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− | | + | ==Lesson 1: Objective== |
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− | |width = "2500" style="background-color:#FFFFFF;"|'''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. | + | |width = "2500" style="background-color:#FFFFFF;"|'''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, and: |
| + | # Convert units using standard/known conversion units. |
| + | # Use appropriate known formulas for the area. |
| + | # Solve multistep problems involving one unit of measure. |
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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. | + | ::* 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. | + | ::* This activity demonstrates how many times bigger Figure A is than Figure B. |
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| '''See Example:''' PowerPoint Lesson 1, Slides 3 and 4. | | '''See Example:''' PowerPoint Lesson 1, Slides 3 and 4. |
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− | # Using a computer program or PowerPoint that contains 2 figures (Figure A and Figure B) with the same area in a grid, students use a switch to determine the area for each figure and verify that they are the same.
| + | <ol start="3"><li> Using a computer program or PowerPoint that contains 2 figures (Figure A and Figure B) with the same area in a grid, students use a switch to determine the area for each figure and verify that they are the same. </li> |
− | ## Students determine if the perimeters are also the same.
| + | :* Students determine if the perimeters are also the same. |
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| '''See Example:''' PowerPoint Lesson 1, Slides 5 and 6. | | '''See Example:''' PowerPoint Lesson 1, Slides 5 and 6. |
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− | # Provide picture and tactile/object representations of relevant vocabulary: inches, feet, yard, centimeter, meter as well as the meanings of each word.
| + | <li> Provide picture and tactile/object representations of relevant vocabulary: inches, feet, yard, centimeter, meter as well as the meanings of each word. </li> |
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− | # When discussing different measurements within the same system (inches, feet, and yards, or centimeters and meters), present students with tactile representations or objects of the different measures.
| + | <li> When discussing different measurements within the same system (inches, feet, and yards, or centimeters and meters), present students with tactile representations or objects of the different measures. </li> |
− | * Students work with peer partners to measure a book using inches marked on a foldable ruler so students feel the inches. | + | :* Students work with peer partners to measure a book using inches marked on a foldable ruler so students feel the inches. |
− | * Students measure a table using feet while attending to how many inches that would be. Again use the foldable ruler. | + | :* Students measure a table using feet while attending to how many inches that would be. Again use the foldable ruler. |
− | * To build understanding of the relationship between the different measurements, students measure the length of the chalkboard/whiteboard using a yardstick while attending to how many feet that would be. | + | :* To build understanding of the relationship between the different measurements, students measure the length of the chalkboard/whiteboard using a yardstick while attending to how many feet that would be. |
− | * Emphasize the difference in the size of an object in relation to the size of the unit used. | + | :* Emphasize the difference in the size of an object in relation to the size of the unit used. |
− | * Students measure a given piece of paper that is 8 inches wide and 2 feet long. | + | :* Students measure a given piece of paper that is 8 inches wide and 2 feet long. |
− | * To emphasize the inches within the foot, use a foldable ruler to show students that the piece of paper can also be measured as 8 inches wide and 24 inches long. | + | :* To emphasize the inches within the foot, use a foldable ruler to show students that the piece of paper can also be measured as 8 inches wide and 24 inches 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.
| + | <li> 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. </li> |
− | ## Provide students with the figure represented on grid paper.
| + | :* Provide students with the figure represented on grid paper. |
− | * Tactilely represent the figure with the original units of inches across and feet down as well as with a rectangle with all measurements converted to inches. | + | :* Tactilely represent the figure with the original units of inches across and feet down as well as with a rectangle with all measurements converted to inches. |
− | * Represent the different units of measure (1foot and 12 inches) tactilely with different thicknesses, so when students are tactilely scanning the inches, they feel the difference when a foot has been reached. | + | :* Represent the different units of measure (1foot and 12 inches) tactilely with different thicknesses, so when students are tactilely scanning the inches, they feel the difference when a foot has been reached. |
− | * Students use a computer program with an alternate keyboard or multi-switch access with each tactile representation on the keyboard or one per switch. | + | :* Students use a computer program with an alternate keyboard or multi-switch access with each tactile representation on the keyboard or one per switch. |
− | * Students locate the original figure and press it so it is represented on the computer screen. | + | :* Students locate the original figure and press it so it is represented on the computer screen. |
− | * The computer program states the original measurements (8 inches by 2 feet), and students locate and press the tactile representation that has been converted to inches. | + | :* The computer program states the original measurements (8 inches by 2 feet), and students locate and press the tactile representation that has been converted to inches. |
− | * The figure is displayed on the screen, and the computer states the converted measurements (8 inches by 24 inches). | + | :* The figure is displayed on the screen, and the computer states the converted measurements (8 inches by 24 inches). |
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| '''See Example:''' PowerPoint Lesson 1, Slide 7. | | '''See Example:''' PowerPoint Lesson 1, Slide 7. |
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| =='''Lesson 1: Practice – 20 minutes'''== | | =='''Lesson 1: Practice – 20 minutes'''== |
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− | |width = "2500" style="background-color:#FFFFFF;"|# In small groups, students work on a variety of problems using different given dimensions such as: | + | |width = "2500" style="background-color:#FFFFFF;"| |
− | * Alex has 140 feet of fencing to place around a rectangular garden he is making. He wants the area of the garden to be as large as possible. What should the length and width of the garden be? | + | # In small groups, students work on a variety of problems using different given dimensions such as: |
− | * Give each student the chart below. | + | :* Alex has 140 feet of fencing to place around a rectangular garden he is making. He wants the area of the garden to be as large as possible. What should the length and width of the garden be? |
− | * Students may use models to explore the various possibilities and complete the chart. | + | :* Give each student the chart below. |
− | | + | :* Students may use models to explore the various possibilities and complete the chart. |
− | Rectangle
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− | Length
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− | Width
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− | Perimeter
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− | Area
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− | A
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− | 40 ft
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− | 30 ft
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− | 140 ft
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− | 1200 ft2
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| + | {|border=1 |
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| + | ||Rectangle |
| + | ||Length |
| + | ||Width |
| + | ||Perimeter |
| + | ||Area |
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| + | ||A |
| + | ||40ft |
| + | ||30ft |
| + | ||140ft |
| + | ||1200ft<sup>2</sup> |
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| + | |height=20| |
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| '''See Resources:''' Pages 20 and 21. | | '''See Resources:''' Pages 20 and 21. |
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− | # Bring the whole group back together.
| + | <ol start="2"><li> Bring the whole group back together. </li> |
− | # Ask one student from each group to discuss the results.
| + | <li> Ask one student from each group to discuss the results. </li> |
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− | # After reviewing students' results, help students realize that when a perimeter is 140 units, length plus width always equals 70 units, but length times width varies.
| + | <li> After reviewing students' results, help students realize that when a perimeter is 140 units, length plus width always equals 70 units, but length times width varies. </li> |
− | # Make a chart with students of the possible lengths and widths of a rectangle in increments of 5 when the perimeter is 140 units. Use information from their charts and organize it in order from smallest length to largest length.
| + | <li> Make a chart with students of the possible lengths and widths of a rectangle in increments of 5 when the perimeter is 140 units. Use information from their charts and organize it in order from smallest length to largest length.</li> |
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− | 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 | + | |align=center|L + W |
− | 70 units = 20 units + 50 units 20 units x 50 units = 1000 units2 | + | |align=center| L x W |
− | 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 | + | ||70 units = 5 units + 65 units || 5 units x 65 units = 325 units<sup>2</sup> |
| + | |- |
| + | ||70 units = 10 units + 60 units || 10 units x 60 units = 600 units2<sup>2</sup> |
| + | |- |
| + | ||70 units = 20 units + 50 units || 20 units x 50 units = 1000 units2<sup>2</sup> |
| + | |- |
| + | ||70 units = 35 units + 35 units || 35 units x 35 units = 1225 units2<sup>2</sup> |
| + | |- |
| + | ||70 units = 50 units + 20 units || 50 units x 20 units = 1000 units2<sup>2</sup> |
| + | |} |
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− | # Demonstrate to students that as the dimensions change, the area gets larger, reaching the highest value, and then gets smaller. Students should conclude that when asked to find the largest area when given a perimeter, a square would always have the greatest area.
| + | <li> Demonstrate to students that as the dimensions change, the area gets larger, reaching the highest value, and then gets smaller. Students should conclude that when asked to find the largest area when given a perimeter, a square would always have the greatest area.</li> |
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− | '''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 representation''': Provide students with a copy of the word problem and the table. Have drawings and manipulatives available for students to use. |
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| '''Multiple means of expression:''' Allow students to solve the problem using formulas and/or models. | | '''Multiple means of expression:''' Allow students to solve the problem using formulas and/or models. |
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| '''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. | | '''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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− | |width = "2500" style="background-color:#FFFFFF;"|# Provide picture representations of the word problem to students as it is being read. | + | |width = "2500" style="background-color:#FFFFFF;"| |
− | * Present word problem electronically using text-to-speech. | + | # Provide picture representations of the word problem to students as it is being read. |
− | * Label each column of the table using picture symbols and include measurements for length and width needed for a perimeter of 140 ft. | + | :* Present word problem electronically using text-to-speech. |
− | * Remind students how to determine perimeter and area. | + | :* Label each column of the table using picture symbols and include measurements for length and width needed for a perimeter of 140 ft. |
− | * Provide formulas and task-analyzed steps for using the formulas: | + | :* Remind students how to determine perimeter and area. |
− | * Perimeter = L+L+W+W or 2L + 2W
| + | ::* Provide formulas and task-analyzed steps for using the formulas: |
− | * Area = L x W
| + | ::: -Perimeter = L+L+W+W or 2L + 2W |
− | ** Perimeter = 140ft: 2L+2W = 140ft or L+W = 70ft
| + | ::: -Area = L x W |
− | * Provide students with models of the various fenced-in areas (rectangles). | + | ::: -Perimeter = 140ft: 2L+2W = 140ft or L+W = 70ft |
− | ** Students use the given formula and calculators to determine area.
| + | :* Provide students with models of the various fenced-in areas (rectangles). |
− | ** Students use the grid paper to identify the rectangle that provides the most area.
| + | :: -Students use the given formula and calculators to determine area. |
| + | :: -Students use the grid paper to identify the rectangle that provides the most area. |
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− | # For steps 3-6, students discuss results by presenting the length and width of the rectangle with the largest area that they discovered in their group, or students point to the actual picture representation of the rectangle with the largest area.
| + | <ol start=2><li> For steps 3-6, students discuss results by presenting the length and width of the rectangle with the largest area that they discovered in their group, or students point to the actual picture representation of the rectangle with the largest area.</li></ol> |
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− | |width = "2500" style="background-color:#FFFFFF;"|# Modify the word problem to include smaller whole numbers. | + | |width = "2500" style="background-color:#FFFFFF;"| |
− | ** For example, Alex has 16 yards of fencing to place around a rectangular garden he is making. He wants the area of the garden to be as large as possible. What should the length and width of the garden be?
| + | # Modify the word problem to include smaller whole numbers. |
− | ** Provide students with picture and/or tactile representations of the important aspects of the problem as it is being read.
| + | :* For example, Alex has 16 yards of fencing to place around a rectangular garden he is making. He wants the area of the garden to be as large as possible. What should the length and width of the garden be? |
− | ** As information is provided, students organize the information in a graphic organizer, baskets, etc.
| + | :* Provide students with picture and/or tactile representations of the important aspects of the problem as it is being read. |
| + | :* As information is provided, students organize the information in a graphic organizer, baskets, etc. |
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− | # Provide students with a computer program or premade PowerPoint as used in previous portions of the lesson to explore rectangles with the same perimeter but different areas.
| + | <ol start=2><li> Provide students with a computer program or pre-made PowerPoint as used in previous portions of the lesson to explore rectangles with the same perimeter but different areas.</li> |
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− | # Using the computer program or PowerPoint with switch access, students verify that the perimeter is 16 yd. in the modified word problem and count the area units to determine the area.
| + | <li> Using the computer program or PowerPoint with switch access, students verify that the perimeter is 16 yd. in the modified word problem and count the area units to determine the area.</li> |
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− | # After students have verified the perimeter or determined the area for a particular rectangle, the program should insert the number of units into the correct portion of the chart. Remember, the alternate keyboard or switches used should have picture or tactile representations of area and perimeter so students determine the correct measurement.
| + | <li> After students have verified the perimeter or determined the area for a particular rectangle, the program should insert the number of units into the correct portion of the chart. Remember, the alternate keyboard or switches used should have picture or tactile representations of area and perimeter so students determine the correct measurement.</li> |
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| '''See Example''': PowerPoint Lesson 1, Slide 8. | | '''See Example''': PowerPoint Lesson 1, Slide 8. |
− | # Students indicate the rectangle with the largest area by choosing rectangle A or B.
| + | <li> Students indicate the rectangle with the largest area by choosing rectangle A or B.</li></ol> |
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− | |width = "2500" style="background-color:#FFFFFF;"|'''Additional Considerations for Emerging Readers and Emerging Communicators''' | + | |width = "2500" style="background-color:#D9D9D9;"|'''Additional Considerations for Emerging Readers and Emerging Communicators''' |
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− | |width = "2500" style="background-color:#FFFFFF;"|# When reviewing the expected outcomes, have students refer to the lesson objectives they recorded in their mathematics journals or their electronic picture versions. | + | |width = "2500" style="background-color:#FFFFFF;"| |
| + | <ol><li> When reviewing the expected outcomes, have students refer to the lesson objectives they recorded in their mathematics journals or their electronic picture versions. </li> |
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− | # Students use the information recorded in their journals to refer back to the lesson objectives key words paired with images. From that information, they share what they have learned based on each of the expectations.
| + | <li> Students use the information recorded in their journals to refer back to the lesson objectives key words paired with images. From that information, they share what they have learned based on each of the expectations. </li> |
− | ** For example, the student may grab the tactile cue for area to state, "I have learned that the area is all the space measured within a figure."
| + | :* For example, the student may grab the tactile cue for area to state, "I have learned that the area is all the space measured within a figure." |
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− | # Students refer back to the photographs or models/tactile representations of examples of real-life situations in which these concepts are used to share when they could use these new skills.
| + | <li> Students refer back to the photographs or models/tactile representations of examples of real-life situations in which these concepts are used to share when they could use these new skills. </li></ol> |
− | ** For example, the student could touch the tactile representations for area and table top to state, "I can use area to determine if an object will fit on my desk."
| + | :* For example, the student could touch the tactile representations for area and table top to state, "I can use area to determine if an object will fit on my desk." |
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− | |width = "2500" style="background-color:#FFFFFF;"|'''Additional Considerations for Emerging Readers and Emerging Communicators''' | + | |width = "2500" style="background-color:#D9D9D9;"|'''Additional Considerations for Emerging Readers and Emerging Communicators''' |
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− | |width = "2500" style="background-color:#FFFFFF;"|# Use the same supports as used in the practice section to solve for the given problem. | + | |width = "2500" style="background-color:#FFFFFF;"| |
| + | # Use the same supports as used in the practice section to solve for the given problem. |
| # Use the supports described in Lesson Body, Step 4: Converting Units of Measure. | | # Use the supports described in Lesson Body, Step 4: Converting Units of Measure. |
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| + | ==Lesson 1: Resources== |
| + | <!--==Lesson 1: Resources== DO NOT REMOVE THIS!--> |
| + | [[Media:UDL_HS_Math_Lesson_1_Resources.pdf|UDL_HS_Math_Lesson_1_Resources.pdf]] |
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− | =='''Lesson 1: Resources '''==
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− | '''The following pages are examples of activities and exercises from Lesson Body, page 8.'''
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− | '''Area and Perimeter of Similar Figures: '''
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− | |width = "125" style="background-color:#FFFFFF;"| | + | Return to [[High School Mathematics UDL Instructional Unit| HS Mathematics UDL Instructional Unit]] Proceed to [[High School Mathematics UDL Instructional Unit-Lesson 2|Lesson 2]] |
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |-
| + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |-
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |-
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |-
| + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |-
| + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
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− | | + | |
− | |width = "125" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |-
| + | |
− | |}
| + | |
− | | + | |
− | 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.'''
| + | |
− | {| border=1
| + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''Model'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''Length'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''Width'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''Perimeter'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''Area'''
| + | |
− | | + | |
− | |-
| + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''A'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''40 ft'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''30 ft'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''140 ft'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''1200 ft2 '''
| + | |
− | | + | |
− | |-
| + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''B'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''45 ft'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''25 ft'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''140 ft'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |-
| + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''C'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''35'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''35'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''140 ft'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |-
| + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''D'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''20'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''50'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|'''140 ft'''
| + | |
− | | + | |
− | |width = "500" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |-
| + | |
− | |}
| + | |
− | | + | |
− | | + | |
− | | + | |
− | | + | |
− | ''''''Lesson 1: Resources– continued ''''''
| + | |
− | | + | |
− | {| border=1
| + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "93" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |-
| + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "93" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |-
| + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
| + | |
− | | + | |
− | |width = "83" style="background-color:#FFFFFF;"|
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