High School Mathematics UDL Instructional Unit-Lesson 5
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<ol><li> Review students' ideas on how to solve the orchard problem. </li> | <ol><li> Review students' ideas on how to solve the orchard problem. </li> | ||
<ol type=lower-alpha><li> Alex and Aldo planted several square apple orchards. </li> | <ol type=lower-alpha><li> Alex and Aldo planted several square apple orchards. </li> | ||
− | <li> The table below shows the number of trees and the size of the orchards.</li> | + | <li> The table below shows the number of trees and the size of the orchards.</li></ol> |
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− | + | <li> Students determine the area of each orchard (e.g., The 2nd orchard has an area of 64 ft<sup>2</sup> because 8 x 8 = 64).</li> | |
− | + | <li> Given the number of apple trees in each orchard, students determine the square footage needed for each tree using ratios and proportions (e.g., <math>\frac{area\ of\ orchard}{number\ of\ trees} = \frac{area}{1\ tree}</math> or the unit rate area per tree).</li> | |
− | area of orchard | + | <li> Using the ratio from orchard 2, students determine the unit rate (e.g., <math>\frac{64^2}{4\ trees} = \frac{?^2}{1\ tree}\ or\ 64ft^2 \div 4\ trees = 16ft^2</math> needed for each tree) and confirm that measurement is true for each orchard (i.e., <math>144 ft^2 \div 9\ trees = 16ft^2 and 256ft^2 \div 16\ trees = 16ft@2).</li> |
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− | area | + | |
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− | + | <li> Given the measurements in the length of each side column, students determine the rate of change in the length of each orchard (i.e., ___, 8, 12, 16 is a +4 pattern). </li> | |
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'''Note:''' Students work in pairs to answer parts 1 - 5 of the problem. | '''Note:''' Students work in pairs to answer parts 1 - 5 of the problem. | ||
− | + | <li> Using the rate of change +4, students determine the length of each side (x) for orchards 1 and 5, and fill in the column of the table. </li> | |
'''Note:''' Use whole group discussion for part 6. | '''Note:''' Use whole group discussion for part 6. | ||
− | + | <li> Students use that information to determine the area of the 1<sup>st</sup> and 5<sup>th</sup> orchards (i.e., the 1<sup>st</sup> orchard has an area of 16 ft<sup>2</sup> because 4ft x 4ft = 16ft<sup>2</sup> and the 5<sup>th</sup> orchard has an area of 400 ft<sup>2</sup> because 20ft x 20ft = 400ft<sup>2</sup>).</li> | |
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− | |width = "2500" style="background-color:#FFFFFF;"| | + | |width = "2500" style="background-color:#FFFFFF;"| |
− | area of orchard | + | <li> Students use the fact that each tree needs 16 ft<sup>2</sup> to determine how many trees can be planted in the 1<sup>st</sup> and 5<sup>th</sup> orchards using <math>\frac{area\ of\ orchard}{area\ per\ tree} = number\ of\ trees</math> (i.e., for the 1<sup>st</sup> orchard, <math>\frac{16ft^2}{16ft^2} = 1\ tree</math> and for the the 5<sup>th</sup> orchard, <math>\frac{400ft^2}{16ft^2} = 25\ trees</math>).</li> |
− | area per tree | + | |
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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> | |
'''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 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. | ||
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− | |width = "2500" style="background-color:#FFFFFF;"|# Refer to the brainstorming ideas for solving the problem. Include picture and/or tactile representations as needed. | + | |width = "2500" style="background-color:#FFFFFF;"| |
+ | # Refer to the brainstorming ideas for solving the problem. Include picture and/or tactile representations as needed. | ||
** 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. |
Revision as of 15:31, 25 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.
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. |
Lesson 5: Body – continued
Additional Considerations for Emerging Readers and Emerging Communicators |
See Example: Manipulative worksheets or PowerPoint Lesson 5, Slide 1.
area of orchard number of trees or 64 2 4 trees = ? 2 1 tree .
64 2 4 trees = ? 2 1 tree or 64 ft 2 4 trees = 16 ft 2 1 tree The unit rate is 16ft2 per tree.
See Example: PowerPoint Lesson 5, Slide 2.
x+4ft = 8ft x + 4ft - 4ft = 8ft – 4ft x=4ft
16 ft + 4 ft = x 20 ft = x 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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