September 9, 2009

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This resource guide provides links to exemplary resources and insight on how to teach mathematics and science concepts at the middle school level. Concepts supported by this particular guide include decimals, fractions, division of whole numbers, and geometry. The guides provide information on the needed content knowledge, science and mathematical pedagogical knowledge, exemplary lessons and activities, career information, and correlations to national mathematics and science standards.

- Mathematics > General

- Grade 6
- Grade 7
- Grade 8

Curriki Rating

On a scale of 0 to 3

3On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of -0001-11-30.

Curriki Review System

September 17, 2009

This resource received a 3* rating because it is part of the larger resource, Math Focal Points: Grade 7, which received a rating of 3-Exemplary in the Curriki Review System. You can learn more about this larger resource by reading its review and comments.

Table of Contents

- Math Focal Points - Grade 7: Introduction
- Math Focal Points - Grade 7: Background Information for Teachers
- Math Focal Points - Grade 7: Ration and Proportion
- Math Focal Points - Grade 7: Surface Area and Volume
- Math Focal Points - Grade 7: Integers and Algebra
- NCTM Standards & Author and Copyright Information

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By decomposing two- and three-dimensional shapes into smaller, component shapes, students find surface areas and develop and justify formulas for the surface areas and volumes of prisms and cylinders. As students decompose prisms and cylinders by slicing them, they develop and understand formulas for their volumes (Volume = Area of base × Height). They apply these formulas in problem solving to determine volumes of prisms and cylinders. Students see that the formula for the area of a circle is plausible by decomposing a circle into a number of wedges and rearranging them into a shape that approximates a parallelogram. They select appropriate two- and three dimensional shapes to model real-world situations and solve a variety of problems (including multistep problems) involving surface areas, areas and circumferences of circles, and volumes of prisms and cylinders.

These activities involve middle school learners in scenarios that challenge them to apply their understanding of measurement of solids. They will also work on circumference and circle area problems, included in this area of emphasis. Keeping cool : when should you buy block ice or crushed ice?

Keeping cool: when should you buy block ice or crushed ice? Which would melt faster: a large block of ice or the same block cut into three cubes? The prime consideration is surface area. A complete solution demonstrates how to calculate the surface area of the cubes as well as the large block of ice. Related problems involve finding surface area and volume for irregular shapes and examining the relationship between surface area and volume in various situations.

Cordwood This problem scenario, set in Alaska, asks students to find the volume of a shed, applying the standard formula, and then to determine the number of cords of wood needed to fill it. Finally, they must calculate the cost of the wood.

Popcorn: if you like popcorn, which one would you buy? Students are directed to use popcorn to compare the volumes of tall and short cylinders formed with 8-by 11-inch sheets of paper. A simple but visual and motivating way of comparing volume to height in cylinders! The solution offered explains clearly all the math underlying the problem.

Windshield wipers: it's raining! Who sees more? The driver of the car or the truck? In this activity, students compare the areas cleaned by different wiper designs. An animation shows the movement of the two windshield wipers, each cleaning off a different geometric shape on the window. Students are encouraged to draw the shape cleaned by each wiper and find its area.

Big tree: have you ever seen a tree big enough to drive a car through? Students must consider the girth and height of ten National Champion trees and determine which, if any, of the trees is large enough to drive a car through. The solution relies on knowledge of the formula for finding the circumference of a circle. MSP full record.

Surface area and volume This applet enables students to form and rotate both rectangular and triangular prisms. They can set the dimensions (width, depth, and height), observing how each change in dimension affects the shape of the prism as well as its volume and surface area. This is a quick way to collect data for a discussion of the relationship between surface area and volume. Users can rotate the figure and call for its frontal, side, or back view — very interesting with a triangular prism!

Three dimensional box applet: working with volume With this applet, students create boxes online in order to explore the relationship between volume and surface area. The screen first shows a rectangular piece of graph paper. Students "cut" four squares of a size determined by the student from the corners of the rectangle. The cut surface then folds to form a box whose dimensions, surface area, and volume are displayed onscreen. Since various sizes of graph paper can be selected, data can quickly be collected and the relationship between volume and surface area explored.

Cylinders and Scale Activity Using a film canister as a pattern, students create a paper cylinder. They measure its height, circumference, and surface area, then scale up by doubling and even tripling the linear dimensions. They can track the effect on these measurements, on the surface area, and finally on the amount of sand that fits into each module (volume). The lesson is carefully described and includes handouts.

Measuring the Circumference of the Earth Here is a real-world project that will engage your class in measuring the circumference of the Earth! You will find all the information you need to enable students to re-create the measurement as done by the Greek librarian Eratosthenes over 2,000 years ago. The procedure is based on measurements of shadows taken at high noon local time on a designated day in March; results from several schools are posted online and used to calculate the circumference. Included are detailed explanations and illustrations of the mathematics involved.

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