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.

Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multistep problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease. They also solve problems about similar objects (including figures) by using scale factors that relate corresponding lengths of the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).

The problems here deal with ratio, in the concrete as well as the abstract. Middle school learners will make actual scale models with paper or clay and find percentages in real-world situations. But they will also work hands-on with online images that make visual the abstractions of ratio and percentage.

Neighborhood Math Questions and hands-on work guide your class in these excellent investigative activities. In Math at the Mall, students calculate the ratio used in making a scale map of the mall, then figure areas and percentage of mall space for each category of shop. Math in the Park or City involves setting up proportions to find heights of buildings. In Gearing Up, students compare the ratio of the turn of the wheel to the turn of the pedal in various bikes.

Capture-recapture: how many fish in the pond? A real application of the ideas of proportion! To estimate the number of fish in a pond, scientists tag a number of them and return them to the pond. The next day, they catch fish from the pond and count the number of tagged fish recaptured. From this, they can set up a proportion to make their estimation. Hints on getting started are given, if needed, and the solution explains the setup of the proportion.

Discovering the Value of Pi Students measure the diameter and circumference of several circles, using a handy applet, record their data, and reach conclusions about the ratio of circumference to diameter. A genuine guided exploration!

Statue of Liberty: is the Statue of Liberty's nose too long? Federal Educational Digital Resources

The full question is: "The arm of the Statue of Liberty is 42 feet. How long is her nose?" To answer the question, students first find the ratio of their own arm length to nose length and then apply their findings to the statue's proportions. The solution sets out different approaches to the problem, including the mathematics involved in determining proportion. Extension problems deal with shrinking a T-shirt and the length-to-width ratios of cereal boxes.What's My Ratio?

What's My Ratio? What would happen to a picture in the pocket of someone who is shrunk or enlarged? This question hooks students into a study of similar figures. As they compare the measurements of corresponding parts of pictures that have been either decreased or increased in size, they can investigate concepts of similarity, constant ratio, and proportionality.

Percentages (grades 9-12) In this interactive activity, students can enter any two of these three numbers: the whole, the part, and the percentage. The missing number is not only calculated but the relationship among the three is illustrated as a colored section of both a circle and a rectangle. The exercise is an excellent help to understanding the meaning of percentage.

Majority vote: what percentage does it take to win a vote? This problem challenges students' understanding of percentage. Two solutions are available, plus hints for getting started. Clicking on "Try these" leads to different but similar problems on percentage. Questions under "Did you know?" include Can you have a percentage over 100? and When can you add, subtract, multiply, or divide percentages? These questions can lead to interesting math conversations.

Perplexing percentages: so how much does it cost? A problem straight from the mall! Here is a rack of clothing, originally on sale for 30 percent off the original price, but now discounted by an additional 50 percent. Is the new price actually 80 percent of the original price? Two complete solutions are set out, and several more problems in the shopping scenario are offered under "Try these."

Math-Kitecture Math-Kitecture is about using architecture to do math (and vice versa). The author provides activities that engage students in doing real-life architecture while learning estimation, measuring skills, proportion, and ratios. In Floor Plan Your Classroom, for example, students make a rough sketch of the classroom, followed by a more exact scale drawing.

Scaling the pyramids Students compare the Great Pyramid to such modern structures as the Statue of Liberty and the Eiffel Tower. The site contains all the information needed, including a template, to construct a scale model of the Great Pyramid. In other activities, they must find the scale heights for the tallest building in their neighborhood and create models for two other pyramids, given only their dimensions. A beautifully illustrated site!

Figure and Ratio of Area A page shows two side-by-side grids, each with a blue rectangle inside. Students can change the height and width of these blue rectangles and then see how their ratios compare — not only of height and width but also, most important, of area. The exercise becomes most impressive visually when a tulip is placed inside the rectangles. As the rectangles' dimensions are changed, the tulips grow tall and widen or shrink and flatten. An excellent visual!

What's round, hard, and sold for 3 million dollars? This activity challenges students to determine which is worth more today: Babe Ruth's 1927 home-run record-breaking ball or Mark McGwire's 70th home-run record-breaking ball that sold in 1999 for three million dollars. The activity involves compound interest and rate of change.

Grid and Percent It Using a 10 x 10 grid, students first represent simple percents, then move to percents less than 1 and greater than 100. Problems involving percent increase and decrease are illustrated on grids, offering visuals that reinforce the instruction in this one-period lesson.

Scaling Away For this one-period lesson, students bring to class either a cylinder or a rectangular prism, and their knowledge of how to find surface area and volume. They apply a scale factor to these dimensions and investigate how the scaled-up model has changed from the original. Activity sheets and overheads are included, as well as a complete step-by-step procedure and questions for class discussion.

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.

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