Problems About Combining Problems About Separating (page 59)

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1 LESSON Name 11 Problems About Combining Problems About Separating (page 59) Story problems have patterns. Addition Pattern Subtraction Pattern Teacher Note: Review Hint #1, Word Problem Cues. + some + some more + total beginning amount some went away what remains To solve these story problems: 1. Always put the larger number on top. 2. Look for the keyword. 3. Work the problem. 4. Check to see if your answer makes sense. Word Problem Keywords + sum total, together, joined (after) difference profit, before, minus; comparisons such as: more than, less than Practice Set (page 61) Check to see if your answer makes sense. a = P 314 total 129 finished still to read b P = total 19 first half second half c. Oscar walked miles on Tuesday. He walked miles on Wednesday. How many did he walk in all? Answer: Saxon Math Course 1 L11-41 Adaptations Lesson 11

2 Written Practice (page 61) l = a. product b. sum + 21 in all + 08 before after a. b. 3. (6 4) (8 5) = = 4. $20 m = $7.75 $ g = $ w = x = y 1000 = w = x = m = 700 y = m = Saxon Math Course 1 L11-42 Adaptations Lesson 11

3 Written Practice (continued) (page 62) (100 10) short division 8 ) long division R 10 ) ) w w = 15. offset w = w = 17. Find the pattern. Continue it = +? +? 2, 6, 10,,,,...,, Saxon Math Course 1 L11-43 Adaptations Lesson 11

4 Written Practice (continued) (page 62) 21. product fraction NOT shaded 24. perimeter 25. sum of the first five odd numbers divided by 6 ) girls boys students 28. Water freezes on the Celsius scale at. See the Student Reference Guide ) 0000 ) Finish this story from the bottom of page 59. Pham had. He earned $ more. Then how m did he have? Answer:. Saxon Math Course 1 L11-44 Adaptations Lesson 11

5 LESSON 12 Place Value Through Trillions Multistep Problems (page 63) Name To determine place value: Use a place value chart. Look at the commas to see which number family the digit is in. Teacher Notes: Introduce Hint #23, Place Value (Digit Lines). Refer students to Place Value on page 11 in the Student Reference Guide. To write large numbers: Use digit lines. A comma is always followed by 3 digit lines. To solve multiple-step problems: Use parentheses. First put in the signs. Then put in the numbers. Practice Set (page 66) a. Which digit is in the millions place in 123,456,789? b. What is the place value of the 1 in 12,453,000,000? c. Use words to write 21,350,608. (Use commas.) d. Use digits to write four billion, five hundred twenty million.,,, e. When the product of 6 and 4 is divided by the difference of 6 and 4, what is the quotient? ( ) ( ) = product difference Saxon Math Course 1 L12-45 Adaptations Lesson 12

6 Written Practice (page 66) 1. ( ) ( ) = product sum 2. ninety-three million miles,, K = l = perimeter 6. 6m = 60 m = 7. a. ) b. ) a. 9. ( 3 x 3 ) ( ) = = b. 10. Find the pattern. Continue it. x? x? x? 1, 2, 4, 8,,,,...,, Saxon Math Course 1 L12-46 Adaptations Lesson 12

7 Written Practice (continued) (page 67) m = n = m = n = sum of the first five even numbers ten-billions place 18. 5,764,283, ,456,789, hundred-thousands place 987,654, = Saxon Math Course 1 L12-47 Adaptations Lesson 12

8 Written Practice (continued) (page 67) 21. $ y = 0 y = w w = m ) ) 000?000 m = divided by red not red total fraction not red If 7 of the marbles are r, then ) 00 of the 10 marbles are n red. 29. four trillion 30. What is the difference between the product of and and the sum of and? ( ) ( ) =,,,, product sum Saxon Math Course 1 L12-48 Adaptations Lesson 12

9 LESSON Name 13 Problems About Comparing Elapsed-Time Problems (page 68) More story-problem patterns: Comparison Pattern greater lesser difference Elapsed-Time Pattern later date earlier date difference These patterns are subtraction patterns. To solve these story problems: 1. Always put the larger number on top. 2. Look for the keyword. 3. Work the problem. 4. Check to see if your answer makes sense. Practice Set (page 70) a. 26,290 18,962 = d 26,290 Castor + 18,962 Weston more b = d 1215 Magna Carta Norman Conquest years between Written Practice (page 71) 1. ( ) ( ) = product sum 2. two hundred fifty thousand miles, Saxon Math Course 1 L13-49 Adaptations Lesson 13

10 Written Practice (continued) (page 71) ,000,000, five million, two hundred thousand words:,, 5. (score 3) = See Counts on page 1 in the Student Reference Guide. A score is, so three score is = T d = miles to Cincinnati miles to Chicago farther 8. mental math = Combine ; then add. 9. mental math = Multiply 9 11; then multiply that by. 10. thousands place 54,321 Saxon Math Course 1 L13-50 Adaptations Lesson 13

11 Written Practice (continued) (page 71) 11. 1,234,567, perimeter Cancel the matching zeros ,000 0,0030 = $ Find the pattern. Continue it , 4, 3, 6, 5, 8,, w = 365 w = Saxon Math Course 1 L13-51 Adaptations Lesson 13

12 Written Practice (continued) (page 72) 21. ( ) 3 = 22. length in inches 3 = 23. To find the perimeter of a s, either a the lengths of the four sides or m the length of one side by four. 25. Water boils on the Fahrenheit scale divided by 7 at. See the Student Reference Guide. ) a = The answer is NOT 3. b 4 = a = b = 12 = d 16 = 61 c c = d = Saxon Math Course 1 L13-52 Adaptations Lesson 13

13 LESSON Name 14 The Number Line: Negative Numbers (page 73) On the number line: Positive numbers are to the right of zero. Negative numbers are to the left of zero. Zero is neither positive nor negative. Opposites are numbers the same distance from zero ( 5 and 5). Integers are all the counting numbers, their opposites, and zero. Example: What number is 7 less than 3? 7 less than 3 means to start with 3 and subtract On the number line, start on 3 and count 7 integers to the left. The answer is 4. Order matters in subtraction. Teacher Notes: Introduce Hint #24, Positive and Negative Numbers. Refer students to Number Line, Definitions, and Number Families on pages 9 and 10 in the Student Reference Guide. 5 2 = 3 is very different from 2 5 = 3 If the first number is what you have in your checking account and the second is the amount of your check, the answer is what you have left in the bank (or what you owe the bank). Practice Set (page 75) a. Compare 8 6 b. Use words to write this number: 8. h. 1 5 = i. All five of these numbers are integers: true or false? 3, 0, 2, 10, 50 c. What number is the opposite of 3? j. The temperature was twelve degrees below zero Fahrenheit. Use a negative number to d. Arrange these numbers in order from least to greatest: 0, 1, 2, 3 least,,, e. What number is 5 less than 0? f. What number is 10 less than 5? greatest write the temperature. k. The desert floor was 186 feet below sea level. Use a negative number to indicate that elevation. l. The stock s price dropped from $18.50 to g. 5 8 = $ Use a negative number to express the change in the stock s value. Saxon Math Course 1 L14-53 Adaptations Lesson 14

14 Written Practice (page 75) 1. ( ) ( ) = sum difference ,654,321, one hundred eighty-six thousand miles per second 4., miles per 5. least to greatest 6. 5, 3, 1, 0, 2,,,, a = perimeter 10. Find the pattern. Continue it.??...,16, 8, 4,,,... Saxon Math Course 1 L14-54 Adaptations Lesson 14,

15 Written Practice (continued) (page 76) = d less than Cancel matching zeros = 36, R 18 ) n 310 = = $3.05 m = $2.98 $3.05 $2.98 n = 20. estimate cm measure cm measure mm m = Saxon Math Course 1 L14-55 Adaptations Lesson 14

16 Written Practice (continued) (page 76) 21. How many zeros do you count? (100) (100) (100) = 22. ten-thousands place 123,456, To find the length of an object in millimeters, m the number of centimeters by t ) 0000 ) (6 2) divided by 6 ) six billion, four hundred million of 12 3,,, 29. opposite of least to greatest 1, 0, 1, 1 2,,, Saxon Math Course 1 L14-56 Adaptations Lesson 14

17 LESSON 15 Problems About Equal Name Groups (page 78) Use multiplication and division to solve equal-groups problems. Look for the keyword, each. The example below shows the steps to solve an equal-groups problem: There are 232 students in 8 classrooms. If there are the same number of students in each classroom, how many students would each classroom have? 1. Name the two things the problem is about. students classrooms 2. Fill in what you know. students classrooms Fill in what you re looking for. students classrooms 232 8? 1 4. Make a diagonal loop and multiply the numbers inside the loop. (The loop will never include the question mark.) students classrooms 232 8? 1 5. If the number outside the loop isn t 1, divide by the outside number. 29 students 8 ) 232 Practice Set (page 79) Teacher Notes: Introduce Hint #25, Rate. Refer students to Proportion (Rate) Problems on page 19 in the Student Reference Guide. a. Multiply the loop. Divide by the outside number. n 25 = 450 b. Multiply the loop = t cents cups ) cups ? spaces rows parking spaces Saxon Math Course 1 L15-57 Adaptations Lesson 15

18 Written Practice (page 79) 1. In the auditorium there were 15 rows of chairs with 20 chairs in each row. How many c were in the a? See the bottom of page = d It is reasonable because 32 plus equals F = t Multiply the loop = d O s ounces 320 1? Subtract 5 from 2. Use words for answer. 7. $ $ Find the pattern. Continue it.?..., 6, 4, 2, 0,,,, Split the difference. digits: words:,, degrees Fahrenheit Saxon Math Course 1 L15-58 Adaptations Lesson 15

19 Written Practice (continued) (page 80) 10. $ $ To which hundred is 587 closest? ) R 36 ) Cancel matching zeros w = w = w = w = 76 = w + $65 = $1000 m m = w = Saxon Math Course 1 L15-59 Adaptations Lesson 15

20 Written Practice (continued) (page 81) n = How many millimeters? n = 23. ( ) 3 = ,345, ten billions place 123,456,789, least to greatest 28. play in band 0, 1, 2, 3 total students 29. Multiply the loop. buttons $ ?,,, 30. not positive not negative See the Student Reference Guide. Saxon Math Course 1 L15-60 Adaptations Lesson 15

21 LESSON Name 16 Rounding Whole Numbers Estimating (page 82) To round whole numbers: 1. Underline the place value you are rounding to. 2. Circle the digit to its right. 3. Ask Is the circled number 5 or more? If so, add one to the underlined number. If not, the underlined number stays the same. 4. Replace the circled number (and any numbers after it) with zero. Teacher Note: Introduce Hint #26, Estimating or Rounding. Example: Round 472 to the nearest hundred Estimating is a quick way to find an answer that is close to the exact answer. To estimate an arithmetic answer, use rounded numbers. To estimate on a chart, look at the scale on the left side of the chart and guess what the measurement is. Practice Set (page 84) Round each number to the nearest ten: a. 5 7 b. 6 3 c. 45 Round each number to the nearest hundred: d e f. 426 Round each number to the nearest thousand: g h i Use rounded numbers to estimate each answer: j = k = l = m. Cancel matching zeros. 29 ) ) Saxon Math Course 1 L16-61 Adaptations Lesson 16

22 Practice Set (continued) (page 84) n. About how many fewer people lived in Ashton in 1980 than in 1990? o. The graph shows an upward trend in the population of Ashton. Based upon the trend, what would be a reasonable projection for the population of Ashton in the year 2010? Written Practice (page 85) 1. ( ) ( ) = product sum = y 1803 Lewis & Clark 1584 Walter Raleigh 3. Multiply the loop. Divide by the outside number. 5 g = 4. hundred-thousands place 159,342,876 cards groups 5 Jacob had groups of cards, and times equals ,068,715 words: , Saxon Math Course 1 L16-62 Adaptations Lesson 16

23 Written Practice (continued) (page 85) ,312 14, ) R 100 ) (5 + 11) 2 = $ $ $ ( ) = (2 + 3) (1 + 2) It felt colder at p.m. because Saxon Math Course 1 L16-63 Adaptations Lesson 16

24 Written Practice (continued) (page 86) = t 22. Multiply the loop. beats minutes 72 1? Hay Eaten by Elephants 23. Father Hay Eaten Daily (in kilograms) Baby Mother Father Baby 24. Father Mother Baby 25. Multiply the loop. 26. Mother eats how many fewer p pounds days 1? per day than f? Answer: 27. 6w = m 60 = n = w = m = 30. n = Saxon Math Course 1 L16-64 Adaptations Lesson 16

25 LESSON Name 17 The Number Line: Fractions and Mixed Numbers (page 87) Point A represents the mixed number 2 3_ 5. The diagram below shows how to read a mixed number on a number line. 1. Count the number of whole units from zero. This is the whole number part. Teacher Notes: Review Hint #17, Reading Inch Rulers. Refer students to Fraction Families Equivalent Fractions on page 12 in the Student Reference Guide. The activity in the Student Edition is optional. 2. Count the number of segments in one whole unit. This is the denominator of the fraction part. 3. Count the number of segments past the whole unit to the point. This is the numerator of the fraction part number of units segments past the unit number of segments in the whole unit The ruler is divided into sixteenths. Count by sixteenths; reduce when possible. Practice Set (page 90) a. Continue this sequence to 1 1_ 2 : Count by 1 s (reduce when you can) ( 2, 16 ) ( 6,,,, 16 ) 3 16 ( 4 16 ) , 16 ( 8, 16 ) , 9 16,( ) 1 8,, ( 2 16 ) 1 8,, ( 2 16 ) 1 8,,, ,( 2 16 ) 1 8,, ( 2 16 ) 1 8,, ( 2 16 ) 1 8,, b. What number is halfway between 2 and 3? c. What number is halfway between 2 and 5? Mark a point on the number line to show this number d. Point A represents what mixed number on this number line? Saxon Math Course 1 L17-65 Adaptations Lesson 17

26 Practice Set (continued) (page 90) Use your ruler to find the length of each line segment to the nearest sixteenth of an inch: e. f. g. Written Practice (page 90) 1. sum = d 3. 6 = y 12, moon landing 1903 first flight Multiply the loop. yards se seconds 6 1? 4. $1000 = v Multiply the loop. coins $ ? 5. Estimate the sum short division = 8. fact family a + b = c = 5 b + b = c 2 + = 5 c b = c 2 =5 c b = c 2 = = 10. A square has equal sides. To find the perimeter, we m the length of one side by. Saxon Math Course 1 L17-66 Adaptations Lesson 17

27 Written Practice (continued) (page 91) 11. Reduce. 12. $3 y = $1.75 $3.00 $1.75 y = 13. m 20 = n = 0 30 $20 m = n = 15. commutative property of addition = 14 + w w = (50 25) = 18. long division ,287 = 20. Find the pattern. Continue it. 5, 10,, 20, 25,... Saxon Math Course 1 L17-67 Adaptations Lesson 17

28 Written Practice (continued) (page 91) 21. hundred-millions place 987,654, Cancel the matching zeros. 250, ,100 = 23. offset $3.750 $ of grams sum of the first six positive odd numbers 26. One way to find 1 4 of 52 is to d 52 by. 27. a. 1 dollar = quarters = = 4 8 b. Multiply the loop. quarter dollar 1? a. b = x 16 sixteenths of an inch Saxon Math Course 1 L17-68 Adaptations Lesson 17

29 LESSON Name 18 Average Line Graphs (page 93) One way to find the average is to make equal groups. Teacher Note: Introduce Hint #27, Average = = 18 Average: Add; then divide by the number of groups. Halfway: Add; then divide by 2. Example: What number is halfway between 27 and 81? Add = 108 Divide by = 54 A line graph shows how a measurement changes over time. Practice Set (page 96) a. average b. average c. halfway ) ) ) d. halfway e. average ) ) Use the information in the line graph to answer these questions: f. How many inches did Margie grow from her eighth to her twelfth birthday? g. During which year did Margie grow the least? between her th and her th birthday h. Based on the information in the graph, would you predict that Margie will grow to be 68 inches tall? Saxon Math Course 1 L18-69 Adaptations Lesson 18

30 Written Practice (page 96) pattern pattern 3. Multiply the loop. $ans cans ? pattern 5. average ) halfway ) less than 2 8. $ Cancel the matching zeros ,180 10, = 11. $3.64 $3.64 $ ,375 13,576 Saxon Math Course 1 L18-70 Adaptations Lesson 18

31 Written Practice (continued) (page 97) = 15. w 84 = w = n = 17. (1 + 2) 3 = (1 2) + m 18. perimeter 5 cm 3 cm m = 19. sum of the first six positive even numbers 20. Find the pattern. Continue it. 1, 2, 4,, 16, 32, 64 Multiply the preceding term by Saxon Math Course 1 L18-71 Adaptations Lesson 18

32 Written Practice (continued) (page 97) ,654, running resting 25. Multiply the loop. minutes beats running 1? 26. How many fewer heartbeats per m are there for a w person than for a r person? Answer: 27. average To be reasonable, the average should 28. a. 1 dollar = dimes b. Multiply the loop. b. dimes dollars 1? be a number between the least and a. the. b _ in. 30. Average problems include: 4 a. b. Saxon Math Course 1 L18-72 Adaptations Lesson 18

33 LESSON Name 19 Factors Prime Numbers (page 99) A factor is a number that divides into another number evenly. To list the factors of whole numbers: 1. Always start with the number Always end with the number given. 3. Then find all the factors of the number. (Use the times table in the Student Reference Guide.) 4. List the factors in order. Write each factor only once. Example: The factors of 12 are 1, 2, 3, 4, 6, 12. A prime number has exactly 2 factors no more, no less. Use the Student Reference Guide. Number Factors , 2 3 1, 3 4 1, 2, 4 5 1, 5 6 1, 2, 3, 6 7 1, 7 8 1, 2, 4, 8 9 1, 3, , 2, 5, 10 Practice Set (page 102) List the factors of the following numbers: Teacher Notes: Introduce Hint #28, Factors of Whole Numbers, and Hint #29, Prime Factorization Using the Factor Tree. Refer students to Factors on page 5 and Prime Numbers on page 9 in the Student Reference Guide. Post reference chart, Primes and Composites. The activity in the Student Edition is optional. Use a factor tree to find the prime factors of a number. 1. List two factors of the given number and write them as branches of the tree. One of the factors must be a prime number. Circle any prime factor. 2. Continue to factor until each factor is a prime number. 3. Write the prime factors in order. Example: Factor 20 into prime factors. List two factors of 20: 2 (prime number) and factors into 2 (prime number) and 5 (prime number) a. 14:,,, b. 15:,,, c. 16:,,,, d. 17:, Circle the number in each group that is a prime number: (See the Student Reference Guide.) e. 21, 23, 25 f. 31, 32, 33 g. 43, 44, 45 Circle the number in each group that is NOT a prime number: h. 41, 42, 43 i. 31, 41, 51 j. 23, 33, 43 Show which prime numbers we multiply to make these products. List two factors. (One factor must be prime.) Example: List two factors of 20: 2 (prime) and 10. Continue to factor until each factor is a prime 10 factors into 2 (prime) and 5 (prime). number. 20 = Write the prime factors in order. k. 16 = l. 18 = Saxon Math Course 1 L19-73 Adaptations Lesson 19

34 Written Practice (page 103) 1.? ) Abraham Lincoln s Gettysburg Address (4 ) + 7 years = = = 4. g = 203 Multiply the loop. Divide by the outside number. turnips rabbits ? 1 5. average Find the pattern. Continue it , 4, 9, 16, 25,, cm = mm 3 cm = mm 9. factors of Factors of 15: How many? 1,,,,, 20 Saxon Math Course 1 L19-74 Adaptations Lesson 19

35 Written Practice (continued) (page 103) 11. prime number Use the Student Reference Guide. A 25 B 27 C Cancel the matching zeros. 250, ,100 = 13. R ) = 15. $3.450 $ $10.00 w = $1.93 $10.00 $01.93 w = 17. w = ab = c 3 = c c ab = b c ab = 19. least to greatest 3, 2, 1, 1 2, 0 w = ,,,, Saxon Math Course 1 L19-75 Adaptations Lesson 19

36 Written Practice (continued) (page 104) 21. ten-millions place , 4 56, ,792,468, perimeter in. $ each side 25. ( ) (51 49) = = 26. prime number A 2 B 22 C factor tree 28. average If a number is even it is divisible by. Odd numbers are not divisible by. Saxon Math Course 1 L19-76 Adaptations Lesson 19

37 LESSON 20 Greatest Common Factor Name (GCF) (page 105) To find the greatest common factor (GCF): 1. List (in order) the factors of the smallest number. 2. Starting with the greatest factor, cross off factors that are NOT factors of the other numbers. 3. Circle the greatest factor that is a factor of all the numbers. This is the GCF. Example: Find the greatest common factor of 6, 9, and 15. 6: 1, 2, 3, 6 Practice Set (page 106) Find the greatest common factor (GCF) of the following: Teacher Note: Introduce Hint #30, Finding the Greatest Common Factor. a. 10 and 15 Here are the factors of 10. Starting with the greatest factor, cross off factors that are NOT factors of 15. Circle the GCF. b. 18 and 27 factors of 18: 1, 2, 3, 6, 9, 18 1, 2, 5, 10 c. 18 and 24 1, 2, 3, 6, 9, 18 d. 12, 18, and 24 1, 2, 3, 4, 6, 12 e. 15 and 25 1, 3, 5, 15 f. 20, 30, and 40 1, 2, 4, 5, 10, 20 g. 12 and 15 1, 2, 3, 4, 6, 12 i. Three numbers whose GCF is 7: Hint: multiples of 7,, h. 20, 40, and 60 1, 2, 4, 5, 10, 20 Saxon Math Course 1 L20-77 Adaptations Lesson 20

38 Written Practice (page 106) 1. ( ) ( ) = product sum 2. one billion, four hundred twenty-nine kilometers,,, 3. ten-millions place ,325, C 0 C 3 C = = 6. average Here are the factors of 12. Starting with the greatest factor, cross off factors that are NOT factors of 20. 1, 2, 3, 4, 6, GCF of 9, 15, and 21 List (in order) the factors of the smallest number, 9. Starting with the greatest factor, cross off factors that are NOT factors of the other numbers, 15 and 21. The greatest factor is the GCF. 9. $ Saxon Math Course 1 L20-78 Adaptations Lesson 20

39 Written Practice (continued) (page 107) = , , , $ = 16. w 76 = w = ,009 w = w = 90 14, , q 365 = w = w = p = , 10, 16, 22, 28,... q = p = Saxon Math Course 1 L20-79 Adaptations Lesson 20

40 Written Practice (continued) (page 107) tenth positive odd number 1,,,,,,,,, 24. perimeter cm each side We d the perimeter by to find each side a. 1 dollar = bits b. Multiply the loop. estimate bits dollars 1? a. measure b. 27. average prime number A 5 B 15 C ,,,,,,, 24 List all numbers that evenly into ,000,000,000,000 1,000,000,000,000 Saxon Math Course 1 L20-80 Adaptations Lesson 20