High School Mathematics UDL Instructional Unit-Lesson 1
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<ol start="2"> Provide students with grid paper with two similar rectangular figures printed on it or grid paper with manipulatives of the figures. | <ol start="2"> Provide students with grid paper with two similar rectangular figures printed on it or grid paper with manipulatives of the figures. | ||
:* Ensure students have a means for sharing how the rectangles are the same and/or different. Students use their math journals or a graphic organizer to record information about the attributes and measurements of each rectangle. Students use the same strategies as were used to determine area and perimeter in the introduction. | :* Ensure students have a means for sharing how the rectangles are the same and/or different. Students use their math journals or a graphic organizer to record information about the attributes and measurements of each rectangle. Students use the same strategies as were used to determine area and perimeter in the introduction. | ||
− | + | :* Students share how the perimeters are the same or different using the information recorded in the journals or the graphic organizer. | |
− | + | :* Students share how the areas are the same or different using the information recorded in the journals or the graphic organizer. | |
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<li> Demonstrate how ratios are used to compare the area of each figure and the perimeter of each figure. </li> | <li> Demonstrate how ratios are used to compare the area of each figure and the perimeter of each figure. </li> | ||
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<li>To build understanding of the relationship between the different measurements, have students measure:</li> | <li>To build understanding of the relationship between the different measurements, have students measure:</li> | ||
:* a book using inches marked on a ruler; | :* a book using inches marked on a ruler; | ||
− | + | :* a table using feet while attending to how many inches that would be; | |
− | + | :* the length of the chalkboard/ whiteboard using a yardstick while attending to how many feet that would be. | |
<li> Repeat measurements using centimeters and meters. </li> | <li> Repeat measurements using centimeters and meters. </li> | ||
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<li> Students measure a given piece of paper that is 8 inches wide and 2 feet long.</li> | <li> Students measure a given piece of paper that is 8 inches wide and 2 feet long.</li> | ||
:* Allow students to explore other units that can be used. | :* Allow students to explore other units that can be used. | ||
− | + | :* Discuss how the paper can be measured using the same unit of measure (i.e., Inches, 8 inches wide and 24 inches long). | |
<li> Provide students with a calculator, the formulas, and task-analyzed steps for converting from one unit to another. Or provide students with a conversion chart with which to match the measured unit to a converted unit. </li></ol> | <li> Provide students with a calculator, the formulas, and task-analyzed steps for converting from one unit to another. Or provide students with a conversion chart with which to match the measured unit to a converted unit. </li></ol> | ||
:* As a whole class or in small groups, work together to convert the units of measure for a rectangle that measures 8 inches wide and 2 feet long. | :* As a whole class or in small groups, work together to convert the units of measure for a rectangle that measures 8 inches wide and 2 feet long. | ||
− | + | :* Students use the conversion formulas or create the figures on grid paper. | |
− | + | :* Students count the units on the grid paper to determine the conversion. | |
'''See Example:''' Lesson 1, Body 4, Converting Units. | '''See Example:''' Lesson 1, Body 4, Converting Units. | ||
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|width = "2500" style="background-color:#FFFFFF;"|# Provide picture and tactile representations of relevant vocabulary: similar rectangle, area, perimeter as well as the meanings of each word. | |width = "2500" style="background-color:#FFFFFF;"|# Provide picture and tactile representations of relevant vocabulary: similar rectangle, area, perimeter as well as the meanings of each word. | ||
# Using manipulatives or a computer program or PowerPoint that contains 2 similar figures (Figure A and Figure B) in a grid, students determine the area of Figures A and B by counting or using one-to-one correspondence to determine the number of units within the figure (area) and number of units around the figure (perimeter). | # Using manipulatives or a computer program or PowerPoint that contains 2 similar figures (Figure A and Figure B) in a grid, students determine the area of Figures A and B by counting or using one-to-one correspondence to determine the number of units within the figure (area) and number of units around the figure (perimeter). | ||
− | + | :* Students compare the areas by moving the smaller figure (Figure B) into the larger figure (Figure A) to see how many are needed to completely cover the larger figure. | |
− | + | :* This activity demonstrates how many times bigger Figure A is than Figure B. | |
'''See Example:''' PowerPoint Lesson 1, Slides 3 and 4. | '''See Example:''' PowerPoint Lesson 1, Slides 3 and 4. |
Revision as of 13:09, 22 July 2013
Grade Span: 9-10 |
Content Area: Mathematics – Measurement
Investigating Measurement in the Real World |
Lesson 1 of the Unit
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Approximate Time Needed: 50 minutes |
Objective: Student will make decisions about units and scales that are appropriate for problem solving situations involving mathematics within mathematics or across disciplines or contexts. |
Essential Question: What are the relationships among the measurements of dimensions, area, and perimeter in problem solving situations? |
Contents |
Lesson 1: Materials
Materials Needed:
Using grid paper or a Geoboard, provide students with rectangles having different dimensions, some of which are similar. Some of the rectangles should have the same perimeter but different areas. For example:
Some should have the same area but different perimeters. For example:
Make chart as used in practice note below to reinforce skills.
Materials needed:
See Resources: See Lesson 1 Resources for example exercises/images. Lesson Vocabulary Area Centimeter Foot Inch Length Meter Perimeter Rectangles Similar Rectangles Width Yards |
Lesson 1: Introduction – 10 minutes
A. Activate Previous Knowledge
Multiple means of representation: Use models and/or drawings during large group instruction. Allow students to have a copy of a drawing or a model at their desks. Multiple means of expression: Provide a list of formulas to determine area and perimeter or provide options for using manipulatives and/or computer models. Multiple means of engagement: Allow students to use paper/pencil, manipulatives, computer, etc. to complete exercises. |
Additional Considerations for Emerging Readers and Emerging Communicators |
See Resources: See PowerPoint, Slides 1 and 2.
Important Note for Communicators Considered Pre-Symbolic: Be sure students have a way to attain peer attention as well as to share and receive information. Limit measurements to one type: standard or metric unit. |
B. Establish Goals/Objectives for the Lesson
Inform students that in this lesson 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 |
Inform students of expected outcomes.
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Lesson 1: Body – 15 minutes
Direct Instruction and/or Facilitation of the Lesson
See Resources: Lesson 1, Pages 15 and 16.
See Resources: Lesson 1, Page 18. Multiple means of representation: Use models and/or drawings during large group instruction; allow students to have a copy of a drawing or a model at their desks. Multiple means of expression: Provide a list of formulas to determine area and perimeter or provide options for using manipulatives and/or computer models. Multiple means of engagement: Allow students to use paper/pencil, manipulatives, computer, etc. to complete exercises. Present information within the context of students' interests such as pets, gardening, new bedroom floor plan, etc.
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Additional Considerations for Emerging Readers |
See Example: Lesson 1, Body 1, Similar Figures. See Example: Lesson 1, Body 2, Same Area.
See Example: Lesson 1, Body 4, Converting Units.
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Additional Considerations for Emerging Communicators |
# Provide picture and tactile representations of relevant vocabulary: similar rectangle, area, perimeter as well as the meanings of each word.
See Example: PowerPoint Lesson 1, Slides 3 and 4.
See Example: PowerPoint Lesson 1, Slides 5 and 6.
See Example: PowerPoint Lesson 1, Slide 7. Important Note for Communicators Considered Pre-Symbolic: Work with only one system: standard or metric units. |
Lesson 1: Practice – 20 minutes
# In small groups, students work on a variety of problems using different given dimensions such as:
Rectangle Length Width Perimeter Area A 40 ft 30 ft 140 ft 1200 ft2
L + W L x W 70 units = 5 units + 65 units 5 units x 65 units = 325 units2 70 units = 10 units + 60 units 10 units x 60 units = 600 units2 70 units = 20 units + 50 units 20 units x 50 units = 1000 units2 70 units = 35 units + 35 units 35 units x 35 units = 1225 units2 70 units = 50 units + 20 units 50 units x 20 units = 1000 units2
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 using formulas and/or models. Multiple means of engagement: Ensure each student is actively involved in the small groups. Present different problems related to students' interests. Use questioning to encourage students to explain their strategies in their groups.
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Additional Considerations for Emerging Readers |
# Provide picture representations of the word problem to students as it is being read.
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Additional Considerations for Emerging Communicators |
# Modify the word problem to include smaller whole numbers.
See Example: PowerPoint Lesson 1, Slide 8.
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Lesson 1: Closure – 5 minutes
A. 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 share what they have learned in different formats: writing, drawing, creative expression, 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 |
# When reviewing the expected outcomes, have students refer to the lesson objectives they recorded in their mathematics journals or their electronic picture versions.
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B. Exit Assessment
New Problem Example: Josh is designing a display for his Science Fair project. His display must have a perimeter of 120 inches or 10 feet. He found two display boards: board one measures 24 in x 3 ft and board two measures 30 in x 30 in.
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 using formulas and/or models. Multiple means of engagement: Ensure students are actively involved in their small groups. Present different problems related to students' interests. Use questioning to encourage students to explain their strategies. |
Additional Considerations for Emerging Readers and Emerging Communicators |
# Use the same supports as used in the practice section to solve for the given problem.
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Lesson 1: Resources
The following pages are examples of activities and exercises from Lesson Body, page 8. Area and Perimeter of Similar Figures:
Figure A A = 12 units x 9 units P = 12 units +12 units + 9 units + 9 units A = 108 units2 P = 42 units Figure B A = 6 units x 4.5 units P = 6 units + 6 units + 4.5 units + 4.5 units A = 27 units2 P = 21 units
Compare Area of figures A and B Compare Perimeter of figures A and B AA/AB = 108/27 PA/PB = 42/21 'AA/AB = 4/1 PA/PB = 2/1 '
Lesson 1: Resources – continued The student can use manipulatives (next 2 images) to compare the two figures by laying rectangle B over rectangle A until completely covered to determine how many times bigger area of A is than B. The student can compare perimeter by laying rectangle B over rectangle A to determine how many are needed to create the same length (2), and how many are needed to create the same width (2). The area of A is 4 times the area of B. The perimeter of A is 2 times the perimeter of B. Tactile representations of similar figures: Cut out figures using construction paper, poster board, card board, sand paper, etc. Representations can also be cut out as templates or frames to lay over grid paper or cut out of transparencies to see grid lines. Rectangle A Rectangle B
Lesson 1: Resources – continued \[\[File:Insert Picture here.jpg\]\]
Is the area of Figure A the same as the area of Figure B?
Figure A: A= 10 units x 3 units A= 30 units (squared) Figure B: A= 6 units x 5 units A= 30 units (squared) Is the perimeter of Figure A the same as the perimeter of Figure B?
Figure A: P= 10 units + 10 units + 3 units + 3 units P= 26 units Figure B: P= 6 units + 6 units + 5 units + 5 units P= 22 units The perimeter of Figure A and Figure B is: The same Different The perimeter of Figure A is more than / less than / the same as the perimeter of Figure B. Lesson 1: Resources – continued \[\[File:Insert Picture here.jpg\]\]
These figures can be represented tactilely with raised, thick, exterior and center lines to represent the height measured in feet. They can also be represented with thinner, raised lines to represent width and height in inches.
Lesson 1: Resources – continued
The following pages are examples of activities /exercises from Lesson Practice, page 11.
Model | Length | Width | Perimeter | Area |
A | 40 ft | 30 ft | 140 ft | 1200 ft2 |
B | 45 ft | 25 ft | 140 ft | |
C | 35 | 35 | 140 ft | |
D | 20 | 50 | 140 ft |
'Lesson 1: Resources– continued '