Section D: "Square and Unsquare" Sec D class 1.notebook. November 15, Oct 11 9:29 AM. Oct 11 8:31 AM. Oct 24 10:41 AM.
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1 Draw a square with the dimensions 3 cm by 3cm. Section D: "Square and Unsquare" How many cm by cm squares completely cover this square? How is squaring related to the area of the square you drew? Oct 8:8 AM Oct 8:3 AM Copy and complete this table filling in the area of the square with the given side lengths. length of side (in cm) area of square (in cm) Is this table a ratio table? Explain why or why not. Oct 8:35 AM Oct 4 0:4 AM Describe the curve of your graph. What does this tell you? Oct 9:7 AM Oct 9:9 AM
2 Draw a square with dimensions of cm by cm. Draw a square with dimensions of cm by cm. What's the area of this square? Using your drawings to explain why: Oct 9:3 AM Oct 9:3 AM Draw a square with dimensions of cm by cm. The number is called a mixed number. It is a whole number and a fraction combined. Use your drawing to calculate the area of the square. Draw a square with side lengths of cm. Using this drawing, calculate the area of the square. Oct 9:3 AM Oct 9:40 AM Use a drawing to calculate: 3 3 x = What does (4 ) mean? Calculate (4 ) Calculate (5 ) Use your results from these problems to add five more points to your graph. Oct 9:46 AM Oct 0:00 AM
3 Oct 6 :38 PM Oct 6 :44 PM Oct 6 :50 PM Oct 8 0:05 AM Oct 8 0:05 AM Oct 8 0: AM 3
4 Nicole uses the pattern in her answers to the previous problem to say, "There is a pattern to squaring these halves! Look, if I want to calculate 6 x 6, I just calculate 6 x 7 and then add. 4 Show how you can use your graph to see whether or not Nicole's idea makes sense. Oct 8 0:5 AM Oct 0:00 AM Use a drawing of a sqaure with side lengths 6 cm to show that Nicole is right. Oct 0:08 AM Oct 8 0:8 AM Oct 8 0:7 AM Nov 8:6 AM 4
5 Nov 8:4 AM Nov :8 AM Directions for Activity. What is the area of this shape?. Fold all four corners so that they meet in the center. What is the shape of this folded paper? What is its area? 3. Measure the length of each side of the shape with a ruler. 4. Fold all four of the new corners so that they meet in the middle. 5. Repeat this process until you have looked at a total of 5 shapes. Each time you fold the four corners, write down the name of the shape, the area of the shape, and the length of one of its sides. How does the area change each time you fold to make a new shape? Number of times folded Name of the shape Area of the shape Length of one side of shape Nov 8:49 AM Oct 0:7 AM In the activity, you measured a side length of a square with an area o 3 square centimeters (cm ). Mr. Ramsdell did the same activity and measured the length as 5.6 cm. When Ms. Bissell did the activity, she measured the length as 5.7 cm. Mr. Cryan, Mrs. Morell, and Mr. Jones are having a conversation about the side length of the square with an area of 3 cm. Mr. Cryan: "Mrs. Morell, I don't think 5.6 cm or 5.7 cm is precise enough. If we take the number out to more decimal places, we will get the exact length. Let's try 5.65 because it is exactly halfway between 5.6 and 5.6 Mrs. Morell: "I don't think that will help, Mr. Cryan. A number with decimals multiplied by itself will never give a whole number as an answer." Mr. Jones: "I figured it out on my calculator and got That has to be the exact answer!" Mr. Cryan: "Great job, Mr. Jones! Let's check it out." At the beginning of the conversation, Mr. Cryan and Mrs. Morell disagree. Who do you think is right? Explain. How do your measurements compare with Mr. Ramsdell's and Ms. Bissell's measurements? How did Mr. Jones find the number with his calculator? When Mrs. Robinson looked at Mr. Ramsdell's and Ms Bissell's answers, she commented that they were clos to the correct answer, but not exact. How could she tell? Mrs. Morell forget her calculator and writes on a piece of paper. She starts figuring whether or not Mr. Jones' number is the exact length of the side of the square. Mr. Jones uses his calculator to check the number he found. How could Mrs. Morell check the number without a calculator? Based on Mrs. Morell's computation, is Mr. Jones' number the exact length of the side of the square? Oct 0:9 AM How could Mr. Jones check the number with his calculator? Do the same with your calculator. Write down your keystrokes and results. Oct 0:34 AM 5
6 You will now use a calculator to find the side length of a square with an area of 5 cm. The length of this side (or the side length of any square) can be found by taking the square root of the area. What does the square root key do? Use Student Activity Sheet 5 to investigate the square root of 5. Write a paragraph describing your findings and what you think about the exact value of 5. Nov :00 PM Oct 0:45 AM Draw a square that has an area of 0cm. For which numbers listed would it be easy to find the square root? Drag them to the correct circle Consider the numbers that you put in the " " circle. Write down the square roots of these numbers. Explain the strategy you used. Consider the numbers that you put in the " " circle. Use your calculator to approximate the square roots of these numbers. Oct 0:50 AM Oct 0:5 AM Nov 4 0: AM Nov 4 0:9 AM 6
7 How can you tell whether or not you can give an exact number for a square root? Nov 4 0:0 AM Oct :04 AM How can you find what whole number is closest to 4? Explain this without using a calculator half of Drag the following numbers to where they belong on the number line. Oct :04 AM Oct :05 AM Nov 5 0: AM Nov 5 0:9 AM 7
8 Nov 5 0:3 AM Nov 8 8:39 AM The floor of Lizzy Mcguire's room is ½ m by 4½ m. His room will be redecorated, and the floor will be redone. In order to estimate the cost of the new floor covering, Lizzy estimates the area of the floor to be about 8¼ m. How did Lizzie arrive at her answer? Show that this answer cannot be right. On the graph paper, make a scale drawing of the floor of Lizzie's room. Use the scale drawing to calculate the area of the floor Nov 8 8:47 AM Oct :5 AM During the fall Superman earns extra money working at the apple orchard. In one hour he fills 3½ bushels of apples. How many bushels will he fill after working 6½ hours? A solution to this problem involves calculating 3½ x 6½. Although bushels of apples and hours are involved, you can use the area model to make a calculation. In this case, the area is 3½ x 6½, and the rectangle is 3½ by 6½. 6 ½ 3 ½ Oct :0 PM Nov 9 :3 AM 8
9 Nov 9 : PM Nov 9 :5 PM Nov 9 :4 PM Nov 9 :48 PM Use the area model to calculate: 3½ x 4½ Use the area model to calculate: 5½ x ½ ½ 3 4 ½ 5 ½ ½ Oct :8 PM Oct :37 PM 9
10 Nov 5 8:30 AM Nov 5 8:47 AM Nov 5 8:0 AM Nov 5 8:54 AM Online Fraction Multiplication with many more examples. Oct :50 PM Oct 0 0:57 AM 0
11 Attachments Math Parabola Graph.swf Math Parabola Graph.swf
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