High School Mathematics UDL Instructional Unit-Lesson 2

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): How does the area of a figure change when one of its dimensions is doubled, tripled, etc.? How can we use ratios and proportions to determine how the area of figures change when at least one of the dimensions change?

Materials Set Up: Provide practice and review worksheets or class discussion about ratio and proportion. Activities will be varied and should include individual and group worksheets, text exercises, and hands-on problem solving activities.

Lesson 2: Materials Needed:

Worksheets Grid paper Grid paper with raised lines Grid paper copied on transparencies for light boxes Square tiles Geoboard Pencils Overhead projector Transparencies 12-inch ruler Yardstick Poster board Chalk board, white board or Smart Board Lesson Vocabulary Area Dimensions Length Perimeter Proportion Ratio Width

Lesson 2: Introduction – 10 minutes

A. Activate Previous Knowledge Lead discussion on meaning of ratio and proportion. Provide practice worksheets on finding ratios and proportions. 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

Provide picture/tactile/object representation of vocabulary words as they are used throughout the discussion. Provide concrete examples when discussing the meaning. During the discussion, students match a picture representation to the example provided which students use as a reference throughout the lesson. Examples can be provided by using a computer program and adaptive software with a talking word processor. Include picture/tactile/object representations of key words in directions and word problems. Provide graphic or manipulative representations of proportional relationships or use a computer program with alternate keyboard or switch access and talking word processor of proportional relationships.

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: Set up and solve proportions. Convert units of measurement using standard/known conversions. Recognize when to multiply and when to divide in converting measurements. Use ratio and proportion to convert measurements. Use appropriate known formulas for area. 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

Provide students with keys words paired with symbols/images/tactile representations. Provide the key words in the lesson objectives paired with images or tactile representations, record into mathematics journals. Students may use an electronic picture writer to record the lesson objectives. Provide students with visual and/or tactile representations of situations when these concepts are used.

Lesson 2: Body – 20 minutes

Direct Instruction and/or Facilitation of the Lesson Students draw rectangles of various dimensions on grid paper or form on Geoboards or with square tiles and to determine the area of each rectangle. Discuss why the area of the rectangles are the same or different. Students draw or form a rectangle A with given dimensions (e.g., 10"x5"). Then have students draw or form rectangle B by doubling the length of first one side and both sides of rectangle A. Find the ratio of the area of rectangle A to the area of rectangle B. 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

Students should determine the area of various given rectangles using the same strategies and supports as used in lesson 1. Draw a model of rectangle A with given dimensions (e.g., 5" x 4") or provide a manipulative model or virtual template of rectangle A. Students place the model on grid paper and verify the length and width by counting the units along the length of the figure and the width of the figure. Students determine the area by counting the units within the figure. Students should keep a record of the length, width, and area of rectangle A. Rectangle Length Width Area A 5 in 4 in 20 in2 B C D Once students have determined the area of rectangle A, provide the rule and/or model for setting up a ratio of area to width. The letters representing length, width, and area can be paired with a picture representation of each measurement. See Example: PowerPoint Lesson 2, Slide 1. The ratio of area to width for rectangle A is $\frac{A}{W}$ 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"). 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. The letters representing length, width, and area can be paired with a picture representation of each measurement. $\frac{A}{W} = \frac{A}{W}$ See Example: PowerPoint Lesson 2, Slide 2. Using the information from the chart, input the numbers into the proportions using the proportions for area and width. $\frac{20in^2}{4in} = \frac{A}{8in}$ Using the templates, students demonstrate that it takes 2 of rectangle B to make the same width of rectangle A. 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 $4 * 2 = 8$) $\frac{20in^2}{4in * 2} = \frac{A}{8in}$ Explain: If you multiply the bottom number by 2, you must multiply the top number by 2. Allow students to use a calculator to determine the area of rectangle B. $\frac{20in^2 * 2}{4in * 2} = \frac{A}{8in}$ $\frac{20in^2 * 2}{4in * 2} = \frac{40in^2}{8in}$ Students place the template on grid paper to determine the area by counting the units within the figure. See Example: PowerPoint Lesson 2, Slide 3. Repeat by providing students with a template for rectangle C (10" x 4"), the length of which is double that of rectangle A. Use the proportional formulas for area and length.

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

Use the same supports as used throughout the lesson body.

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: Set up and solve proportions. Convert units of measurement using standard/known conversions. Recognize when to multiply and when to divide in converting measurements. Use ratio and proportion to convert measurements. Use appropriate known formulas for area. 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

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. 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." 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.

B. Exit Assessment Generalize the effect on the area of the rectangle when one and/or both dimensions are multiplied by a factor of "n." 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 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

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."

Lesson 2: Resources

UDL_HS_Math_Lesson_2_Resources.pdf

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