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Measure and use formulas to find volume and surface area of right rectangular and triangular prisms
volume and surface area
Find volume and surface area
Rectangular prism, triangular prism, face, base, lateral face, base area, volume, surface area.
Ways to Gain/Maintain Attention (Primacy):
Manipulatives, sketches, predicting, journaling, calculators, music, game, cooperative groups.
Lesson Segment 1: What is a right rectangular prism? A Triangular Prism?
Sorting is an excellent way for students to begin to identify attributes of geometric figures. The following activity will help students review ideas from past years cores and to scaffold their understanding for volume and surface area.
Give teams of students a set of Geometric solids. Using the Classifying Solids worksheet as a guide, have student teams sort the three dimensional objects in the set. Have them write their information on the worksheet. As teams report on their classification rules, help them use the vocabulary terms like faces, parallel faces, bases, edges, and vertices.
Then, showing models and having students hold up examples from their Geosolids set build a discussion to help students fill in the information on the Geometry Words For Three-dimensional Shapes Foldable.
To help students remember the type of units needed for measuring geometric shapes, have them make and complete the foldable for Units of Measure For Geometric Objects.
Lesson Segment 2: What is the shape for each of the faces, bases or surfaces of a three-dimensional shape? What information is essential in finding the surface area? How can the area for each face and the total surface be found?
Have students take out rectangular prisms from Geo-Solids. Review vocabulary by asking a team member to point to a base, then to point to a face. Ask another team member to show an edge where the length could be measured, then to show where the width could be measured, then show where the height could be measured. Ask another team member to show the team how many faces and bases the prism has. (Demonstrate which faces are the bases and which are the lateral faces or lateral surface.) If we want to find the area for the entire surface, we need to know what shape each face is and how many faces there are. Have the students use the solids to complete the attached Prism Bases and Faces worksheet.
If we could find the area for each of the faces of a prism, we would be able to find the area of the entire surface by adding these face areas together. Have students look on their Math 7 Class Reference Sheet and write the formulas for each face on the prisms from the Prism Bases and Faces worksheet. They can write the formula beside the face it applies to. When there are more than one of the same size face, the students can use an arrow to show they would use the same formula.
Lesson Segment 3: How are the units of measurement for surface area different from those used for volume? What information is essential in finding volume? How can we find the volume of a prism?
As we are told in the song (sing it again), volume is measured with cubes. Tell students if they can find the base area, then stack up the bases, they can find the volume.
As you demonstrate and discuss the following volumes, have students sketch, label, write the formulas and find the volumes on an assignment paper.
Lesson Segment 4: Practice finding surface area and volume
Comparing Rectangular Prisms
Give students the worksheet, Linker Cube Volume and Surface Area Comparisons and a bag of 100 Linking Cubes. Do a round robin reading to read all the questions for this worksheet. Show them a 1x3x8 rectangular prism and a 2x3x4 rectangular prism that you have made previously. Both prisms have a volume of 24 cubic units. Have the student write the hypothesis as indicated on the top of the worksheet for whether or not the surface area will be the same if the volumes are the same. Remind students to build the base area or l x w first and then stack layers for the h. Have pairs at each team work together to build one of the prisms. Then, the team sets the prisms in the center of the desks and discusses the number of cubes needed for volume and the number of squares needed for the area of all the surfaces. Give about 10 minutes for them to build and discuss each set of prisms. Discuss questions and answers for # 1-6 as a class.
Spin To Win Game
Materials needed: overhead spinner divided into three sections and labeled 1, 2, 3. Transparency problem for each team.
Directions: Cut each transparency containing the three shapes (attached) into three parts. Give each team one of the parts of the transparency. Ask each team to use their journal notes and class reference sheet, and calculators to find the volume or the surface area as directed on their transparency. They should all record this on an assignment sheet. Each person on the team must be prepared to explain how they found the answer.
Divide the class in half-Team 1 and Team 2. Have a person from one team come to the overhead to show the class their transparency. The class members work with their teams to find the answer, recording the problem on their assignment paper. The person at the overhead then calls on a person from the other side of the room to explain how to find the answer. That person comes to the overhead to show how. If he/she explains correctly, they get to spin the spinner. Spinning a 1 earns the team 1 point. Spinning a 2 earns the team 2 points. Spinning a 3 earns the team 3 points AND subtracts 1 point from the other team. If the person asked cannot explain cannot correctly, the student who you selected to bring the transparency up to show the class explains the problem and gets to spin the spinner for points for their half of the class.
The side with the most points when all the problems have been presented wins. Students should use the reference sheets, journal and calculators to avoid tedium and to be able to use the reference sheet effectively for the CRT later in the year.
Assign text practice as needed.
Performance tasks, questions, observation
This lesson plan was created by Linda Bolin.