Elementary Measurement - Lesson 4

Return to Lesson 3 or return to Elementary Mathematics UDL Instructional Unit

Objectives

• Students will be able to distinguish between perimeter and area.
• Students will be able to calculate perimeter and area.
• Students will be able to relate the concepts of area and perimeter to real life situations.

Essential Questions

• What is perimeter, and how is it calculated?
• What is area, and how is it calculated?
• How could perimeter and area be used in real life situations?

Vocabulary

Area - the amount of space an object occupies

Centimeter - a standard unit of length in the metric system equal to 1/100 of a meter

Foot - a standard unit of length in the US Customary system equal to 12 inches

Inch - a standard unit of length in the US Customary system equal to 1/12 of a foot

Length - a measurement of the distance from one point to another

Measure - to determine a quantity/amount

Measurement - a determined quantity/amount

Meter - a standard unit of length in the metric system equal to 100 centimeters

Perimeter - the distance around a figure along its edges

Quantity - an amount of something

Rectangle - a 4-sided figure in which opposite sides are equal and angles measure 90º

Ruler - a wooden or plastic tool used to measure lengths up to 12 inches

Square - a figure that has four equal sides and angles that measure 90º

Standardized - the same

Tape Measure - a tool consisting of a flexible ribbon of cloth or metal used to measure lengths up to several feet

Unit - a set amount used to consistently determine quantities

US Customary System of Measurement - a system of measurement that includes units such as inches, feet, yards and miles (for length); also referred to as imperial units or English units; This system is not commonly used outside of the United States.

Width - measurement of the distance from one side or edge to the opposite side or edge

Yard Stick - a usually wooden tool used to measure lengths up to 3 feet (1 yard)

Materials

• Masking or painter's tape
• Math journals
• Index cards (Each student will get one card. Some cards should have a "P" on them, while others should have an "A" on them. It is recommended that you have more "A" cards than "P" cards.)
• Chart paper
• Lesson 4 Perimeter Area PowerPoint presentation (print out slides for the students)
• Lesson 4 Practice Perimeter Area PowerPoint presentation (do not need to print out the slides for the students, but if you do remove the answers from the slides)
• Whiteboards and dry erase markers
• Lesson 4 Practice Worksheet document printed for each student
• Grid paper
• Lesson 4 Word Problem document printed for each student

Introduction

Activate Previous Knowledge

1. Using masking or painter's tape, tape off a large rectangle on the classroom floor. (If you still have the tape on the floor from Lessons 1 and 2, you could just use that initial line as one of the sides of the rectangle. If you need more space than you have available in your classroom, you could do this activity in the cafeteria or gym.)
2. Divide the class into two groups. Give each student in the first group an index card with the letter "P" written on it. Give each student in the second group an index card with the letter "A" written on it. (It is a good idea to have more students in the "A" group than in the "P" group.)
3. Have the students in the "P" group get up and walk along/on the taped edges of the rectangle while the students in the "A" group watch.
4. Have the students in the "A" group get up and fill the inside space of the rectangle while the students in the "P" group watch.
5. Ask the students, "What is the difference between the "P" group and the "A" group?
6. Explain to the students that the "P" group demonstrated the word perimeter whereas the "A" group demonstrated the word area.
7. Have the students verbally come up with definitions for perimeter and area, and write those definitions on chart paper to be displayed in the classroom.

Additional Considerations for Emerging Readers and Emerging Communicators

1. Provide a graphic representation, enhanced with tactile (e.g. outlined with glue, rough and smooth textures) and color qualities (e.g. perimeter in pink, area in blue) as appropriate, of the area and perimeter of the taped off section of the floor. A picture frame with a think frame could be used as a model of perimeter and area.
2. No accommodations.
3. No accommodations.
4. No accommodations.
5. Provide vocabulary options (word bank) for the student to choose from ("perimeter"", area"", outside", "inside", "more", "less", etc.). Put them in a format that allows the student to use his/her preferred mode of communication, including AAC and/or AT.
6. As the teacher explains, show the student the concepts on his/her graphic representation.
7. Have the student put the class definitions of perimeter and area in his/her math journal. The student can enter the definitions by writing, tracing (if the student is working on fine motor skills), keyboarding, drawing, cutting and/or pasting pictures, symbols, icons, text, selecting pictures, symbols, icons, text, tactile representations, concrete objects or any combination of those which a partner scribes, or saving symbols, icons, pictures, etc. into a digital journal using assistive technology.

Body

1. Present the students with the Lesson 4 Perimeter Area PowerPoint presentation. (The presentation is scripted, so be sure to consult the speaker's notes before you begin for information concerning how the animations are sequenced as you explain each step.) Provide the students with handouts of the PowerPoint. The presentation guides students in:

a. finding perimeter of a square given the lengths of all four sides

b. finding perimeter of a square given only one length

c. finding area of a square using tiles and the formula for area (length x width)

d. finding perimeter of a rectangle given the lengths of all four sides

e. finding perimeter of a rectangle given one length and one width

f. finding area of a rectangle using tiles and the formula for area (length x width)

2. As you go through the part of the presentation concerning rectangles, you will need to point out the difference/similarity of "length" and "width". Up until now, students have primarily been dealing with length only, so they will need to add "width" to their vocabulary.

3. Be sure to note the importance of including the appropriate units when providing answers to perimeter and area problems (i.e., perimeter = in vs. area = in2).

Additional Considerations for Emerging Readers and Emerging Communicators

1. Provide a copy of the PowerPoint.

• Enhance with tactile qualities as necessary.
• Provide the PowerPoint digitally with animations and sound.
• Guide the student through his/her PowerPoint copy, presenting graphic or tactile representations of salient vocabulary (e.g., perimeter, area, names of shapes, length, width) as needed. Provide a model or template of the formulas as they are discussed on the slides
• Provide a 3-dimensional representation that the student can manipulate during the presentation, such as a geoboard or pegboard that can be altered to reflect the shapes in the PowerPoint where pegs can be used to count perimeter and the grid cells to count area. Cubes or tiles might also be used to fill in the area.
• Provide a personal digital device that can be programmed with the shapes from the PowerPoint, and have the student manipulate the perimeter and area measurements, with or without AT.
• Allow student to use a calculator (talking, large button, etc.) to mirror the calculations during the PowerPoint.
• Have the student place tiles or cubes used in the perimeter/area demonstrations on a number line to count to the correct answer.

2. Have the student put the definitions of length and width in his/her math journal. The student can enter the definitions by writing, tracing (if the student is working on fine motor skills), keyboarding, drawing, cutting and/or pasting pictures, symbols, icons, text, selecting pictures, symbols, tactile representations, concrete objects, or any combination of these which a partner scribes, or saving symbols, icons, pictures, etc. into a digital journal using assistive technology.

3. Have the student add to the definition of area that area is always stated as square units and that exponent of 2 is used to when recording area. Have the student use the same strategy as in 2) above to add this information to the math journal.

Practice

1. Present the students with the Lesson 4 Practice Perimeter Area PowerPoint presentation. (You do not necessarily need to give handouts of this one. If you do, remember to remove the answers from the slides before printing.)

a. Each slide presents the students with a perimeter and/or area problem.

b. Students are asked to use the information provided to find the perimeter and/or area as shown. (Remind students they may refer to their PowerPoint notes. You should point out that the figures shown on screen are to scale drawings.)

c. Students are asked to write and complete each problem on their whiteboards.

2. Have students complete the Lesson 4 Practice Worksheet individually.

a. There are only 4 problems on the worksheet.

b. Remind the students that they may refer to their PowerPoint notes if needed.

c. Students may show their work in the blank space on the worksheet or on a separate sheet of paper.

d. Remind students to include the appropriate units in each of their answers.

Additional Considerations for Emerging Readers and Emerging Communicators

1. Provide models for the problems that the student can use to find perimeter and area.

• Provide templates with the formulas for area and perimeter, which the student can use to "write the problems". Students may also choose which formula is needed to solve for area/perimeter (touching, moving, selecting, etc.).
• Prewrite the problems on the whiteboard.
• Provide the problems digitally and allow the student to solve the problems digitally. Allow the student access to the digital problems using assistive technology.
• Provide math function options for the student to choose from. Allow the student to use a calculator (traditional or digital, talking, large button, etc.) to solve the problems.
• Provide number cards that the student can use as answers for the problems instead of writing them.

2. Adapt the worksheet to include needed supports.

• Provide a formula template for the student to complete.
• Provide the shapes drawn on grid paper so that the student may count versus calculate.
• Provide cutouts of grid units or other manipulatives that the student can use to solve for area and perimeter.
• Provide number cards that the student can use as answers for the problems instead of writing them.
• Provide visual cues to help the student distinguish between length and width (i.e., graphic representation with arrow up to indicate length and arrow right indicating width).
• Allow the student to use a calculator (traditional or digital) to solve the problems.
• Reduce the number of problems to solve, remembering that the student may need extra practice at a later time.
• As this is still instructional, not assessment, provide guidance so that the student completes the worksheet correctly. Techniques such as errorless learning and systematic instruction could be used.

Closure

a. Revisit/Review Lesson and Objectives –

1) Remind students that the goal for this lesson was to learn the difference between perimeter and area as well as how to "find" perimeter and area of squares and rectangles.

2) Review the definitions of perimeter and area that were charted at the beginning of the lesson. Ask the students to verbally explain any additional information they learned about perimeter and area throughout the lesson (e.g., perimeter is calculated in units, area in squared units; when calculating perimeter and area of a square, you really only need to know the length of one side since all four sides are the same; when calculating the perimeter and area of a rectangle, you really only need to know the length of one side and the width of one side since opposite sides are the same, etc.)

Additional Considerations for Emerging Readers and Emerging Communicators

1) & 2) Provide access to math journal and PowerPoint presentations. Assist the student in finding the review information as the teacher goes over it and the class discusses. Provide answer options to the questions. Have the student select an answer(s) and use his/her preferred mode of communication to contribute to the review. Pre-plan a question and answer for the student to contribute.

b. Exit Assessment

1. Have each student draw a square or a rectangle on a sheet of grid paper and illustrate the difference between perimeter and area (e.g., outline the figure in one color to demonstrate perimeter, and shade the inside of the figure in another color to demonstrate area).
2. Provide each student with a copy of the Lesson 4 Word Problem document. Read the problem to the students, and have the students solve the problem in their math journals. (You'll go over the problem and its answer at the beginning of the next and final lesson in this unit.)

Jane and Luis are in charge of the 4th grade booth at their school's Spring Festival, which will be held on the school's parking lot. Space on the parking lot is very limited, and so the parking lot has been divided so that each grade will have a section that measures only 2 feet by 3 feet. Jane and Luis want to make sure they will have room for their popcorn popper and snow cone machine as well as the serving table.

a. What is the perimeter of class' section of the parking lot?

b. Convert the perimeter of the class' section into inches.

c. What is the area of the class' section of the parking lot?

d. Which is likely more helpful to Jane and Luis in determining whether or not they have enough space for all of their equipment—knowing the perimeter of their section or knowing the area of their section? Why?

e. Based on your calculations, do you think Jane and Luis will have enough room for the popcorn popper, the snow cone machine, and the table? How do you know?

Additional Considerations for Emerging Readers and Emerging Communicators

1. Provide grid paper (enlarged or raised line if either of those has been used successfully by the student during instruction) on which the student should draw a square or rectangle.

• Allow the student to trace the square or rectangle (shape and size should be the student's choice).
• Allow the student to create or select shape, digitally using AAC and/or AT.

Have the student indicate where the perimeter and area would be found or measured.

• This could be done verbally/vocally, by touch, selection from an indicated choice (e.g., "Is this the perimeter or is this the perimeter?"), outlining, coloring, digitally, etc.
• Allow the student to use the method of performance that will give him/her the most success. For instance, if the student has difficulty with fine motor skills, he/she might indicate more successfully by answering questions (including use of AAC/AT) rather than coloring. After a successful response, the student may want to color or highlight as well, but the accuracy of the response would be on the answer given, not the ability to highlight or color.
• Since this is now assessment and not instruction, it is important to assess the student's independent performance. If the answer is incorrect, he/she can be prompted to give a correct performance, but the data should reflect the student's independent (incorrect) response.

2. Provide an adapted story problem worksheet:

a. read the problem to the student

b. simply/summarize text of story problem

c. highlight the important information

d. provide a graphic or 3-dimensional representation of the problem (with manipulatives if necessary)

e. provide formulas for perimeter and area

f. provide visual cues for determining perimeter and area

g. provide answer selections for the student to choose from (these should include plausible distractors or incorrect answers, the number of which could vary from student to student)

h. provide a number line

i. provide a conversion chart

Provide and allow the student to use any of the accommodations or supports he/she used in this lesson (Lesson 4), Practice 2 to solve the problem. Reduce number of questions required for assessment. Since this is now assessment and not instruction, it is important to assess the student's independent performance. If the answer is incorrect, he/she can be prompted to give a correct performance, but the data should reflect the student's independent (incorrect) response.

Return to Lesson 3 Proceed to Lesson 5