Remaining Fraction Two-Step Equations

Transcription

1 LESSON 61 Name page 394 Remaining Fraction Two-Step Equations Teacher Note: For additional practice, students may complete Fraction Activity 61. New Concept Remaining Fraction If we know the size of one portion of a whole, we can figure out the size of the other portion. 3 8 is shaded. 5 is not shaded. 8 Two Step Equations To solve a two step equation: 2n = Find the answer to one side of the equation. 2n = Find the letter (variable) n = 12 2 A raised dot shows multiplication. 4 6 means 4 times 6. n = 6 Example 3m = 4 6 3m = 24 m = 8 1. Find the answer to one side. 2. Divide to find the variable. Saxon Math Intermediate Adaptations Lesson 61

2 Lesson Practice Use fraction pieces for help. a. What fraction of this rectangle is not shaded? b. Three fifths of the race was over. What fraction of the race was left? Find each missing number: c. 2n = d. 2 + n = 2 8 2n = 2 + n = n = n = Written Practice page Find the radius. 2. lunches bought 24 in. apple slices per lunch total The d is twice the r, so 24 =. = n Saxon Math Intermediate Adaptations Lesson 61

3 Written Practice, continued page Two nickels a. fraction b. decimal 4. Multiply the loop. Divide by the outside number. cups days =? 1 ) a. b to Ariana s house to restaurant back to Ariana s back to Maya s 6. What fraction of this rectangle is not shaded? total 7. Use the multiplication table. 8. What fraction is left (not shaded)? Which of these numbers is not a factor of 10? A 2 B 5 C 10 D Use fraction pieces. Saxon Math Intermediate Adaptations Lesson 61

4 Written Practice, continued page Use fraction pieces. 100% answers 60% true cm 4 cm false a. perimeter b. area More true answers or more false answers? a. b. 13. $ $ n = n = n = (110 9) n = $ Saxon Math Intermediate Adaptations Lesson 61

5 Written Practice, continued page $ ) 3 9 R ) 3 9 R ) 3 9 R = = = = 26. Point A represents what number on this number line? A a b Saxon Math Intermediate Adaptations Lesson 61

6 Written Practice, continued page a. fraction not shaded b. decimal not shaded c. percent not shaded a. 100 b. 0. c. 29. AB is parallel to. is perpendicular to. is perpendicular to. Angle is a right angle. A B Angle is a right angle. Angle is obtuse. C D Angle is acute. 30. postcards stamps elapsed years Saxon Math Intermediate Adaptations Lesson 61

7 LESSON Name 62 Teacher Note: page 399 Multiplying Three or More Factors Exponents Refer students to Exponents on page 21 in the Student Reference Guide. New Concept Multiplying Three or More Factors To find the product of three numbers: 1. Multiply any two of the numbers. 2. Multiply that answer by the third number. It does not matter which numbers are multiplied first = = = = 60 Exponents Math Language Exponents are numbers that show how many times another number (the base) is to be used as a factor. base 5 2 exponent If the exponent is 2, we say squared. 5 2 is read five squared. If the exponent is 3, we say cubed. 5 3 is read five cubed. Exponents can be used in formulas: area of a square A = s 2 area = (length of side) means = 25 Lesson Practice Simplify: a = b = c. 8 2 = d. 3 3 = Saxon Math Intermediate Adaptations Lesson 62

8 Lesson Practice, continued e = f = = = g. Rewrite this expression using an exponent: = h. Formula for area of a square: 2 5 in. Area of this square = = Written Practice page missing factor Divide. 2h = peacocks 2. 00$1.98 paper 00$.98 pen 00$.98 pen 00$. tax total I will round each number to see if my answer is r. $ + $ + $ + $ = $ My estimate is close to the actual sum of $. Saxon Math Intermediate Adaptations Lesson 62

9 Written Practice, continued page Use your student clock. time class starts: Count minutes back. 4. Finish the table. How many miles in 4 hours? miles hours 60 1 =? 2 Hours Miles miles hours =? miles hours =? Fraction of race over: 2_ 3 Fraction of race left: 6. $ $ = 100 y = = y y = Saxon Math Intermediate Adaptations Lesson 62

10 Written Practice, continued page Which are prime numbers? A prime number has exactly two factors (itself and 1). A 7 B 8 C 9 D 10 Use fraction pieces. 10. According to this calendar, July 4, 2014, is what day of the week? S JULY 2014 M T W T F S ) ) 12. Associative Property of Multiplication = , , = 15. $20.00 $ c 19,434 45, $ c = Saxon Math Intermediate Adaptations Lesson 62

11 Written Practice, continued page $ R 4 ) R 8 ) R 5 ) = = = % students 40% boys girls 27. a. perimeter b. area 6 in. 28. What type of angle is each angle of a square? A acute C obtuse B right D straight a. b. Saxon Math Intermediate Adaptations Lesson 62

12 Written Practice, continued page Colors of Candles in One Package 10 Number of Candles Red Orange Yellow Green White a. How many red candles? b. How many more green than orange candles? a. b. 30. Show 1 1_ 2, 1.25, and 1 3_ Saxon Math Intermediate Adaptations Lesson 62

13 LESSON Name 63 Teacher Note: page 405 Refer students to Common Polygons on page 14 in the Student Reference Guide. Polygons New Concept Polygons are closed, flat shapes made from line segments. Math Language A vertex is a corner of a polygon (plural is vertices). Regular polygons have: sides the same length. angles the same size. Three-sided polygons are triangles. Four-sided polygons are quadrilaterals. Five-sided polygons are pentagons. (Regular triangle) (Regular quadrilateral, or square) Six-sided polygons are hexagons. (Regular pentagon) Eight-sided polygons are octagons. (Regular hexagon) Ten-sided polygons are decagons. (Regular octagon) (Regular decagon) Saxon Math Intermediate Adaptations Lesson 63

14 Lesson Practice Draw an example of each polygon. a. triangle b. quadrilateral c. pentagon d. hexagon e. octagon f. decagon Name each polygon shown and describe its angles: g. h. angles angles i. j. angles angles k. and l. m. more vertices Written Practice page ft yd 3 1 = 0? ) ) ) Saxon Math Intermediate Adaptations Lesson 63

15 Written Practice, continued page quarters $ dimes $ pennies $ Find the sum of all even numbers greater than 10 but less than $ 7.15 $ Use containers to solve. 1 gallon = cups product of 4 and 3 pieces of cornbread eaten: 7 sum of 4 and 3 fraction of cornbread left: Saxon Math Intermediate Adaptations Lesson 63

16 Written Practice, continued page a. name b. perimeter cm a. b. 12. Multiply the loop. Divide by the outside number. 13. berries minutes 00 1 =? 5 berries minutes 00 8 =? 1 ) 14. $40.00 d $ n = = 16. Associative Property of Multiplication = n = d = n = = Saxon Math Intermediate Adaptations Lesson 63

17 Written Practice, continued page $1.00 ($ $0.57) = 00$ $ $ $ $ R 6 ) R 8 ) R 5 ) = 27. = n 8 R ) n = The remainder represents players. If only 4 m are used, then those players would not have a ride. minivans will be needed to fit all of the p. Saxon Math Intermediate Adaptations Lesson 63

18 Written Practice, continued page Use the multiplication table. Which of these numbers is a multiple of 10? A 3 B 5 C 15 D 40 1,,, a. fraction shaded b. decimal not shaded c. percent not shaded a. b. c. 30. a. type of polygons: b. angles line segments line segments Saxon Math Intermediate Adaptations Lesson 63

19 LESSON Name 64 Teacher Notes: page 411 Division with Two-Digit Answers, Part 1 Introduce Hint #35 Short Division. For additional practice, students may complete Targeted Practice 64. New Concept Example Short division rules: 1. Any number left over goes in front of the next digit. 2. There must be a digit above each digit. 3. Use zero as a placeholder. 4. Any final number left over becomes the remainder. Solve 78 3 using short division. 2 3 ) ) ) divides into 7 two times. 2. Multiply: 2 3 = 6. Subtract 6 from Put the leftover 1 in front of the divides into 18 six times. 5. Multiply: 6 3 = 18. Subtract 18 from 18. There is no remainder. Example ) R 1 3 ) Tests for Divisibility A number is able to be divided by: 2 if the last digit is even. 5 if the last digit is 0 or if the last digit is 0. Already know 3 if the sum of the digits can be divided by 3. New Saxon Math Intermediate Adaptations Lesson 64

20 New Concept, continued Example Use the divisibility rules to divide 87 by = 15 Since 15 is a multiple of 3, 87 can be divided by 3 with no remainder. Lesson Practice Use short division. a. 3 ) 5 1 b. 4 ) 5 2 c. 5 ) 7 5 d. 3 ) 7 2 e. 4 ) 9 6 f. 2 ) 7 4 g. Find the missing factor: 3n = 45 ) n = h. Which of these numbers can be divided by 3 with no remainder? A 75 B 76 C 77 D 79 The sum of and is 12, which is a multiple of 3. i. There are 6 students per row. 29 students fill the first available seat. What is a reasonable estimate of the number of rows that will be filled? 29 is close to, and 30 seats 6 students = rows. Saxon Math Intermediate Adaptations Lesson 64

21 Written Practice page twenty-seven million, eight hundred seventy-eight thousand, four hundred square feet,, 2. number in each group number of groups 3. has = m more will hold m = 4. Multiply the loop. 5. sides of a stop sign days weeks 7 1 = 0? ) stop signs 6. inch ,912 expanded form: words: Saxon Math Intermediate Adaptations Lesson 64

22 Written Practice, continued page Multiply the loop. 9. The students washed 8 cars in 90 minutes. ft in. 1 0 = 4? Estimate the number of minutes spent washing each car. I can use com numbers. is close to = minutes a b Use fraction pieces. 12. last week this week 112 total I will round to the nearest 10 to see if my answer is r. + = papers 13. $ $ ,036 7, Saxon Math Intermediate Adaptations Lesson 64

23 Written Practice, continued page short division 17. short division 18. short division 5n = 75 ) ) ) 9 2 n = 19. short division 6 ) 5 8 R 20. Carry on your fingers $ $ short division 2 ) n = 36 ) n = = ( ) = + = = Saxon Math Intermediate Adaptations Lesson 64

24 Written Practice, continued page See page 416. List ways to pair two bills: $5 and $10 $10 and $5 and $ and and $20 and 28. fraction of game over: 3_ 4 fraction of game remaining: 29. a. fraction shaded b. decimal shaded. c. percent not shaded % 30. prime = 2 factors The first two prime numbers are 2 and 3. What are the next two prime numbers? A 4 and 5 B 5 and 6 C 5 and 7 D 7 and 9 Saxon Math Intermediate Adaptations Lesson 64

25 LESSON Name 65 Teacher Notes: page 417 Review Hint #35 Short Division. Division with Two-Digit Answers, Part 2 Refer students to Division on page 8 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 65. New Concept The numbers in a division problem are called the divisor, dividend, and quotient. dividend quotient 78 3 = 26 dividend 78 = 26 divisor 3 = quotient divisor divisor 26 3 ) 78 quotient dividend Tests for Divisibility A number is able to be divided by: 2 if the last digit is even. 5 if the last digit is 0 or if the last digit is 0. Already know 3 if the sum of the digits can be divided by 3. 9 if the sum of the digits can be divided by 9. New Use short division: ) Any number left over goes in front of the next digit. Place a digit above each digit. Use zero as a placeholder. Saxon Math Intermediate Adaptations Lesson 65

26 Lesson Practice In the division fact 32 8 = 4, a. What number is the divisor? b. What number is the dividend? c. What number is the quotient? Use short division. d. 0 3 ) e. 0 4 ) f. 0 6 ) g. 0 5 ) h. 0 7 ) i. 0 8 ) j. Which of these numbers can be divided by 9 without a remainder? A 288 B 377 C 466 D 555 How do you know? The sum of the digits,, and equals, which is a multiple of 9. k. Find the missing factor in this equation: 5m = 125 ) m = l. An oil change business sold 157 quarts of motor oil. About how many gallons is that? Round quarts quarts quarts galons 0? = quarts is close to quarts. There are quarts in each gallon. A reasonable estimate is =. Saxon Math Intermediate Adaptations Lesson 65

27 Written Practice page missing factor Divide end 3. years months 1 12 = 0? ) begin minutes long 4. 7 half gallons = how many gallons? half gallons gallons 2 1 = 7? ) The quotient is between and. R 5. miles hours ) 36 4 =? 1 Madeline purchases or gallons of juice each month. 6. Finish the table. How many miles in 5 days? Find the pattern. 7. Days Miles a. fraction not shaded b. perimeter a. b. Saxon Math Intermediate Adaptations Lesson 65

28 Written Practice, continued page see page 422. Average Annual Precipitation Amount of Rain (in inches) Phoenix Reno Boise Albuquerque City 9. 8:05 to 10:05 is how many hours? hr 10. What is the diameter? 10:05 to 10:25 is how many minutes? min 18 in. 11. How long is segment BC? A B C cm Saxon Math Intermediate Adaptations Lesson 65

29 Written Practice, continued page Which of these words names the answer to a division problem? A product C divisor B dividend D quotient 14. $ $ $60.00 $ short division = 18. short division = = short division 23. short division 24. short division 4 ) ) ) Saxon Math Intermediate Adaptations Lesson 65

30 Written Practice, continued page n = First, add and. The sum is. Then divide by. The answer is. n = 26. Associative Property of Multiplication 27. See page = 28. three quarters a. fraction b. percent 29. See page 16 in the Student Reference Guide Draw a quadrilateral. A quadrilateral has how many vertices? a. b. 30. a. Which side is parallel to side CB? A D b. Which angle appears to be obtuse? B C a. b. Saxon Math Intermediate Adaptations Lesson 65

31 LESSON Name 66 Teacher Note: page 424 Use Lesson Activity 29 for the activity. Similar and Congruent Figures New Concept Congruent figures match exactly (the same shape and the same size). C X A B Z Y Triangle ABC and triangle XYZ are congruent. A corresponds to X. AB corresponds to XY. Similar figures have the same shape but not necessarily the same size. Similar A B C D not similar or congruent Congruent Saxon Math Intermediate Adaptations Lesson 66

32 New Concept, continued Activity page 426 Determining Similarity and Congruence Use Lesson Activity 29 to complete this activity. 1. Is the first shape similar to the bike sign? Is the shape congruent to the bike sign? Cut out the shape on the left and place it on top of the bike sign to check your answers. 2. Is the triangle similar to the yield sign? Is the triangle congruent to the yield sign? Cut out the triangle and place it on top of the yield sign to check your answers. 3. How can you tell if the octagon on the left is congruent to the stop sign? The octagon is c They are the same s to the stop sign. and the same s Are these shapes similar?, congruent shapes are also s. Lesson Practice A B C D a. Which are similar (same shape)? b. Which are congruent (match exactly)? Saxon Math Intermediate Adaptations Lesson 66

33 Written Practice page earned each hour hours per day earned each day 2. There are 141 beads. Every third bead is red. How many beads are red? missing factor Divide. ) % square 25% shaded not shaded 4. North 20 km 15 km South 5. Time now: Count minutes forward. Count hours forward. 6. a. perimeter: units 6 units area: square units 3 units b. Draw a rectangle with 18 square units arranged in two rows. Saxon Math Intermediate Adaptations Lesson 66

34 Written Practice, continued page mi gal 30 1 =? 0 8. I multiplied miles by gallons. cheered wildly: 2_ 7 The answer is miles. stood quietly: 9. Make 3-digit numbers using 4, 2, and 7. Label even or odd. 2 7 odd different numbers n + 2 = 3 12 = n = n = Saxon Math Intermediate Adaptations Lesson 66

35 Written Practice, continued page ( ) = = = 14. $10.00 $ , Associative Property of Multiplication = 17. $ $ short division 2 ) short division 22. short division 23. short division 24. short division 6 ) ) = 91 7 = Saxon Math Intermediate Adaptations Lesson 66

36 Written Practice, continued page short division = 26. a. 8 $. b. $ $. 27. a in words: b. 2.3 in words: 28. a. Which two triangles are congruent? congruent exactly the same 29. Draw a pentagon. A pentagon has how many vertices? A B C D b. Triangles and are congruent because they have the same s and the same s. 30. Are all squares similar? Why or why not? All squares similar because every square has equal sides and right angles. Saxon Math Intermediate Adaptations Lesson 66

37 Example LESSON 67 page 429 Name Multiplying by Multiples of 10 Teacher Note: For additional practice, students may complete Targeted Practice 67. New Concept To multiply a whole number by 10, attach a zero after the number = = 370 Multiples of 10 10, 20, 30, 40, 50, 60, 70 Use offset multiplication to multiply a whole or decimal number by a multiple of Write the multiple of 10 as the bottom number. 2. Let the zero hang out (offset to the right). 3. Copy the zero into the answer. 4. Multiply. Example Zero hangs out to the right When multiplying a money amount by a multiple of 10, put two decimal places in the answer. $ $28.60 Saxon Math Intermediate Adaptations Lesson 67

38 Lesson Practice Multiply. a = b = c = d e. $ f g. Write as a product of 10 and two other factors. Then multiply. See Example 1 on page = Written Practice page missing factor Divide. ) 2. a. perimeter: 8 units 3 units area: b. Sketch a rectangle that is four units wide with the same area as the rectangle above. Area = length width perimeter: Saxon Math Intermediate Adaptations Lesson 67

39 Written Practice, continued page The server placed a full pitcher of water on the table. Which of the following is a reasonable estimate of the amount of water in the pitcher? 4. Which of these numbers is not a factor of 12? Use the multiplication table. A 6 B 5 C 4 D 3 A 2 gallons C 2 cups B 2 quarts D 2 ounces 1,,,,, Starting time Stopping time 6. 3,097,600 sq. yd words: The starting time was before dawn. The stopping time was in the afternoon. What was the difference in the two times? 7. a. fraction not shaded 8. last Saturday of the month b. shaded part: more or less than 50%? a. b., Saxon Math Intermediate Adaptations Lesson 67

40 Written Practice, continued page See page mixed number The exact product of 5 12 is. Round 12 to the nearest ten. Then multiply = The estimate is than the exact product. 11. See page 433. A better e would be to round 68 to the nearest instead of to the nearest hundred: 4 = $6.25 $0.00 $ $30.25 b $ ,384 98, b = Saxon Math Intermediate Adaptations Lesson 67

41 Written Practice, continued page $ $ = 21. short division 22. short division 23. short division 6 ) ) ) short division 95 5 = 25. short division = 26. fraction and decimal shaded Saxon Math Intermediate Adaptations Lesson 67

42 Written Practice, continued page a. Which two figures are congruent? congruent exactly the same A B C D b. If one of them is flipped, they are the same and the same. a. and b. 28. How much money is 1_ of a dollar? Draw a hexagon. A hexagon has how many vertices? 30. a. The first temperature of the morning was recorded at. What was that temperature? b. Was the noon temperature warmer or colder than the 10 a.m. temperature? How many degrees warmer or colder was the noon temperature? Saxon Math Intermediate Adaptations Lesson 67

43 LESSON Name 68 Teacher Notes: page 435 Review Hint #35 Short Division. Division with Two-Digit Answers and a Remainder For additional practice, students may complete Targeted Practice 68. New Concept Use short division: 1. Any number left over goes in front of the next digit. 2. Place a digit above each digit. 3. Use zero as a placeholder. 4. Any final number left over becomes the remainder. To check a division answer that has a remainder: 1. Multiply the quotient by the divisor. 2. Add the remainder. 3. The answer should match the dividend. Example R 2 5 ) Check: dividend Lesson Practice Divide. Use short division. a. d. 0 R 3 ) b. 0 R 8 ) e. 0 R 7 ) c. R 4 ) 9 5 f. 5 ) 8 8 R 0 R 6 ) Saxon Math Intermediate Adaptations Lesson 68

44 Lesson Practice, continued g. Shou divided 235 by 4 and got 58 R 3 for her answer. Describe how to check Shou s calculation. To check her calculation, I would m 58 by. Then I would a 3 to the product. The answer should be. h. 175 birds live in the 9-acre marsh. What is a reasonable estimate of the number of birds in each acre? Explain why your estimate is reasonable. 175 is close to 180. The number is a factor of both 18 and 180. A reasonable estimate is 180, which equals birds per acre. Written Practice page Finish the table. How many miles in 3 hours? Find the pattern. 2. perimeter and area 6 units Hours 1 3 Miles units 3. twelve and fourteen hundredths seconds. Saxon Math Intermediate Adaptations Lesson 68

45 Written Practice, continued page octagon pentagon 5. Offset = total 6. Offset = 7. Offset = 8. a. fraction of the course ran: 3_ 5 fraction of the course walked: b. ran: more or less than 50%? Show 0, 1, 2, 1 2_, and 2 1_ four thousand, three hundred ninety-two meters Saxon Math Intermediate Adaptations Lesson 68,

46 Written Practice, continued page knots minutes 35 0 =? 1 ) $12.15 $ 15. $20 ($ ) = $ 5.95 $ $8.95 $0.75 $20.00 $.00 estimate: actual sum: $ $ Change to multiplication and solve: = Saxon Math Intermediate Adaptations Lesson 68

47 Written Practice, continued page short division 22. short division 23. short division 5 ) 9 6 R 7 ) R 3 ) short division 25. short division 26. short division = 4r = 156 ) = r = 27. Use an inch ruler to find the lengths of segments AB, BC, and AC. A B C AB BC AC 28. a. Which word makes the following sentence not true? All squares are. A polygons B rectangles C similar D congruent b. Not all s are because quarts they are not all the same s. 1_ 2 gallon See page 1 in the Student Reference Guide. Saxon Math Intermediate Adaptations Lesson 68

48 Written Practice, continued page Length (in feet) Land Tunnels in the United States Dingess, WV Cumberland Gap, KY/TN Hanging Lake, CO Tunnel Name and State a. Tunnels from shortest to longest: shortest longest b. How many feet longer is the Hanging Lake Tunnel than the Dingess Tunnel? Hanging Lake Dingess feet longer c. 1 mile = 5280 feet Are the combined lengths of the tunnels more than or less than 2 miles? miles feet = 2? 2 miles = feet The combined length of the t Dingess Cumberland Gap Hanging Lake total feet is than 2 miles. Saxon Math Intermediate Adaptations Lesson 68

49 LESSON Name 69 Teacher Notes: page 440 Introduce Hint #36 Reading Metric Rulers. Review Equivalence Table for Millimeters Units on page 1 in the Student Reference Guide. Use rulers to illustrate the examples. New Concept 1 centimeter = 10 millimeters Millimeter mm Centimeter cm The length of the segment below is 35 mm. It is also 3.5 centimeters. mm Metric measures are always written as decimal numbers instead of fractions. To convert: from centimeters to millimeters Multiply by 10. from millimeters to centimeters Divide by 10. Activity page 442 Measuring with Metric Units Use your text book to complete this activity. Saxon Math Intermediate Adaptations Lesson 69

50 Lesson Practice a. The thickness of a dime is about 1 mm. How many dimes would it take to form a stack that is about 1 cm high? b. Write the length of the segment below twice, once in millimeters and once in centimeters. Millimeter mm Centimeter cm c. Each side of this square is 1 cm long. What is the perimeter of this square in millimeters? 1 cm d. The diameter of a penny is about 19 mm. How many centimeters is that? e. Write a decimal subtraction problem that shows how to find the length of segment XY. W X Y 3.2 cm cm f. Write 3.4 cm as a fraction. Saxon Math Intermediate Adaptations Lesson 69

51 Written Practice page Celeste 2. students per bus Will buses more total students 3. How many millimeters? 4. A B C point A decimal fraction 5.2 cm point B decimal fraction point C decimal fraction 5. Shade one sixth. 6. mm cm a. centimeters b. millimeters a. b. Saxon Math Intermediate Adaptations Lesson 69

52 Written Practice, continued page % students 25% completed on Thursday 8. Find the perimeter of the square in feet. completed on Friday yd ft 1 3 = 00? 1 yd 1 yd 1 yd 1 yd I rounded each number to the nearest h and then added. + + = A reasonable e is. 10. A 3.5 cm B? C 11.6 cm 11.6 cm. Saxon Math Intermediate Adaptations Lesson 69

53 Written Practice, continued page a. mi hr b. mi hr =? =? prime = 2 factors The first three prime numbers are 2, 3, and 5. Next three prime numbers:,, and. a. b. 13. $7.95 $ short division = 15. short division = short division = 18. 4w = $4.63 = 20. $ w = 21. $10.00 $ ,428 27, short division 4 ) Saxon Math Intermediate Adaptations Lesson 69

54 Written Practice, continued page short division 26. short division 27. a + 5 = ) R 5 ) = a = a = ( ) = First s 1.7 from cm 20 mm 2 cm 30 mm a. perimeter in millimeters b. area in square centimeters The difference is. Then subtract from 4.7. The answer is. a. b. 30. Each angle of this triangle is. A acute B right C obtuse D straight Saxon Math Intermediate Adaptations Lesson 69

55 LESSON Name 70 Teacher Note: page 446 Word Problems About a Fraction of a Group Introduce Hint #37 Fraction of a Group, Part 1. New Concept Example One fourth of the team s 32 points were scored by Thi. Thi scored how many points? The whole rectangle stands for 32 points. Thi scored 1_ of the points, so we divide the rectangle into 4 4 equal parts. 1 scored 4 by Thi 3 not scored 4 by Thi 32 points 8 points 8 points 8 points 8 points 8 points 4 ) 32 points Thi scored 8 points. Here are some shortcuts: To find 1_ 2 To find 1_ 3 To find 1_ 4 of a number Divide by 2. of a number Divide by 3. of a number Divide by 4. Saxon Math Intermediate Adaptations Lesson 70

56 Lesson Practice a. What is 1_ of 60? b. What is 1_ of 60? ) ) 60 c. What is 1_ of 60? d. What is 1_ of 60? ) ) 60 e. One half of the 32 children were boys. How many boys were there? 1_ of = boys ) were 2 boys. 1 were 2 girls. 32 children children children f. One third of the 24 coins were quarters. How many quarters were there? 1_ of = quarters ) were quarters. were not quarters. 24 coins coins coins coins Saxon Math Intermediate Adaptations Lesson 70

57 Written Practice page seats 128 filled empty seconds Angela Marion faster 3. 42,000, price of lunch lunches per week greater spent during week 5. perimeter and area 4 units 5 units M T W Th F in all I can use compatible n to check my answer. 30 is about is close to, and 26 is near 25. a = b. Saxon Math Intermediate Adaptations Lesson 70

58 Written Practice, continued page a. 1_ of 74 ) seeds 2 1 sprouted. seeds 2 b. 1 1 did not 2 = % seeds 2 sprout. a. b. 8. Show all the ways to arrange these bills in a row: $1, $10, $1,,,,,,,,,, 9. 1_ 6 of 60 ) Finish the table. How many miles in 3 hours? Hours 1 2 Miles 65 mi hr 65 1 =? 00 Saxon Math Intermediate Adaptations Lesson 70

59 Written Practice, continued page mi hr =? 1 ) 12. a. diameter in centimeters cm 1 2 b. radius in millimeters a. b. 13. A 2.7 cm B? 4.8 cm C $ $. 00$ cm 4.8 cm $ $ ,102 18, = 19. Offset. 20. Offset. = 0 00$ = Saxon Math Intermediate Adaptations Lesson 70

60 Written Practice, continued page $ short division 23. short division 3 ) 8 9 R 9 ) short division 90 6 = 25. short division = 26. short division 5m = 355 m = n = Write twelve and three tenths as a: mixed number decimal number n = 29. Which of these numbers is a factor of both 12 and 20? A 3 B 4 C 5 D 6 Factors of 12: 1,,,,, 12 Factors of 20: 1,,,,, Draw a triangle that has one right angle. Saxon Math Intermediate Adaptations Lesson 70

61 INVESTIGATION 7 Name page 451 Focus on Collecting Data with Surveys A survey gathers specific information about a group. The group in a survey is called a population. A sample is part of a population. How survey questions are asked can affect the results of a survey. Which of these school lunches is your favorite? tuna pizza turkey chicken Which lunch from the school menu is your favorite? Multiple Choice: Answers limited to the choices given Open-Ended: Open to many answers 1. Write two questions to find out students favorite drink to have with lunch. Make one question multiple-choice. For the other, leave the question open (do not list options). Question 1: Saxon Math Intermediate Adaptations Investigation 7

62 INVESTIGATION 7 continued Question 2: Survey questions should be written without bias. Bias makes one choice sound better than another choice. 2. Describe the bias in the following question: Which drink do you prefer with lunch: cool, sweet lemonade or milk that has been out of the refrigerator for an hour? The words c and s bias the question to favor l. 3. Cross off words to remove the bias: Which drink do you prefer with lunch: cool, sweet lemonade or milk that has been out of the refrigerator for an hour? When using a sample to find information about a larger population, the sample must be very similar to the population. 4. You will survey students in your class. (Your class is the sample.) Which of the following larger populations will your survey apply to most? (State why or why not each larger population is like your sample.) Saxon Math Intermediate Adaptations Investigation 7

63 INVESTIGATION 7 continued A all the students in the school The d between ages might be too great. B all the school children your age in your community This p because the a is most similar to the sample and region are the same. C all the children your age in the country The differences in r might be too great. D all the parents of students in the class Parents might make different choices than their c. Saxon Math Intermediate Adaptations Investigation 7

64 INVESTIGATION 7 continued We can track survey answers with a tally sheet. On the tally sheet, we make tally marks: Make four vertical marks. Cross them with a fifth diagonal mark. This counts as five. Question: Which of these school lunches is your favorite? tuna, turkey, pizza, chicken Answer: tuna turkey pizza chicken 5. According to the tally marks, how many students named tuna as their favorite lunch? 6. Make a tally sheet to show favorite drinks to have with lunch. Write a multiple-choice question. List the possible answers. One choice may be no opinion. Question: Answer Choices: Tally: Saxon Math Intermediate Adaptations Investigation 7

65 INVESTIGATION 7 continued Duplicating data occurs when information is counted more than once. Omitting data occurs when information is left out. 7. Brad found that 11 students in his class had dogs. Dena found that 9 students in the same class had cats. Brad and Dena concluded that 20 students in the class had dogs or cats for pets. Is this conclusion correct? Why or why not? Their c might not be correct. Some students may have both a and a for pets. Dena and Brad may have counted these students t times. Saxon Math Intermediate Adaptations Investigation 7

66 INVESTIGATION 7 continued 8. Brad and Dena also concluded that 20 students in the class have pets. Is this conclusion correct? Why or why not? Their c might not be correct. Brad and Dena did not count some students who may have other, such as birds or fish. Brad and Dena may have counted some students t times-those who may have both a c and a d for pets. Activity page 453 Class Survey This activity is optional. Saxon Math Intermediate Adaptations Investigation 7