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Springboard - Slope as a Rate of Change Cameron Kubota 0
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A Ab boou utt T Th hiiss L Leessssoon n DESCRIPTION SWBAT determine and analyze a line’s slope SWBAT create proportional slopes SWBAT understand slope as a rate of change −In order for the students to reach the objective, they will need to develop a thorough understanding of slope as a rate of change and be able to utilize slope in order to answer real life situations −First, we will frame slope as depicted by a wheelchair ramp. We will use this analogy in order to understand how rise and run play key roles in determining slope −Then, we will mathematically prove that slope is a rate of change and develop our own formula for calculating slope −Finally, we will apply slope and topics covered in Unit 1 to solve real life situations that tie back to the wheelchair ramps via material costs and income rates (Short-term goal) Students will achieve 100% mastery of determining the slope from tables and points and be able to apply slopes to real-life situations. (Medium-term goal) Students will master this content so that they can apply the steps they took to solving for slope to forthcoming activities and topics, like graphing linear functions and solving systems of linear equations via graphing. (Long-term goal) Students will need to understand slope as a rate of change and utilize the slope formula because it becomes vital and integrated in all math and science courses. Slope is the underlying building block for a lot of what the students will see as they move on in both the math and science tracks.
PREREQUISITES − Substituting inputs to determine outputs − Graphing inputs and outputs − Knowledge of points on a graph − Ratios
ESTIMATED TIME 1.5 hours
P Pootteen nttiiaall U Ussee PURPOSE: GRADES: CONTENT AREAS: COMMON CORE:
Classroom Instruction 8 - 10 Math Mathematics
G Gooaallss INSTRUCTIONAL GOALS Students will understand that slope is a rate of change between two quantities, the inputs and outputs. They will also be able to take the slope of a function and create proportional slopes.
OBJECTIVES SWBAT determine and analyze a line’s slope SWBAT understand slope as a rate of change SWBAT create proportional slopes
VARIABILITY Students will undoubtedly enter this lesson with varying level of understanding. This lesson will serve as a great introduction to slope for those that don't understand what slope is as it teaches slope as a rate of change between the inputs and outputs, but will also enrich the knowledge of students that already understand slope as a rate of change by teaching how to analyze slope and create proportional slopes to extend reach of the functions.
A Asssseessssm meen nttss FORMATIVE ASSESSMENTS
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(Springboard pg. 96 Check Your Understanding #2-7) Answers are bolded and italicized
2. Find the slope given a table
x
y
5
5
7
3
9
1
11
-1
Slope of the function is -1
3. Find the slope of a line that passes through the points (0,4) and (3,9). Reduce if possible. Slope of the line is 5/3 4. Find the slope of a line that passes through the points (-2,4) and (3,-3). Reduce if possible. Slope of the line is -7/5 5. Find two points that make a slope of -5/7 Various Answers. Sample Answer: (14,5) and (7,10) 6. Determine the slope of a given line. (Graph is displayed in Springboard books) Slope is 2 7. How does slope represent a rate of change?
Slope represents a rate of change, because it is a ratio between the change in the vertical and a change in the horizontal direction. It tells us how much our function will move vertically when the function moves so many units horizontally
SUMMATIVE ASSESSMENTS
IIn nssttrru uccttiioon naall M Meetth hood dss OPENING Introduction and Activation of Prior Knowledge - Welcome Students to class - Activate Background Knowledge of slope o BELLWORK: On page 87, write the ratio we use to solve for slope and then determine the slope of a line from a graph. - Give students 5 minutes for Bellwork. I will walk around the class to get a feeling of who’s done and who isn’t - Cold Call on a student to give their answer for bellwork. Go over for all the students how to solve for slope from a graph
“Today, we’ll be using what we learned yesterday about rise over run and ratios in order to apply slope to real life situations
DURING Guided Practice/Group Discussion - Draw a line at the bottom of the page and write the following questions on the line “How would an increase in the rise of the ramp affect the slope? What about a decrease?” “Why was it important to change inches to feet in parts a & b?”
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- You will have 20 minutes to work in your groups and answer number 16. Be sure to answer each part and show all of your work. If you finish early, answer the questions we wrote on the line. Everyone will be expected to answer these questions, either during the 20 minutes or in our class discussion. - (After 20 minutes, get the class’s attention) Let’s go over the answers you got to part b and f, but before you share your answers whole group, please open your iPads and log on to your Seariders Gmail account. - In your Gmail, you will find a link that I sent to you to a Google Forms. Please input your answers on Google Forms so that you can contribute to our classroom discussion. The responses to Google Forms will be projected onto the board and even though it will ask you to input your name, I will not display your name. - (The Google Form will ask, From the data they gave us in the representation, what is the slope of the ramp that they designed? How did you determine the slope? Does the ramp meet the ADA recommendations? Why?) (Students will have 5 minutes to input their answers) - (10 minute discussion of the responses and to sum up the lessons in the first chunk of problems)
- Please close your iPads. Now, draw a line on the bottom of page 89 and write the following question on the line “Provide a second way to write the expression to calculate slope and prove it works.” - You will have 10 minutes to complete numbers 17-19 silently and independently and then another 10 minutes to check your answers with your group and then complete what you haven’t already in your group. Again, once you finish, answer the finish early question and make sure your entire group is on the same page. - (During the 20 minutes, hand whiteboards out, one to each group, and have them write down their answer for g and c on the whiteboards) - (After 20 minutes, get the class’s attention) Let’s go over the answer to part g and c. Hold up your whiteboards and read to me what you wrote. - We will spend 5 minutes analyzing all of the answers and determine which answers are correct and fix the answers and thinking that are incorrect - “In summary, either way you write your slope expression is correct, ie x1-x2 or x2-x1, as we saw through answering g.”
CLOSING -
What did we learn today? o How to determine slope, create proportional slopes, and apply it to real-life situations”
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Now, you will work on problems #2-7 on pg. 96 to prove that you have mastered today’s lesson
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We will work independently and individually
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We will work silently and complete each of the problems fully
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We will show all our work
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This will be your ticket out of the class, so work efficiently and thoroughly
You will have 15 minutes to complete the exit ticket. You will raise your hands when you are finished (Exit ticket is Check Your Understanding on page. 96 in Springboard book)
M Maatteerriiaallss MATERIALS AND SUPPLIES Student Springboard Books Student Whiteboards and Dry Erase Markers iPads/Laptops/Access to internet Gmail accounts
RESOURCES INCLUDED
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C Coom mm meen nttss
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