Area and perimeter are two important and fundamental parts of mathematics. The unit and topics of area and perimeter are important to mathematics because they are the physical aspects of mathematics. They are the foundation for understanding other aspects of geometry such as volume and mathematical theorems that help us understand algebra, trigonometry, and calculus.
Since math builds upon itself, it is important for students to learn about area and perimeter. Learning about area and perimeter will give the students a chance to use math that “real” people need and use outside of school. Many careers like architecture, aeronautical and graphics design, engineering, the coast guard, and many others include the use of area and perimeter on a regular basis. With some of these careers (like aeronautical design and the coast guard), it is crucial to know and understand the importance of these topics. These topics will also be important for them to understand one day when they need to remodel, buy, or build a new home because they will want to get the maximum use of their house.
Once students understand the importance of area and perimeter and that it is useful outside of the classroom in so many places, they will be more willing to learn about them. It is also important for teachers to come up with creative activities to capture students’ interests. As long as the activity is fun or is similar to a career the students will have some day, they will want to learn.
The Principles & Standards 2000 and 1997 Illinois Learning Goals (Standards) both suggest that middle school students should understand and draw two-dimensional shapes, communicate logical arguments about geometry, and compute distances and lengths. The students must understand two-dimensional objects in order for them to compute area and perimeter, with and without technology. They will have to know the difference and relationship between the two, which they must show the teacher through participation in activities, discussions, and homework. The students will perform activities that do and do not use technology, like geometer’s sketch pad and geoboards consecutively, to give them a variety of ways to learn about area and perimeter.
This unit plan is based on the abilities of a sixth grade classroom, but could be incorporated into higher level math classes. The lessons and activities were created to challenge the students’ mental abilities and encourage further exploration of these subjects and in mathematics overall.
The main goal for the students is to learn and understand the importance
of area and perimeter in real life situations. By the end of the
unit, the students should know how to calculate the area of rectangles,
triangles, and squares, and know how to find the perimeter of any shape.
Day 1: Spaghetti & Meatballs for AllMeasuring Area & Perimeter
Day 2: Go over examples of possible layouts while showing the number of tiles & rails for each. Let students work with tiles on their own to find the different arrangement of a certain number of tiles. Have groups share their results.Measuring Odd Shapes
Day 3: Let students explore a few different layouts and find the perimeter & area of each. Discuss as a class their strategies for finding these.
Day 4: Students examine different floor patterns to find perimeter, area, as well as the different costs, depending on the perimeter and area.
Day 5: Students work with the previous day's plans to answer questions about finding different plans with same area or perimeter.
Day 6: Students will find the perimeter and area of irregular shapes, including their own hands and feet, by comparing them to a square grid.Constant Area, Changing Perimeter
Day 7: More problems with irregular shapes
Day 8: See Constant Area, Changing PerimeterConstant Perimeter, Changing Area
Day 9: Have students take a certain area and cut an interesting shape out of the side of it, tape to the opposite side and compare the perimeter with the original object. Notice (& have students notice) that each rectangle has the same area, but the perimeters change.
Day 10: Give students a problem with certain perimeter (amount of fence) and they need to find the different possible areas.Measuring Parallelograms
Day 11: Have students find the smallest and largest amount of tiles needed to make shapes of certain perimeters.
Day 12: Students will look at different parallelograms and determine the area of each by comparing it to a grid. Students should use what they have learned from previous lessons to find this.Unit Project
Day 13: Go over the meanings of base and height of a parallelogram. Have students work together to find rectangles and parallelograms that meat certain characteristics.
See Unit ProjectReview
Day 19: Powerpoint Presentation and Quiz Show similar to these.
For our unit plan, as far as assessment is concerned, we decided to have warm up activities on a daily basis instead of weekly quizzes. Homework will be assigned on a daily to every other day basis. As the unit comes to a close, with about a week left before the exam, we plan to have a unit activity that allows students to synthesize their learning of the unit. After students have presented their projects, we well have a day set aside for review over the material, and last minute questions, and then we will have an exam to close the unit.
As educators at the sixth grade level, we decided against having quizzes on a weekly basis. We thought that at this level there would be better ways to see if children are learning. On a daily basis, we plan to have warm up activities that will provide a review of the material from the previous day. Warm up activities would mainly consist of 2 to 3 problems that would be solved together as a class. The teacher will be able to sense the level of understanding by his or her students by the facial expressions and the general responses students give. This will also give the educator an idea of what pace to take for that day's lesson. If students do completely not understand the warm up, it might be wise for the teacher to review the previous day's lesson, and make a slower transition into the new material. If the case seems to be that the students understand the general idea but not a minor point, the teacher will know to reiterate that topic when it comes up again.
If students take quizzes, we believe that it will only measure how much as student has memorized in order to take the quiz. It doesn't necessarily show how well a student understands a concept. Quizzes are usually taken without the book or notes as a resource, so a student may encounter feelings of anxiety to do well on a quiz when the might have forgotten what needs to be done when they know and can explain the process verbally rather than on paper.
Through daily warm-up exercises, the teacher can follow students' general train of thought, and at the same time, combat some of the misunderstandings one student has with the rest of the class as an audience. Chances are there are other student's that are confused about the same thing. Or even if a student believes that he or she understands, but they misunderstood an idea that they believe is right, it should be cleared up during the warm-up activity, (this may occur with or without the teacher's knowledge).
Homework will be assigned on a regular basis in order for the students to gain practice of the material learned on a daily basis. Usually it will be in the form of a worksheet, a number of problems from the book, or gathering data from their everyday world (*). If a lesson is not completed by the time the bell rings, we suggest that students attempt to do part or all of the homework depending on how much/little the lesson covered. Students should have questions/comments ready for the next day, (of course the teacher must probe for these, "What did you think of the homework? Easy, hard, okay??).
(*) If we ask students to gather data, it will be used for an activity for the following day. If homework consists of gathering data, students should be given a general direction to which the data will be used. If no general direction is given, students may either be curious about the activity, or they will find the assignment to be pointless.
If time permits, is wise to have students start on the homework in class. If they have questions the teachers will readily available to answer them. Another benefit to having homework started in class is that if one student has a question that might have reflected something that wasn't focused on as much as it should have been in the lesson, then the teacher can pass the information onto the rest of the students.
Homework is likely to be handed in the next day, or maybe reviewed together with the entire class. If a teacher plans to review the homework in class, we must take in consideration the difficulty of the material. If the material is easy, it may be best to have students turn in the homework and grade it for an actual score. If the material was hard for the students to understand, and we could not give the students time to start the homework in class the previous day, we will have students grade their own homework and correct any errors. This way students can see where they might have made mistakes.
If the homework is graded by each student, then these assignments should be handed in, but not considered in calculating students' overall grade. It should most likely be a credit/no credit assignment. Credit would be granted upon completion with a grade of a B or higher. If a student does not achieve about 85% on the assignment, then it should be returned to the student to redo. Credit will be given when the student has received 85% or higher on the assignment.
***By no means do we suggest that if a student were handed back an assignment should that student be neglected, as teachers we should be available to help the student with where problems occur. If the student does not usually ask for help, it is our responsibility to ensure that the student knows we are readily available to help. Whether this means pulling a student out from their study hall or asking them to come if for extra tutoring (for maybe 10 minutes out of recess or their lunch), if the student does not make an effort to get help, the teacher should take the initiative.
In determining whether material was hard or easy for students, is where the warm up activities come into play. As stated before, the warm up activity will help not only the students as a review, but it will also benefit the teacher. Through the how smooth (or how rocky the warm-up activity goes, the teacher will have a better idea what general areas are difficult for the class as a whole.
The homework would provide a more individualized report for the teacher. In grading homework, the teacher can decide which students are having difficulty with what material.
As the unit comes to a close, we plan to have one day for a review, then the following day will be the exam.
The exam would consist of problems encountered throughout the unit. It will ask students what the general formulas for area and perimeter. It will have problems asking students to find he area and perimeter of different shapes, and include problems similar to the banquet seating, keeping area constant changing area, as well as keeping area constant and changing the perimeter.
How well/poorly students to on the final project as well as the exam
will show how well a student understood the lesson.
As the unit has about a week before the exam, we plan to have a unit activity that will encompass all the ideas in our unit plan. The final project for our unit on "Area and Perimeter" would be to have students build a one-floor dream home. We would give the students the amount of land they have to build on, say 45 feet x 55 feet of land. The students can plan to have anything in their home. If a student want three cars, or a pool they must take in consideration the dimension as well as the amount of area each item will have. Students will be given a poster board to put all of this information. Before putting info on poster board, inform students to thin of the things they want in their home. Please start with a pencil and a large eraser... just in case you change your mind.
Some general guidelines.
Each home must at least have:
-at least 6 different rooms (bath, bed, kitchen, living room, closet,
dining room / family room (entertainment room)
-each bedroom should have a closet
-If you want more than 2 cars you will need to have a garage to fit at least one car
-if you have dog, there must be a doghouse
-any other pets, you must say where it's home will be
-you want a backyard of at least 300 square feet (in case you decide later to get a pool)
ALL ROOMS MUST HAVE THE DIMENSIONS LABELED!!!
Each room must have enough space so that necessary things can fit in
(a bathroom must be able to fit a bathtub, sink and toilet)
When introducing the lesson to the children, remind them even though they are not required to find the dimensions of each item, it must be enough space for the item to fit in the room.
Students must identify at least fit 3 different items in each room (if you want more things, make sure you say where things will be and everything fits!!!) Closets can have the same items.
~ a bedroom could have a bed, a TV, a night stand
~ a closet might have a pair of shoes, hanger, a storage bin.
***Again remind students that everything must fit in any given room... a closet must be wide enough so that the hanger can fit width-wise
Nice but not necessary
a backyard pool
a foosball table
a big screen TV
a swing in the backyard
a place to grow plants, vegetables in the yard
The students will have about a week to work on this with a day or two in class to ask questions that might have not been answered through the unit.
The day the project is due students will have about 5 minute to present
it to the class. This will give the students and the teacher the opportunity
to get to know each other's likes and dislikes. And more importantly, student
will explain there reasoning in how certain things fit in different rooms.
Source: Connected Mathematics, Grade 6, Covering & Surrounding