We are starting a new unit called "Covering and Surrounding." I gave a very short pre-unit assessment yesterday and discovered some who are unfamiliar with concepts and terminology that are foundations of this unit. They must know how to find the area of rectangles, which is Length x Width. The ability to find perimeter is also needed for success in this unit. This is Length + Length + Width + Width or (2 x length) + (2 x width). The most alarming result of the pre-assessment: many are still struggling with the factors of a number. We will be finding links between area (which is the product of length and width OR the factors that create the area of a rectangle) and the length of the sides. The sides are the factors of the number that is the area. I will be adding refresher problems to each day's bellwork. Being fluent with the factors of a number (or what numbers can we divide a given number by to find whole number quotients), will allow the flexibility of thinking needed in the unit. I will attempt to post examples of student thinking this week. You can check their classwork notes and thinking, as well as their homework notes and thinking.
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All division problems are made of 3 elements, the dividend, the divisor, and the quotient (Sample A). Each division problem asks the same basic question: how many groups of the divisor are in the dividend? Fraction division is no different.
Fraction divided by a fraction is shown in Sample B and C. Sample D is a whole number divided by a fraction. Sample E is a mixed number divided by a fraction. Finally Sample F shows a fraction divided by a whole number. I have shown samples of all these so you can understand how we modeled the concepts in math. The final picture is the traditional method used for fraction division: Copy, Change, Flip. The models show HOW it works. Copy, Change, Flip is the method to work the problems mathematically. Copy, Change, Flip-has to be done step by step. Skipping steps leads to careless mistakes. Our evaluation this week will concentrate on fractions, decimals, and percents. The class has practiced finding equivalent fractions (and ratios). Much of this evaluation will require students to be able to find percents and decimals if given a fraction, decimals and fractions if given a percent, or fractions and percents if given a decimal. They will also be required to put various numbers in order when the numbers are given as a combination of fractions, decimals, and percents. I have noticed the students are already in the habit of changing fractions into decimals so that they can compare values more easily.
Equivalent fractions and ratios are found in much the same way, by multiplying or dividing each part of the ratio by the same number (Ex: the ratio 8:10 can be divided by 2 to find an equivalent ratio of 4:5 OR it could be multiplied by 2 to find an equivalent ratio of 16:20). Now, to find equivalents between fractions, decimals and percents (which all give the same basic numerical information, as we have discovered). A fraction is really a division problem 2/5, or 2 divided by 5. 2 divided by 5 is 0.4, a decimal! The decimal 0.4 = 0.40, which is 40/100. Today we made the connection that 0.40 = 40%, it's just a matter of moving the decimal point two places to the right. So 2/5 = 0.4 = 40%. If I don't have time to upload specific 'how to' instructions, the I have indicated which lessons (and they are pink almost all the time) and what homework (usually white sheets) will help them study.
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September 2015
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