High School Mathematics UDL Instructional Unit-Lesson 5
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<li> Students graph the rate of change in the length of each side and the consequent number of trees for each orchard (i.e., (x, y) where x = length of each side and y = the number of apple trees. </li> | <li> Students graph the rate of change in the length of each side and the consequent number of trees for each orchard (i.e., (x, y) where x = length of each side and y = the number of apple trees. </li> | ||
− | '''Multiple means of representation: '''Allow students to refer to their brainstorming notes during discussion. When discussing unit rate, provide familiar examples (e.g., miles per hour). Provide students with a copy of the word problem and the table under | + | '''Multiple means of representation: '''Allow students to refer to their brainstorming notes during discussion. When discussing unit rate, provide familiar examples (e.g., miles per hour). Provide students with a copy of the word problem and the table under #1. Have drawings and manipulatives available for students to use. |
'''Multiple means of expression: '''Allow students to solve the problem by using formulas and/or models and record information into the tables using various formats: computer, premade or original graphic organizer, etc. Allow students to use a reference of formulas. | '''Multiple means of expression: '''Allow students to solve the problem by using formulas and/or models and record information into the tables using various formats: computer, premade or original graphic organizer, etc. Allow students to use a reference of formulas. | ||
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::* Provide students with copies of the table as well as word/picture/tactile representations of the words orchard and apple trees. | ::* Provide students with copies of the table as well as word/picture/tactile representations of the words orchard and apple trees. | ||
::* Knowing that the orchards are square, students should determine that the length and width are the same. | ::* Knowing that the orchards are square, students should determine that the length and width are the same. | ||
− | ::* Students determine the area of orchard | + | ::* Students determine the area of orchard #2 by using the formula length x length = area or 8ft x 8ft = 64 ft2 and/or students may also draw the orchard on grid paper to determine the area. |
− | ::* Students can also be provided with a manipulative model or virtual template of orchard | + | ::* Students can also be provided with a manipulative model or virtual template of orchard #2 so they can determine the area by counting the units. |
::* Since the numbers will be quite large, provide students with a means to skip count to determine area. | ::* Since the numbers will be quite large, provide students with a means to skip count to determine area. | ||
:::* Students can be given units grouped by 8 and a calculator set up to add 8 so each time students place a row of units into the template, they hit enter on the calculator to add 8. | :::* Students can be given units grouped by 8 and a calculator set up to add 8 so each time students place a row of units into the template, they hit enter on the calculator to add 8. | ||
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<li> Review the concept of unit rate (area/tree) or the amount of space needed per tree. </li> | <li> Review the concept of unit rate (area/tree) or the amount of space needed per tree. </li> | ||
− | ::* If orchard | + | ::* If orchard #2 is 64 ft<sup>2</sup> and has 4 trees, how many square feet is needed for one tree? Students should set up the ratio as <math>\frac{area\ of\ orchard}{number\ of\ trees} or \frac{64^2}{64\ trees} = \frac{?^2}{1\ tree}</math> |
::* Allow students to review strategies used in lesson 3 for using ratios and proportions to solve problems. | ::* Allow students to review strategies used in lesson 3 for using ratios and proportions to solve problems. | ||
::* Students should remember that the equation must remain balanced and that whatever was done to the top portion must be done to the bottom. | ::* Students should remember that the equation must remain balanced and that whatever was done to the top portion must be done to the bottom. | ||
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::* Students determine the pattern (x, 8, 12, 16, x; pattern is +4). | ::* Students determine the pattern (x, 8, 12, 16, x; pattern is +4). | ||
::* Students draw each orchard and lay them on top of each other to determine how the side lengths change or add/subtract the difference between unit lengths of the consecutive orchards to determine that each orchard changes by 4 ft. | ::* Students draw each orchard and lay them on top of each other to determine how the side lengths change or add/subtract the difference between unit lengths of the consecutive orchards to determine that each orchard changes by 4 ft. | ||
− | ::* Students use that information to determine the unit length of orchard | + | ::* Students use that information to determine the unit length of orchard #1 and orchard #5. |
:::* For example: <math>length\ of\ orchard \#1 + 4ft = length of orchard \#22</math> | :::* For example: <math>length\ of\ orchard \#1 + 4ft = length of orchard \#22</math> | ||
<math> x+4ft = 8ft</math> | <math> x+4ft = 8ft</math> | ||
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<math>20 ft = x</math> | <math>20 ft = x</math> | ||
'''See Example:''' PowerPoint lesson 5, Slide 3. | '''See Example:''' PowerPoint lesson 5, Slide 3. | ||
− | <li> Students use the information of unit length to determine the area of orchards | + | <li> Students use the information of unit length to determine the area of orchards #1 and #5.</li> |
::* Students use given formula for a square (length x length = area) and/or draw the orchards on grid paper and count the squares to determine the area. | ::* Students use given formula for a square (length x length = area) and/or draw the orchards on grid paper and count the squares to determine the area. | ||
− | ::* Students use manipulatives of the rate of change by placing a unit length of four, starting at the end of the length and width on orchard | + | ::* Students use manipulatives of the rate of change by placing a unit length of four, starting at the end of the length and width on orchard #2 to determine the unit length for orchard #1. |
::* Students draw or model the orchards on grid paper and count the squares to determine the area. | ::* Students draw or model the orchards on grid paper and count the squares to determine the area. | ||
'''See Example:''' PowerPoint Lesson 5, Slide 4. | '''See Example:''' PowerPoint Lesson 5, Slide 4. | ||
− | ::* Students use the rate of change by adding it onto the length of orchard | + | ::* Students use the rate of change by adding it onto the length of orchard #4 to determine the length of orchard #6. |
'''See Example:''' PowerPoint Lesson 5, Slide 5. | '''See Example:''' PowerPoint Lesson 5, Slide 5. | ||
− | <li> Now that students have determined the unit rate, they determine the number of trees per orchard for orchard | + | <li> Now that students have determined the unit rate, they determine the number of trees per orchard for orchard #5. </li> |
** Using unit length determined in step 3, students use the formulas and ratios to determine the area of the orchard and the number of trees that can be planted in the orchard. | ** Using unit length determined in step 3, students use the formulas and ratios to determine the area of the orchard and the number of trees that can be planted in the orchard. | ||
− | ** Students can also use grid paper to draw orchard | + | ** Students can also use grid paper to draw orchard #5 (based on the dimensions of 20 ft x 20 ft) and by using a cut out of the unit rate, determine how many trees can be planted. |
'''See Example:''' Lesson 5 or students use virtual manipulatives as in PowerPoint Lesson 5 Slide 2. | '''See Example:''' Lesson 5 or students use virtual manipulatives as in PowerPoint Lesson 5 Slide 2. | ||
− | + | <li> Tell students they will be graphing the relationship between the size of the garden and the number of trees that can be planted. </li></ol> | |
::* Provide students with a coordinate grid with the x- and y- axes labeled. | ::* Provide students with a coordinate grid with the x- and y- axes labeled. | ||
::* Students must use the information from their tables to create ordered pairs and complete the graph. | ::* Students must use the information from their tables to create ordered pairs and complete the graph. |
Revision as of 12:40, 26 July 2013
Contents |
Lesson 5: Objective
Grade Span: 9 - 10 | Content Area: Math - Geometry |
Lesson 5 of the Unit
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Approximate Time Needed: 90 minutes or two 45 minute blocks |
Objectives:
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Essential Question(s):
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Materials Needed:
Lesson Vocabulary: Area Centimeter Foot Inch Length Meter Ratio Unit of Measure Unit Rate Width Yard |
Lesson 5: Introduction – 15 minutes
A. Activate Previous Knowledge (unit rate)
Multiple means of representation: Present real life problems using drawings, models, and video representations of orchards of various sizes. Multiple means of expression: Allow students to present ideas for problem solving using computer models, demonstrations, visuals, etc. Record problem solving ideas in different formats: mathematics journals, computer, premade or original graphic organizers, etc. Multiple means of engagement: Students may choose the type of orchard when presenting problem. Allow students to work individually or in small groups based on learning style. | |||||||||||||||
Additional Considerations for Emerging Readers and Emerging Communicators | |||||||||||||||
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B. Establish Goals/Objectives for the Lesson
Inform students that they will make decisions about units and scales that are appropriate for problem solving situations involving mathematics within mathematics or across disciplines or contexts and:
Multiple means of representation: Along with posting lesson objectives in the classroom, provide individual copies for students. Multiple means of expression: Allow students to record lesson objectives in different formats: mathematics journals, computer, premade or original graphic organizers, etc. Multiple means of engagement: Brainstorm ideas of how and when these skills might be relevant to "me." |
Additional Considerations for Emerging Readers and Emerging Communicators |
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Lesson 5: Body – 30 minutes
Direct Instruction and/or Facilitation of the Lesson
During this portion of the lesson, students will generalize relationships and determine the appropriate scale to express the relationship between two quantities.
Note: Students work in pairs to answer parts 1 - 5 of the problem. Note: Use whole group discussion for part 6. Multiple means of representation: Allow students to refer to their brainstorming notes during discussion. When discussing unit rate, provide familiar examples (e.g., miles per hour). Provide students with a copy of the word problem and the table under #1. Have drawings and manipulatives available for students to use. Multiple means of expression: Allow students to solve the problem by using formulas and/or models and record information into the tables using various formats: computer, premade or original graphic organizer, etc. Allow students to use a reference of formulas. Multiple means of engagement: Ensure all students are actively involved in their partnerships. Use scenarios related to students' interests. For example, if a student is interested in animals instead of orchard trees, the scenario could involve the rate of grazing area per horse. Use questioning to encourage students to explain their strategies. |
Additional Considerations for Emerging Readers and Emerging Communicators |
See Example: Manipulative worksheets or PowerPoint Lesson 5, Slide 1.
See Example: PowerPoint Lesson 5, Slide 2. See Example: PowerPoint lesson 5, Slide 3. See Example: PowerPoint Lesson 5, Slide 4. See Example: PowerPoint Lesson 5, Slide 5. See Example: Lesson 5 or students use virtual manipulatives as in PowerPoint Lesson 5 Slide 2.
See Example: PowerPoint Lesson 5, Slide 6. Important Consideration: For some students, the difficulty/complexity can be reduced by using only the first quadrant of the coordinate grid. |
Lesson 5: Practice – 30 minutes
Multiple means of representation: Provide students with a copy of the word problem and the table. Have drawings and manipulatives available for students to use. Multiple means of expression: Allow students to solve the problem by using formulas and/or models and record information into the tables using various formats: computer, premade or original graphic organizer, etc. Allow students to use a reference of formulas. Multiple means of engagement: Ensure all students are actively involved in their partnerships. Use scenarios related to students' interests. For example, if a student is interested in animals instead of orchard trees, the scenario could involve a rate of grazing area per horse. Use questioning to encourage students to explain their strategies. |
Additional Considerations for Emerging Readers and Emerging Communicators |
See Example: Manipulatives or PowerPoint Lesson 5, Slides 7 & 8. |
Lesson 5: Closure - 15 minutes
a. Revisit/Review Lesson and Objectives
Remind students that they were to make decisions about units and scales that are appropriate for problem solving situations within mathematics or across disciplines or contexts and:
Multiple means of representation: Along with posting lesson objectives in the classroom, students may refer to their individual copies. Multiple means of expression: Students can share what they have learned in different formats: writing, drawing, creative expression, etc. Multiple means of engagement: Share ideas of how and when these skills might be relevant to "me." |
Additional Considerations for Emerging Readers and Emerging Communicators |
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B. Exit Assessment
Multiple means of representation: Ensure students have the previous word problems from this lesson and/or lesson 4 to review and model. Have previous drawings, models, and manipulatives available for students to use. Multiple means of expression: Allow students to create the problem using various formats: computer, premade or original graphic organizer, models, etc. Allow students to use a reference of formulas. Multiple means of engagement: Ensure all students are actively involved in creating their problems. Encourage students to use scenarios related to their interests. For example, if a student is interested in animals instead of orchard trees, the scenario could involve a rate of grazing area per horse. Use questioning to encourage students to explain their strategies. |
Additional Considerations for Emerging Readers and Emerging Communicators |
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