Divisibility (page 112)

LESSON 21 Divisibility (page 112) Name Tests for divisibility: Last-Digit Tests Inspect the last digit the number. A number is divisible by Teacher Notes: Introduce Hint #, Tests for Divisibility. Refer students to Tests for Divisibility on page 5 in the Student Reference Guide. 2 if the last digit is even. 5 if the last digit is 0 or 5. 10 if the last digit is 0. Sum--Digits Tests Add the digits the number and inspect the total. A number is divisible by if the sum the digits is divisible by. 9 if the sum the digits is divisible by 9. Practice Set (page 11) a. Which these numbers is divisible by 2? 12 2 5 b. Which these numbers is divisible by? 12 25 56 Use the divisibility tests to decide which the numbers 2,, 5, 9, and 10 are factors the following numbers: c. 120,,, d. 102, Written Practice (page 11) 1. ( ) ( ) = sum difference 2. 1959 = d 1959 Hawaii 1787 Delaware Saxon Math Course 1 L21-81 Adaptations Lesson 21

Written Practice (continued) (page 11). 16 w = Multiply the loop. Divide by the outside number.. fraction left pounds bowling balls 20 _ 000 000 _ 000 5. girls students _ 6. three hundredths 7. 8. 987,65,21 $2. 9. 1,, 16, 6,,... 10. 6 1 6 + 1 M the preceding term by. 11. Divisible by 9 means the sum the digits can be divided by 9. A 65 B 1179 C 1556 12. Estimate the sum. 96 197 20 Saxon Math Course 1 L21-82 Adaptations Lesson 21

Written Practice (continued) (page 115) 1. GCF 12 and 16 List (in order) the factors the smaller number, 12. Starting with the greatest factor, cross f factors that are NOT factors the larger number, 16. The greatest factor is the GCF. 1. 00 0100 = 1,,,,, 12 15. 2 ) _ 8,80 16. 6 7 8 17. $.75 18. $10 w = 87 $10.00 + $10.00 w = 19. 6 + 27 + m = 500 20. least to greatest 1,, 0, 2, 2 21. average 12 16 + 2 m = 22. factors 28,,,, 1,,,,, 28 Saxon Math Course 1 L21-8 Adaptations Lesson 21

Written Practice (continued) (page 115) 2. Multiply the loop. sides centimeters 1? 2. in. 25. (12 12) (11 1) = 26. Show clock divided into thirds. = and 27. 2 < 28. a. 1 dollar = bits b. Multiply the loop. < bits _ dollars 1? 1_ 2 a. Use work area. b. 29. Here are the factors 20. Cross f the factors that are NOT factors 0. 1, 2,, 5, 10, 20 0. Draw a. In the circle draw a p sign. Then draw a t sign in the circle.,,, Use work area. Saxon Math Course 1 L21-8 Adaptations Lesson 21

LESSON 22 Equal Groups Stories with Name Fractions (page 117) The textbook shows how to solve fraction a group problems with a diagram: What number is _ 16? 1. Draw a rectangle and divide it into the number equal parts shown by the denominator the fraction. (four parts) 2. Divide the number by the denominator and write that number in each part the rectangle. (16 = ). Count the number parts the rectangle shown by the numerator the fraction and find the answer. ( = 12) _ { { is 12 16 _ 16 { Teacher Notes: Introduce Hint #5, Fraction a Group, Part 2. Refer students to Finding a Part When the Whole is Known on page 1 in the Student Reference Guide. You can also solve these problems using an is/ loop. Notice the words is and appear in these problems: What number is _ 16? 1. Set up a loop problem using the words is and. 2. Write the given fraction first.. Then fill in the number given. If the is number is given, write it as the numerator. If the number is given, write it as the denominator.. Solve the problem. (1) Draw the loop. (2) Multiply the numbers in the loop. () Divide by the outside number. When working percent problems, remember that a whole is 100%. Practice Set (page 119)? 16? 16 (16 ) = 12 Answer using either the diagram or the is/ loop. a. 12 = b. 2 $.50 = c. 60 = 5? is 2 12 $.50 5 Saxon Math Course 1 L22-85 Adaptations Lesson 22

Practice Set (continued) (page 119) d. 10 80 = e. 5 6 2 = f. 9 10 10 5 6 100% =? 100% Written Practice (page 119) 1. ( ) ( ) = 2. original states 00000 all states 00000. 26 mi plus 85 yd Multiply the loop. mi yd 1 26?. 2 12 Multiply the loop. Divide by the outside number. 2 5. 16 7. 600 ft 0 = = 100 ft 6. 10 $.50 10 8. w 15 = 8 9. w 15 = 5 10. $.09 $.09 + $.09 w = w = Saxon Math Course 1 L22-86 Adaptations Lesson 22

Written Practice (continued) (page 120) 11. ) $1 2. 5 12. R 5 ) 1000 1. 7 + 9 + 1 = 1. 6 9 $1.2 $1.25 a. estimate b. First multiply $1.25. Then multiply that answer times. Use work area. 15. ten-millions place 75,26,198,000 16. GCF 12 and 15 List (in order) the factors the smaller number, 12. Starting with the greatest factor, cross f factors that are NOT factors the larger number, 15. The greatest factor is the GCF.,,,,, 17. 0 18. 100 2 5 9 10 19. 5 = %,,,,,,,,,? 100% 20. Use fraction manipulatives. 2 Saxon Math Course 1 L22-87 Adaptations Lesson 22

Written Practice (continued) (page 120) 21. NOT prime A 19 B 29 C 9 22. ( + ) ( ) = = 2. halfway between 27 and 2. perimeter 25. 26. Use fraction manipulatives. 6 5 27. 2 5 28. 29. a. 1 dollar = bits b. dollar = bits a. Use work area. 0. c p = t c = p + = t + = b. Use work area. Saxon Math Course 1 L22-88 Adaptations Lesson 22

LESSON 2 Ratio Name Rate (page 122) A ratio is a way to describe a relationship between numbers. Each the following forms is read the same: Thirteen to fifteen. 1 1 to 15 1:15 15 Write the ratio in the order asked. Always reduce ratios. 12 16 = _ Teacher Notes: Review Hint #25, Rate. Refer students to Proportion (Rate) Problems on page 19 and Ratio on page 22 in the Student Reference Guide. Leave ratios in top-heavy fraction form. (Never convert a ratio to a mixed number.) 7_ A rate is a ratio measures. Name Rate Measures Example Alternate Form Speed distance time Mileage distance fuel used Unit Price price quantity 55 miles 1 hour 28 miles 1 gallon $2.89 pound 55 miles per hour 28 miles per gallon $2.89 per pound Rate problems are solved just as you did equal-groups problems: 1. Name what the problem is about. 2. Fill in what you know.. Fill in what you are looking for.. Multiply the loop. 5. Divide by the outside number. Practice Set (page 12) a. What is the ratio dogs to cats in a neighborhood that has 19 cats and 12 dogs? dogs cats Multiply the loop. Divide by the outside number. b. What is the girl-boy ratio in a class 0 students with 17 boys? girls boys d. How long will it take a trucker to drive 00 miles at 50 miles per hour? miles hours? c. If the ratio cars to trucks in the parking lot is 7 to 2, then what is the ratio trucks to cars in the parking lot? trucks cars e. If a four-quart container milk costs $2.8, what is the cost per quart? quarts $? Saxon Math Course 1 L2-89 Adaptations Lesson 2

Written Practice (page 125) 1. Multiply the loop. cm mm 1 0 2. 2 0. One large pace is about one yard.. Multiply the loop. 100 large paces = yards Divide by the outside number. mi gal. 5. 25 5 6. 7 10 is $6.00 i s 7. Use fraction manipulatives to add. 8. mixed number 8 + 8 9 8 = 9. Reduce. 2 8 = % 10. $.75 Saxon Math Course 1 L2-90 Adaptations Lesson 2

Written Practice (continued) (page 125) 11. 12. 6,17,591 $.75 1. One way to find 2_ a is to first 1. $0.5n = $5.00 divide the number by ; then that answer by 2. Use work area. n = 15. $10.20 m = $.6 16. Use fraction manipulatives. $10.20 $1.6 1 m = 17. 18. 2,, 8, 16,,, To find a number, multiply the number before it by. 19. See the thermometer in the Student Reference Guide. Fahrenheit or Celsius? 1 is below freezing on the 20. 12 6 2 12 (6 2) scale, but is above freezing on the scale. Use work area. Saxon Math Course 1 L2-91 Adaptations Lesson 2

Written Practice (continued) (page 125) 21. GCF 2 and 2 Here are the factors 2. Starting with the greatest factor cross f factors that are NOT factors 2. Circle the GCF. 22. sum the first seven positive odd numbers 1, 2,,, 6, 8, 12, 2 2. Use fraction manipulatives. 2. 8 = % a. b. 25. 8 = 2 26. 16 on team freestyle not freestyle _ 27. See the Student Reference Guide. 28. Which represents a line? A B C 29. Use tests for divisibility by 2 and 5. A 252 B 525 C 250, 0. win loss win _ loss Saxon Math Course 1 L2-92 Adaptations Lesson 2

LESSON Name 2 Adding and Subtracting Fractions That Have Common Denominators (page 127) Use fraction manipulatives to help you see that the denominator does not change. To add or subtract fractions with like denominators, add or subtract the numerators. 1 8 1 8 1 8 1 8 1 8 8 + 2 = 8 5 8 Practice Set (page 129) a. 8 + 8 = b. + = c. 8 + 8 + 8 = d. 8 8 = e. 2 = f. = g. Use words to write the subtraction problem in exercise d. eighths minus eighth equals eighths. Saxon Math Course 1 L2-9 Adaptations Lesson 2

Written Practice (page 129) 1. Multiply the loop. $ hr 1 5 $5.00 car $5.00 yard $ 5.00 altogether Equal g pattern; then a pattern. 2. 1 dozen. 1760 8 I divided by.. Use fraction manipulatives. + 2 = 5. 7 8 8 = 6. 2 + 2 = 7. 2 2 = 8. 2 + = % Fred had a carrot. He ate it. How much did he have? 9. fiction nonfiction _ 10. halfway A 12 and 21 and d by. Use work area. Saxon Math Course 1 L2-9 Adaptations Lesson 2

Written Practice (continued) (page 10) 11. 12. NOT prime A 21 B 1 C 1 1. R 9 ) _ 1 0 0 0 1. R ) _ 22,22 15. 16. 2 $50 17. Seattle to Portland 172 mi Portland to San Francisco 66 mi 18. Multiply the loop. Divide by the outside number. Circle one. I rounded He (will, will not) be charged extra. 172 66 mi hr _ 172? Use work area. 19. Split the difference. 20. 2, 9 87,15 Saxon Math Course 1 L2-95 Adaptations Lesson 2

Written Practice (continued) (page 10) 21. GCF 21 and 28 List (in order) the factors the smaller number, 21. Starting with the greatest factor, cross f factors that are NOT factors the larger number, 28. The greatest factor is the GCF. 22. Use tests for divisibility by 9. A 12 B 2 C 5,,, 2. Use fraction manipulatives. 1 = x 2. w 8 = 20 w = 25. 7x = 8 26. 76 + w = 81 81 76 x = w = 27. m 286 = 592 592 286 28. twice the population Eaton m = 29. Madison Chester 0. Use work area. Saxon Math Course 1 L2-96 Adaptations Lesson 2

LESSON Name 25 Writing Division Answers as Mixed Numbers Multiples (page 12) In some division problems, the answer must be shown as a mixed number. A mixed number is a whole number plus a fraction. whole number 2 _ fraction mixed number } Put the remainder over the divisor to make the fraction. Example 1: Write 25 as a mixed number. 6 Example 2: A whole circle is 100% a circle. One third a circle is what percent a circle? We find multiples a number by multiplying the number by 1, 2,,, 5, 6, and so on. Example: The first six multiples are, 6, 9, 12, 15, and 18. Practice Set (page 1) Teacher Notes: Review Hint #, Improper Fractions. Refer students to Multiples on page 5 in the Student Reference Guide. a. ) 28 b. ) 1 0 0% c. ) 67 The times table will give you the multiples a number. d. first four multiples 12,,, e. first six multiples 8,,,,, f. rd multiple 8 2nd multiple 12 Divide to change the improper (top heavy) fractions to mixed numbers: g. 5 6 = h. 9 10 = i. 65 12 = Saxon Math Course 1 L25-97 Adaptations Lesson 25

Written Practice (page 1) 1. ( ) ( ) = 2. Carlos can find the a distance the t punts by adding yd, yd, and yd, and then d the sum by. Use work area.. one hundred forty-nine million, six hundred thousand kilometers. perimeter,, 5. p = 6. Show the answer as a mixed number. ) 0 7. 2 12 12 8. Use fraction manipulatives for help. Half 2 = Now, half that = 9. Show the answer as a mixed number. ) 1 0 0% 10. Use fraction manipulatives for help. a. Saxon Math Course 1 L25-98 Adaptations Lesson 25 b.

Written Practice (continued) (page 15) 11. 1_ % is what fraction? 12. mixed number 6 5 1. 2 + 2 + 2 = 1. 6 6 5 6 = 15. 0 0 60 = 16. 5 12 5 12 = 17. win loss 000 _ 000 18. 10 = t pens cost x x? 19. GCF 2 and 0 List (in order) the factors the smaller number, 2. Starting with the greatest factor, cross f factors that are NOT factors the larger number, 0. 20. _ 1 100 100 The greatest factor is the GCF.,,,,,,, Saxon Math Course 1 L25-99 Adaptations Lesson 25

Written Practice (continued) (page 15) 21. 5 8 + m = 1 1 5 8 1 5 8 22. 1 _ n = 12 m = n = 2. estimate 2. 2 12 628 7 xx xx xx xx 25. 26. Jan could draw segments from the center to estimate the 12, the, and the. measure Use work area. Use work area. 27. mixed number 28. 15 = 5 Use work area. 29. Multiples: Think times table. 0. Circle the number that is divisible by 9 and 10. Use tests for divisibility by 9 and 10. A 910 B 8910 C 78,910 The sum the digits is, which is divisible by. The last digit is so it is divisible by. 25,,, Use work area. Saxon Math Course 1 L25-100 Adaptations Lesson 25

LESSON Name 26 Using Manipulatives to Reduce Fractions Adding and Subtracting Mixed Numbers (page 16) Use fraction manipulatives to reduce fractions. We reduce when we use the fewest number fraction pieces to show the amount. When adding mixed numbers: 1. Add the whole numbers. 2. Add the fractions.. Reduce or convert the fraction if needed. We convert when we change an improper (top-heavy) fraction to a mixed number or a whole number. Simplify is another way to say convert or reduce. Practice Set (page 18) Use fraction manipulatives to reduce: a. 2 8 = Teacher Notes: Introduce Hint #6, Reducing Fractions (Manipulatives and Shortcuts). Review Fraction Families Equivalent Fractions on page 12 in the Student Reference Guide. b. 6 8 = Add and reduce when possible: c. 12 2 % + 12 2 % d. 16 2 % + 66 2 % e. + 2 = = = f. 1 8 + 2 7 8 = g. + 2 2 = h. + = i. Use words to write problem f. plus equals. Saxon Math Course 1 L26-101 Adaptations Lesson 26

Written Practice (page 19) 1. 2. _ years x _ mi months 1 6. 2 dozen Is this enough? 2 1 dozen = 1 dozen = 2 dozen =. mc cm 1 1000? 5. perimeter 6. 2 + 2 2 2 7. Convert and reduce. 8. 8 5 7 8 + 7 5 8 = = 12 2 % 8 = % 9. 1 = 12 10. GCF 15 and 25 List (in order) the factors the smaller number, 15. Starting with the greatest factor, cross f factors that are NOT factors the larger number, 25. The greatest factor is the GCF. 1,,, 15 Saxon Math Course 1 L26-102 Adaptations Lesson 26

Written Practice (continued) (page 19) 11. Find the pattern. Continue it. 8, 16, 2, 2, 0,,,... Add to the preceding term. 12. mixed number 1 5 = 1. Simplify. 2 5 + 5 = 1. 2 + n = 1 1 2 5 2 + n = 15. GCF 12 and 18 List (in order) the factors the smaller number, 12. Starting with the greatest factor, cross f factors that are NOT factors the larger number, 18. The greatest factor is the GCF. 16. 1 1,,,,, 17. + 18. 2 2 2 2 19. Use tests for divisibility by 2 and. A 671 B 858 C 69 20. prime numbers between 0 and 0 See the Student Reference Guide. Saxon Math Course 1 L26-10 Adaptations Lesson 26 and

Written Practice (continued) (page 10) 21. 506 987 22. Use fraction manipulatives to reduce. 6 8 = 2. $ounds _ pounds xx xx? xx 2. $0 5 xxx _ xxx xxx _ xxx 25. 26. least to greatest, 0, 1, 1 2 a. in millimeters b. in inches a. b.,,,, 27. 2nd year 1st year 28. average 29. average 1st year 0. In the year it rained inches. In the year it rained inches. Altogether, how many did it rain? Answer: Use work area. Saxon Math Course 1 L26-10 Adaptations Lesson 26

LESSON 27 Measures a Circle (page 11) Name The circumference is the distance around the circle (perimeter). The diameter is the distance across a circle through the center. The radius is the distance from the center to the circle. The diameter is twice the radius. D = 2r The radius is half the diameter. r = 1_ 2 D A compass is a tool for drawing a circle. Concentric circles are circles with the same center like a bull s-eye target. C i r e c c u n m e f e r Diameter Teacher Notes: Refer students to Circle on page 17 in the Student Reference Guide. Post reference chart, Circles. The activity in the Student Edition is optional. Radius Practice Set (page 12) Give the name for: a. The distance across a circle d b. The distance around a circle c c. The distance from the center to the circle r d. If the diameter is 10 in., what is the radius? The radius is h the diameter. Written Practice (page 1) 1. ( ) ( ) = sum difference 2. xx xx xx xx Saxon Math Course 1 L27-105 Adaptations Lesson 27

Written Practice (continued) (page 1). 06 = d. a. radius b. The d is 06 twice the radius a c. a. 5. Use tests for divisibility. A 122 B 12 C 12 6. 1,2,567 7. 10p = lb $ 010 _ 010 010 _ 010 8. denominator See the Student Reference Guide. 2 2 9. 65 5 xx xx xx xx 10. 2 $15 xx xx xx xx 11. Use fraction manipulatives for help. Simplify. 6 + 2 6 + 6 = 12. Reduce. 7 8 8 = Saxon Math Course 1 L27-106 Adaptations Lesson 27

Written Practice (continued) (page 1) 1. 6 6 5 6 = 1. 2 8 + 5 8 = 15. a. 1 = 0 8 16. 6 = b. 2 = 0 8 a. b. 17. 2 18. 50% = 19. R 52 ) 2100 00 20. sides inches / 1? 0 6 21. Convert. 7 6 = 22. 2 _ 18 = Saxon Math Course 1 L27-107 Adaptations Lesson 27

Written Practice (continued) (page 1) 2. (55 + 5) (55 5) = = 2. Use tests for divisibility by 2 and 5. A 502 B 205 C 250 25. Add the d the number. 26. prime but NOT odd If the s the digits can be divided by, the number can be by 9. Use work area. 27. perimeter a circle 28. 1 2 There are even numbers 5 6 and odd numbers. 7 8 9 even odd 00 00 Use work area. 29. 7 2 % 12 2 % 0. Convert. % + 16 2 % = Saxon Math Course 1 L27-108 Adaptations Lesson 27

LESSON 28 Angles (page 15) Name A plane is a flat surface like a tabletop. Parallel lines never meet, like railroad tracks. Lines intersect when they cross. Perpendicular lines intersect and make square corners like the corner a piece paper. Oblique lines intersect but do not make square corners. Teacher Notes: Introduce Hint #7, Geometry Vocabulary. Refer students to Types Lines and Types Angles on pages 17 and 18 in the Student Reference Guide. Post reference chart, Angles and Triangles. Two rays that start at the same point make an angle. The vertex an angle is the point where the rays start. The square corner fits a cute little angle more than a right angle the corner your paper. Angles can be named with letters or numbers. You can name an angle with just the letter the vertex. If three letters are used to name the angle, the letter the vertex must be in the middle. This angle is named angle B ( B), angle ABC ( ABC), angle CBA ( CBA), or angle 1( 1). Practice Set (page 17) a. With your thumb and forefinger, show an acute angle, a right angle, and try to make an obtuse angle. Describe each angle below as acute, right, or obtuse. b. c. d. e. What type angle is formed by the hands a clock at :00 o clock? angle f. What type angle is formed at the corner a door in your classroom? angle g. Which two angles formed by these obtuse lines appear to be acute angles? and. Saxon Math Course 1 L28-109 Adaptations Lesson 28

Practice Set (continued) (page 17) h. Draw two parallel line segments. i. Draw two perpendicular lines. Refer to the triangle to answer questions j and k. j. Angle H is an acute angle; name another acute angle. k. Name an obtuse angle. Written Practice (page 18) 1. Convert. + 2 + = 2. 2 20 million 5. 2g = 768. 1776 = d peanuts children _ 768? 1 + 1776 this year + 1776 Declaration Independence 5. Convert. 2 = 6. Convert. 1 2 + 1 2 7. 2 + 2 8. 5 6 1 6 9. Reduce. 8 = 10. 2 $2 Saxon Math Course 1 L28-110 Adaptations Lesson 28

Written Practice (continued) (page 18) 11. a. 1 100% = 10 b. 100% = 10 12. What fraction? 25% = a. b. 1. mi gal 1? 1. + m = 1 1 1 m = 15. 2 w = 297 2 297 16. a. obtuse angle b. acute angle a. w = b. 17. average 22 20 2 + 2 18. inches sides? 1 19. GCF 2, 6, and 60 List (in order) the factors the smaller number, 2. Starting with the greatest factor, cross f factors that are NOT factors the other numbers, 6 and 60. The greatest factor is the GCF. 20. 10,010 10,010,,,,,,, Saxon Math Course 1 L28-111 Adaptations Lesson 28

Written Practice (continued) (page 19) 21. (100 100) (100 99) = 22. 1 10 = % = 2. Show the answer as a mixed number. long division 2. 2 dozen 5097 25. a. in inches b. in centimeters 26. Multiples: Think times table. first five multiples 6:,,,, first five multiples 8:,,,, Circle the common multiple. a. b. 27. Use fraction manipulatives for help. 28. red white 2 29. factor tree 0. Use tests for divisibility by 9. A 2 B 5 C 567 Saxon Math Course 1 L28-112 Adaptations Lesson 28

LESSON Name 29 Multiplying Fractions Reducing Fractions by Dividing by Common Factors (page 152) Multiplying fractions: Of means multiply. Set up whole numbers as fractions. ( = 1 ) Multiply across. Convert and reduce answers. Example: 2 Example: 2 5 Reducing fractions: 1 2 = 8 = 2 2 means 2 5 = 8 15 What number will divide evenly into both the numerator and the denominator? (the GCF) Example: Reduce 6. The GCF and 6 is 2. 2 6 2 = 2 Practice Set (page 15) Multiply; then reduce: a. 2 5 Multiply; then convert: d. 5 6 6 5 = b. 2 = c. 2 = = e. Write the whole number f. 2 = as a fraction. Teacher Notes: Review Hint #0, Finding the Greatest Common Factor, and Hint #6, Reducing Fractions (Manipulatives and Shortcuts). Review Fraction Families Equivalent Fractions on page 12 in the Student Reference Guide. Reduce: g. 9 12 = h. 6 10 5 2 = = 2 = = i. 18 2 = j. In a class 0, there were 20 girls. What was the ratio boys to girls? Reduce. boys girls boys girls = Saxon Math Course 1 L29-11 Adaptations Lesson 29

Written Practice (page 15) 1. tons pounds 1 8? 2. beans ounces 16 1?. ( ) ( ) =. Reduce. win loss = 5. 16 2 = 6. Reduce. 8 + 8 = 7. Reduce. 8. Reduce. 2 2 = 7 12 12 = 9. 8 96 10. 1,, 7, 10,,,, Saxon Math Course 1 L29-11 Adaptations Lesson 29

Written Practice (continued) (page 15) 11. 5 out 12 months passed 12. fset $.60 1. Cancel the matching zeros. 50,000 _ 50,100 = 1. Convert and reduce. 18 = 15. 15 0 8 = = 16. m + 96 + 268 = 217 m = 17. 1000 n = 857 18. 2x = 80 1000 8857 n = x = 19. 7 11 1 = 20. To estimate 96 9, first r 96 to and r 9 to. Then divide by. Use work area. Saxon Math Course 1 L29-115 Adaptations Lesson 29

Written Practice (continued) (page 155) 21. 2 2 1 22. perimeter one width both widths so both lengths one length 2. Think! 12 0 = 2. ( 2 2 ) = 00 00 = 25. a. acute angles b. obtuse angles 26. Reduce. 2 5 a. and b. and 27. product 28. Reduce. radius diameter = 29. 0. 2 5 = % a circle is %, so 2 5 5 is. Saxon Math Course 1 L29-116 Adaptations Lesson 29

LESSON 0 Least Common Multiple (LCM) Reciprocals (page 158) Name Multiples remind us multiplication. Multiples: Think times table. Example: Find the least common multiple (LCM) and. Multiples :, 6, 9, 12, 15, 18, 21, 2, Multiples :, 8, 12, 16, 20, 2, 28, 12 and 2 are common multiples. 12 is the least common multiple (LCM). Reciprocal flip the fraction Example: = _, so the reciprocal is 1_ 1. Rule: The product any fraction and its reciprocal always equals 1. Examples: = 12 12 = 1 7 9 9 7 = 6 6 = 1 Teacher Notes: Introduce Hint #8, Finding the Least Common Multiple, and Hint #9, Reciprocal. Refer students to Multiples on page 5 in the Student Reference Guide. Practice Set (page 158) Find the least common multiple each pair: a. Go down the 6s and 8s. Find the first number in common. 6 and 8 b. Go down the s and 5s. Find the first number in common. and 5 c. 5 and 10 Write the reciprocal each number: d. 6 e. 2 f. 8 5 g. Use the rule reciprocals to find the number that goes in the box: h. 8 = 1 i. = 1 j. 6 l. How many 2_ 5 s are in 1? (reciprocal) m. How many 5 s are in 1? 12 = 1 k. 7 8 = 1 Saxon Math Course 1 L0-117 Adaptations Lesson 0

Written Practice (page 159) 1. Multiples: Think times table. ( ) ( ) = 2. 2. 2 = p. Multiples: Think times table. 15 min = 1_ hour 2 hours = 1_ -hours Multiply the loop. Divide by the outside number. popcorn 2 1_? -hours 12,,, 5. LCM and 6 Go down the s and 6 s. Find the first one in common. 6. Reduce. one hour = commercials non commercials min 00000 00000 = One hour is minutes, so if minutes were commercials, then minutes were not commercials. 7. Convert. 2 5 + 2 5 + 2 5 = 8. 1 1 10 = 9. Reduce. 11 12 1 12 = 10. rule reciprocals = Saxon Math Course 1 L0-118 Adaptations Lesson 0

Written Practice (continued) (page 159) 11. 5 = 12. Convert. 5 2 5 = 1. Count the factors 2. 1. $6.50 $6.50 $6.50 15. $5.00 + $6.50 16. 596 05 17. obtuse angle 18. 2 2 2 1 19. 500,000 500,100 = 20. 5 ) 850 Saxon Math Course 1 L0-119 Adaptations Lesson 0

Written Practice (continued) (page 159) 21. Write the answer as a mixed number. short division 1 0 0% 22. 12 = 2. average 75 62 + 571 2. Multiply the loop. Divide by the outside number. sides inches 6? 25. rule reciprocals 26. Think reciprocal. 27. 8 = 1 28. The only even prime number is. The reciprocal that is: 29. Convert and reduce. 5 10 = 0. = Saxon Math Course 1 L0-120 Adaptations Lesson 0