High School Mathematics UDL Instructional Unit-Lesson 2
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|width = "1250" style="background-color:#FFFFFF;"|'''Grade Span:''' 9 - 10 | |width = "1250" style="background-color:#FFFFFF;"|'''Grade Span:''' 9 - 10 | ||
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* Activities will be varied and should include individual and group worksheets, text exercises, and hands-on problem solving activities. | * Activities will be varied and should include individual and group worksheets, text exercises, and hands-on problem solving activities. | ||
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− | '''Materials Needed:''' | + | ==Lesson 2: '''Materials Needed:'''== |
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* Worksheets | * Worksheets | ||
* Grid paper | * Grid paper | ||
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− | |width = "2500" style="background-color:# | + | |width = "2500" style="background-color:#D9D9D9;"|'''Additional Considerations for Emerging Readers and Emerging Communicators''' |
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− | {|border=1 border-collapse | + | {|border=1 style="border-collapse:collapse;" align=center |
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||Rectangle | ||Rectangle | ||
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||5 in | ||5 in | ||
||4 in | ||4 in | ||
− | ||20 | + | ||20 in<sup>2</sup> |
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||B | ||B | ||
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|} | |} | ||
− | + | <ol start=3><li> Once students have determined the area of rectangle A, provide the rule and/or model for setting up a ratio of area to width. </li> | |
− | + | :* The letters representing length, width, and area can be paired with a picture representation of each measurement. | |
'''See Example:''' PowerPoint Lesson 2, Slide 1. | '''See Example:''' PowerPoint Lesson 2, Slide 1. | ||
− | + | <li>The ratio of area to width for rectangle A is <math>\frac{A}{W}</math></li> | |
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− | W | + | |
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− | + | <li> Provide a template of rectangle B with given dimensions as the width twice as wide as rectangle A. Students should keep a record of the length and width of rectangle B (e.g., 5" x 8").</li> | |
− | + | <li> Once students have recorded the length and width of rectangle B, provide the rule and/or model for setting up the ratios of rectangles A and B to determine the area of B.</li> | |
− | + | :* The letters representing length, width, and area can be paired with a picture representation of each measurement. | |
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+ | <math>\frac{A}{W} = \frac{A}{W}</math> | ||
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'''See Example:''' PowerPoint Lesson 2, Slide 2. | '''See Example:''' PowerPoint Lesson 2, Slide 2. | ||
− | + | <li> Using the information from the chart, input the numbers into the proportions using the proportions for area and width. </li> | |
− | + | <math>\frac{20in^2}{4in} = \frac{A}{8in}</math> | |
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− | + | <li> Using the templates, students demonstrate that it takes 2 of rectangle B to make the same width of rectangle A. </li> | |
− | + | :* Students should conclude that the width of rectangle B is 2 times the width of rectangle A. | |
− | + | :* Allow students to use a calculator to verify that multiplying the width of A by 2 will give students the width of B <math> 4 * 2 = 8</math>) | |
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− | + | <math>\frac{20in^2}{4in * 2} = \frac{A}{8in}</math> | |
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− | + | <li> Explain: If you multiply the bottom number by 2, you must multiply the top number by 2.</li> | |
− | 2 | + | :* Allow students to use a calculator to determine the area of rectangle B. |
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+ | <math>\frac{20in^2 * 2}{4in * 2} = \frac{A}{8in}</math> | ||
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− | + | <math>\frac{20in^2 * 2}{4in * 2} = \frac{40in^2}{8in}</math> | |
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− | 4in | + | |
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− | + | <li> Students place the template on grid paper to determine the area by counting the units within the figure. </li> | |
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'''See Example:''' PowerPoint Lesson 2, Slide 3. | '''See Example:''' PowerPoint Lesson 2, Slide 3. | ||
− | + | <li> Repeat by providing students with a template for rectangle C (10" x 4"), the length of which is double that of rectangle A. </li></ol> | |
− | + | :* Use the proportional formulas for area and length. | |
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'''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 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. | ||
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'''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 expression: '''Provide a list of formulas to determine area and perimeter, or provide options for using manipulatives and/or computer models. | ||
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'''Multiple means of engagement: '''Allow students to use paper/pencil, manipulatives, computer, etc., to complete exercises. | '''Multiple means of engagement: '''Allow students to use paper/pencil, manipulatives, computer, etc., to complete exercises. | ||
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− | |width = "2500" style="background-color:# | + | |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 throughout the lesson body. | + | |width = "2500" style="background-color:#FFFFFF;"| |
+ | * Use the same supports as used throughout the lesson body. | ||
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− | |width = "2500" style="background-color:# | + | |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 in their electronic picture versions. | + | |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 in their electronic picture versions. | ||
# Students use the information recorded in their journals to refer back to the lesson objectives' key words paired with images or tactile/objects representations so they can share what they have learned based on each of the expectations. | # Students use the information recorded in their journals to refer back to the lesson objectives' key words paired with images or tactile/objects representations so they can share what they have learned based on each of the expectations. | ||
− | + | :* For example, a student may touch the tactile cues for ratio and area to state, "I have learned how to compare areas of similar figures by using ratios." | |
− | + | <ol start=3><li> Students refer back to the photographs or 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> | |
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# Generalize the effect on the area of the rectangle when one and/or both dimensions are multiplied by a factor of "n." | # Generalize the effect on the area of the rectangle when one and/or both dimensions are multiplied by a factor of "n." | ||
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# Students review their work from the lesson and conclude that when only one dimension is changed, the area is affected by the same amount of change, but if both dimensions are changed, the area is affected by the change of width times the change of length. | # Students review their work from the lesson and conclude that when only one dimension is changed, the area is affected by the same amount of change, but if both dimensions are changed, the area is affected by the change of width times the change of length. | ||
'''Multiple means of representation:''''''' ''''Allow students to refer back to their work samples, models, drawing, notes, etc. | '''Multiple means of representation:''''''' ''''Allow students to refer back to their work samples, models, drawing, notes, etc. | ||
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'''Multiple means of expression: '''Students share what they have learned in different formats: writing, drawing, creative expression, etc. | '''Multiple means of expression: '''Students share what they have learned in different formats: writing, drawing, creative expression, etc. | ||
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'''Multiple means of engagement: '''Allow students to review work independently or to review with a partner or small group. | '''Multiple means of engagement: '''Allow students to review work independently or to review with a partner or small group. | ||
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− | |width = "2500" style="background-color:# | + | |width = "2500" style="background-color:#D9D9D9;"|'''Additional Considerations for Emerging Readers and Emerging Communicators''' |
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− | |width = "2500" style="background-color:#FFFFFF;"|# Students show the effect on the area of the rectangle when one and/or both dimensions are multiplied by a factor of "n" by drawing models or using manipulatives to demonstrate how many of one figure is needed to cover the other. | + | |width = "2500" style="background-color:#FFFFFF;"| |
− | + | # Students show the effect on the area of the rectangle when one and/or both dimensions are multiplied by a factor of "n" by drawing models or using manipulatives to demonstrate how many of one figure is needed to cover the other. | |
# Use ratios and proportions to show the relationship between the areas of the original rectangle and the new rectangle that was created by changing dimensions by a factor of "n." | # Use ratios and proportions to show the relationship between the areas of the original rectangle and the new rectangle that was created by changing dimensions by a factor of "n." | ||
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− | '''Lesson 2: Resources''' | + | =='''Lesson 2: Resources'''== |
− | + | [[Media:UDL_HS_Math_Lesson_2_Resources.pdf|UDL_HS_Math_Lesson_2_Resources.pdf]] | |
+ | Return to [[High School Mathematics UDL Instructional Unit-Lesson 1| Lesson 1]] Proceed to [[High School Mathematics UDL Instructional Unit-Lesson 3|Lesson 3]] | ||
− | + | [[Category: High]] | |
− | + | [[Category:Math]] | |
+ | [[Category:UDL]] |
Latest revision as of 14:47, 7 January 2014
Contents |
[edit] Lesson 2:Objective
Grade Span: 9 - 10 | Content Area: Mathematics - Measurement |
Lesson 2 of the Unit | Approximate Time Needed: 50 minutes |
Objective: Students will make decisions about units and scales that are appropriate for problem solving situations involving mathematics or across disciplines or contexts. |
Essential Question(s):
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Materials Set Up:
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[edit] Lesson 2: Materials Needed:
Lesson Vocabulary
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[edit] Lesson 2: Introduction – 10 minutes
A. Activate Previous Knowledge
Multiple means of representation: Provide definitions of ratio and proportion. Provide drawings or models of ratios and proportions. Worksheets can be presented with fewer items per page. Worksheets may be printed on various color sheets. Worksheets may be presented using a computer. Multiple means of expression: Students may express the meaning of ratio and proportion by describing a situation that represents a ratio or proportion. Students may create a model by drawing or using manipulatives to express the meaning of ratio and proportion. Students may use drawings or models to complete worksheets. Students may complete work on a computer. Multiple means of engagement: Provide examples of ratios and proportions based on students' interests or real life situations in which they would be used. |
Additional Considerations for Emerging Readers and Emerging Communicators |
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B. Establish Goals/Objectives for the Lesson
Inform students that in this lesson the will make decisions about units and scales that are appropriate for problem solving situations within mathematics or across disciplines or contexts. Explain that they will:
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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[edit] Lesson 2: Body – 20 minutes
Direct Instruction and/or Facilitation of the Lesson
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 Example: PowerPoint Lesson 2, Slide 1.
See Example: PowerPoint Lesson 2, Slide 2.
See Example: PowerPoint Lesson 2, Slide 3.
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[edit] Lesson 2: Practice – 10 minutes
Repeat the exercise by tripling the dimensions and/or by reducing the dimensions by one-half.
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 |
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[edit] Lesson 2: Closure – 10 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 posted 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: through 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 |
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B. Exit Assessment
Multiple means of representation:'' ''Allow students to refer back to their work samples, models, drawing, notes, etc. Multiple means of expression: Students share what they have learned in different formats: writing, drawing, creative expression, etc. Multiple means of engagement: Allow students to review work independently or to review with a partner or small group. |
Additional Considerations for Emerging Readers and Emerging Communicators |
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