PROBLEM-BASED LESSON PLANMathematics Learning and Teaching, Task 3

GENERAL INFORMATION

Lesson Title & Subject(s): Surface Area of a Rectangle Topic or Unit of Study: Geometry

Grade/Level: 6Th grade

Instructional Setting:Classroom setting. Students are asked to think on their own and then with a partner that is seated close in proximity. Teacher displays powerpoint presentation on the SmartBoard.

STANDARDS AND OBJECTIVES

State or Common Core State Standard(s):CCSS.MATH.CONTENT.6.G.A.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Lesson Objective(s):Find the surface area of a rectangular prism. (Condition) Students are guided through the steps of calculating each of the three pairs of faces of the rectangle and finding the sum of all 6 faces as a whole. (Behavior) The students should earn at least 3 of the 4 points on the attached surface area assignment.(Criteria)

STUDENTS’ NEEDS

Prior Knowledge:Students must already know how to find the dimensions of 2D objects. They must be able to distinguish between 2D and 3D shapes. Earlier math topics must be used, as well. This includes addition and multiplication.

English Language Learners:During the lesson, certain accommodations for English Language Learners are considered. When teaching to ELL, academic vocabulary is very important. When defining the new terms for this lesson, the teacher should take into consideration that the mathematical definition of a word and other definitions of that word are very different and could confuse an ELL. The teacher will encourage students to offer support from their peers. When pairing students, the teacher should take into consideration who the ELL student is paired with. Making sure the ELL is paired with a student that is proficient at both English and math will help the ELL excel.

Lastly, the teacher takes into consideration that ELL students learn best when a real world example is used. When the example of painting the surface area of a home is used, the ELL can visualize a real world situation and better comprehend the topic. The teacher should also walk over to each ELL during the think-pair-share time and individually ask the student if they have any questions about the new equation.

Students with Special Needs:There are many students in every school that have ADHD. These students also need to have a sort of differentiated instruction than the rest of the class. ADHD students should be seated closer to the teacher so they can focus and sustain their attention. This can also be enforced when grouping the students or pairing them with their peers. The ADHD student must always be encouraged to stay on topic, so placing them in the least distractive environment will greater their success. Additionally, ADHD students thrive when the main topics are presented multiple times, or are highlighted. The teacher should make sure that they highlight the surface area equation so the ADHD student knows it is important information.

MATERIALS AND RESOURCES

Instructional Materials:Powerpoint PresentationAssignment Handout

Resources:"Grade 6 . Geometry." Common Core State Standards Initiative. 1 Dec. 2015. Web. 9

Jan. 2016. <http://www.corestandards.org/Math/Content/6/G/>.

INSTRUCTIONAL PLANBefore Phase of the Lesson:

The surface are of rectangular prisms brings together learning about the area of two-dimensional polygons with the idea that the surface area of three-dimensional shapes are a composite of a set number of two-dimensional shapes. Before the lesson begins, the teacher will present a warm up that involves finding the area of two-dimensional figures. This is the first slide of the powerpoint presentation. This will remind the students the relationship of finding the areas of 2-D before starting the surface area of 3-D polygons.

Students are asked to “think-pair-share” about finding the surface area of 3-D polygons. This will include thinking by themselves, then pairing off with a peer, and sharing their ideas about the problem with another student. Students are asked how they believe a painter would find the area of the surface he is assigned to paint. What information would be needed in order for the painter to come up with a valid answer?

Additionally, the teacher should introduce the learning objective before the lesson begins. The teacher should clarify each aspect to the class, this includes the behavior, condition, and the criteria. When the teacher tells the class exactly what

they need to accomplish, the students will know how they are going to be assessed and will hopefully pay closer attention to those aspects. The teacher should tell the students that they are going to find the surface area of a rectangular prism. (Condition) Students are guided through the steps of calculating each of the three pairs of faces of the rectangle and finding the sum of all 6 faces as a whole. (Behavior) This will be done by finding the surface area of a building that a painter must paint. (Criteria)

During Phase of the Lesson:A problem is presented to the class as a whole. The teacher gives an example

of a home’s exterior that needs to be repainted. The students are asked to find the amount of paint they will need in order to complete the project without buying too much paint.

Before the students have a chance to work on the problem, the teacher introduces new vocabulary to the class. Surface area and the “faces” of a rectangular prism are defined. These new vocabulary terms will help the students solve the paint problem.

The rectangular prism (the house) is shown “unfolded” to display the different sides of the prism. It shows the student each shape that they might have to paint during their problem. It also shows the three pairs of faces in the prism.

In order to monitor student understanding, the teacher should then prompt the students to participate in a hand signal activity. The hand signals are used to indicate the class’s understanding of the subject. Students are asked signal with their thumbs if they can complete a surface area equation on their own. The thumbs up means that they understand and can explain the topic, thumbs sideways means that they are unsure, and thumbs down indicates that they are confused and do not yet understand. This strategy makes the entire class participate and allows the teacher to check for the understanding of a large group. If the majority of the class is thumbs up or thumbs sideways, the teacher could continue to the next step of the lesson, the example equation.

The next step would be to let the students attempt an example equation.

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Let students work in pairs to attempt to find the surface area of the prism. Give a few minutes to see if they are able to figure out the faces of the rectangular polygon. Students may struggle with finding the dimensions of every face, so the teacher may need to remind them how to “unfold” the prism.

The last equation reverts back to the initial question about the amount of paint that you should buy to paint a house. The surface area of a house must be found. Ask the students to complete this on their own. Once the entire class is complete, or ten minutes has passed, teachers are to assess their students using Kahoot.

After Phase of the Lesson:After the lesson, the teacher will ask for student feedback. The students are asked to discuss in small groups what challenges they ran into during their work. Each group is asked to write their main issue on the whiteboard. The teacher will discuss the entire class’s issues as a whole. As an assignment, the students are given the attached worksheet to complete and have graded.

ASSESSMENT PLAN

Observations: When students are working in groups or with a partner, the teacher is listening in on

conversations. It is likely that students will understand the idea of finding the surface area, but they might be “stuck” on a certain part. The most difficult concept for students in this lesson might be finding the appropriate dimensions on the 3-dimensional object. The teacher will be able to show the students how to “unfold” the prism to find each face’s dimensions.

If students are able to explain to each other how they answered their problem, they have met the learning objective. If the student can “teach the lesson” back to the teacher, they have grasped the new math objective. Students should be able to explain how they got their surface area, not just have the answer.

Questions: The teacher will circulate the classroom when students are working in pairs and in

groups. They will be available to answer questions and guide students in the right way.

After their problems are solved, the teacher uses Kahoot to question the students. Kahoot will ask the class different questions about the topic. This will give both the teacher and the students the feedback about if everyone understood the new math topic. While using this technology, both the class and the teacher are able to see everyone’s responses.

Questions includeo During the lesson

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What is the difference between area and surface area? Are they interchangeable?

What information is needed in order to find the surface area? Can surface area and area both be found on the same polygon?

o After What problems did you run into during your work? What was the most difficult part of find the surface area? What is a simple error that could occur during a surface area equation?

When these questions are asked, they are checking to see if the students are meeting the learning objective. The questions help clarify if the teacher must spend more time clarifying the topic, or the students are ready to be accessed.

Worksheet or quiz: The lesson includes an assignment that students are to complete after the lesson is

over. It will be collected and graded by the teacher.

In order to assure that the teacher successfully taught their class, they should check for the lesson’s alignment with the objective. The goal of the lesson was stated in the lesson objective “Find the surface area of a rectangular prism. (Condition) Students are guided through the steps of calculating each of the three pairs of faces of the rectangle and finding the sum of all 6 faces as a whole. (Behavior) The students should earn at least 3 of the 4 points on the attached surface area assignment.(Criteria)”.

The lesson begins with much more simple mathematical problems that grow in difficulty as new aspects are introduced. The teacher should make sure the students do not lost interest or become confused as the lesson plan progresses, so ensuring the lesson starts easier and ends with new, more difficult information is the best method. This lesson plan starts with 2-D polygons surface areas and eventually ends with the surface area and real-life situations.

Just like every new lesson, there are always misconceptions or barriers that students might run into. One of the most difficult aspects of surface area of a regular polygon would most likely be finding the dimensions of the object. When a picture of the polygon is given, a student must determine how many sides and the length of each side in order to find the surface area. Most of the time, a picture is not able to show every side of the object, so the student may have a difficult time visualizing every side of the object. The teacher should explain how to “unfold” the polygon’s sides so every side can be shown and each dimension can be written out and visualized. A second misconception of surface area is often finding the volumeof a polygon. Because the formula of surface area and of volume are similar, a student can easily get confused on which they need to use. The teacher should remind students that the surface area is only the surface of the object, whereas the volume includes the interior of the object.

The questions used in both the during and the after phases of this lesson are higher-level questions. This means that the questions involve making connections, analyze information, and draw conclusions on the topic. The questions on the attached assignment do just that. They use real-world examples that make the students relate the lesson plan to everyday life. Also, the worksheet has questions that have visual examples and word problems. This makes the student analyze the questions further

and makes them decide what steps they need to make in order to answer each different question. Some of the questions included in the discussion will include: What problems did you run into during your work? What was the most difficult part of find the surface area? What is a simple error that could occur during a surface area equation? What steps were taken in order to visualize each dimension that needed to be used

to calculate the surface area? Have you thought of another way the surface area could be calculated?

All in all, the lesson plan aligns with the objective, assessment, and questions asked during the lesson. All aspects of the class period reflect the objective of the lesson plan. The assessment ensures that each individual student learned the new topic of surface area of a rectangular polygon. If they are able to answer the questions on the assessment, they have successfully learned the steps of calculating each of the three pairs of faces of the rectangle and finding the sum of all 6 faces as a whole.

Surface Area AssignmentMs. Kendall 6th Grade Math

1. Find the dimensions of each face of the rectangular prisma. Side A ________________________b. Side B________________________c. Front________________________d. Back________________________e. Top________________________f. Bottom________________________

2. Find the surface area of the rectangular prism from Question 1.____________________________________________________________

3. A painter wants to know the square footage of the Empire State Building. Assume that the building is a rectangular prism. The height is 1,250 and the square base is 100 ft by 100 ft. Draw the building and find the surface area of the building.

____________________________________________________________________________________________________________________________________________________

4. Find the surface area of the following rectangular prisms.

A. B. with dimensions of 10 in X 2 in X 5 in

_________________________ __________________________