A formula is a rule expressed in symbols. If we wish to express the rule above in symbols, we let the symbol I stand for the number of units in the length, the symbol w stand for the number of units in the width, and the symbol A stand for the number of square units in the area. This gives us the formula A = lw. The main thing to remember in formulas is that symbols placed side by side are to be multiplied, not added. In this formula lw means I times w. The length of a rectangle is usually called its base, and its width is called its altitude. Altitude means the same as height and is usually represented by the letter h. The base is represented by the letter b. So the formula A lw may also be written = Illustrative Example. Find the area of a rectangle 8 inches long and 5 inches wide. Note that we substitute 8 for 1 and 5 for w, just as one player is substituted for another in football. The Formula Brings Us to Algebra. In our formulas we saw that A was a symbol for all areas. The letter l is a symbol for any length. This use of letters brings us to another branch of the New Mathematics which uses letters as well as figures to represent numbers. This branch of mathematics we call Algebra. Algebra uses the processes of arithmetic besides some special ones of its own. It uses the same signs: +, -, X, . The most important thing to remember in algebra, as in the case of formulas, is that two letters or letters and figures, when written side by side, are to be multiplied. Thus bh means b times h; 2l means 2 times l. Squares in Algebra. The use of squares is very common in algebra. There is a simple formula for getting the area of a square. If s represents the number of units in the side of the square, then A sxs. We do not usually write s times s as ss but write it s2 instead. This gives us the formula = A = s2. This is read " A equals s square.' 8 A = 82 8 Here the 2 is called an exponent. It is a small figure written above and at the right of a letter or number to show how many times the letter or number is to be used as a factor. Here it means that s is multiplied by s, or 2 s's are multiplied together. How much is 22? 32? 52? 62? 82? 102? Illustrative Example. Find the area of a square whose side is 15 inches. Using Algebra in Perimeter Problems. If the sides of a figure are straight-line seg ments, we may find the perim- 8 ft. Rectangle 4 ft. 8 ft. Figure 1 6 ft. Figure 3 write 4 Xs as in the line above we wrote 4 X 6. I. R. B. Test [1]. Prepare a chart for Chapter VI (three tests). Enter First s. ft. Trial scores. Use examples 1-10 for s. ft. Squares. ft. this test. Let the Steering Committee determine the standard time. s. ft. Figure 4 DO-IT-IN-YOUR-HEAD PLUS PENCIL-PAPER PRACTICE Divide the class into three teams. Let the first and second teams compete in an oral contest, members of each team alternating in giving the answers to the following 16 examples. In case of a Let the third team check the answers. wrong answer let the member of the third team who first gives the right answer replace the pupil of either the first or second team who fails. Score one for each correct answer given by the first and second teams; score two to the credit of the third team for each member replacing a member of either the first or second team. In case an answer cannot be given orally let the solution be given on the blackboard. Your teacher and Steering Committee will make additional examples, if necessary, to complete the contest. Area Exercise Find the areas of the following rectangles: 1. Length 7 feet, width 4 feet. 2. Length 6 inches, width 4 inches. 3. Length 18 rods, width 61 rods. 4. Length 8 feet, width 5g feet. Find the area of the following squares : 5. Length of one side, 12 inches. 6. One side is 5 yards. 7. One side is 7 inches. 8. What are the perimeters of each of the squares in examples 5, 6, and 7? 9. Find the number of square feet in a rectangular garden 20 feet wide and 35 feet long. 10. How long must a fence be to inclose the garden in example 9? 11. Give the table of square measure in the Appendix of the book. 12. Measure the top of your desk. How many square inches does it contain? How many square feet? What is its perimeter? 13. A small farm was in the shape of a rectangle. It was 45 rods long and 22 rods wide. How many acres did it contain? 14. How long a fence will be required to inclose it? What part of a mile is this? 15. The ground floor of a house had the shape and dimensions shown in the diagram. How many square feet of floor space were there? Hint: Draw lines to 30 divide the floor into rectangles and a square. 20' 6'10' 25 5 16. A football field is a rectangle 300 feet long and 160 feet wide. How much lime will it take to mark its perimeter, using a pound of lime for each four feet? Draw a plan of the field by letting 1 inch represent 60 feet. Then draw parallel lines to the end lines to represent the lines which are 5 yards apart and generally spoken of as the 5-yard lines. The Habit of Systematic Review 1. The number of 8th grade graduates in the state of Illinois in 1913 was 41,361. The number of graduates in 1923 was 70,698. Find the increase and the ratio of the graduates in 1913 to those in 1923. 2. The average number of persons employed in agriculture for every 1000 acres of land is |