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RATIOS Day 1 Introduce ratios A ratio is a comparison of two numbers by division. You can write a ratio three ways: o 3 to 4 o 3:4 o ¾ Give the following examples for students to write ratios the three different ways. o The United Stated Census Bureau predicts that in the year 2010 there will be about 64 males for every 100 females who are 75 years old or older. Write this information as a ratio in three ways. 64 to 100 64 : 100 64/100 o Why is writing the above ratio of males to females as 100 : 64 wrong? You need to write the ratio in the order the information is given. There are only 64 males, not 100, and males should be listed first. o The Untied States Census Bureau predicts by the year 2010 there will be about 73 million people under the age of 18 and 39 million people 65 and older. Use the information to write a ratio in three ways. 73 to 39 73 : 39 73/39 You can also use a decimal to express and compare ratios o To change a ratio to a decimal, divide the numerator by they denominator when the ratio is expressed as a fraction. o Examples: An official United States flag has a lengthto-width ratio of 19:10. The larges U.S. flag measures 505 ft by 255 ft. Is this an official U.S. flag? Original flag – 19/10 = 1.9 Largest flag – 505/255 1.98 The ratio 1.98 is not equal to the ratio 1.9, so the largest flag is not an official U.S. flag. Express each ratio as a decimal. Round to the nearest hundredth, if necessary. ¾ (0.75) 16 to 5 (3.2) 8:9 (0.89) 7/3 (2.33) Day 2 o o o o Assign the homework: Page 234-135 1-20 Ask the students for questions on the homework. Have volunteers work any questions the students had on the board. Correct the homework Assign the worksheet 6-1 Day 3-4 o Correct the worksheet going over any questions the students have. o Introduce the “Go for the Gold Activity” (note: this activity is taken directly from the TI-73 Explorations book.) Divide students into groups of 4. Assign each group the label of G1, G2, G3 etc. Pass out the worksheet, “Go for the Gold” and have each student make the necessary measurements on the picture and record their answers one number 1 on their worksheets. All measurements should be done vertically or horizontally. Skip to number 3 on the worksheet. Have the student measure each other while filling our number 3 on the worksheet. Pass out the graphing calculators Set the decimal place in the mode function to 3. Have the students use the calculator to calculate the required ratios on the worksheet. (Problems 2 and 3). Have the fill out the table worksheet with their individual ratios Have the student average their group’s ratio and record those numbers in the second column. To average the ratios together, have the students add up all the ratios in their group, then divide this answer by 4 (there should be four in each group). When these averages are found, have a member of the group record them on the teacher transparency under their group number. When all the groups have recorded their numbers, display the transparency and have the students fill in the table on their worksheet. Enter these values into the graphing calculator using the list function. Name the lists – RAT, G1, G2, G3, . . . , AVE o Name the lists first by pressing [2nd ] [INS] o Then press [2nd] [STAT] 2 [ENTER] to rename the list. o Type in the name using letters and numbers. When you click on [DONE] and press [ENTER] the name will be recorded and you will be on the first line to enter data. In the RAT column, enter in the text for the ratios. Example: A/G, E/D, etc. Enter the averages in the other columns. In the AVE column, enter the following formula. o AVE = (G1 + G2 + G3 . . . +GN)/N N = the number or groups. Go back to the home screen. [2nd] [QUIT] [CLEAR] Enter in the mean function [2nd] [STAT] [→] [→] [↓] [↓] (to select mean) [ENTER] Select the lists named G1, G2, etc by pressing [2nd] [STAT] Find the mean for each column and enter it into the table on the worksheet. Have the students answer question 4. When the students are done using the calculators have them reset the lists by going to the memory function and resetting all RAM. o Further extension: Have the students draw a strange face using the “Golden Ratio”. Draw the Greek face without any using the “Golden Ratio”. Day 5 – Introduction to spreadsheets. o Let students know that they may not always have access to a graphing calculator, but if they have a computer, they most likely have a spreadsheet program available for them to use. Introduce spreadsheets by projecting the software onto a TV using a linking cord. Give each student a paper copy of a spreadsheet. Give the students cell names and have them mark the cells as you tell them to. Example: Put a smiley face in cell C5 Go through each icon on the spreadsheet and explain what they do. Talk about formulas and how to put them in the spreadsheet program. Work a few formulas out with the students and have them write the formulas in the cells. o =AVERAGE(B3:G3) this will average the row of cells going from B3 to G3 Have the students fill out another copy of the spreadsheet putting in all their data from the golden ratio worksheet. o See the attached spreadsheet for a sample of what their spreadsheet should look like. Day 6 o Go to the computer lab and have the students enter in their numbers and formulas from their worksheet of the spreadsheet. o When students finish, have them change a few of the numbers to see what happens to the other numbers and to the “Golden Ratio”. o Evaluate the students’ abilities by using the attached rubric. Day 7 o Evaluate the students’ knowledge of ratios and spreadsheets by giving them a test. (See attachment.)

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RATIOS

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