High School Mathematics UDL Instructional Unit-Lesson 3
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− | + | <ol><li> Model a problem with the class that involves making decisions about units and scales, and determine various ways to solve it. </li> | |
<ol type=lower-alpha><li> Problem 1: A floor is 9 ft wide and 12 ft long. How many tiles (12" on a side) are needed to completely cover the floor? </li> | <ol type=lower-alpha><li> Problem 1: A floor is 9 ft wide and 12 ft long. How many tiles (12" on a side) are needed to completely cover the floor? </li> | ||
− | <li> Draw a rectangle to represent dimensions 9 ft by 12 ft or make a scale drawing of it.</li> | + | <li> Draw a rectangle to represent dimensions 9 ft by 12 ft or make a scale drawing of it.</li></ol> |
− | + | <li> Model a second problem for students. </li> | |
<ol type=lower-alpha><li> Problem 2: A floor is 9 ft wide and 12 ft long. How many tiles (18" on a side) are needed to completely cover the floor? </li> | <ol type=lower-alpha><li> Problem 2: A floor is 9 ft wide and 12 ft long. How many tiles (18" on a side) are needed to completely cover the floor? </li> | ||
<li> Students recommend whether to convert the floor plan to inches or the tiles to feet.</li> | <li> Students recommend whether to convert the floor plan to inches or the tiles to feet.</li> | ||
− | <li> If students recommend converting 9 ft and 12 ft to inches, then find the area of the rectangle in square inches (108in x 144in) and divide by the area of a tile (12in x 12in).</li></ol> | + | <li> If students recommend converting 9 ft and 12 ft to inches, then find the area of the rectangle in square inches (108in x 144in) and divide by the area of a tile (12in x 12in).</li></ol></ol> |
For example: | For example: | ||
* 9 x12in = 108 in 12 x 12in = 144 inches | * 9 x12in = 108 in 12 x 12in = 144 inches | ||
− | * Area of the floor in inches: 108 in x 144 in = 15,522 | + | * Area of the floor in inches: 108 in x 144 in = 15,522 in<sup>2<sup> |
− | * Area of the tile in inches: 18 in x 18 in = 324 | + | * Area of the tile in inches: 18 in x 18 in = 324 in<sup>2<sup> |
− | * 1552 | + | * 1552 in<sup>2<sup> ÷ 324 in<sup>2<sup> = 48 in<sup>2<sup>, so 48 tiles are needed |
'''Multiple means of representation: '''Allow students to have a written copy of the problem, drawn models of the situation, and/or conversion formulas as needed/requested. | '''Multiple means of representation: '''Allow students to have a written copy of the problem, drawn models of the situation, and/or conversion formulas as needed/requested. | ||
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<ol><li> Provide the written problem to include picture representations of relevant words so students can follow along as the problem is introduced.</li> | <ol><li> Provide the written problem to include picture representations of relevant words so students can follow along as the problem is introduced.</li> | ||
<ul><li> Provide students a scale drawing of the rectangle (floor) on grid paper measuring 9 units by 12 units with each unit representing a foot.</li> | <ul><li> Provide students a scale drawing of the rectangle (floor) on grid paper measuring 9 units by 12 units with each unit representing a foot.</li> | ||
− | <li> Label the rectangle "floor" using word and picture representation. </li> | + | <ul><li> Label the rectangle "floor" using word and picture representation. </li> |
<li> Each square in the grid represents 1 inch in length and 1 inch in width.</li> | <li> Each square in the grid represents 1 inch in length and 1 inch in width.</li> | ||
<li> Highlight around 12 in x 12 in to represent 1 ft x 1 ft.</li> | <li> Highlight around 12 in x 12 in to represent 1 ft x 1 ft.</li> | ||
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<li> Convert the floor to inches or convert the tiles to feet.</li></ul> | <li> Convert the floor to inches or convert the tiles to feet.</li></ul> | ||
<li> Once students have made the conversion, determine the area of the tile using the equation length x width. </li> | <li> Once students have made the conversion, determine the area of the tile using the equation length x width. </li> | ||
− | <li> Students should discover that the area of the tile is 1ft<sup>2</sup>. </li> | + | <ul><li> Students should discover that the area of the tile is 1ft<sup>2</sup>. </li> |
<li> Use the ratio <math>\frac{1 tile}{1ft^2}</math> to determine how many tiles are needed to cover the area of the floor: | <li> Use the ratio <math>\frac{1 tile}{1ft^2}</math> to determine how many tiles are needed to cover the area of the floor: | ||
− | <math>\frac{1 tile}{1ft^2} = \frac{? tiles}{108 ft^2}</math></li> | + | <math>\frac{1 tile}{1ft^2} = \frac{? tiles}{108 ft^2}</math></li></ul> |
<li> Students use a calculator to determine and solve the proportions. </li> | <li> Students use a calculator to determine and solve the proportions. </li> | ||
− | <li> Or students determine how many tiles are needed to complete the length of one side of the floor by placing a manipulative tile on the floor plan and count 9 tiles needed and repeat for the width, counting 12 tiles. </li> | + | <ul><li> Or students determine how many tiles are needed to complete the length of one side of the floor by placing a manipulative tile on the floor plan and count 9 tiles needed and repeat for the width, counting 12 tiles. </li> |
− | <li> Students multiply 9x12 to determine the number of tiles needed to complete the floor.</li></ul> | + | <li> Students multiply 9x12 to determine the number of tiles needed to complete the floor.</li></ul></ul> |
− | < | + | <li> Provide the written problem to students to include picture representations of relevant words so students can follow along as the problem is introduced.</li> |
<ul><li> Be sure students have the picture representations of inches, feet, tile, and floor so they can give an opinion as to which rectangle should be converted to which unit of measure.</li> | <ul><li> Be sure students have the picture representations of inches, feet, tile, and floor so they can give an opinion as to which rectangle should be converted to which unit of measure.</li> | ||
<li> Students should still have the scale drawing of the rectangle (floor) on grid paper measuring 9 units by 12 units with each unit representing a foot and the rectangle labeled "floor" using word and picture representations.</li> | <li> Students should still have the scale drawing of the rectangle (floor) on grid paper measuring 9 units by 12 units with each unit representing a foot and the rectangle labeled "floor" using word and picture representations.</li> |
Revision as of 12:24, 25 July 2013
Grade Span: 9 - 10 | Content Area: Mathematics – Measurement
Investigating Measurement in the Real World |
Lesson 3 of the Unit
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Approximate Time Needed: 90 minutes |
Objective: Students will make decisions about units and scales that are appropriate for problem solving situations within mathematics or across disciplines or contexts. |
Essential Question: How can we use proportion to convert measurements from one unit to another in the same system? |
Materials Set Up:
Materials Needed:
Lesson Vocabulary: Area Centimeter Conversion Foot Inch Length Meter Proportion Ratio Width Yards |
Contents |
Lesson 3: Introduction – 15 minutes
A. Activate Previous Knowledge
Multiple means of representation: Present illustrations or models of ratio and proportions during discussions. Multiple means of expression: Allow students to use paper and pencil, models, computers, etc. to practice the concepts of ratios and proportions. Multiple means of engagement: Present real life uses for ratios and proportions related to students' interests. |
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 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 3: Body – 30 minutes
Direct Instruction and/or Facilitation of the Lesson
Multiple means of expression: Allow students to use paper/pencil, manipulatives, computer, etc., to complete exercises. Multiple means of engagement: Allow students to brainstorm ideas by writing descriptions of examples, drawing examples, acting out examples, etc. |
Additional Considerations for Emerging Readers |
See Example: Lesson 3 Conversions. |
Additional Considerations for Emerging Communicators |
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Lesson 3: Practice – 30 minutes
For example:
Multiple means of representation: Allow students to have a written copy of the problem, drawn models of the situation, and/or conversion formulas as needed/requested. Multiple means of expression: Students may draw or use manipulatives to model solutions or use the computer. Multiple means of engagement: Create situations that include areas of interest to students. |
Additional Considerations for Emerging Readers |
(___ft x 12 inches) and a calculator, students convert the length and the width of the floor from feet to inches.
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Additional Considerations for Emerging Communicators |
# Provide students with relevant picture or tactile/object representations of relevant words/concepts as the problem is introduced.
Important Note for Communicators Considered Pre Symbolic: The number load may need to be reduced.
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Lesson 3: 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 involving 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 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
1. Students solve a third problem using models and paper and pencil.
Multiple means of representation: Allow students to have a written copy of the problem, drawn models of the situation, and/or conversion formulas as needed/requested. Multiple means of expression: Students may draw or use manipulatives to model solutions or use the computer. Multiple means of engagement: Create situations that include areas of interest to students. |
Additional Considerations for Emerging Readers and Emerging Communicators |
* Use the same supports as used in the practice section. |