Evaluations with Positive and Negative Numbers (page 631)

Transcription

1 LESSON Name 91 Evaluations with Positive and Negative Numbers (page 631) When evaluating expressions with negative numbers, use parentheses to help prevent making mistakes with signs. Example: Evaluate x xy y if x = 2 and y = 3 Practice Set (page 632) 1. Write parentheses for each variable. ( ) ( )( ) ( ) 2. Insert the numbers within the parentheses. ( 2) ( 2)( 3) ( 3) 3. Follow the order of operations. Multiply first. ( 2)( 3) = +6 Add algebraically from left to right. ( 2) (+6) ( 3) = 5 Evaluate each expression. Write parentheses as the first step. x + xy y m + n mn if x = 3 and y = 2 if m = 2 and n = 5 Teacher Note: Review Order of Operations on page 22 and charts of operations with signed numbers on page 26 in the Student Reference Guide. Check each solution by substituting it into the original equation. c. 4x + 25 = 9 solution: x = 4 d. 3x + 7 = 8 solution: x = 5 4( 4) + 25 = 9 3( 5) + 7 = = 9 = 8 9 = 9 = 8 Solve and check: e. 4x = 20 f. 2x = 16 4x 4 = x 2 = 16 2 x = x = g. How did you check your solutions for e and f? I checked my s by substituting the value into the original e. If the two sides were equal, then I was correct. Saxon Math Course 2 L Adaptations Lesson 91

2 Written Practice (page 632) , 5, 6, 7, 9, 12, 18, 28 9 mean + 12 median 3. mi hr? % = is of is of? =? in. 2 ft in. ft in. = 10. is of 3 4 were 4? were not Saxon Math Course 2 L Adaptations Lesson 91

3 Written Practice (continued) (page 633) 11. Evaluate x y xy if x = 3 and y = people hours = people-hours (3 people)(12 hours) = people-hours (4 people)( hours) = people-hours 13. A = 1 2 (b 1 + b 2 )h 14. a + (b + c) = (a + b) + c Property of ab = ba Property of c. a(b + c) = ab + ac Property c. d. Use work are 15. Label the figure. Then find the perimeter. 16. ( )( ) = C = πd area c. Use 3.14 for π. 19. The graph shows yd ft direct variation. The points are aligned. As one variable increases the other Use work are. 20. What is m X? What is m Y? c. What is m A? d. Are the two triangles similar? Why or why not? Answer:. The triangles have matching a. Use work are Saxon Math Course 2 L Adaptations Lesson 91

4 Written Practice (continued) (page 634) 21. 3x 3 x 1 = ( 3x)( 3)( x)( 1) = 22. Use work are 23. Segment AB is how many millimeters longer than segment BC? = y = y y = ( y) = 15 2 = y Use work are y = Use work are 26. 9x = 414 9x = 414 x = ft 1 s 60 s 1 min = Use work are 28. mixed-number answer 29. decimal answer = = = ( 3) ( 4)(+5) ( 2) = 3(+4) 5(+6) 7 = 2 3_ _ Saxon Math Course 2 L Adaptations Lesson 91

5 LESSON 92 Percent of Change (page 636) Name Use a percent box to find percent of change: 1. Use 100 as the original percent. 2. Put other known facts into the original, change, and new boxes. If the change is an increase, add to the original. If the change is a decrease, subtract from the original. Teacher Note: Refer students to Percent of Change on page 14 in the Student Reference Guide. 3. Use the percent box to write a proportion. Always use the row that is full and the row that answers the question. Example: The county s population increased 15 percent from 1980 to If the population in 1980 was 120,000, what was the population in 1990? Example: The price was reduced 30%. If the sale price was $24.50, what was the original price? original new = R original new = 120,000 N Practice Set (page 638) The regular price was $24.50, but the item was on sale for 30 percent off. What was the sale price? The number of students taking algebra increased 20 percent in one year. If 60 students are taking algebra this year, how many took algebra last year? c. Bikes were on sale for 20 percent off. Tomas bought one for $120. How much money did he save by buying the bike at the sale price instead of at the regular price? change new = c 120 Saxon Math Course 2 L Adaptations Lesson 92

6 Practice Set (continued) (page 638) d. The clothing store bought shirts for $15 each and marked up the price 80% to sell the shirts at retail. What was the retail price of each shirt? e. The problems above in which the change was an increase are and. Written Practice (page 639) 1. ( ) ( ) = min = hr miles hours? = dozen ft 2 min yd ft min hr = is of is of = =? 100? 100 Saxon Math Course 2 L Adaptations Lesson 92

7 Written Practice (continued) (page 640) 11. x = 5 and y = 3x % of 20 20% of 30 y = 13. area Draw a line of symmetry on figure above. 14. Use work are 15. ( )( ) = 16. Use work are 17. aces left: % = cards left is of? aces cards = Use work are Round to the nearest inch. Use 3.14 for π. Saxon Math Course 2 L Adaptations Lesson 92

8 Written Practice (continued) (page 640) 21. y = 2x + 1 c. Are x and y directly proportional?, the x, y pairs do not form proportions. Use work are x + y x y 1 = (3x)(2x) + (3x)(2) = c. (x 3 y) 2 = c x = 66 ( x) = 66 x = 26. w 0.15 = 4.9 w 0.15 = y = 600 8y = 600 Use work are w = y = Use work are Use work are Saxon Math Course 2 L Adaptations Lesson 92

9 Written Practice (continued) (page 640) 28. (2 3) 2 2(3 2 ) = ( ) = = 30. ( 8)( 6)( 5) ( 4)( 3)( 2) = 6 5( 4) 3( 2)( 1) = Saxon Math Course 2 L Adaptations Lesson 92

10

11 LESSON Name 93 Two-Step Equations and Inequalities (page 642) To balance two-step equations, isolate the variable using two steps. 1. First add or subtract on both sides of the equation to isolate the variable term. 2. Then multiply or divide on both sides to isolate the variable. Example: Solve this two-step equation. 2x + 5 = 35 2x = x = 30 2x 2 = 30 2 subtracted 5 from both sides simplified divided both sides by 2 x = 15 simplified To solve inequalities, isolate the variable in the same way as two-step equations. Example: Solve this inequality. 2x 5 = 1 2x added 5 2x 6 2x x 3 simplified divided by 2 simplified Graph the solution x 3. This graph indicates that all numbers greater than or equal to 3 satisfy the original inequality. Practice Set (page 645) Solve each equation. Show all steps. 8x 15 = y = 3.7 c. 3 4 m 1 3 = 1 2 x = y = m = d n = 14 e. 6p + 36 = 12 f. 38 = 4w 26 n = p = w = Solve and graph these inequalities. g. 2x x h. 2x 5 < 1 x < Saxon Math Course 2 L Adaptations Lesson 93

12 Written Practice (page 645) 1. round-trip = km km hr? 2 1_ , 4, 4, 5, 5, 5, 7, 8, 8, 9, 10, hr = min ( 3x 2 )(2xy)( x)(3y 2 ) = 7. blue total 8. 7 days 000 dahr 000 days 000 min 000 mhr = % 11. Evaluate: ab a b if a = 3 and b = Saxon Math Course 2 L Adaptations Lesson 93

13 Written Practice (continued) (page 646) Use work are ( )( ) = x + 2x x x 2 = 20. c. Are x and y directly proportional?, the x, y pairs do not form proportions. Use work are Saxon Math Course 2 L Adaptations Lesson 93

14 Written Practice (continued) (page 647) 21. is of? 22. 2x 5 > 1 2x 5 > 1 2x > x > Use work are 23. m x = m y = m z = Answer:. The triangles are the s shape. Their corresponding a are congruent. Use work are x + 2 = 9 3x + 2 = 9 x = w + 4 = w + 4 = 14 = x = Use work are w = Use work are y 1 = 7 0.2y 1 = 7 = y = Use work are m = 6 ( 2 3 m ) = 6 m = 29. 3( ) = 30. ( 9)(+6)( 5) ( 4) ( 1) = Use work are 3(4) + 2(3) 1 = Saxon Math Course 2 L Adaptations Lesson 93

15 LESSON 94 Probability of Dependent Name Events (page 648) When past events do not affect the probability of a series of events, the events are independent. The probability of independent events occurring in a certain order is the product of the probabilities of each event. Teacher Note: Review Probability, Chance, Odds on page 25 in the Student Reference Guide. Example: What is the probability of getting three heads in a row on three tosses of a coin? The probability of getting heads each time is 1_ 2. P(H, H, H) = 1_ 2 1_ 2 1_ 2 = 1_ 8 When past events do affect the probability of a series of events, the events are dependent. The probability of dependent events occurring in a certain order is the product of the first event and the recalculated probabilities of each subsequent event. Example: Two red marbles, three white marbles, and four blue marbles are in a bag. If one marble is drawn and not replaced, and a second marble is drawn, what is the probability that both marbles will be red? 1st Draw: P(Red) = 2_ 9 2nd Draw: P(Red) = 1_ 8 (because there is now 1 red in 8 total) Multiply the probabilities: = 1 36 Practice Set (page 650) 1 4 In a bag are two red marbles, three white marbles, and four blue marbles. If one marble is drawn from the bag and not replaced and then a second marble is drawn from the bag, what is the probability of drawing two blue marbles? 1st Draw: P(Blue) = 9 2nd Draw: P(Blue) = 8 Multiply: 9 8 = If two cards are drawn from a regular shuffled deck, what is the probability that both cards will be diamonds? 1st Draw: P(Diamond) = 52 = 4 2nd Draw: P(Diamond) = 51 = 17 Multiply: = Saxon Math Course 2 L Adaptations Lesson 94

16 Written Practice (page 650) Which box costs more per pound? lb $ 1? 4. faces edges lb $ 1? per ft 2 yd ft yd ft = 10. is of? 1 km km km mm mm = 11. See the Student Reference Guide c. 36 total written needs to write 12. y = 4x 3 and x = 2 c. y = Saxon Math Course 2 L Adaptations Lesson 94

17 Written Practice (continued) (page 651) 13. perimeter ft each side 14. $18,500 $18,500 $18,500 $18,500 c. $18,500 $18,500 area c % = is of? Use work are 17. ( )( ) = 18. cubes 19. area of square area of circle ) y = 3x c. Are x and y directly proportional?, the x, y pairs form proportions. Use work are Saxon Math Course 2 L Adaptations Lesson 94

18 Written Practice (continued) (page 652) 22. 2x 5 < x < p + 4 = 28 = = m = ( m) = m = p = Use work are Use work are 27. 6x 2 + 3x 2x 1 = 28. ( 8) ( 6) (4) 3 (5x)(3x) (5x)( 4) = 5( 4) 3( 2) 1 = 29. Evaluate b 2 4ac if a = 1, b = 2, and c = st Draw: P(White) = 9 2nd Draw: P(White) = 9 Multiply: = dependent or independent? 1st Draw: P(White) = 9 2nd Draw: P(White) = 8 Multiply: = dependent or independent? Use work are Saxon Math Course 2 L Adaptations Lesson 94

19 LESSON 95 Volume of a Right Name Solid (page 653) A right solid is a geometric solid whose sides are perpendicular to the base. If the base of a right solid is a polygon, the solid is called a prism. If the base of a right solid is a circle, the solid is called a right circular cylinder. The volume of a right solid equals the area of the base times the height. volume = area of base height Teacher Note: Review Geometric Formulas on page 29 in the Student Reference Guide. Practice Set (page 656) Find the volume of each right solid shown. Dimensions are in centimeters. The triangle is the base. c = d. volume of whole box minus the volume cut out e. The circle is the base. Leave π as π. f. What is the approximate volume of the shed? List the steps to find the volume. 1. Round measurements to whole numbers. 2. Divide the shed into sections, a rectangular prism and a t prism. 3. Find the v of each. 4. Add the volumes. Saxon Math Course 2 L Adaptations Lesson 95

20 Written Practice (page 656) 1. ( 4 mi $ 0.1 mi ) + $1.40 = 2. See Investigation total students lower quartile upper quartile median 3. A( 1, 1), B( 1, 4), C( 3, 2) Reflect across the y-axis. per A (, ), B (, ), C (, ) 4. 4 hr 20 min = minutes $ min 60? Use work are 5. The area of the unshaded trapezoid is. The area of the shaded triangle is. So the ratio of the shaded to unshaded area is ton = lb lb $? mm 2 cm mm cm mm = Saxon Math Course 2 L Adaptations Lesson 95

21 Written Practice (continued) (page 657) 10. is of 60? total play do not 11. rate time = distance 6 10 = = Evaluate m(m + n) if m = 2 and n = See the Student Reference Guide rectangular prism triangular prism Use 3.14 for π. The circle is the base. 16. tacos drinks salad P(White, Blue) = = P(Blue, White) = = 18. ( 2xy)( 2x)(x 2 y) = So the order of the draws affect the probability. 19. ( )( ) = Use work are 6x 4y + 3 6x 5y 8 = Saxon Math Course 2 L Adaptations Lesson 95

22 Written Practice (continued) (page 658) 20. y = 1 2 x + 1 c. Where does the graph intercept the y-axis? (, ) Use work are c. Use work are 23. average 24. 5w + 11 = 51 5w + 11 = 51 = w = Use work are x 2 = x x 2 = 14 ( 4 3 x ) = x = Use work are x = (1 + 2) 3 = ( ) = 30. ( 10) + ( 8) ( 6) ( 2)(+3) = 8 + 3( 2) 6 = Saxon Math Course 2 L Adaptations Lesson 95

23 LESSON Name 96 Estimating Angle Measures Distributive Property with Algebraic Terms (page 660) The ability to measure an angle with a protractor is an important skill. The ability to estimate the measure of an angle is also a valuable skill. To estimate angle measure, use a mental image of a degree scale a mental protractor. Build a mental image of a protractor from the face of a clock. A clock is a full circle, which measures 360. There are 12 hours on the clock face. From one hour mark to the next is 30. ( = 30 ) At 1 o clock, the angle formed by the clock hands measures 30. At 2 o clock, the angle formed by the clock hands measures 60. At 3 o clock, the angle formed by the clock hands measures 90. There are 60 minutes on the clock face. From one minute mark to the next is 6. ( = 6 ) The distributive property distributes multiplication over terms that are algebraically added. a(b + c) = ab + ac Examples: Simplify: 2(x 3) 2 x 2 3 = 2x 6 Simplify: 2(x + 3) 2 x + ( 2)(3) = 2x 6 Practice Set (page 663) By counting minute marks, find the measure of each angle shown on the clock face: A D O B m AOB = C m AOC = c. m AOD = d. x(x y) = e. 3(2x 1) = f. x(x 2) = g. 2(4 3x) = h. x 2 + 2x 3(x + 2) = i. x 2 2x 3(x 2) = In problems j m, estimate the measure of each angle as shown on page 664. Then use a protractor and measure each angle. By how many degrees did your estimate miss your measurement? j. BOC k. DOC l. FOE estimate actual measure difference m. FOB Saxon Math Course 2 L Adaptations Lesson 96

24 Written Practice (page 664) 1. $280 $ $ = 3. miles gallons? tanks gallons? 4. The number of vertices is. 5. The number of edges is. So the ratio is, which reduces to. Use work are is of is of =? =? 9. $12 1 hr mhr min $ = per 10. Corresponding Angles Corresponding Sides A and B and ACB and AB and BC and AC and m ABC = 53 m ECD = proportional Use work are Saxon Math Course 2 L Adaptations Lesson 96

25 Written Practice (continued) (page 665) = 48 1 = 48 2 = 48 Which has the smallest perimeter? 12. Evaluate: c(a + b) if a = 4, b = 3, and c = 2 4 = 48 6 = perimeter in. 14. each side area volume = area of base height 16. [ $ yd 2? ] + tax % = Use work are 19. ( )( ) = m Leave π as π. Saxon Math Course 2 L Adaptations Lesson 96

26 Written Practice (continued) (page 666) 21. each minute = = Interior and exterior angles are supplementary. c. 23. Translate 4 right and 4 down x < Q (8, 4), R (, ), S (, ), T (, ) x < x 7 = x 7 = 13 = x = 26. 3x + 8 = 10 3x + 8 = 10 = x = 27. 3(x 4) = x(x + y) = 28. ( 4) ( 8)( 3)( 2) 2 ( 3) = Use work are = 29. ( 4ab 2 )( 3b 2 c)(5a) = a 2 + ab ab b 2 = Use work are 30. She has 2 of each letter = Saxon Math Course 2 L Adaptations Lesson 96

27 LESSON Name 97 Similar Triangles Indirect Measure (page 668) Tick marks show equal angles. Similar triangles have: 3 pairs of corresponding sides 3 pairs of corresponding angles equal corresponding angles Teacher Notes: Introduce Hint #58, Proportion Setups. Review Similar and Congruent Triangles on page 28 in the Student Reference Guide. The activity in the Student Edition is optional. Corresponding Sides Corresponding Angles Equal Corresponding Angles AB and ZY A and Z m A = m Z BC and YX B and Y m B = m Y CA and XZ C and X m C = m X The lengths of corresponding sides of similar triangles are proportional. The ratios formed by corresponding sides are equal. Use this to find the length of an unknown side. Example: Find the length of side YZ = 3 equal ratios x 6 x = 10 3 cross-multiplied 6x 6 = 30 divided by known factor 6 x = 5 solved Proportions can be used to help find lengths of objects too large to actually measure. The lengths of the shadows cast by two objects are proportional to the heights of the two objects. Use this to find the indirect measure of an unknown length or height. Example: About how tall is the telephone pole? cm ft = H p H p = H p = 2400 H p = H p = 60 ft Saxon Math Course 2 L Adaptations Lesson 97

28 Practice Set (page 673) Corresponding Angles Corresponding Sides W and YW and Y and WX and X and XY and Estimate the length of x. c. Find the length of x. 6 9 = x 12 x = d. Estimate the length of y. e. Find the length of y. 6 9 = y = y f. A tree casts a shadow 18 ft long while a 6 ft pole casts a shadow 9 ft long. How tall is the tree? x 18 = 9 g. As Donald stood next to a pole supporting a basketball hoop, he noticed that the shadow of the pole was about twice the length of his own shadow. If Donald is 5 ft 6 in. tall, what is a reasonable estimate of the height of the pole? 5 ft 6 in. = 5 1_ 2 ft The pole s shadow is twice his shadow. Written Practice (page 673) 1. $8.95 $8.95 $8.95 $8.95 $10.00 $ ,000,000,000,000 2,000,000,000, , 2, 3, 3, 3, 4, 6, 7, 7 median Which has more protein? mode white bread + pasta = g 4. range bran muffin + bagel = g Use work are Saxon Math Course 2 L Adaptations Lesson 97

29 Written Practice (continued) (page 674) t units to the r Use work are of in. 8. Leeks Radishes % = is of? 10. is of =? 11. decimal answer 40% = is of? average Use work are 15. rate time = distance 3 15 = 5 = 16. ( )( ) = mm Saxon Math Course 2 L Adaptations Lesson 97

30 Written Practice (continued) (page 674) volume = area of base height c. x = Change all dimensions into feet. x 72 = 23. (38,470)(607) 79 (38,470)(607) m = y 2 = 12 m = y = 26. 3x y x + y 2 = 27. 3(x y) = 29. ( 2) (+3) + ( 4)( 3) ( 2) + (+3) (+4) x(y 3) = = ( ) = = 5 4 = Saxon Math Course 2 L Adaptations Lesson 97

31 LESSON Name 98 Scale Scale Factor (page 677) Scale is stated as a ratio. Scale models are examples of similar shapes. Example: A model airplane is built on a scale of 1:24. If the wingspan of the model is 18 inches, the wingspan of the actual airplane is how many feet? Model 1 Object = 18 W W = W = 432 in. Teacher Notes: Introduce Hint #59, Scale Factor. Refer students to Scale Factor on page 31 in the Student Reference Guide. Review Similar and Congruent Triangles on page 28 in the Student Reference Guide. Then change to feet. 432 in. 1 ft = 36 ft 12 in. Scale factor is the number of times larger (or smaller) the terms of one ratio are when compared to the other ratio. In this book scale factor will be expressed in decimal form. Example: These two triangles are similar. Calculate the scale factor from the smaller triangle to the larger triangle A 20 B To calculate the scale factor: Write an equation using f to stand for the scale factor. (side of figure starting from) f = (side of figure going to) 20 f = 25 f = f = 1.25 A shortcut to calculating the scale factor is to divide corresponding sides. Place side of figure going to in numerator. Place side of figure starting from in denominator = 1.25 The relationship between the areas of two similar figures is the scale factor squared. Example: The area of B is how many times larger than the area of A? The area of B is times larger than the area of A. The relationship between the volumes of two similar figures is the scale factor cubed. Saxon Math Course 2 L Adaptations Lesson 98

32 Practice Set (page 682) The blueprints were drawn to a scale of 1:24. If a length of a wall on the blueprint was 6 in., what was the length in feet of the wall in the house? Bret is carving a model ship from balsa wood using a scale of 1:36. If the ship is 54 feet long, the model ship should be how many inches long? Model 1 Object 24 6 in. Change to feet. Change to inches. c. 5 7 = 15 w w = d. x 3 = x = e. These two rectangles are similar. Calculate the scale factor from the smaller rectangle to the larger rectangle. 25 mm f. The area of the larger rectangle below is how many times the area of the smaller rectangle? Square the scale factor. 10 mm 10 mm 4 mm g. The scale of the car model is 1:36. This means 1 inch on the model corresponds to 36 inches (3 feet) on the actual car. Draw a line on the graph to show this relationship. The horizontal axis represents the car in feet. The vertical axis represents the model in inches. h. The statue of the standing World War II general was 1 1_ times life-size. 2 Circle the most reasonable estimate for the height of the statue? A person is about 6 ft. A 4 ft B 6 ft C 9 ft D 15 ft Written Practice (page 683) 1. There are cards and As. After picking one A, there are cards and As. So the probability of another A is. Use work are Saxon Math Course 2 L Adaptations Lesson 98

33 Written Practice (continued) (page 683) 5. (3x)(x) (x)(2x) = ,010 43,764 mi gal mi hr 12? 1? 8. is of? 9. ( 3, 2), (3, 2), ( 3, 2) 4th vertex 90 clockwise rotation (, ) (2, 3), (, ), (, ), (, ) Use work are 10. { 3, 2, 1, 0, 1, 2} 11. Find a 2 if a = 3. counting numbers integers = is of =? Saxon Math Course 2 L Adaptations Lesson 98

34 Written Practice (continued) (page 684) % = is of? 15. Segment BC is how much longer than segment AB? inch AC in centimeters in cm 1 in. = 16. x Fraction Decimal Percent 1.4% Use work are Use work are 18. Complete the table and graph the function. (, ) Are x and y directly proportional? go up to the right., the graph does not Use work are Estimate the angle measure. Then extend the sides and measure angle ABC with a 2 ft protractor. Saxon Math Course 2 L Adaptations Lesson 98

35 Written Practice (continued) (page 684) f = in. 30 in. 50 in. x = f = in. x 30 = 16 y = A = bh 2 y = area = 23. ( )( ) = m + 8 = m + 8 = 20 ( 3 5 m ) = m = Use work are x 2.7 = = 0.3x 2.7 = 9 0.3x = x = Use work are gal 1 qt 1 pt 1 qt 1 pt 28. (0.25) ( ) = ( ) 3.5 = 30. ( 2)(3) (3)( 4) ( 2)( 3) (4) = Saxon Math Course 2 L Adaptations Lesson 98

36

37 LESSON 99 Pythagorean Theorem (page 686) Name The longest side of a right triangle is called the hypotenuse. The other two sides are called legs. leg hypotenuse Teacher Note: Refer students to Pythagorean Theorem on page 29 in the Student Reference Guide. leg Every right triangle has a property that makes it special. This property is called the Pythagorean Theorem, which states: The area of the square drawn on the hypotenuse of a right triangle equals the sum of the areas of the squares drawn on the legs a 2 + b 2 = c The Pythagorean Theorem is commonly expressed algebraically as a 2 + b 2 = c 2. (a and b represent the two legs of a right triangle. c represents the hypotenuse.) Use the Pythagorean Theorem to find the missing length of a side of a right triangle. Example: Use the Pythagorean Theorem to find a 2 + b 2 = c 2 a = 5 2 a = 25 a 2 = 9 a = 3 Practice Set (page 689) Draw squares on the sides of the triangles as you work problems a c. Use the Pythagorean Theorem to find a = 26 2 a 2 = a 2 = 26 a = 24 Saxon Math Course 2 L Adaptations Lesson 99

38 Practice Set (continued) (page 689) Use the Pythagorean Theorem to find = b 2 b 2 = 12 b = 9 c. Find the perimeter of this triangle. Dimensions are in feet = c c 2 = c = perimeter = d. Which triangle below is a right triangle? A B 9 15 C = = = 20 2 = 15 2 = 10 2 = Triangle is a right triangle, because + =. Written Practice (page 690) 1. $ J 31 F 29 M A M J J A S O N D 4. 2 lb = oz oz $ oz $ 1? 1? 5. per c. d of oz 8 Saxon Math Course 2 L Adaptations Lesson 99

39 Written Practice (continued) (page 690) 8. 10% = 9. See the Student Reference Guide. is of is of? =? c (6, 3) Then change to feet. in. units 2 ft (ax 2 )( 2ax)( a 2 ) = 1 2 π π π = Use work are 16. ( )( ) 17. c 2 b 2 if c = 15 and b = 12 Saxon Math Course 2 L Adaptations Lesson 99

40 Written Practice (continued) (page 691) c 2 = Find the area of the base and multiply it by the of the right solid Use 3.14 for π = x 12 8 c. (scale factor) x = c. c. 22. Estimate: (41,392)(395) n = 2 = x 1 = 49 = = = n = x = Use work are Use work are = m = = m = 28. Convert 0.75 to a fraction. ( ) (0.75)(40) (6)( 3) = 30. 3(x 2) = ( 12) ( 6) + (3) Saxon Math Course 2 L Adaptations Lesson 99

41 LESSON Name 100 Estimating Square Roots Irrational Numbers (page 693) These counting numbers are perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, The square root of a number that is between two perfect squares can be estimated. Example: Show the location of 29 on a number line. Think of each number on the number line as the square root of a perfect square. 4 = 16 5 = 25 6 = 36 7 = 49 Since 29 is between 25 and 36, we graph 29 between 5 and 6. We decide that 29 is a little closer to 25, so we place 29 a little closer to 5. Example: Between which two consecutive whole numbers is 200? Use the times table in the Student Reference Guide. 196 = =? 225 = is between the consecutive whole numbers 14 and 15. Irrational numbers are numbers that cannot be expressed exactly as decimals or fractions. Even when using the 0 key on a calculator the answer will not be exact. Examples of irrational numbers include π, 2, and the square roots of counting numbers that are not perfect squares. Rational numbers (Lesson 86) are numbers that can be expressed exactly as decimals or fractions. The irrational numbers plus the rational numbers make up the set of real numbers. Real Numbers Rational Numbers Example: On the number line show the approximate location of the points representing the following real numbers. Then describe each number as rational or irrational. π Irrational Numbers π 3.14 Position π between 3 and 4, closer to 3. 2 is between 1 (= 1) and 4 (= 2). Position 2 between 1 and 2, closer to = 2 1 Position 2. 3 between 2 and 3, closer to is exactly halfway between 0 and 1. 2 The rational numbers are 2. 3 and 1. (Repeating decimal numbers are rational.) 2 The irrational numbers are π and 2. (Neither π nor 2 can be expressed exactly as a fraction or a decimal.) Saxon Math Course 2 L Adaptations Lesson 100

42 Practice Set (continued) (page 696) Each square root below is between which two consecutive whole numbers? 7 and 70 and c. 700 and d. Find x = x 2 e. Find y. y = 2 2 x 2 = y 2 = x = y = f. On the number line show the approximate location of the points representing these real numbers π 1 3 Which are irrational?, Written Practice (page 696) 1. ( ) + (2 ) 2. $30.00 $30.00 The two spins are i events. M the probabilities. 3. average of first 10 counting numbers 4. mi hr? Saxon Math Course 2 L Adaptations Lesson 100

43 Written Practice (continued) (page 696) 8. is of? 1 2 of = 9. 6% = is of is of? =? 10. $40 $40 $ x(x + 3) = 12. (0, 0), ( 2, 4), (2, 4) ft Convert to inches. 48f = 2 c. 7 in. c. (, ) 14. 2f = 6 (scale factor) c. (scale factor) 3 c. sample space: {,, AC,,,, CA,, } Use work are 17. ( )( ) = Use work are Saxon Math Course 2 L Adaptations Lesson 100

44 Written Practice (continued) (page 698) a = and Use 22 for π. 7 and 21. volume = area of base height 22. volume = area of base height Use 3.14 for π. 23. m a = x + 80 = w = m b = m c = x = w = = ( ) = = = (2)( 3) ( 3) + ( 2) ( 4) = 30. On the number line show the approximate locations of 5, 0.5, and 1.5. Use work are Saxon Math Course 2 L Adaptations Lesson 100