High School Mathematics UDL Instructional Unit-Lesson 4

Lesson 4: Objective

Grade Span: 9 - 10	Content Area: Math - Geometry
Lesson 4 of the Unit	Approximate Time Needed: 55 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 Questions: What are the relationships among the measurements of dimensions, area, and perimeter in problem solving situations? How does changing the sides of a square affect the area?
Materials Set Up: Set up problem and question on overhead/whiteboard. Mark off floor in varying size squares up to 25 square feet. (e.g., 1'x1', 2'x2', 3'x3', 4'x4', 5'x5') to demonstrate size needed for dancing. Create or select manipulatives to represent area and people. Lesson 4: Materials Needed: Calculator Pencils, paper, graph paper, masking tape Manipulatives CD player with various types of music Blank table with columns for name and dance space Measuring tape, yardstick, ruler Lesson Vocabulary Area Length, Width Ratio Unit of Measure Unit Rate

Lesson 4: Introduction – 10 minutes

A. Activate Previous Knowledge Remind students that they have been working on the concepts of perimeter and area of shapes of different sizes. Review ratios. Discuss how they can use this knowledge to solve problems they may encounter in the real world. Present the following idea/problem: Introduce the idea of planning a dance party in the classroom. How many people would you expect to attend? How large will the dance floor need to be? Students use previous knowledge to brainstorm ways to solve this problem. Multiple means of representation: Present real life problems using drawings, models, and video representations of people dancing on a dance floor. Multiple means of expression: Allow students to present ideas for problem solving using computer models, demonstrations, visuals, etc. Record problem solving ideas in different formats: mathematics journals, computer, premade or original graphic organizers, etc. Multiple means of engagement: Use student-chosen dance styles and music when presenting problem. Allow students to work individually or in small groups based on learning style.

Additional Considerations for Emerging Readers and Emerging Communicators

During the review, be sure students have graphic and/or tactile representations of relevant vocabulary (area, perimeter, length, width) as well as related materials/drawings/objects representations from previous lessons. Provide examples through pictures, tactile cues and/or videos of couples on various dance floors that are very crowded, average, and very empty, etc. Point out how much space people have to dance. Ask guiding questions: "Do the dancers have enough space?" "Is there room for more people?" etc. Students attempt to add more people to an object representation or virtual representation of the dance floor. Create a list of possible dance styles by using words paired with pictures. Students use their math journals to refer to previous strategies used for solving problems. Ensure students have a way to contribute to the brainstorming.

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: Identify, quantify, and compare the attributes of the objects, situations, and/or events that need to be measured to solve the problem/situation. Use appropriate units of measure to identify, quantify, and compare objects, situations, and/or events to solve a real world problem. Convert units when necessary. Represent data in various forms 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 (i.e., units of measure, inch, foot, yard, centimeter, and meter). Provide the key words in the lesson objective paired with symbols/images/tactile representations to paste into their mathematics journals or collect in a mathematics basket or bag. Students may use an electronic picture writer to record the lesson objectives. Provide students with photographs, models, or tactile representations of examples of situations when these concepts are used.

Lesson 4: Body – 15 minutes

Direct Instruction and/or Facilitation of the Lesson Whole Group Discussion: Review students' ideas on how to solve the dance floor problem. Pull out relevant ideas to try making sure the following are included: Measure a square/rectangular area in the classroom that could be used as a dance floor. Choose the best unit of measurement to measure the space. Explore strategies for determining how much space each person needs to dance depending on type of music. What is the best unit of measurement to use? Introduce unit rate, square feet per couple. In small groups, students list at least three types of dance/music they will model and measure to determine how much floor space is needed per person. Allow students to volunteer to dance. Students demonstrate different styles of dancing, slow or fast. Students who did not want to dance should measure and record the dance space needed per person and per style of dance in a table using appropriate unit of measurement, square footage. Be sure the amount of dance space needed for students in wheelchairs is considered. Display the information in the table at the front of the classroom. Dance Style Space Needed for a Person Length Width Area Slow dance 2 ft 2 ft 4 ft2 Multiple means of representation: Allow students to refer to their brainstorming notes during discussion. When discussing unit rate, provide familiar examples (e.g., miles per hour). Provide students with a copy of the word problem and the table above. Have drawings and manipulatives available for students to use. Provide options for demonstrating different dance styles (e.g. volunteers demonstrate, bring dancers into the classroom to demonstrate, watch video demonstrations, etc.) Multiple means of expression: Allow students to solve the problem using formulas and/or models and record information into the tables using various formats paper and pencil, computer, etc. Multiple means of engagement: Ensure all students are actively involved in their small groups. Use music and dance styles related to students' interests. Use questioning to encourage students to explain their strategies.

Additional Considerations for Emerging Readers

Introduce the concept of unit rate as area per person or the amount of space needed per person to have enough room to dance. Provide a list of brainstorming ideas for solving the problem. Include picture and/or tactile representations of different dance styles as needed. Be sure all students have a job in their small groups that relates to the mathematical concept of measuring. When students are measuring, be sure they have the needed supports for reading the ruler/yardstick to the nearest foot and inch. Provide students with a copy of the table as well as word/picture representations of the different dance styles that can be used to complete column one.

Additional Considerations for Emerging Communicators

Introduce the concept of unit rate as area per person or the amount of space needed per person to have enough room to dance. Represent some of the brainstorming ideas they came up with in the introductory lesson using tactile and object representations to review the ideas with the class. Provide some new ideas in tactile representation that students share with the class. Be sure all students have a job in their small groups that relates to the mathematical concept of measuring. When students are measuring, they keep track of the number of feet by working with a peer. Each time the peer lays the ruler and measures a foot, the other student places a tactile representation of a foot long in a basket for length and a tactile representation of a foot wide for width. When finished, students count how many feet were collected/measured for length and width. Observe how students communicate within their groups. Ensure they have a means for sharing ideas and gaining peers' attention. If not, allow opportunities to practice within the group. Be sure activities are engaging to encourage communication. Provide students with a copy of the table as well as word/picture/tactile representations of the different dance styles that can be used to complete column one. If students are completing the table, they place a tactile representation for each dance style in column one. Record the number of feet for length and width by tallying each time a foot is measured.

Lesson 4: Practice – 15 minute

Break into small groups to solve the problem. Pose the problem: Your class is having a party and wants a dance floor. The biggest dance floor in the classroom is 8ft x 8ft. Based on each dancer's estimation of the dance space needed for one person preforming one style of dance, how many people can dance at one time on the dance floor? Calculate each style separately by using unit rate. Dance Style Space Needed for a Person Number of People Who Can Dance at One Time Length Width Area Slow dance 2 ft 2 ft 4 ft2 16 Based on the information in the table, what style of music would you play? Explain why. Bring the whole group back together. Fill in the table to indicate the number of dancers who can dance at one time based on the style of dance. Unit rate of couple per square feet needed based on different dance styles. Discuss the style of music the class would choose. Multiple means of representation: Provide students with a copy of the word problem, a template of the formulas for the unit rate/ratios and the table. Have drawings and manipulatives available for students to use. Multiple means of expression: Allow students to solve the problem using the formulas, drawings, computer graphics, and/or models, etc. Record the number of people into the tables using various formats: paper and pencil, Smart Board, computer, etc. Multiple means of engagement: Ensure all students are actively involved in their small groups, and use music and dance styles related to students' interests. Use questioning to encourage students to explain their strategies.

Additional Considerations for Emerging Readers

Present students with the problem written with words paired with picture and/or object representations of the most salient vocabulary from the problem. Determine the area of the dance floor, using previous learned strategies (e.g., 8ft x 8ft = 64ft2). Using information from the table, use the unit rate and equivalent ratios to determine how many people can dance on the floor at one time: Slow dance $\frac{1 person}{4ft^2} = \frac{x\ person}{64 ft^2}$ Repeat for each style of music. Individuals from groups share their results to complete the class table. Students should have their own copies of the table for reference. Provide picture/number representations for students to use to communicate results if needed.

Additional Considerations for Emerging Communicators

Present the problem to students written with words paired with pictures or object representations. Have a section of the classroom floor measured out and taped in an 8ft x 8ft square. Students move around the perimeter of the dance floor and within the area. If the floor has one foot square tiles, students skip count the tiles by 8, hitting a preprogrammed switch or placing a representation of each long foot (1x8) in a basket and determine the total of 64. Students stop hitting the switch at the end of the length or stop adding a long foot to indicate understanding/performance of area. Repeat process for each style of music. Students should collect a representation of their group's results as the group collects information on each style. Individuals from groups share the results to complete the class table. Students should use their own copies of the group results, which they collected in their mode of communication, to contribute to the whole class table.

Lesson 4: 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 within mathematics or across disciplines or contexts, and: Identify, quantify, and compare the attributes of the objects, situations, and/or events that need to be measured to solve the problem/situation. Use appropriate units of measure to identify, quantify, and compare objects, situations, and/or events to solve a real world problem. Convert units when necessary. Multiple means of representation: Along with posting lesson objectives in the classroom, students may refer to their individual copies. Multiple means of expression: Students can 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

When reviewing the expected outcomes, have students refer to the lesson objectives they recorded in their mathematics journals or their electronic picture versions. 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. For example, students grab the tactile cue for area to state, "I have learned that the area is all the space measured within a figure." Students should also refer back to the photographs or tactile representations of real-life situations in which these concepts are used to share when they could use these new skills. For example, students touch the tactile representations for area and tabletop to state, "I can use area to determine if an object will fit on my desk."

B. Exit Assessment Tell students: "This will be your ticket out the door": If you have a party at your house and have a 10ft x 10ft dance floor, determine how many people could dance at the same. Use the information from the table created during the lesson body. Observe how students solve the problems. Take anecdotal notes or assess students using a rubric. The situation/problem dictates the type of measurement to use. Did students determine the area of the dance floor correctly? Could students use the area to compute the answer to the question? Did students use the rate and equivalent ratios to determine how many people could dance a certain style at one time? Students return to whole group. Small groups present their solutions to the class and explain their process for determining their answers. Multiple means of representation: Provide students with a copy of the word problem, a template of the formulas for the unit rate/ratios and the table. Have drawings and manipulatives available for students to use. Multiple means of expression: Allow students to solve the problem using formulas, drawings, computer graphics, and/or models, etc. Record the number of dancers into the tables using various formats: paper and pencil, Smart Board, computer, etc. Multiple means of engagement: Ensure all students are actively involved in their small groups, and use music and dance styles related to students' interests. As you observe group work, use questioning to encourage students to explain their strategies.

Additional Considerations for Emerging Readers

Present students with the problem written with words paired with picture symbols of the most salient vocabulary from the problem. Determine the area of the dance floor, using previous learned strategies (e.g., 8ft x 8ft = 64ft2). Using information from the table, use the unit rate and equivalent ratios to determine how many people can dance on the floor at one time: Slow dance $\frac{1 person}{4ft^2} = \frac{x\ person}{64 ft^2}$ Repeat for each style of music. Provide students with a copy of a modified rubric and review expectations. Allow students to use all supports provided throughout the unit lesson so far. Students should have their own copies of the table for reference. Provide picture/number representations for students to use to communicate results if needed.

Additional Considerations for Emerging Communicators

Present students with the problem written with words paired with pictures or an object representation of the problem. Have a section of the classroom floor measured out and taped in an 8ft x 8 ft square. Students move around the perimeter of the dance floor and within the area. If the floor has one foot square tiles, students skip count the tiles by 8, hitting a preprogrammed switch or placing a representation of each long foot (1 x 8) in a basket and to determine the total of 64. Students stop hitting the switch at the end of the length or stop adding a long foot to indicate understanding/performance of area. Repeat for each style of music. Provide students with a copy of a modified rubric in picture and/or tactile representation and review expectations. Allow students to use all supports provided throughout the unit lesson so far. Students have their own copies of the group results to the dances in the form of visual and/or tactile representations of the dance style paired with the number of people. Students contribute to the class table by handing the paired representations to the teacher.

Lesson 4: Resources

UDL_HS_Math_Lesson_4_Resources.pdf

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