Reading and Writing Decimal Numbers (page 221)

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1 LESSON Name 31 Reading and Writing Decimal Numbers (page 221) To read the decimal number : We say and for the decimal point. One hundred twenty-three and one hundred twenty-three thousandths We say thousandths to conclude naming the number. Decimal numbers and fractions are two ways to name parts of a whole. They are read the same way. 0.3 = 3 Both are read three tenths = 21 Both are read twenty-one hundredths. 100 Practice Set (page 224) Teacher Notes: Introduce Hint #46, Decimal Place Value (Digit Lines), Hint #47, Writing Numbers, and Hint #48, Tenths and Hundredths. Review Spelling Numbers on page 9 and Place Value on page 11 in the Student Reference Guide. Color tiles, available in the Adaptations Manipulative Kit, can be used to demonstrate tenths and hundredths. Write three hundredths as a fraction. Then write three hundredths as a decimal. Name the shaded part of this circle both as a fraction and as a decimal., ,. c. In the number , which digit is in the thousandths place? d. The number has how many decimal places? Use words: e and f and Use digits: g. one hundred two and three tenths. h. one hundred twenty-five ten-thousandths. i. three hundred and seventy-five thousandths. j. What little word tells you that a number will have both whole-number and fraction parts? a Saxon Math Course 2 L Adaptations Lesson 31

2 Written Practice (page 225) 1. $32.54 $26.47 $89.89 $ average months $ ? Jamestown Columbus 5. Divide the perimeter of the s by to find the length of a side. Then m the length of a side by to find the p of the 6. 80% = used left h. Use work are ,462 nearest hundred-thousand nearest thousand 8. 49,623 20, fraction decimal c. percent 10. hundredths place c. Saxon Math Course 2 L Adaptations Lesson 31

3 Written Practice (continued) (page 226) (3, 3), (3, 3), ( 3, 3) and ( 3, 3) = = c. 0 6 = 4 24 c. units c. units Follow the instructions in the textbook to complete the drawing = Take half of the exponent of each prime factor. Multiply. 16. not red total = ( 3 4 ) x = ( ) x = x = x = Given A Property C c. I x = = 1 3 Use work are Saxon Math Course 2 L Adaptations Lesson 31

4 Written Practice (continued) (page 227) 18. 9n = b = = = 0 0 n = b = ( ) = = = = = = = = = = a = 3 b = 4 b a + a b = 29. k = 10 n the 6th term in words 10, 100, 1000, 30. a full circle = 360 1_ 2 1_ 4 c. 1_ 8 of a circle of a circle of a circle c. Saxon Math Course 2 L Adaptations Lesson 31

5 LESSON 32 Metric System (page 228) Name The metric system is a system of measurement used throughout most of the world. Use decimal numbers with the metric system. Units of length in the metric system are the meter, kilometer, centimeter, and millimeter. Teacher Notes: Introduce Hint #49, Reading Metric Rulers, and Hint #50, Gram/ Kilogram Manipulatives. Review Equivalence Table for Units and Formula for Celsius to Fahrenheit Conversion on pages 1 and 2 in the Student Reference Guide. Gram and kilogram weights can be found in the Adaptations Manipulative Kit. Use the chart below to convert metric length to U.S. Customary length. Temperature in the metric system is measured in degrees Celsius ( C). Units of liquid capacity in the metric system are liters and milliliters. Units of weight in the metric system are grams and kilograms. Practice Set (page 231) The closet door is about 2 meters tall. A 1-gallon plastic jug can hold about how many How many centimeters is 2 meters? liters of milk? One quart is a little more than one liter. mc cm 1 2 The metric system is based on powers of 10. A prefix tells what power of 10 the base unit is multiplied by. For instance, the prefix kilo tells to multiply a unit by So 1 kilometer is 1000 meters. Examples of Metric Prefixes Prefix Unit Relationship kilohectodeka- deci- centi- milli- kilometer (km) hectometer (hm) dekameter (dkm) meter (m) decimeter (dm) centimeter (cm) millimeter (mm) 1000 meters 100 meters 10 meters 0.1 meter 0.01 meter meter Check the label on a gallon bottle to be exact. Saxon Math Course 2 L Adaptations Lesson 32

6 Practice Set (continued) (page 231) c. A metric ton is 1000 kilograms, so a metric ton is about how many pounds? A kg mass weighs about 2.2 pounds. kg lb e. After running 800 meters of a 3-kilometer race, Michelle still had how many meters to run? km m 1 3? 800 d. A temperature increase of 10 on the Celsius scale is equivalent to an increase of how many degrees on the Fahrenheit scale? (See Example 4 in textbook.) C F f. A 30-cm ruler broke into two pieces. One piece was 120 mm long. How long was the other piece? cm mm 1 30? 120 g. About how many inches long was the ruler in exercise f. before it broke? Round off. in. cm 1? 30 Written Practice (page 232) 1. average hr min 1? = 4. sides cm 4 1? Now find the perimeter of the pentagon. D the perimeter of the square by to find 5. 3,197,270 nearest million nearest hundred-thousand the length of a side. Then m the length of a side by to find the perimeter of the p. 7. about love and chivalry not about love and chivalry 8. not shaded fraction decimal c. percent. c. Saxon Math Course 2 L Adaptations Lesson 32

7 Written Practice (continued) (page 232) in words and 10. seven and forty hundredths meters 11. $ Use work are in expanded notation 13. liters $ 35 1 ( ) + ( ) c. ) 2500 = Take half of the exponent of each prime factor. Multiply. c. 14. Complete the triangle. Measure the angles to check that they measure 45. Use work are 15. area of smaller square area of larger square c. total area c. 16. perimeter = 4w s = = 3 8 = w = = 3 4 = s = = Saxon Math Course 2 L Adaptations Lesson 32

8 Written Practice (continued) (page 233) = 3 20 = = = = = ( ) = = 27. estimated and exact answers = 28. estimated and exact answers 29. ( 5, 3), ( 5, 2), and (2, 2) = = 30. chord but not a diameter central right angle c. inscribed angle coordinates of the fourth vertex area (, ) c. Saxon Math Course 2 L Adaptations Lesson 32

9 LESSON Name 33 Comparing Decimals Rounding Decimals (page 235) To compare decimal numbers, write the numbers vertically with the decimal points aligned. Then compare each place value. Examples: > = Terminal zeros to the right of the decimal point have no value: 1.3 = 1.30 = = To round a decimal number: 1. Underline the place value you are rounding to. 2. Circle the digit to the right. 3. If the circled digit is 5 or more, add 1 to the underlined number. If the circled digit is less than 5, do not change the underlined number. 4. Everything after the underline becomes zero. 5. Remove all terminal zeros after the decimal point. Examples: Practice Set (page 238) Teacher Note: Review Hint #12, Comparing Numbers, and Hint #42, Estimating or Rounding c d. Round to the nearest ten-thousandth. e. Round to the nearest hundred.. f. Round to the nearest whole number. g. Simplify by removing extraneous zeros.. h. Estimate the sum of 8.65, 21.7, and by rounding each decimal number to the nearest whole number before adding Saxon Math Course 2 L Adaptations Lesson 33

10 Written Practice (page 239) 1. We m 5 times 12 inches to find the number of inches in 5 f. Then we a 8 inches to find the t number of inches in 5 feet, 8 inches. (5 12) + 8 = 62 inches Use work are 2. average , , Complete the function table. Use work are 5. perimeter of hexagon cm each side of hexagon cm perimeter of octagon Divide the p of the h by 6. to find the length of a side. Multiply the length of a side by the o. to find the perimeter of Use work are c nearest hundredth Saxon Math Course 2 L Adaptations Lesson 33

11 Written Practice (continued) (page 239) words: words: and 10. one hundred twenty-five thousandths one hundred and twentyfive thousandths. Use work are centimeters millimeters 13. Draw ray OD so that angle COD measures whole number but not a counting number Use work are n = m = 4 18 = a = = = = m = a = Saxon Math Course 2 L Adaptations Lesson 33

12 Written Practice (continued) (page 240) = = = = x x x x x x = x x x x = x x x x = = = ( ) 26. There are 4 aces in a deck. not aces/ cards in deck = = 54 + y y = I Property of a The quotient will be than 1 because a larger number is d by a s number. Use work are Use work are 29. The mixed numbers are g than and 5, so the sum is g than. The numbers are l than 9 and, so the s is 30. Complete the triangle. Label the 30 angle and the 60 angle. less than 15. Use work are Use work are Saxon Math Course 2 L Adaptations Lesson 33

13 LESSON Name 34 Decimal Numbers on the Number Line (page 241) If each centimeter on a centimeter ruler is divided into 10 equal parts, then each part is 0.1-centimeter (1-millimeter) long. Find the length of this segment in millimeters. 23 mm in centimeters. 2.3 cm If a number line is divided so there are 100 equal parts between whole numbers, then each mark is one hundredth (0.01) from the next mark. Find the number on the number line indicated by each arrow. Practice Set (page 243) Find the length of this segment in Find the length of the segment to the nearest centimeters.. millimeter. c. The scale above can be precise within what fraction of a millimeter? d. Seventy-five centimeters is how many e. Carmen s wardrobe closet is 1.57 meters tall. meters? 1 cm = 0.01 m How many centimeters tall is it? 1 m = 100 cm. f. What point on a number g. What decimal number names the point marked by A on this line is halfway between number line? 2.6 and 2.7?.. h. Estimate the length of this segment in centimeters. Then i use a centimeter ruler to measure its length j. 2.5 cm 25 mm 1 cm = 10 mm Saxon Math Course 2 L Adaptations Lesson 34

14 Written Practice (page 244) 1. average parts per cubic meter $12.55 $13.95 parts per Wright brothers flight years later landed on the moon 6. 40% = $12 perimeter of square each side of square 7. First round the length to and 8. nearest thousandth the width to. Then m the l and the w. Use work are words: words: and 10. one hundred seventy-five millionths three thousand, thirty and three hundredths Use work are.. Saxon Math Course 2 L Adaptations Lesson 34

15 Written Practice (continued) (page 245) centimeters millimeters. 13. What decimal number? halfway between 7 and 8. halfway between 0.7 and (, ) c = 12y = 74 + c = x 2 3 = x = x y = c = = x = x = x = x Saxon Math Course 2 L Adaptations Lesson 34

16 Written Practice (continued) (page 245) x x x x = x x x x = = x = x ( ) = mm = 0.1 cm 1 cm = 10 mm 24 mm = cm 3.6 cm = mm Now find the difference 27. equivalent to Add the exponents. A 2 5 B 2 6 C 12 D 24 in cm in mm 28. least to greatest x = 5 y = 10 y x x = 30. red total c. blue total x x x x,, = white total d. green total x x x x = = Use work are Saxon Math Course 2 L Adaptations Lesson 34

17 LESSON Name 35 Adding, Subtracting, Multiplying, and Dividing Decimal Numbers (page 247) The chart below summarizes the rules for adding, subtracting, multiplying and dividing decimal numbers. Notice that there are two kinds of decimal division problems: dividing by a whole number and dividing by a decimal number. For the next few lessons, we will divide only by a whole number. Following are examples using the Decimals Chart: When multiplying or dividing a decimal by 10, 100, or 1000, there is a shortcut. Shift the decimal point one place for each zero. When multiplying, shift the decimal to the right. When dividing, shift the decimal to the left. Examples: shift shift = = Practice Set (page 251) Teacher Notes: Introduce Hint #51, Decimal Arithmetic Reminders Chart. Refer students to Multiplication and Division of Decimal Numbers by 10, 100, 1000 and Decimal Arithmetic Reminders Chart on pages 6 and 7 in the Student Reference Guide. + by whole by decimal A Line up the decimal points. B Multiply. Then count decimal places. Decimals Chart C Decimal point is up. E 1. Place a decimal point to the right of a whole number. F 2. Fill empty places with zeros. D Decimal point is over, over, up A and E A, E, and F B C and F places ) places places c. What is the perimeter of this rectangle? d. Drew ran.50 meters in 8.46 seconds e f Mathea ran 50 meters in 8.52 seconds. Drew ran how many seconds faster than Mathea? Saxon Math Course 2 L Adaptations Lesson 35

18 Practice Set (continued) (page 251) g. 4.2 h. (0.06) 2 i. Six inches is how many centimeters? (1 in. = 2.54 cm) in cm? j = k. shift l. What is the area of (0.04)(10) = this rectangle? m n o p short division ) ) ) ) q. A loop of string 0.6 meter long is arranged to form a square. sides How long is each side of the square? m 4 1? Written Practice (page 251) 1. A all the bills together and d by. Use work are = x = x 3. mo $o x ? Now compare. 4. Faster means less time. (1 ) + 22 = s 1 min =?s Now find Li Jinyi s time. 5. perimeter of square of = each side of square area of area of 6 6 c. area of figure 8. not shaded. c. c. Saxon Math Course 2 L Adaptations Lesson 35

19 Written Practice (continued) (page 251) and twenty-five hundred-thousandths. Use work are (, ) gal $ What decimal number? It is p to pay 9 of one cent. 10 Use work are. 14. This figure illustrates the multiplication of which two decimal numbers? What is their product? 15. = x = f = y = 46.4 x = f = y= Saxon Math Course 2 L Adaptations Lesson 35

20 Written Practice (continued) (page 253) 19. w 3.4 = = x = x = x w = ( ) = 1 2 = x = x = x = x 25. shift 26. (0.3) (0.4) (0.5) = = = I Property of multiplication 28. Inches Centimeters Rule: For every i there are Use work are cm. Use work are estimate calculate estimate calculate 30. Complete the triangle. Label the 45 angles. Use work are Use work are Saxon Math Course 2 L Adaptations Lesson 35

21 LESSON Name 36 Ratio Sample Space (page 255) Ratio is a way to describe a relationship between two numbers. The ratio of 3 to 4 can be written several ways: with the word to 3 to 4 as a fraction 3_ 4 as a decimal number 0.75 with a colon 3:4 Write ratios as reduced fractions but not as mixed numbers. Example: In a class of 28 students, there are 12 boys. What is the boy-girl ratio? First find the number of girls in the class. 12 boys 12 boys + 1? girls + 16 girls 28 total 28 total Write the ratio as a reduced fraction. boys 12 girls 16 = 3_ 4 The sample space is a list of all possible outcomes in a probability experiment. The sample space can be shown in different ways. Example: A coin is tossed once, and then it is tossed again. Each time a coin is tossed, it can land either heads (H) or tails (T). A tree diagram shows the process of the probability experiment. 1st toss H 2nd toss H T Outcomes HH HT H TH T T TT The outcomes from the tree diagram can be summarized in braces or a table. {HH, HT, TH, TT} The fundamental counting principle says that you multiply the number of outcomes of each part of an experiment to find the total number of outcomes. Tossing a coin has 2 outcomes (heads or tails). So tossing a coin twice has 2 2 = 4 outcomes. Practice Set (page 260) big little Outcomes for 2 Coin Tosses HH HT TH T T = boys + 14 girls. 30 total Teacher Notes: Review Hint #29, Probability. Refer students to Ratio on page 22 and Number Cube Chart on page 25 in the Student Reference Guide. Review Probability, Chance, Odds on page 25 in the Student Reference Guide. boys girls = Saxon Math Course 2 L Adaptations Lesson 36

22 Practice Set (continued) (page 260) c. 3 won + lost 8 total d. 5 red + 3 blue total won lost blue total i. Which sample space below is the better way to show the possible outcomes of rolling two number cubes? Why? Use the better sample space to find the probability of rolling a sum of 7. Sample space 1: {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Sample space 2: e. The name for the list of all possible outcomes of a probability experiment is s s. f. {, H T,, } g. The better way is sample space # because it shows more than one way to roll most sums. It shows all combinations. h. tails, less than 3 total possible = combinations of 7 total possible = Written Practice (page 261) 1. cities with more cities with less = 2. average to 5. 40% = never played rugby had played never played = 3. pages days 1? 7 to Saxon Math Course 2 L Adaptations Lesson 36

23 Written Practice (continued) (page 261) 6. One way to find BC in m is to first convert AB to mm and AC to mm. Then s 40 mm from 7. length = width + 5 cm area perimeter mm. Use work are 8. estimate Round to three decimal places = 10. twelve million 11. heads, even total possible = twelve millionths % = = 600 = List two factors of each given number. Continue to factor until each factor is a prime number. Write the prime factors in order. Cancel matching factors. = 15. estimate hr $10.90 She earned a little than. Use work are Saxon Math Course 2 L Adaptations Lesson 36

24 Written Practice (continued) (page 262) y = w 4 = 1.2 c. y = w = 19. estimated and exact estimated and exact Convert = = = = ( ) = 2 3 = 1 2 = = = 25. Multiply the reciprocal = 26. Multiply the reciprocal. 5 ( ) = = 28. (0.2)(0.3)(0.4) = 29. shift = shift = 30. area = 25 units 2 each side = units (, ), (, ), (, ), (, ) Use work are Saxon Math Course 2 L Adaptations Lesson 36

25 LESSON Name 37 Area of a Triangle Rectangular Area, Part 2 (page 264) A triangle has a base (b) and a height (h). The base is any of the three sides. The height is the perpendicular distance from the base to the opposite vertex of the triangle. Since a triangle has three sides and any side can be the base, a triangle may have three base-height orientations, as shown by rotating these triangles. Teacher Notes: Review Hint #33, Perimeter of Complex Shapes. (Students must find the length of missing sides to find the area of a complex shape.) Review Geometric Formulas on page 29 in the Student Reference Guide. Students will need paper, a ruler, a protractor, and scissors to complete the activity in this lesson. Do the Activity on pages 265 and 266 of the Student Editon to understand this formula: area of a triangle = 1 2 bh or bh 2 To find the area of a complex shape: Example: 1. Divide the shape into rectangular parts. 2. Find the area of each part. 3. Add the areas to find the total are Sometimes subtracting a ghost area (the area that is missing) from a rectangle is easier. There are three ways to find the area of this shape. Practice Set (page 269) Find the area of each triangle. Dimensions are in centimeters. area of a triangle = 1_ 2 bh or bh 2 d. Find the are 14 m 10 m A B 5 m c. 6 e. Find the area by subtracting the area of the small square from the area of the large rectangle in. 4 in. 4 in. 20 m 12 in. Saxon Math Course 2 L Adaptations Lesson 37

26 Practice Set (continued) (page 270) f. Find the are 6 in. g. I found my answer to f by a the areas 24 in. A of two r. B 20 in. 8 in. h. Write two formulas for finding the area of a triangle. A = A = Written Practice (page 270) played + 2 cancelled 3 total games played cancelled to 2. average Subtract $1.30 from $ to find how much the gallons of milk cost. Then d that number by to find how much e gallon cost. Use work are perimeter x = y = in. in. 7. Two methods: 1. Add area of both parts. 2. S area of cut-out part from =? 18? 8 = 9 24 b rectangle. Now find the are c. 3 4 = 15? c. Saxon Math Course 2 L Adaptations Lesson 37

27 Written Practice (continued) (page 271) 9. decimal shaded decimal not shaded c. percent not shaded two decimal places nearest hundred. c sixty and seven hundredths % = = = Use work are 13. Find the length of segment BC. 14. Intersect with oblique parallel lines. Then shade the enclosed region. Use work are 15. perimeter area area of triangle = 1_ 2 bh { { 17. { AA,,,, BB,,,, CC } = 4x { = 4x A total possible Use work are x = Saxon Math Course 2 L Adaptations Lesson 37

28 Written Practice (continued) (page 272) = y 20. m 3.6 = w = y = m = w = = ( ) = = 1 2 = = = = = 26. a = a b = a b b = = 2 n 28. shift = = n = 29. Plot (3, 3). Which quadrant is the point in? 30. perimeter Saxon Math Course 2 L Adaptations Lesson 37

29 LESSON 38 Interpreting Graphs (page 273) Name In a pictograph, each picture in the chart represents a certain number of items. The legend tells how many items each picture represents. Jan. Fe Mar. Adventure Tire Sales Represents 100 tires A bar graph shows comparisons between categories (such as classrooms or months of the year). Number of Aluminum Cans Collected by Each Homeroom 10,000 Number of Aluminum Cans Room Number A line graph shows how a measurement changes over time. A circle graph (pie graph) shows parts of a whole. Where Ayisha Spends Her Day At home 12 hr Elsewhere 4 hr At school 8 hr Practice Set (page 276) Use the information from the graphs in the lesson area above to answer each question. How many more tires were sold in February than How many aluminum cans were collected by all in January? tires four homerooms? cans c. On which game was Paul s score lower than his d. What fraction of Ayisha s day is spent somewhere score on the previous game? Game # other than at home or at school? e. Which type of graph best displays the relationships between parts of a whole? graph f. Which type of graph best displays change over time? graph g. Which type of graph is best for comparing categories of data? graph Saxon Math Course 2 L Adaptations Lesson 38

30 Written Practice (page 277) walkers joggers total athletes 2. pages days 345 x?x 1 walkers total athletes x x 3. (5 ) + 52 = 1 min =? s 4. Number of Aluminum Cans Room 16 Collected by Each Homeroom 10,000 Room 18 Number of Aluminum Cans Room Number 5. Paul s Bowling Scores 200 Number of Points Scored average Game 7 = Game 6. What is the d between Paul s h score and his l score? Use work are pages read 48 pages pages to halfway Mira read Mira did not read =? 18 c. 4 5 = 24? 384 pages 48 pages 48 pages 48 pages 48 pages 48 pages 48 pages? 9 = d. l Property 8. area perimeter y x x = in. y = in nearest thousand three decimal places of m c.. Saxon Math Course 2 L Adaptations Lesson 38

31 Written Practice (continued) (page 278) 11. most likely least likely c. Better sample space is 12. cm centimeters # because it lists all the p millimeters. outcomes. 13. perimeter in centimeters 10 mm = cm 1.2 cm 10 mm 14. A B C D The number 3.4 is between 5 and and is nearly h between. Point B is too c to 3 to be 3.4. So the best choice is. Use work are area of ACD area of a triangle = 1_ 2 bh perpendicular to AD parallel to AD area of CAB ( CAB is congruent to ACD) c. total area c a = m 3.6 = w = a = m = x 2.5 = 2.5 w = x = Saxon Math Course 2 L Adaptations Lesson 38

32 Written Practice (continued) (page 279) = = = 3 4 = = = ( ) = 1 2 = 1 5 = = = A B 2 8 C 4 8 D How many milliliters? 200 ml 30. How much less than a liter? 100 ml y 1 liter = 1000 milliliters 29. Compare the numbers to tell which books are out of order x and Saxon Math Course 2 L Adaptations Lesson 38

33 LESSON 39 Proportions (page 280) Name A proportion is a statement that two ratios are equal. You can cross-multiply to check that ratios are equal. If the cross-products are equal, then the ratios are equal = = = 4 5 Solve a proportion by finding the missing number. 1. Cross-multiply. 2. Divide by known factor. Example: 3 5 = 6 w 3 w = 5 6 3w = 30 w = 30 3 w = 10 You have done this before: Multiply the loop. Divide by the outside number. The missing number will always be outside the loop. Practice Set (page 282) Teacher Note: Refer students to Proportion (Rate) Problems on page 19 in the Student Reference Guide. Multiply the loop. Divide by the outside number. 30 b = b = a 12 = 6 8 a = c = c 15 c = e = n 40 n = d = 24 d d = f. m 100 = 9 12 m = Saxon Math Course 2 L Adaptations Lesson 39

34 Written Practice (page 282) months 19 months 2. Between his and months. Use work are 3. trumpet flute x x = 4. average Weeks Dollars fewer 5 or more 3 5 Use work are 7. area x = mm 8. perimeter x y y = mm 9. decimal number nearest hundredth nearest hundredthousandth. mixed number. Saxon Math Course 2 L Adaptations Lesson 39

35 Written Practice (continued) (page 283) 11. $ one hundred and seventy-five thousandths one hundred seventy-five thousandths R Q P S acute obtuse 14., 100, 10, 1, 0.1,,,, Divide a term by to find the next term of the sequence. c. straight c. Use work are 15. Multiply the loop. Divide by the outside number = 6 x y = 2 3 x = y = = n m = n = m = w = x = w = x = Saxon Math Course 2 L Adaptations Lesson 39

36 Written Practice (continued) (page 284) 21. y = estimated and exact answer y = 23. estimated and exact answer 3.15 ( ) = = x = x = x = = x = 28. A C perimeter B 29. 1, 2, 3, 4, 5, 6 odd prime total numbers x x = area = 1_ 2 bh 30. least to greatest , 2, 6, = x = x = x 12,,, Saxon Math Course 2 L Adaptations Lesson 39

37 LESSON Name 40 Sum of the Angle Measures of a Triangle Angle Pairs (page 285) A square has four angles and each one measures 90. By drawing a diagonal segment from one corner to the opposite corner, the square divides into two congruent triangles. Do the Activity on pages 286 and 287 to understand: A triangle has three angles and the sum of these angles is = º 90º 45º 90º 90º 45º 90º Teacher Notes: Refer students to Angle Pairs on page 27 in the Student Reference Guide. Review Angles on page 27 in the Student Reference Guide. Students will need paper, a ruler, a protractor, and scissors to complete the activity in this lesson Adjacent angles share a common side. Examples: 1 and 4, x and y Supplementary angles are two angles whose sum is 180. Examples: y and z, 3 and 4 Complementary angles are two angles whose sum is 90. Example: A and B Vertical angles are a pair of non-adjacent angles formed by intersecting lines. Vertical angles have the same measure. Examples: 1 and 3, 2 and 4, x and z Practice Set (page 289) The sides of a regular triangle are equal in length, and the angles are equal in measure. What is the measure of each angle of a regular triangle and why? Each a measures because they equally share. Refer to rectangle ABCD to answer questions b d. What is the measure of ACB and why? Answer: ; Angle ACB and ACD are c. c. What is the measure of CAB and why? CAB measures because it is the third a of a triangle whose other angles measure and. d. Are angles ACD and CAB vertical angles? Why or why not? They are n vertical a. Their angles are equal in m but they are n non-adjacent angles formed by two i lines. Saxon Math Course 2 L Adaptations Lesson 40

38 Practice Set (continued) (page 290) e. Find the measure of x, y, and z in this figure. x y z m x = m y = m z = = m x = m y Written Practice (page 290) redite + 2 white total fraction white white total x x 2. ( 6 ) + 20 = 1 min =? s laps seconds 4 1? 3. miles gallons 1? Round off the difference ft F 550 1? 5. The length is twice the width. perimeter area 7. Find BC in centimeters. 6. grazed nearest thousandth drank cm mm 1? nearest tenth.. Saxon Math Course 2 L Adaptations Lesson 40

39 Written Practice (continued) (page 290) and 10. area of triangle = 1_ 2 bh and Use work are 11. What decimal number? 12. Sum of angles in triangle is 180. A B D C B E c. 13. Name an angle supplementary to ACB that is not ACD. 14. I Property of m = = w n 1.5 = = 15 m = a w = n = m = = t m 12 cm = m cm 1? m 4.00 a = t = Saxon Math Course 2 L Adaptations Lesson 40

40 Written Practice (continued) (page 292) 21. (0.15)(0.05) = = (4 1.25) = ( ) = = x x = = x = x = x = x 30. Perimeter is m m each side area Saxon Math Course 2 L Adaptations Lesson 40

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