# UNIT DESIGN FOR LINEAR FUNCTIONS DEVELOPED BY CANISE STEWARTSINGLETON

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## Understanding By Design

Unit Design

for

Linear Functions

Developed by

Canise Stewart-Singleton

Detroit Community Schools

Unit Design Worksheet

 Unit Title: Functions Subject/Course: Algebra 1 Topic: Linear Functions Grade(s): 9 Staff Name: Canise Singleton

 Stage 1 - Desired Results Established Goals (HSCE’s, etc.): A3.1.1 Write the symbolic forms of linear functions (standard, point slope, and slope intercept) and convert between forms. A3.1.2 Graph lines such as x = h and y = k given appropriate information. A3.1.4 Find an equation of a line parallel and perpendicular to a given line. Understandings: Students will understand that... Linear functions are written in various forms. Linear functions can be graphed using input/output tables. Linear functions can be graphed using x and y-intercepts. Finding the slope of an equation is determined by the rate of change. Lines can be horizontal or vertical. Lines are parallel if their slopes are equal If non-vertical lines are perpendicular, then their slopes multiply to equal -1. Given a line and a point, a parallel or perpendicular equation can be found. Essential Questions: What forms can linear functions be written in? How can an input/output table be used to graph a linear function? How can linear equations be graphed using the x and y-intercept? How can the slope be found between two points? What types of equations graph horizontal or vertical lines? How are lines determined to be parallel? What proof can be used to show that lines are perpendicular? How do you write the equation of a line that is parallel or perpendicular to a given line? Students will know… Linear equations can be converted from one form to another. Rise over run is another way to represent slope. Perpendicular lines have slopes that are negative reciprocals of each other. Students will be able to... Explain different methods that are useful when graphing and writing linear functions. Unit Enduring Understanding: Linear functions can be graphed or used to graph and interpret real life situations. Unit Question: How are linear functions graphed to interpret real life situations?

Stage 2 - Assessment Evidence

Performance Tasks: (Summary in GRASPS form, end of the unit)(Summative)(After)

Goal: Your task is to show mastery of linear functions by creating an illustrated magazine article about functions.

Role: You have been hired as a writer for Ebony, Jet, Sports Illustrated or a magazine name that you choose. You have been asked to create school piece this month. You must come up with a four page spread about linear functions. Your spread must include illustrations, and appeal to readers who don’t know much about linear functions.

Audience: Your target is high school students, and families who do not have math backgrounds.

Situation: The challenge involves creating a 4 page illustrated spread that is eye appealing and interesting to the reader.

Product: Four page article explaining linear functions.

Standards: Your work will be judged using a rubric.

Key Criteria: (Rubrics, etc.)

Rubric for GRASPS

 CATEGORY 5 4 3 2 Diagrams and Sketches Diagrams and sketches have exceptionally attractive formatting and well-organized information. Diagrams and sketches have attractive formatting and well-organized information. Diagrams and sketches exist, but are done with little effort or creativity. The magazine's diagrams and sketches are confusing to the reader. Information Gathering At least 4 different resources were used and cited to create the lesson such as internet, textbook etc. 3 resources were used and cited to create the lesson. 2 resources were used and cited to create the lesson. 1 resource was used and cited to create the lesson. Article Content Accuracy/Linear Function Knowledge All facts, terminology, and notation in the article are accurate, indicating an accurate understanding of linear functions. 99-90% of the facts, terminology, and notation are accurate, indicating a substantially accurate understanding of linear functions. 89-80% of the facts, terminology, and notations in the article are accurate. Fewer than 80% of the facts, terminology, and notations in the article are accurate. Article Writing Mechanics Capitalization and punctuation are correct throughout the article. Writing is creative and witty. Capitalization and punctuation are correct throughout the article after feedback from an adult. Writing is enjoyable. There are 1-2 capitalization and/or punctuation errors in the magazine even after feedback from an adult. Writing is tolerable. There are several capitalization or punctuation errors in the magazine even after feedback from an adult. Writing is confusing and inconsistent. Article Organization and Readability Each article in the magazine has a clear beginning, middle, and end. Very enjoyable to read. Article has beginning, middle, and end. Enjoyable to read. Article has beginning and end. Tolerable to read. Article is unclear and poorly written.

 Holistic Rubric for (Tests) 4 3 2 1 Student understands the concept, but made minor arithmetic errors which affected the rest of the work causing the answer to be incorrect. Student understands the concept, but missed a step and/or is confusing learned rules. Student work has a lot of errors showing the student has not fully grasped the concept. They are mixing up concepts or rules, and work lacks clarity. Student attempted the problem, but clearly does not understand the concept.

Other Evidence: (Quizzes, Tests, Prompts, Observations, Dialogs, Work samples, etc.)(Before, During)(For learning)

Journals, vocabulary activity, tiered assignment-(differentiation), worksheet, textbook, concept map, bingo, classroom jeopardy set, TI-83

Before During After

Pre-test jeopardy, double bubble maps, quizzes Post-test grasps

Create crossword puzzles, journal prompts,

Vocabulary quiz

Describe the assessment/s and state the prompt if applicable. □ F X S

What type of scoring tools will be used for evaluation?

□ Analytic rubric □ Checklist

X Holistic rubric □ Answer Key

X Criterion rubric □ Other

Student Self-Assessment and Reflection:

Students can write journals explaining what they understood specifically about that day’s concept or what they are having trouble with. They may be asked to describe what they found to be the best part of the unit. Students may also be given a questionnaire at the end of the unit.

Unit Design Worksheet

 Stage 3 - Learning Plan Differentiated Instruction (Layers, Tiered, etc.): Level C- 45 pts. (Choose 3 of the following) Use the calculator to graph equations in slope intercept form in order to identify their x and y-intercepts. (15 pts) Create 10 equations to be graphed using x and y-intercepts, and then pass them to another group to graph them. (15 pts.) Create a matching game to identify different forms of linear equations. (15 pts.) Create vocabulary words using the bubble maps. (15pts.) Level B- 30 pts. (Both activities are required) Use the graphics calculator to discover slope-intercept form on the graphing linear equations activity sheet. (20 pts.) Draw 5 linear equations using the slope triangle method to identify the slope and identify the y-intercepts. (10 pts.) Level A- 25 pts. (Choose 1 of the following). Create equations of parallel and perpendicular lines. (25 pts.) Create an original 20 question test for the unit. Give to a class-member and grade. Turn in blank copy, key copy, and student copy. (25 pts.) Create a poster on linear functions using the poster rubric as a guide. (25 pts.) Learning Activities: (consider the WHERE TO elements) The end of the unit project asks students to answer the question of (W) where are we going. They will have to (R) rethink and (O) organize what they have learned into information to create a magazine on linear functions. Students will use technology to understand slope intercept form. Students will be given Texas Instruments guided practice in order to discover what happens when m and b change. This will (T) tailor learning to varied needs, interests, and styles. Ring toss—Comparing negative slopes. Students will work in groups tossing pennies into rings with various diameters. They will then graph the results of the number of times the six pennies fell into each of the circles based on the distance away from the circle. The data will be collected and graphed in order to determine the slope and make predictions. This will (H) hook and hold students’ interest. Vocabulary activity- students are given a choice of six activities to choose from to show mastery of the unit vocabulary. At the end of the unit students will reflect on what they learned using a survey or a questionnaire. This is the (E) evaluation. Students will be (E) equipped with materials and supplies to complete each learning activity.

Unit Design Worksheet

 Essential Vocabulary (Identify and define) Standard form: a linear equation of the form Ax + By = C where A, B, and C are real numbers and A and B are not both zero. Slope intercept form: A linear equation of the form y = mx + b where m is the slope and b is the y-intercept. Point-slope form: A linear equation of the form y –y = m(x –x) X-intercept: The x-coordinate of a point where the graph crosses the x-axis. Y-intercept: The y-coordinate of a point where the graph crosses the y-axis. Slope: The ratio of the vertical change to the horizontal change between any two points on the line. (m = rise/run) Parallel lines: Two non-vertical lines in the same plane with the same slope. Perpendicular lines: Two non-vertical lines in the same plane whose slopes are negative reciprocals of each other. Sequencing the Learning Monday (pre-test) Identify different forms or linear equations in their various forms. Write equations in their different forms such as slope intercept form, point-slope form. Tuesday Graph lines using input/output tables. (group activity) Wednesday Graph lines using x and y-intercepts. Group C work day Thursday Slope formula song and activity (kuta worksheet) Friday Ring toss activity (slope activity) Slope quiz Monday Layer B work day Graph lines using y = mx + b (TI calculator activity slope-intercept form). Tuesday Layer B work day Wednesday Parallel lines (textbook) Thursday Perpendicular lines Friday Vocabulary activity workday Monday Jeopardy game Tuesday Layer A workday Wednesday GRASPS (double bubble map) Thursday GRASPS Friday Linear functions test (post test)

Linear Functions Test

Name Date Section

(Show all work)

1. Draw and label the coordinate plane including the quadrants.

Convert the following linear equations into slope intercept form.

2. 3x + 4y = 12 3. –9x + y = 5

4. x – 6y = 10 5. 5x + 3y = –15

Graph the following linear equations by creating an input/output table.

6. y = 7x – 3 7. y = 3/4x

1. y = –x + 4 9. y = x

1. Write an equation parallel to y = 4x + 7 passing through the point (–1, 5)

1. Write an equation perpendicular to y = –2x passing through the point (4, –3).

12. Write an equation of the line passing through the given points. (1, 4), (6, –1)

Find the x and y-intercepts.

13. –5x + y = 20 14. –4x + 5y = 30

UBD Unit Design Worksheet / Saginaw Valley State University 7