The two examples that follow model the concept that squares (or rectangles closer to square shapes) have the greatest area for a fixed perimeter. With a fixed area of 18 units squared, the perimeter was as much as 38 units or as small as 18 units. With a fixed area of 36 units squared, the perimeter was as much as 74 units or as small as 24 units. Long and thin areas = greater perimeter. Square areas (or as close as we can get) = smaller perimeter.
These are student samples of some of the things we are learning about area (Length x Width, or the number of tiles) and perimeter (2Length + 2Width). We have learned (and their examples will show) learned that you can have an unchanging perimeter and a changing area OR you can have an unchanging area and a changing perimeter. The first four examples show an unchanging area of 6 square units and changing perimeters. The following four examples show a fixed area of 24 square units and changing perimeters.
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.
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. |
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
September 2015
Categories |