Parallelograms (page 368)

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1 LESSON 71 Parallelograms (page 368) Name A parallelogram has two pairs of opposite, parallel sides. The opposite angles of a parallelogram have equal measures. The adjacent angles of a parallelogram are supplementary (add to 180 ). A parallelogram can be cut in half and rearranged to form a rectangle: Teacher Notes: Review Geometric Formulas on page 29 in the Student Reference Guide. The activity in the Student Edition is optional. You know how to find the area of a rectangle, so you can use this method to find the area of a parallelogram. Imagine cutting the parallelogram on the dashed line. Move the part on the left under the part on the right. To get the area, multiply the base times the height. A = bh A = (3)(3) A = 9 sq. cm Do not be fooled by the slanted side. Example: Find the area of this parallelogram. A = bh A = (6)(5) A = 30 sq. cm When the angles of a parallelogram change the area changes. The perimeter does not change. Practice Set (page 371) Refer to parallelogram QRST to answer questions a d. Which angle is opposite Q? Which angle is opposite T? c. Name two angles that are supplements of T? and d. If the measure of R is 100, what is the measure of Q? Saxon Math Course 1 L Adaptations Lesson 71

2 Practice Set (continued) (page 371) Find the perimeter and area of each parallelogram: e. f. perimeter area perimeter area g. Here is the same parallelogram in two different positions. The area is the same in both drawings. A = bh so h = A b What is the height in the figure to the right? 12 cm 6 cm = 72 cm 2 9 cm h = 72 cm 2 Written Practice (page 372) 1. LCM of 6 and Mt. Everest 29,035 ft sea level 0 ft Dead Sea 1371 ft = = minutes = hours minutes time start 1:15 p.m. Count forward hours = = Count forward minutes = = 8. 6 = = = Saxon Math Course 1 L Adaptations Lesson 71

3 Written Practice (continued) (page 372) (3.5) 2 = ) 5 1 $ = = 13. ( ) (1 0.6) = 14. $ tax total c. change c. 15. name of point (0, 0) on coordinate plane 16. Always begin at the origin. Next, move on the x-axis. Last, move on the y-axis. c. (, ) d. (, ) f = = 1.2 f = ) 210 ) ) ) ) ) ) ) ) ) ) ) 224 f = f = = 20. perimeter each side area Saxon Math Course 1 L Adaptations Lesson 71

4 Written Practice (continued) (page 373) 21. not shaded 22. I multiplied the r by to find the diameter. Then I m the diameter by. 23. How many centimeters long is your little finger? % = is of 26. Name this geometric solid. 27. perimeter each side so, perimeter of triangle 28. area of your state 29. perimeter A = bh A square inches B square yards C square miles 30. In this figure BMD is a right angle. Name two angles that are supplementary. supplementary = 180 complementary. complementary = 90 and and Saxon Math Course 1 L Adaptations Lesson 71

5 LESSON Name 72 Fractions Chart Multiplying Three Fractions (page 375) To use the S.O.S. method in the Fractions Chart: Step 1. Write the problem in the correct shape. Step 2. Perform the operation. Step 3. Simplify the answer. To multiply three or more fractions, cancel vertically and diagonally but never horizontally. Practice Set (page 376) Fill in the fractions chart for this lesson. Write fractions with common d. Write numbers in f form. Add or subtract the n. Find the r of the divisor, then cancel. R fractions. C improper fractions. Describe the three steps for adding fractions. 1. Write the f so that the d are the same. 2. Add the n but not the d. 3. Reduce and/or c the answer if possible. Saxon Math Course 1 L Adaptations Lesson 72

6 Practice Set (continued) (page 376) c. Describe the steps for dividing fractions. 1. Write any mixed numbers in f form. 2. Find the r of the divisor. 3. C. 4. M the fractions. d = Cancel. e = 5. S the answer if possible. Written Practice (page 377) 1. average tablespoons cups 4? 1_ º 110º = = m = cm c. c 6. Write in cents. nickel dollar = 7. n 1 2 = = 1 2 = 8. 1 w = w = = = w = n = w = w = w = Saxon Math Course 1 L Adaptations Lesson 72

7 Written Practice (continued) (page 378) 11. (6 10) + ( ) + ( ) 12. closest to 1 A 1 B 0.1 C Largest prime number less than Which of these figures is not a parallelogram? 15. perimeter in. each side area 16. Figure ABCD is a rectangle. complementary = 90 supplementary = sandwiches 1 green salad 1 small juice 2 medium juices Menu Grilled Chicken Sandwich $3.49 Juice: Small $0.89 Green Salad $3.29 Medium $1.09 Pasta Salad $2.89 Large $ $20.00 $ List the items for an order. Then find the total not including tax. Saxon Math Course 1 L Adaptations Lesson 72

8 Written Practice (continued) (page 379) 20. A = l w l = 2.5 w = A = = ) 00 ) 00 ) 00 ) 00 ) 72 ) 000 ) 000 ) 000 ) 000 ) 120 = 22. K 23. (3, 4) F ( 3, 0) point point 24. Draw a pair of parallel lines perpendicular to the parallel lines below. Always begin at the origin. Next, move on the x-axis. Last, move on the y-axis. Is the quadrilateral a rectangle? (, ) (, ) Use work are = = = = 29. (0.12)(0.24) = = ) Saxon Math Course 1 L Adaptations Lesson 72

9 LESSON Name 73 Exponents Writing Decimal Numbers as Fractions, Part 2 (page 380) The exponent shows how many times the base number is multiplied by itself. The exponent 2 is read squared. The exponent 3 is read cubed. Examples: 5 2 = 5 5 = 25 (5 squared) 3 4 = = 81 (three to the fourth power) 2 5 = = 32 (two to the fifth power) To write decimal numbers as fractions or mixed numbers: The denominator (10 or 100 or 1000 ) is indicated by the number of decimal places in the decimal number. The numerator is the digits to the right of the decimal point. Examples: 0.5 = 5 10 = = = Practice Set (page 382) Find the value of each expression: 10 4 =, = c = d. Write the prime factorization of 72 using exponents. Teacher Notes: Introduce Hint #57, Prime Factorization of Powers of Ten. Review Exponents on page 8 in the Student Reference Guide. 72 = = Write each decimal number as a fraction or mixed number. Reduce. e = 12 5 = f = = g = = 10 h = = i = = j = = Saxon Math Course 1 L Adaptations Lesson 73

10 Written Practice (page 382) = d = d average pages to finish in 3 days 3p = 4. mixed number 2.5 = 5. reduced fraction 6. total plus tax 0.35 = $12.60 $12.60 $12.60 $ ( ) 5 2 = = 9. 3 = = = = = Saxon Math Course 1 L Adaptations Lesson 73

11 Written Practice (continued) (page 383) = = C = π d radius diameter m = y = m = y = 17. ten-thousands place 18. least to greatest 123, , 1 2, 1 10, 1 4, ,,,, 19. Use exponents % of $ % = is of = $18.00 $18.00 Saxon Math Course 1 L Adaptations Lesson 73

12 Written Practice (continued) (page 383) Find the are Then take 1_ of it = 25. Before we multiply fractions, we write any m numbers as i fractions. Use work are 26. Always begin at the origin. Next, move on the x-axis. Last, move on the y-axis. 27. ( 4, 3) (3, 0) point H L 29. See the Student Reference Guide. (, ) (, ) c. point 28. s = 9 s 2 = 30. What is the measure of X? What is the measure of Y? d. Saxon Math Course 1 L Adaptations Lesson 73

13 LESSON Name 74 Writing Fractions as Decimal Numbers Writing Ratios as Decimal Numbers (page 385) To write a fraction as a decimal: Divide the numerator by the denominator. Keep any whole number Examples: 3_ 4 ) _ 5 ) Ratios (such as probability) are often written as fractions, so they can be converted to decimals in the same way as any fraction. Practice Set (page 387) You may use a calculator to convert these fractions to decimals: Teacher Note: Instruct students on calculator usage. See page 386 in the Student Edition. 3 4 = =. c. 1 8 =. d =. e =. f =. g =. h =. i =. j. In a bag are three red marbles and two blue marbles. If Chad pulls one marble from the bag, what is the probability that the marble will be blue? Express the probability ratio as a fraction and as a decimal number. blue total fraction decimal Saxon Math Course 1 L Adaptations Lesson 74

14 Written Practice (page 387) 1. (4 3 ) ( ) = 2. in. mi 1 3? =. 4. sample space Write the probability as a fraction and a decimal. greater than 1 total numbers {,,,, }. 5. reduced fraction = d 0.24 = yd ft 1 300? 7. A = bh b = 12 h = = 2 3 = A = = = = Saxon Math Course 1 L Adaptations Lesson 74

15 Written Practice (continued) (page 388) = = = 14. ( ) 0.01 = Complete the triangular prism g = golf balls $ 12 1? Use work are average LCM of 6, 8, and c + 96 = c = Saxon Math Course 1 L Adaptations Lesson 74

16 Written Practice (continued) (page 388) = 22. perimeter 40 cm each side 23. mountain bikes all cyclists 24. All f sides of a square are the same l. Some rectangles are longer than they are w, so not all the s are the same l. Use work are Name a pair of parallel segments that are not AB and DC % = is of 300 (, ) (, ) and Saxon Math Course 1 L Adaptations Lesson 74

17 LESSON 75 Writing Fractions and Decimals as Percents, Name Part 1 (page 390) Percent means per hundred. Examples: = 23% 3 10 = = 30% = 1 2 = = 50% To change a decimal to a percent, shift the decimal point two places to the right. Examples: 0.08 = 8% 0.40 = 40% Practice Set (page 392) Write each fraction as a percent: Teacher Note: Review Fraction Decimal Percent on page 13 in the Student Reference Guide = = c = 100 = d = 100 = e = 100 = f. 2 5 = 100 = g. Twelve of the 30 students earned a B on the test. What percent of the students earned a B? = 10 = 100 = h. Jorge correctly answered 18 of the 20 questions on the test. What percent of the questions did he answer correctly? = 10 = 100 = Write each decimal number as a percent: shift i = j. 0.3 = k = l. 1.0 = m. 0.7 = n = Saxon Math Course 1 L Adaptations Lesson 75

18 Written Practice (page 392) 1. reciprocal = 5 2. time start Count forward hours. Count forward minutes pound = 16 ounces oz $z ? 4. $4.000 $4.000 $ Round 94 to $ and $6.35 to $. Add the items to get $. Tax is 8 per dollar, so the tax is about. This is close to my answer. 5. part 50% 6. Connect the correct corners. part whole 100% = = Write 12% as a reduced fraction and a decimal = n 100. n = Saxon Math Course 1 L Adaptations Lesson 75

19 Written Practice (continued) (page 393) m = x w = m = w = 13. m = = = 14. ( ) 1 6 = 1 2 = 1 3 = m = = 16. (0.43)(2.6) Add zeros. ) = 100 = % 19. Round to the nearest foot = ) ) ) 000 ) ) ) 300 = Saxon Math Course 1 L Adaptations Lesson 75

20 Written Practice (continued) (page 393) 22. GCF of 18 and product of 2 numbers is 1 1,,,,, 18 A equal C opposites B reciprocals D prime 24. A q is a four-sided p, and every r has four s. 25. b = 8 h = 6 bh 2 = Use work are 26. Use exponents. 27. Always begin at the origin. Next, move on the x-axis. Last, move on the y-axis. (3, 1), (3, 1), ( 1, 1), ( 1, 1) 28. perimeter area. 29. perimeter A = bh Use work are 30. Connect the endpoints to form a quadrilateral. Is it a rectangle? Use work are Saxon Math Course 1 L Adaptations Lesson 75

21 LESSON Name 76 Comparing Fractions by Converting to Decimal Form (page 395) To compare two fractions: 1. Cross-multiply. 2. Compare the numbers above the fractions. Examples: 18 > 12 6 < Convert to decimals if the problem is mixed (fraction and decimal). Example: < Teacher Note: Review Hint #47, Comparing Fractions. Practice Set (page 396) Compare by cross-multiplying c Convert; then compare. d e f ) ) ) Written Practice (page 396) ( )( ) = 2. halfway: Add; then divide by Saxon Math Course 1 L Adaptations Lesson 76

22 Written Practice (continued) (page 396) = y human dog 7 1? shaded 6. circumference of a juice glass. A centimeters B meters C kilometers c = 3.75 = = 100 = 0.04 =. 9. Answer with a mixed number. half of each { = = = = =? ( ) ( ) ( ) = Saxon Math Course 1 L Adaptations Lesson 76

23 Written Practice (continued) (page 397) = n = n = d = d = 17. shift median First, put the numbers in order. 0.3, 0.25, 0.313, 0.2, = prime numbers between 40 and = 100 = 22. perimeter,, Saxon Math Course 1 L Adaptations Lesson 76

24 Written Practice (continued) (page 397) 23. complementary = millimeters 25. two congruent triangles 26. A = bh area of one of the triangles bottom layer all layers cubes 27. Always begin at the origin. Next, move on the x-axis. Last, move on the y-axis. 30. Draw a fourth line that intersects but is NOT perpendicular to the parallel lines. Is the A (1, 2) B ( 3, 2) C (1, 2) 28. perpendicular to AC right angle 29. b = 12 h = 9 bh 2 = quadrilateral a rectangle? Use work are Saxon Math Course 1 L Adaptations Lesson 76

25 LESSON Name 77 Finding Unstated Information in Fraction Problems (page 399) Work through the Practice Set. Teacher Note: Review Hint #35, Fraction of a Group, Part 2. Practice Set (page 401) 3 of the 40 little engines could. 8 parts that could total parts parts that could not total parts Into how many parts was the group divided? How many engines were in each part? c. How many parts could climb the hill? e. How many parts could not climb the hill? d. How many engines could climb the hill? f. How many engines could not climb the hill? The face of a spinner is divided into 12 equal sectors. The probability of spinning red on one spin is 1_ 4. g. How many sectors are red? part red 1_ 4 part not red whole 1 h. How many sectors are not red? i. What is the probability of spinning not red in one spin? 1 of 12 = 4 j. What is the sum of the probabilities of spinning red and not red? How are the events related? The events are c. Written Practice (page 401) 1. 1 of is of A desk might weigh about 24 pounds. is of 1 6 Saxon Math Course 1 L Adaptations Lesson 77

26 Written Practice (continued) (page 401) 3. hits times = 4. 3 of 30 students are boys 5 c. d. 5. shaded =. c a = x = 1 a = x = 9. part 60% part whole 100% = 100 = % There is a g chance that it will rain because than %. % is greater Use work are 11. Water freezes at F. 0 = 3 = Saxon Math Course 1 L Adaptations Lesson 77

27 Written Practice (continued) (page 402) = = = = = 3 4 = = = = = 19. perimeter 20. area 21. Use exponents. ) 1000 ) 1000 ) 1000 ) 1000 ) 1000 ) % = is of $80 $80 $80 Saxon Math Course 1 L Adaptations Lesson 77

28 Written Practice (continued) (page 403) 23. $38.80 $38.80 $38.80 $ A polygon is a straight-sided closed figure. Is every quadrilateral a polygon? 25. time start 12:00 p.m. Count back hours. Count back minutes. 26. What percent appears to be shaded? A 20% B 40% C 60% D 80% 27. W(2, 3), X(1, 0), Y( 3, 0), Z( 2, 3) 28. parallel to WX parallel to XY = ) 210 ) 350 ) 210 ) 350 ) 210 ) 350 ) 210 ) 350 = Always begin at the origin. Next, move on the x-axis. Last, move on the y-axis. 30. What shape? Round the circumference to the nearest ten miles. Use work are Saxon Math Course 1 L Adaptations Lesson 77

29 LESSON 78 Capacity (page 404) Name Measuring liquids: U.S. Customary System: ounces, cups, pints, quarts, gallons Metric system: milliliters, liters One liter is a little more than one quart. Liquids Teacher Notes: Introduce Hint #58, Measuring Liquids and Capacities of Containers. Refer students to Liquids and Equivalence Table for Units on page 1 in the Student Reference Guide. Post reference chart, Liquids. Milk Half & Half Equivalence Table for Units of Liquid Measure U.S. Customary System Metric System 1 gallon = 4 quarts 1 quart = 2 pints 1 liter = 1000 milliliters 1 pint = 2 cups 1 cup = 8 ounces Practice Set (page 405) What fraction of a gallon is a quart? gallon quarts A 2-liter bottle has a capacity of how many milliliters? ml L ml 1 2? c. A half gallon of orange juice will fill how many 8-ounce cups? cups d. The entire contents of a full 2-liter bottle are poured into an empty half-gallon carton. Will the half-gallon container overflow? Why or why not? The half-gallon c will o because 2 liters is a little m than half a gallon. Saxon Math Course 1 L Adaptations Lesson 78

30 Written Practice (page 406) 1. ( ) ( ) = 2. cm mm 1? 3. Go down the 3s and 4s columns of the 60 lights were on. 5 c. d. 5. not prime, not composite m = 1 m = w = x = y 4 5 = w = 10. shaded x =. y = c. Saxon Math Course 1 L Adaptations Lesson 78

31 Written Practice (continued) (page 406) = = 1 2 = = = = 2 3 = = = = = The opposite sides of a rectangle are parallel. True or false? Saxon Math Course 1 L Adaptations Lesson 78

32 Written Practice (continued) (page 407) 21. average 22. ) ft. in _ 2? Draw a quadrilateral that is NOT a rectangle. 26. See the Student Reference Guide. Use work are 27. (5, 3), (5, 1), ( 1, 1) 29. A liter is like a: (, ) 30. one pint = ounces teaspoons = 1 tablespoon 16 tablespoons = 1 cup 2 cups = 1 pint 2 pints = 1 quart 4 quarts = 1 gallon A pint B quart C 1 gallon D gallon 2 Saxon Math Course 1 L Adaptations Lesson 78

33 LESSON 79 Area of a Triangle (page 408) Name Notice that the area of any triangle is: 1 the area of a parallelogram with the same base and height 2 Teacher Notes: Review Geometric Formulas on page 29 in the Student Reference Guide. The activity in the Student Edition is optional. So the formula for the area of a triangle is: A = 1 2 bh or A = bh 2 The height must be perpendicular to the base. Area must be expressed in square units (16 cm 2 ). A = 1 (8 cm)(4 cm) 2 A = 16 cm 2 Practice Set (page 410) Find the area of each triangle: c. d. e. If the height of the triangle in c is doubled to 30 mm, would the area double? 1 (56)(30) = 2 = Written Practice (page 410) 1. Divide the p by 2 and s the length from the quotient liters = 2 quarts ounces 1 liter 1 quart Use work are Saxon Math Course 1 L Adaptations Lesson 79

34 Written Practice (continued) (page 410) See the Student Reference Guide % = is of = birch all others 30 c. 7. A = 1 2 bh = (0.12) = = = Saxon Math Course 1 L Adaptations Lesson 79

35 Written Practice (continued) (page 411) = q = q = m = n = = = m = n = 17. w = = 1 4 = 18. perimeter each side area 19. (9 10) + (6 1) + ( ) 20. circumference 21. closest to zero A 2 B 0.2 C 1 D Round 6.7 to and 7.3 to. Then m. Saxon Math Course 1 L Adaptations Lesson 79

36 Written Practice (continued) (page 411) = = 24. halfway only one pair of parallel sides 27. ( 5, 5), (1, 5), (3, 1), ( 3, 1) 28. area of square 100 cm 2 each side perimeter of square 29. each side of hexagon perimeter of hexagon = ) 32 ) 32 ) 32 ) 32 ) 32 ) 32 ) 32 ) 32 ) 32 ) 48 = Saxon Math Course 1 L Adaptations Lesson 79

37 LESSON Name 80 Using a Constant Factor to Solve Ratio Problems (page 413) Ratio can be used to express an actual count. Ratios and actual counts are related by a constant factor. Multiply the terms of a ratio by the constant factor to find the actual count. A ratio box can help to sort the numbers out. To find the constant factor ask: What did they multiply by to get the actual count? That number is your constant factor. You will multiply the other ratio term by the same thing. Example: To make green paint, the ratio of blue paint to yellow paint is 3 to 2. For 6 ounces of yellow paint, how much blue paint is needed? Draw a ratio box. Blue Paint Yellow Paint Ratio Actual Count Blue Paint Yellow Paint Ratio 3 constant factor 2 constant factor Actual Count? 6 A ratio term and an actual count are given for yellow paint. What number times 2 (ratio term) equals 6 (actual count)? 3 3 is the constant factor. Multiply the ratio term for blue paint by the constant factor. 3 3 = 9 9 ounces of blue paint are needed. Practice Set (page 414) Draw a ratio box and use a constant factor to illustrate and solve these ratio problems. The ratio of boys to girls in the cafeteria was 6 to 5. If there were 60 girls, how many boys were there? The ratio of ants to flies at the picnic was 8 to 3. If there were 24 flies, how many ants were there? Written Practice (page 414) 1. mean range ) = 2.5 mi ft 1 2.5? Use work are Saxon Math Course 1 L Adaptations Lesson 80

38 Written Practice (continued) (page 415) 3. 12p = 4. perimeter players teams 168? 1 A = bh 5. perimeter 6. one pair of parallel sides A = 1 2 bh 7. See the Student Reference Guide of 30 present 5 5 is of of 30 absent = 100 = 0.6 = 11. square sides qt 1 gal. Saxon Math Course 1 L Adaptations Lesson 80

39 Written Practice (continued) (page 415) = ) = = = 1 4 = = a = a = 19. 3n = x = 0.36 n = x = y = y = Saxon Math Course 1 L Adaptations Lesson 80

40 Written Practice (continued) (page 416) 23. Frosted Rice 24. Coco Flakes sugar cereal 100? How many f grams of sugar 26. one quart = cups does have than Coco Flakes? Answer: Use work are 27. (3, 0), (3, 3), (0, 3) 28. complement = 90 A (, ) B C 29. b = 6 h = 8 A = 1 2 bh 30. Connect the endpoints. Is the quadrilateral a parallelogram? A = Use work are Saxon Math Course 1 L Adaptations Lesson 80

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