This lesson will take several days to complete. It could be used as an introduction to length, width, height, area, volume and surface area. The lesson begins with an art project where the students assemble an object that will help them to visualize the concepts they are to learn later on. As a warm up, the teacher could ask the students what they think length is and then ask them to give an example. The teacher could go through all of the concepts in this way. Another way that this could be approached would be to ask the students what all of these terms mean on their own bodies. Start with height and have them each measure their height. Next move onto their width and their length. Ask them what makes up the front of their bodies (area). Repeat this process with all of the new terms

Next the teacher should give out a vocabulary list and go over each of the terms with the students. Have them write sentences that uses each word correctly. Hopefully, they will become familiar with these terms and fully understand them after the project is complete.

Measure

Height

Length

Width

Area

Surface Area

Volume

1. Each student gets 12 strips of each color
2. The students lay out one set (8 of the 1/2 inch strips) in an order that they like
3. Tape these eight next to each other on their desks
4. Take each of the other eight strips and weave them through the other strips already laid out To weave, each strip goes over one and then under the next one
5. While weaving, occasionally put glue on the strips so that they hold together
6. After the student has a square using eight strips in each direction, cut the ends so that there is only 1 inch of paper left on any side of the weave
7. Fold the ends that have just been cut inward and glue them down to the weave that has just been created
8. Put glue on a cardboard piece and glue the woven strips to the square with the weave side up
9. Repeat this process until each student has six squares
10. With glue or staples, attached the flaps on the squares so that the object resembles a cube

For the next week, each day can be devoted to a new concept dealing with the shape. The first one should be height, length, and width. Have the students measure each of these on their cube. Next, have them measure one square that is created by the weave. Count how many squares are on a side and then using math, check to see that this measurement makes sense with the first one. (Multiply the number of squares by the length of one of the squares.)

For Area, have the students measure the length and width of one box in the weave on one side of the cube. Ask them to count how many squares there are on a side. Explain to them that this is the area of one side of the cube. Another way to express the area other than the amount of squares is in inches. Have them measure the length and the height of an entire side of the cube. Explain that when they multiply these two measurements, the result is the area in inches squared (or whatever other unit they use to measure). Next, have them find the area of one weave on the side of the cube by measuring the length and height of that single square. Ask them what they think that they need to do in order to get the area of an entire side. After listening to their guesses, explain that you need to add up the area of all of the squares. Since they are all the same size, you can multiply the area of one cube by the number of all of the cubes to obtain this answer.

The next topic would be Surface Area. Since they have already found and understand the area of one side, ask them what they think the entire area of all the sides would be. After the guesses, explain that the area of the entire cube would be the area of each side added together. Have them find the area of each side for practice and then have them add them all up. The students will find that the area of each side is the same, so explain that they could also have found the area of one side and multiplied that number by the number of different sides, in this case six. The teacher should explain that this is called the surface area of the object because it is the area on the surface of the cube.

The last topic that could be used with this shape is Volume. Ask the students how they think they could find out how much could fit into the cube. After all of the guesses, Explain that this is called the volume of the cube. Have them measure what one little cube inside of the big cube would be by measuring the length, height and now width of one of the corners. Explain that if they multiply these three measurements, they will get the volume of the small cube. The teacher can show it to the students as taking the area of one side and seeing how many of that one need to be "stacked" on top of each other to get the width to be the same as the height and the length. Next, ask the students how they would get the volume of the entire cube. First have them measure the length, height and width of the cube and multiply the three numbers together. Another way would be to find the area of one cube. which they have done, and then to count how many cubes would be needed. This might be hard for them because there will be many cubes on the inside that they will have to understand are there without seeing them.

Note: The teacher could supply a sheet that has all of these formulas on them for the students to keep in their notebooks.

To evaluate what subjects the students might need more instruction in, a test could be given that requires the students to label the length, height, width, area, surface area and volume of a three dimensional drawing of a cube and then to actually find these values.

The students could also be tested on their knowledge of these concepts by having to verbally explain them. Each student could be responsible for one term and s/he would have to use some object in the classroom to explain the concept.

The students could also be divided into groups of six and each student in the group would be assigned a different term. After working together, each group would be required to present what they had done to the rest of the class.

MATHEMATICS CONTENT STANDARD 1- NUMBER SYSTEMS: ARITHMETIC, RELATIONSHIPS, AND THEORY

Beginning here, benchmark four states that students should "develop, analyze, and explain procedures for computation and techniques for estimation." In figuring out the different measurements of the cube, the students will have to estimate and guess the values before they are taught the formulas. Still in standard one, benchmark six states the students will "estimate results within reasonable limits."

MATHEMATICS CONTENT STANDARD 2- MEASUREMENTS

This project allows the students to relate dimensions such as length, area and volume" (2.2) as well as "work with geometric measurements of length' area, surface area, volume and angles..." (2.7).

MATHEMATICS CONTENT STANDARD 3- GEOMETRY

Benchmark two of this standard says that students must be able to "identify, describe, compare, classify, and construct various two and three dimensional objects...." In the same standard, benchmark four states that the students must "visualize and represent geometric figures with special attention to developing spatial sense.- In benchmark five of standard three, the students must "know and use the formulas for area, surface area, and volume of various figures...."

MATHEMATICS CONTENT STANDARD - PROBLEM SOLVING AND REASONING

Benchmark eight of this standard says each student will be able to "Break a problem into simpler parts which is done while counting the smaller squares to find the length, area, surface area and volume of the larger object. Benchmark eleven in the same standard states that the students must "work effectively in teams and independently" which will be tested in the follow up activities.

MATHEMATICS CONTENT STANDARD 9- USE OF TOOLS AND TECHNOLOGY

In this standard, benchmark three says each student will "choose a correct tool to measure length, area, volume...."

This project involves choosing patterns in the colored strips as well as other artistic qualities. While brainstorming how to find the different measurements before learning the formulas, the students are using the scientific method to observe and then hypothesize what the result should be. This project also uses many of the different intelligences such as verbal, mathematical, spatial, artistic and written.