Understanding By Design
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Unit Design
for
Linear Functions
Developed by
Canise Stewart-Singleton
Detroit Community Schools
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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: |Essential Questions: |
|Students will understand that... |What forms can linear functions be written in? |
|Linear functions are written in various forms. |How can an input/output table be used to graph a linear function? |
|Linear functions can be graphed using input/output tables. |How can linear equations be graphed using the x and y-intercept? |
|Linear functions can be graphed using x and y-intercepts. |How can the slope be found between two points? |
|Finding the slope of an equation is determined by the rate of change. |What types of equations graph horizontal or vertical lines? |
|Lines can be horizontal or vertical. |How are lines determined to be parallel? |
|Lines are parallel if their slopes are equal |What proof can be used to show that lines are perpendicular? |
|If non-vertical lines are perpendicular, then their slopes multiply to equal |How do you write the equation of a line that is parallel or perpendicular to a |
|-1. |given line? |
|Given a line and a point, a parallel or perpendicular equation can be found. | |
|Students will know… |Students will be able to... |
| | |
|Linear equations can be converted from one form to another. |Explain different methods that are useful when graphing and writing linear |
|Rise over run is another way to represent slope. |functions. |
|Perpendicular lines have slopes that are negative reciprocals of each other. | |
|Unit Enduring Understanding: |Unit Question: |
| | |
|Linear functions can be graphed or used to graph and interpret real life |How are linear functions graphed to interpret real life situations? |
|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 |Tuesday |Wednesday |Thursday |Friday |
| | | | | |
|(pre-test) |Graph lines using input/output |Graph lines using x and |Slope formula song and activity|Ring toss activity (slope |
|Identify different forms or |tables. |y-intercepts. |(kuta worksheet) |activity) |
|linear equations in their | | | | |
|various forms. |(group activity) |Group C work day | |Slope quiz |
| | | | | |
|Write equations in their | | | | |
|different forms such as slope | | | | |
|intercept form, point-slope | | | | |
|form. | | | | |
|Monday |Tuesday |Wednesday |Thursday |Friday |
| | | | | |
|Layer B work day |Layer B work day |Parallel lines |Perpendicular lines |Vocabulary activity workday |
| | |(textbook) | | |
|Graph lines using | | | | |
|y = mx + b | | | | |
| | | | | |
|(TI calculator activity | | | | |
|slope-intercept form). | | | | |
|Monday |Tuesday |Wednesday |Thursday |Friday |
| | | | | |
|Jeopardy game |Layer A workday |GRASPS |GRASPS |Linear functions test |
| | | | |(post test) |
| | |(double bubble map) | | |
| | | | | |
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
8. y = –x + 4 9. y = x
10. Write an equation parallel to y = 4x + 7 passing through the point (–1, 5)
11. 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
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