is a rule that assigns to each input exactly one output and that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output
* Compare the properties of two functions, each represented in a different way (for example, in a table, graph, equation, or description)
* Determine the rate of change and initial value of a function based on a description of a proportional relationship or at least two given (x, y) values
Sample task: Filling a pool
In the graph below, an Olympic-sized swimming pool is being filled with an average-sized garden hose.
a. At what hourly rate is the pool in the graph above being filled? Use mathematical reasoning to justify your response.
b. Is the hourly rate at which the pool is filing the same as the slope of the line? Why or why not? Explain your reasoning in words.
c. Determine the equation of the line in the graph avove. Show how you determined your answer.
d. How long will it take to fill the 660,000-gallon pool? Use mathematical reasoning to justify yoru response.
ENGLISH
Reading literature
* Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot. Students also provide an objective summary of the text.
* Analyze how differences in the points of view of the characters and the audience or reader create such effects as suspense or humor.
Reading for information
* Cite evidence from the text that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.
* Evaluate the advantages and disadvantages of using different mediums (such as print, digital text, video, multimedia) to present a particular topic or idea.
Writing
* Introduce a topic clearly, previewing what is to follow, and develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information.
* Provide a concluding statement or section that follows from and supports the information or explanation presented.
* Organize ideas, concepts, and information into broader categories.
* Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.
* Use precise language and subject-specific vocabulary.
Sample task: Write argument letter
Students watch several videos and read articles on the pressures and dangers faced by student athletes. Assignment:
“Imagine that the mayor or the school board is having a meeting to decide whether or not to keep funding school sports. You have an opportunity to present an essay, in the form of a letter, to the decision makers. What would you say? What claim would you make about school sports being good or bad for kids? What research will you call on to back up your claim? Be sure to cite important references.”
ANSWER — FILLING A POOL
a. 1,000 gallons an hour
b. no, because the slope is the change in the y-axis compared to the change in the x-axis. The hourly rate is the change in the x-axis compared to the change in the y-axis.
c. X=1,000 y because of the 1,000 gallons per hour
d. It will take 660 hours because if you divide 660,000 by the 1,000 gallons, it fills in one hour.