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1 LESSON 51 Rounding Decimal Name To round decimal numbers: Numbers (page 268) 1. Underline the place value you are rounding to. 2. Circle the digit to its right. 3. If the circled number is 5 or more, add 1 to the underlined number. If the circled number is 4 or less, the underlined number stays the same. 4. Drop all digits after the underlined digit. Example: Round to the hundredths place: Practice Set (page 270) Round to the nearest cent: Teacher Note: Review Hint #26, Estimating or Rounding. a. $ b. $ c. $ Round to the nearest tenth: d e f Round to the nearest whole number or whole dollar: g h i. $ j. If the sales-tax rate is 6%, then how much sales tax is there on a $3.79 purchase? (Round the answer to the nearest cent.) $3.79 $3.79 rounded k. Describe how to estimate a 7.75% sales tax on a $7.89 item. 27 Harcourt Achieve Inc. To estimate a 7.75% sales tax on a $7.89 item, I would round 7.75% to, and round $7.89 to $ and then m. Saxon Math Course 1 L Adaptations Lesson 51

2 Written Practice (page 270) 1. ( ) ( ) 2. Home 3.5 mi School d 1804 crowned Emperor 1769 Napoleon born 4. a. tax $12.89 b. total a. b. 5. a. diameter 6. The whole number part of is b. Round to the nearest inch. C πd m. The next digit is 7. It is 5 or, so we round up to the next a. w number, which is. b. Use work area w over, over, up Add zeros. 4 ) 0. 5 w 27 Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 51

3 Written Practice (continued) (page 270) 11. shift Reduce ? as a fraction 17. decimal number (6 10) + ( ) 18. area each side perimeter 27 Harcourt Achieve Inc LCM of 2, 3, and Convert and reduce Saxon Math Course 1 L Adaptations Lesson 51

4 Written Practice (continued) (page 271) reciprocal of estimate common factors of 16 and estimate ,,, 26. average of x and y 27. Cancel the matching factors $0.79 The problem is to multiply by, so s the d p one place to the 29. mixed number r. 30. a , 80, 90, 75, 85, 1, 90, 80, 90 in order: 75,,,,,,,, 1 median mode b. 27 Harcourt Achieve Inc. Use work area. Use work area. Saxon Math Course 1 L Adaptations Lesson 51

5 LESSON Name 52 Mentally Dividing Decimal Numbers by 10 and 1 (page 272) Shift the decimal left for division one place for each zero in the divisor. Fill empty places with zeros. Example: shift left Teacher Note: Review Multiplication and Division of Decimal Numbers by 10, 1, 10 on page 6 in the Student Reference Guide. Practice Set (page 273) Mentally calculate each quotient. Write each answer as a decimal number. a b c d e f g h i. A stack of 10 pennies is 1.5 cm high. How thick is one penny in centimeters? In millimeters? 1.5 cm mm Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 52

6 Written Practice (page 273) 1. product piano 88 white black Now compare. 3. Puerto Rico Trench in Atlantic Ocean twenty-eight thousand, two hundred thirty-two feet 4. shift a To m by 10, s the decimal point one place to the. b To d by 10, s the decimal point one place to the. a. b. 5. students teachers 6. The answer is NOT (4)(0.125 ) over, over, up ( ) (1 0.2 ) Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 52

7 Written Practice (continued) (page 274) m m m m 13. $10 w $0.10 $10. $ Round to nearest cent. $8.59 $0.10 w 15. Round to the nearest inch. C πd 16. least to greatest ,,, , 2, 4, 7, 11,, perimeter each side area 27 Harcourt Achieve Inc. 19. What fraction of a foot is 3 inches? 20. is of tiles Saxon Math Course 1 L Adaptations Lesson 52

8 Written Practice (continued) (page 274) 21. reciprocal of LCM of 2, 4, and D 12 by. 23. a Use a meterstick. b a. b. 25. What decimal number? Answer with a mixed number perimeter each side 28. Gases in Earth s Atmosphere a. Nitrogen rounded to Gas Percent Composition nearest whole-number percent Nitrogen 78.08% Shade 50%. Oxygen 20.95% Argon 0.93% Other 0.04% b. Write as an unreduced fraction and as a decimal number. 29. Oxygen a. percent rounded to nearest ten b. Write as a reduced fraction. Use work area. a. 30. Complete the circle graph for the gases. Round each to the nearest whole number. Group Argon and Other together in one sector. A circle graph shows parts of b., 27 Harcourt Achieve Inc. a. b. a w. Use work area. Saxon Math Course 1 L Adaptations Lesson 52

9 LESSON Name 53 Decimals Chart Simplifying Fractions (page 276) The chart below summarizes the rules for adding, subtracting, multiplying, and dividing decimal numbers. Operations + by whole by decimal line up ; then count up over, over, up memory._._. cue ±._._ w )..0 D ).0._._ You may need to Place a decimal point to the right of whole number Fill empty places with zeroes Teacher Notes: Introduce Hint #46, Decimal Arithmetic Reminders Chart. Refer students to Decimal Arithmetic Reminders Chart on page 7 in the Student Reference Guide. Remember, fractions that do not have common denominators can be renamed to have common denominators. To reduce fractions to lowest terms: Divide both numbers by the largest number that will go into both evenly. (This is the GCF.) To convert and reduce improper fractions to mixed numbers: 1. Fix the top heavy number. 2. Add it to the whole number. Practice Set (page 277) Example: 4 8 Example: a. Write the letters from the chart that apply to each problem. Decimal Arithmetic Reminders Divide the numerator and denominator by 4 (not 2) Fix the top heavy number Add to the whole number Harcourt Achieve Inc. + by whole by decimal Line up the Multiply. Then count Decimal over, decimal points. decimals places. point is up. over, up A B C D E F 1. Place a decimal point to the right of a whole number. 2. Fill empty places with zeros E F F E Look at arithmetic symbols (+,,, ). b. Fill in the missing words on the decimals chart. + by whole by decimal Line up the decimal. Decimal Arithmetic Reminders Multiply. Then decimal. Decimal point is. 1. Place a decimal point to the of a whole number. 2. Fill empty places with. over, F, up Saxon Math Course 1 L Adaptations Lesson 53

10 Practice Set (continued) (page 277) Simplify: c d e Written Practice (page 278) 1. We only add or su digits that have the same place v. If we line up the de points, we also line up the di with the same p value hours 45 minutes before 3: p.m. Time Count back hours. Count back minutes. Use work area mean (average) and range What would x be to shift the decimal point two places right? 0.375x shift m x m 7. fraction and decimal number 1% 9. over, over, up Add zeros. 27 Harcourt Achieve Inc Saxon Math Course 1 L Adaptations Lesson 53

11 Written Practice (continued) (page 278) a. tax to the nearest cent $ 5.20 b. total 16. Which number is closest to one? A 1.2 B 0.9 C 0.1 D a. b. 17. C πd Round to the nearest foot Cancel the 8 and Harcourt Achieve Inc a. factors of 11:, b. p n Use work area. Saxon Math Course 1 L Adaptations Lesson 53

12 Written Practice (continued) (page 278) 21. compare 22. LCM of 6 and Cancel the matching factors Use work area ? Shade 2 3. Use work area % is of Add. 29. Use decimal numbers to tell how much less point A is than point B. 30. reciprocal of Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 53

13 LESSON Name 54 Reducing by Grouping Factors Equal to 1 Dividing Fractions (page 280) To reduce fractions in factored form: 1. Arrange factors in order. 2. Cancel the matching factors in dividend and divisor. Example: To divide fractions: Cancel the matching factors. Teacher Notes: Review Hint #36, Reducing Fractions (Manipulatives and Shortcuts), and Hint #40, Canceling Fractions. Review Fraction Families Equivalent Fractions on page 12 in the Student Reference Guide. 1. Copy the first fraction. 2. Change sign to. 3. Flip the second fraction. 4. Cancel. 5. Multiply across. Practice Set (page 282) } a b Cancel the matching factors. Cancel the matching factors. c. How many 3 8 s are in 1 2? d. How many 1 2 s are in 3 8? 2 ) ( ) ( Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 54

14 Written Practice (page 283) 1. Complete the chart. 2. ) 0 Decimal Arithmetic Reminders + by whole by decimal Line up the Multiply. Then Decimal point over, decimal. decimal. is., up 1. Place a decimal point to the of a whole number. 2. Fill empty places with. 3. estimate 151,325, ,212, d (1 1) 6. Give a mixed number answer. ) 0 7. Halfway: Add; then divide by $3 n $3. $3. 9. m shift n 27 Harcourt Achieve Inc m Saxon Math Course 1 L Adaptations Lesson 54

15 Written Practice (continued) (page 283) 11. ( ) (1.2) over, over, up 12. ( 4 3 ) 2 ) hundred-thousands place 123,456, tax $ Use rulers to compare. 2 cm inch 17. double minus area 1, 3, 5, 7, 9,,,,,,, 27 Harcourt Achieve Inc. 19. a. 30 b. played did not play 20. a. 5 6? 24 b. 5 8? 24 a. a. b. b. Saxon Math Course 1 L Adaptations Lesson 54

16 Written Practice (continued) (page 284) 21. LCM of 3, 4, and % is of 24. shift in. cm 1 1? 25. Cancel the matching factors Cancel the matching factors C πd Round to the nearest inch. 1 2 Estimate: 15 Add. 29. a. perimeter b. area } } 27 Harcourt Achieve Inc. a. b. Saxon Math Course 1 L Adaptations Lesson 54

17 LESSON Name 55 Common Denominators, Part 1 (page 285) Fractions with the same denominator have common denominators. The common denominator is 5. These fractions do not have common denominators. To add or subtract fractions that do not have common denominators: 1. Find a common denominator. Example: 2. Rename the fractions. 3. Add or subtract Practice Set (page 287) a. 1 2 b. 8 c d. 1 2 e. 5 8 f g. This exercise is optional. 27 Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 55

18 Written Practice (page 287) 1. When we divide a decimal number by a w number using a division box, we place a d point in the quotient directly u from the decimal p in the dividend. Use work area. 3. pumpkins pounds over, over, up ) Shift Shift. (0.17)( 1 ) 27 Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 55

19 Written Practice (continued) (page 287) ? Mt. McKinley standard form (2 10,0) + (3 1) + (2 10) 15. Round the product to the nearest hundredth C πd 18. perimeter Round to the nearest kilometer. each side area 27 Harcourt Achieve Inc dimes LCM of 3 and 4 Saxon Math Course 1 L Adaptations Lesson 55

20 Written Practice (continued) (page 288) 21. a. factors of 23:, b. p ? 1 n Use work area height width 27. fraction shaded 28. Cancel the matching factors :45 p.m. to 10:25 p.m. 7:45 p.m. to hr to 10:25 p.m. min 30. a. triangle with one right angle b. triangle with one obtuse angle 27 Harcourt Achieve Inc. a. triangle b. triangle Saxon Math Course 1 L Adaptations Lesson 55

21 LESSON Name 56 Common Denominators, Part 2 (page 289) To find a common denominator (when both fractions must be renamed): 1. Find the LCM. (Use the times table for help.) 2. Rename fractions using the LCM as the common denominator. 3. Add or subtract. Simplify as necessary. Example: Practice Set (page 292) Teacher Notes: Introduce Hint #47, Comparing Fractions. Review Hint #38, Finding the Least Common Multiple. 1. Look down the 3s and 4s columns in the times table to find the LCM (12). 2. Rename the fractions ( 8 12 and 6 12 ). 3. Add and simplify. a b c d e f Before comparing, write each pair of fractions with common denominators. g h i Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 56

22 Written Practice (page 292) a. white piano b. black white 0 0 a. b $3.0 0 $3.0 0 $ over, over, up Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 56

23 Written Practice (continued) (page 292) a. 40% b. is of decimal number (8 10) + ( ) + ( ) a. b C πd Molly s estimate reasonable. is close to 3.14 for π. So the tire would go a l more than 6 feet on one turn. Use work area. 17. mean perimeter each side area 27 Harcourt Achieve Inc w 0 w Saxon Math Course 1 L Adaptations Lesson 56

24 Written Practice (continued) (page 293) 21. rule of reciprocals 2 3 m n 0 m n 23. The graph shows how much money was NOT spent. Naeem spent. 24. $30 0 Lisa $30 0 Donato 25. Donato total 26. What percent of the did save? 27. Cancel the matching factors Complete the rectangles. Then show three different ways to divide them in half. horizontal vertical diagonal Harcourt Achieve Inc. Use work area. Saxon Math Course 1 L Adaptations Lesson 56

25 LESSON Name 57 Adding and Subtracting Fractions: Three Steps (page 295) When adding and subtracting fractions, remember the S. O. S. method. 1. Shape Write the problem in the correct shape. Rename fractions to have common denominators. (Find the LCM. Use the times table for help.) 2. Operate Add or subtract. 3. Simplify Reduce or convert. Practice Set (page 296) a b c d e f Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 57

26 Written Practice (page 296) 1. ( ) ( ) d 18 Jefferson president 1743 Jefferson born Cancel. 8. $ ( ) 10. over, over, up 6 27 Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 57

27 Written Practice (continued) (page 296) Cancel area of the shaded part % 15. Round to the nearest tenth. ) least to greatest ,, th term 18. aces all cards 0 0 2, 4, 6, 8, 27 Harcourt Achieve Inc. 19. a. perimeter 20. is of b. area a. b. Saxon Math Course 1 L Adaptations Lesson 57

28 Written Practice (continued) (page 297) 21. factors of LCM Go down the 12s and 18s. Find the first number in common below zero Cancel the matching factors fraction shaded 28. Cancel _ 8 3 9_, which is a little 8 more than. If 3 CDs are in about inch, then there should be about CDs in 9 inches circumference 27 Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 57

29 LESSON 58 Probability and Name Chance (page 299) Probability and chance both tell how likely an event is to happen. Probability tells it with a (reduced) fraction. Chance tells it with a percent. The probability is the reduced ratio of the number of favorable outcomes (what you want to happen) to the number of possible outcomes (everything that can happen). Teacher Notes: Introduce Hint #48, Probability and Chance. Refer students to Probability, Chance, Odds on page 25 in the Student Reference Guide. Students will require a number cube to complete this lesson. Example: Example: a. What is the probability that the spinner will stop on a number greater than 1? number of favorable outcomes number of possible outcomes numbers greater than 1 3_ total numbers 4 b. What is the chance of spinning a number greater than 1? 75% What is the probability of pulling a blue marble out of the bag? number of favorable outcomes number of possible outcomes number of blue marbles 3_ total marbles 6 Then reduce. 3_ 6 1_ 2 The complement of an event is the opposite of the event. The probability of an event plus the probability of its complement equal 1. The sample space is the set of total possible outcomes. Practice Set (page 303) Juan is waiting for the roller coaster at an amusement park. He has been told there is a 40% chance that he will have to wait for more than 15 minutes. a. Find the probability that Juan s wait will be more than 15 minutes. Write the probability both as a decimal and as a reduced fraction. 27 Harcourt Achieve Inc. b. Find the probability that Juan s wait will NOT be more than 15 minutes. Express your answer as a decimal and as a fraction. c. What word names the relationship between the events in a and b? See the bottom of page 301. c A number cube is rolled. The faces of the cube are numbered 1 through 6. d. What is the sample space? See Example 3 on page 302. {,,,,, } e. What is the probability that the number rolled will be odd? Saxon Math Course 1 L Adaptations Lesson 58

30 Practice Set (continued) (page 303) f. What is the probability that the number rolled will be less than 6? g. State the complement to the event in f and find its probability. n l than ; Refer to the spinner at right for problems h k. h. What is the probability that the spinner will land in the gray sector? In the black sector? In either of the white sectors? gray black white i. What is the probability that the spinner will NOT land on white? j. State the complement of the event in i and find its probability. l on ; k. If you spin this spinner 30 times, roughly how many times would you expect to land in each sector? gray: of 30 black: of 30 white: of 30 l. Roll a number cube 24 times, and tally your results in the frequency table. Which outcomes occurred more than was predicted? Written Practice (page 304) Numbers Rolled Number Tally Predicted Outcomes Actual Outcomes 1 ( 1_ 6 of 24 ) ( ) ( ) 2. (2 ) dozen dozen 3. ) $4 4, Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 58

31 Written Practice (continued) (page 304) m n m n 8. 3 f $ f 11. over, over, up ) 12. over, over, up ) total $9.79 $9.79 $9.79 $ Harcourt Achieve Inc. 17., 0.6, 0.7, 0.8, 0.9,, 18. perimeter each side area Saxon Math Course 1 L Adaptations Lesson 58

32 Written Practice (continued) (page 305) What would w be to shift the decimal point two places right? 0.32w x w x 22. even numbers total numbers least to greatest Use a ruler. 1 inch, 3 cm, 20 cm,, % a. more or less than 1 2? b. reduced fraction a. b. 25. Finding 1 10 of $12.50 is like d $12.50 by. We shift the d point in $12.50 one place to 26. Cancel the matching factors the l, which makes $ Then we remove the trailing z. The answer is $. Use work area. 27. sum of the decimal numbers at x and y 28. Complete the rectangle and draw a diagonal segment. 29. perimeter 30. A lw Use work area. 27 Harcourt Achieve Inc. l 1.5 w 0.75 A Saxon Math Course 1 L Adaptations Lesson 58

33 LESSON 59 Adding Mixed Name Numbers (page 306) To add mixed numbers with unlike denominators, remember the S. O. S. method. 1. Shape Write the problem in the correct shape. Rename fractions to have common denominators. (Find the LCM. Use the times table for help.) 2. Operate Add. 3. Simplify Reduce or convert. Example: Practice Set (page 307) a b c d e f Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 59

34 Written Practice (page 307) :45 p.m. to 8:30 a.m. 9:45 p.m. to 7:45 a.m. hr 7:45 a.m. to 8:30 a.m. min 3. five billion, nine hundred million kilometers Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 59

35 Written Practice (continued) (page 308) d Halfway: Add; then divide by 2. d 15. nearest million 36,428, ? 17. Round to the nearest inch ft 1 ft 1 sq. ft 12 in. 12 in. sq. in. 27 Harcourt Achieve Inc. 19. m cm a. Shift. b. Shift a. b. Saxon Math Course 1 L Adaptations Lesson 59

36 Written Practice (continued) (page 308) (0.8) a. probability of less than 3 b. Write the complement of a.: n l than. Find the a. probability. b. 23. range highest lowest 24. Saturday noon 25. How many degrees did it drop between Answer: and? Use work area % 8 % 28. Shift. $ least to greatest 4, the reciprocal of 3 4, P 2l + 2w l 4 w 3 27 Harcourt Achieve Inc.,, P Saxon Math Course 1 L Adaptations Lesson 59

37 LESSON 60 Polygons (page 310) Name Polygons are closed flat shapes made from straight lines. Two sides of a polygon meet at a vertex. A quadrilateral is a polygon with four sides. The sides of a regular polygon are the same length. The angles of a regular polygon are equal. A square is a regular quadrilateral. Polygons are congruent when the same size and same shape. Practice Set (page 312) a. What is the name of this six-sided shape? h b. How many sides does a pentagon have? c. Can a polygon have 19 sides? 27 Harcourt Achieve Inc. d. What is the name for a corner of a polygon? v e. What is the name for a polygon with four vertices? q Saxon Math Course 1 L Adaptations Lesson 60

38 Written Practice (page 312) c $1.26 ounces $ 42 1? 2. a b. A little more than one g would cost a l more than $ a. 3. largest 3 digit whole number ( ) is of Harcourt Achieve Inc. Saxon Math Course 1 L Adaptations Lesson 60

39 Written Practice (continued) (page 312) 11. Add zeros. 12. How many sides? Round the product of 0.24 and 0.26 to the nearest hundredth average , 3, 5, 7,,,, m cm x Harcourt Achieve Inc y m x y m Saxon Math Course 1 L Adaptations Lesson 60

40 Written Practice (continued) (page 313) w prime numbers 40 to 50 w,, 23. Round to the nearest centimeter. 24. a. What decimal number? b. Round to a whole number. a. b. 25. sample space {,,, } probability of a 3 Use work area. 27. commercials total First divide both by. Then solve total price $6.89 $6.89 $6.89 $ a b Harcourt Achieve Inc. a. b. Saxon Math Course 1 L Adaptations Lesson 60