CAN YOU BUILD A RECTANGULAR PRISM?

Name: Janie Abplanalp

Date of Lesson: September 19, 2002

Subject/Topic: Mathematics/Geometry

Grade: 3^rd

Standards:

Geometry – use visualization, spatial reasoning, and geometric modeling to solve problems.

 

Communication – students will communicate their mathematical thinking clearly to peers, teachers and others.

Problem Solving – build new mathematical knowledge and strategies through problem solving.

Outcomes/Objectives:

The third grade students will be able to show all the rectangular regions they can make using 24, 1-inch tile squares in their cooperating groups of two or three while listing the results on a grid with the teacher.

The third grade students will be able to use geometric models to solve problems in other areas of mathematics, such as measurement and number while working in cooperating groups of two or three.

Materials:

Table/grid of regions

24, 1-inch tile squares

Overhead Projector

Vocabulary Words:

Prisms – a solid figure whose ends are parallel and equal in size and shape, and whose sides are parallelogram.

Rectangles – a four-sided plane figure with four right angles.

Area – the measure, in square units, of a surface.

Perimeter – the outer boundary of a figure or area.

Factor – any of the quantities which form a product when multiplied together.

Multiple – a number which is a product of another number.

Grid:

*students put in the numbers after class discussion of answers with teacher

Procedure:

Engage – Open with discussion of rectangles and prisms and make sure the students understand the meaning of them. Show pictures of different rectangular prisms on the overhead and note to the students about the different shape/size of the rectangle. Next, go over the formula of perimeter and area of a rectangular prism and practice on some problems. By now, the students will be able to start the project with complete understanding. Have student’s practice drawing the shapes, letting them understand form of them.

Explore – Hand out the tiles to each group, directing them to not touch them. Next, hand out the grid. Point out that one student will be the recorder and the other will be the builder. Tell the students to show all the rectangular regions they can make by using 24, 1-inch tile squares. Remind them to use all of the tiles. Finally say to count and keep a record of the area and perimeter of each rectangle and then look for and describe any relationships you notice. Ask for any questions. If okay, then tell them to start. Give them about ten minutes to get all of the results.

Explain – When the students are ready to discuss their results, ask if anyone had a rectangle with a length of one, of two, of three, and so on, and model a way to organize the information. Use the overhead projector with a blank grid to show the classroom solutions on. Ask if anyone tried to form a rectangle of length five or more and, if so, what happened. See how many results there were. Let each group give their answers. Mention that LxW=A and how the first two columns multiplied together will get 24 (area). Also mention that the long, skinny rectangles have a larger perimeter than the fatter rectangles. Explain the vocabulary words of this lesson in great detail. This lesson provides opportunities for students to consider the relationship between area and perimeter, to use particular vocabulary, to record data in an organized way, and to review basic number combinations. Also, having the students communicate in class will allow them to accomplish good problem solving tasks.

 

 

Expand/Extend/Apply:

Reflecting on different ways of thinking about this problem solution is to consider a different representation. Use a square of 36 dots and have students find several ways to determine the number of dots on the boundary of the square. Then represent their solutions as equations. The students should be able to see the different patterns just like in the assignment before. Students should compare how they are alike and different. Give plenty of time for the students to discuss this answer with each other.

Evaluate:

Have students write in their journals over the new vocabulary terms with definitions. Have them list what we did and how we came up with our results. This will allow the students to review the lesson and ask questions if they still do not understand. Assess the students with new vocabulary, and have them list two of the answers of how to get a rectangular prism. Let them explain their results.

Expand:

Before going on to the next lesson on the next day or week, review over all the information they learned in the rectangular prism lesson. Go over vocabulary terms and formulas. Make sure you call on the students who were having a little trouble on it. Once you are sure the students know, then go on to the next lesson. If not, then you will need to create another way of teaching that concept.

References:

Principles and Standards for School Mathematics. (2000). Reston, VA: The National Council of Teachers of Mathematics, Inc.

Reflection:

This is a great lesson plan because this involves all the students. It allows them to work in groups and a classroom as a whole. It teaches multiple tasks that are combined in curriculum. The only problem I see is that this might be a little advanced for some 3^rd grade students. So you might need to go slow and expand it to a couple of days.

 

Ideas for Integration: