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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