Ratio Problems Involving Name Totals (page 528)

LESSON 101 Ratio Problems Involving Name Totals (page 528) In some ratio problems a total is needed in order to solve the problem. 1. Fill in the ratio box with things you know. 2. Write a proportion. Use the row that answers the question asked. Use the row that is already complete. Example: The ratio of boys to girls in a class was 5 to 4. If there were 27 students in the class, how many girls were there? 4 9 = g 27 3 g = 4 27 9 1 g = 12 Practice Set (page 530) Sparrows and crows perched on the wire had the ratio of 5 to 3. If the total number of sparrows and crows on the wire was 72, how many were crows? crows total? 72 72 3 8 Cancel. = Raisins and nuts were mixed by weight in a ratio of 2 to 3. If 60 ounces of mix were prepared, how many ounces of raisins were used? raisins total? = Cancel. c. There are 20 green and blue markers in a ratio of 3 to 2. How many of each color are there? green blue Saxon Math Course 1 L101-401 Adaptations Lesson 101

Written Practice (page 530) 1. 2. See the Student Reference Guide. r p 3. x 6 = 12 4. radius 5. pounds $ 1.65 6. AC = 12 cm AB = 1 of AC 4 BC = 4 of AC 7. 3 + 4 = +5 + 5 = c. 6 + +3 = 8. 3 4 = +5 5 = c. 6 +3 = d. 6 6 = e. Change the s of the d. +6 + 3 = 9. 10. subtrahend and a. Saxon Math Course 1 L101-402 Adaptations Lesson 101

Written Practice (continued) (page 531) 11. 12. 13. 1 1 2 4 14. 6 1 1 2 15. (0.4) 2 2 3 16. x + 2 1 2 = 5 5 2 1 2 x = 17. 8 5 = 40 x 18. 0.06n = $0.15 x = 19. 6n = 21 4 20. Nia s garage is 20 feet long, 20 feet wide, and 8 feet high. bottom layer n = all layers n = Saxon Math Course 1 L101-403 Adaptations Lesson 101

= = Written Practice (continued) (page 531) 21. circumference 22. 9 2 9 10 2 4 2 = A 2 1 2 in. B 5 in. C 7 3 4 in. D 9 1 4 in. 23. What kind of polygon? 24. The sum of the angles of each triangle is. 25. 15 0 8 26. 27. 1, 2, 3, 4, 5, 6 perfect squares total numbers 29. Divide 18 feet by per yard. yd ft 1 3 18 28. (4, 0), (0, 3), (0, 0) area 30. 1 gal = qt qt $ 3.80 1 Saxon Math Course 1 L101-404 Adaptations Lesson 101

LESSON 102 Mass and Weight (page 533) Name Physical objects are composed of matter. The amount of matter in an object is its mass. Mass does not change with changes in gravity. Weight does change with gravity changes. The weight of an astronaut changes on the moon. His or her mass does not change on the moon. Teacher Notes: Introduce Hint #60, Gram/Kilogram Manipulatives. Review Equivalence Table for Units on page 1 in the Student Reference Guide. Metric weight manipulatives can be found in the Adaptations Manipulative Kit. Practice Set (page 535) Half of a kilogram is how many grams? The mass of a liter of water is one kilogram. The mass of two liters of beverage is about how many grams? L g 1 2? c. 5 lb 10 oz + 1 lb 9 oz d. 9 lb 8 oz 6 lb 10 oz e. A half-ton pickup truck can haul a half-ton load. Half of a ton is how many pounds? Saxon Math Course 1 L102-405 Adaptations Lesson 102

Written Practice (page 535) 1. 84, 90, 92, 92, 92, 96 3. 18 one-point baskets 2. average (mean) 84 90 92 92 92 + 96 6 three-point baskets total points from one- and three-point baskets points from whole game points from one- and three-point baskets points from two-point baskets number of two-point baskets 4. 4 7 = 5. 4 5 = 20 A 7 4 B 14 17 C 12 21 D 2 3 6. least to greatest 1, 1, 0.1, 0.1, 0 7. 10 3 10 2,,,, 8. The area of the square in this figure is 100 mm 2. radius diameter c. area of the circle (Use 3.14 for π.) A = π r 2 A 10 9 B 10 6 C 10 5 D 10 9. c. 10. Saxon Math Course 1 L102-406 Adaptations Lesson 102

Written Practice (continued) (page 536) 11. 12. 1 2 3 = 3 1 2 = + 4 1 6 = 13. 5 6 3 10 4 = 14. 6 1 4 100 15. 6.437.. 16. ) 1. 0 0 0. 17. octagon pentagon 18. 4 5 2 50 4 + ( 3 2 2 3 ) = 19. Multiply the probabilities. 90 360 = 20. probability of sector 1 = 4 4 of 100 = Saxon Math Course 1 L102-407 Adaptations Lesson 102

Written Practice (continued) (page 536) 21. top layer 22. x 4 = 5 all layers 23. 10 lb 1 oz 08 lb 4 oz 24. m 1 =, m 2 = 25. x 1 2 4 5 26. 3x 5 2 1 7? 27. 28. g mg 1? c. 29. (3, 1) and (3, 5) 30. ) 31 (, ) Saxon Math Course 1 L102-408 Adaptations Lesson 102

LESSON 103 Perimeter of Complex Name Shapes (page 538) Perimeter means to add all the sides. Some sides will not be labeled. Subtract to find labels for these sides. Hint: Sometimes it helps to use two different colors. Trace over all horizontal lines in one color. Trace over all vertical lines in another color. Teacher Note: Introduce Hint #61, Perimeter of Complex Shapes. 10 4 = m 8 2 = n 6 in. = m 6 in. = n Practice Set (page 540) Find the perimeter of each complex shape: 12 5 = y 8 3 = x perimeter = 20 = x 15 = y perimeter = Saxon Math Course 1 L103-409 Adaptations Lesson 103

Written Practice (page 540) 1. ( ) ( ) = 2. x 3 = 24 x = (22 + 22 + ) 3 = 24 3. 1 yd = inches perimeter inches 4. 5 3 = 30 each side area 5. 6. 7. 100 10 2 + 3 ( 2 3 16 ) = 8. pounds = 1 ton probability of something impossible 9. Fraction Decimal Percent 10. Saxon Math Course 1 L103-410 Adaptations Lesson 103

Written Practice (continued) (page 540) 11. 12. 10 1 2 3 1 2 13. (6 + 2.4) 0.04 = 14. 7 1 2 + 6 3 4 + n = 15 3 8 7 1 2 = 6 3 4 = 15 3 8 = = n = 15. x 1 3 4 = 7 1 2 16. 10 1 2 ( 2) 17. 7 1 2 = 3 1 2 ( 2) 1 3 4 = x =. 18. Use exponents. 19. prime numbers between 40 and 50 20,500,000 ( ) + ( ) 20. 3 + 8 = 3 8 = c. 8 + +3 = 21. The sum of the angles in a triangle is 180. m C = m B,, d. 8 +3 = Saxon Math Course 1 L103-411 Adaptations Lesson 103

Written Practice (continued) (page 541) 22. perimeter: 23. area: c. 20 mm side longest side fraction: decimal: 24. queen of spades 52 cards 25. 26. 50 = x 20 = y 28. ( 3, 2) and (5, 2) 27. 29. 16 oz = lb 1 gal = pt 1 gal = 2 pt 1 gal = 2 pounds c. (, ) 30. 360 = 180 = Saxon Math Course 1 L103-412 Adaptations Lesson 103

LESSON 104 Algebraic Addition Name Activity (page 543) Activity Sign Game Level 1 During the game, positive and negative pairs are neutralized. After the game, count the remaining positives and negatives to see what remains. Tell what remains for these games: Level 2 Now the positives and negatives are shown in clusters of more than 1. The same rules apply as in Level 1. The suggested strategy is to group all the signs first. So +3 combines with +1 to make +4, and 5 combines with 2 to make 7. Since there are three more negatives than positives, 3 remain. Tell what remains for these games: Level 3 Now the clusters take on a disguise. Sometimes a cluster will have no sign, sometimes it will have one sign, sometimes it will even have two signs. First, remove the disguise. Positive clusters will have: no sign + + Negative clusters will have: + + Sometimes the cluster has a shield (parentheses). Don t be fooled. Look through the shield to see the sign ( 3) is really +3 (+3) is really 3 Tell what remains for these games: Level 4 Extend Level 3 to a line of clusters: 3 + ( 4) ( 5) (+2) + (+6) Use the following steps to find the answer: Step 1: Remove the disguises: 3 4 + 5 2 + 6 Step 2: Group signs: 9 + 11 Step 3: Find what remains: +2 Saxon Math Course 1 L104-413 Adaptations Lesson 104

Practice Set (page 545) 2 + 3 4 + 5 = 3 + (+2) (+5) ( 6) = c. +3 + 4 +6 + +7 1 = d. 2 + ( 3) ( 9) (+7) + (+1) = e. 3 5 + 4 +2 + +8 = f. ( 10) (+20) ( 30) + ( 40) = Written Practice (page 545) 1. edges vertices 2. 12 lb 6 oz 7 lb 8 oz 3. fish snails 4. 5. Multiply the probabilities. 1 1 = 6. 7. 8. 9. 2 3 = A 2 4 B 3 4 C 4 6 D 3 2 Saxon Math Course 1 L104-414 Adaptations Lesson 104

Written Practice (continued) (page 546) 10. 6 8 = a 12 11. 13 = x 12 = y a = 12. 13. 14. 15. 40% off $6.95 $6.95 16. See the Student Reference Guide. 200 17. ( 1 2 ) 3 the probability of three heads in three coin tosses and 18. Round to a whole number. ) 0.624 20. ) ) ) ) ) 450 19. x 3 = 20 21. 3 + 5 4 +2 = Saxon Math Course 1 L104-415 Adaptations Lesson 104

Written Practice (continued) (page 547) 22. 3 4 + 5 2 4 100 2 3 = 23. 24. 3 of 60 played 4 25. km hr 88 1? 4 of 60 did not is of 26. area 27. average 3.12 3.2 3.15 3.1 c.. 28. There are 90 two-digit counting numbers. 29. (3, 5), ( 1, 5), ( 1, 3) Since Hector was t of only area o number, the probability of 30. correctly guessing the n in one try is. 2 gal 1 4 qt 1 gal 2 pt 1 qt = Saxon Math Course 1 L104-416 Adaptations Lesson 104

LESSON Name 105 Using Proportions to Solve Percent Problems (page 548) A ratio box may be used to solve percent problems. Remember: A percent may be expressed as a fraction. 30% equals 30 100 Example: Thirty percent of the students earned an A on the test. If twelve students earned an A, how many students were there in all? 30 100 = 12 t t = 4 10 12 100 30 3 1 = 40 Practice Set (page 550) Forty percent of the cameras in a store are Seventy percent of the team members played digital cameras. If 24 cameras are not digital, in the game. If 21 team members played, how how many cameras are in the store in all? many team members did not play? c. Referring to problem b, what proportion d. Joan walked 0.6 mile in 10 minutes. How far would we use to find the number of members can she walk in 25 minutes at that rate? Write on the team? and solve a proportion to find the answer. = t 0.6 10 = d e. Ninety percent of the 30 students loved math. How many of the students? Answer: Saxon Math Course 1 L105-417 Adaptations Lesson 105

Written Practice (page 551) 1. 2 1 2 = 2.5 2. in. mi 1? mi hr 50 1? 3. Ratio Actual Count 4. Volume = lwh 5. +10 + 10 = 6. lb kg 1? 10 10 = c. +6 + 5 4 = c. 7. 8. 9. 10. Saxon Math Course 1 L105-418 Adaptations Lesson 105

Written Practice (continued) (page 551) 11. 12. 4 1 12 = 5 1 6 = + 2 1 4 = 13. 4 5 3 1 = 14. 0.125 80 15. (1 + 0.5) (1 0.5) = 16. c 12 = 3 4 c = 17. $8.75 $8.75 18. one hundred five and five hundredths 19. The sum of the angles in a quadrilateral is 360. 20. ) ) ) ) ) 500 m B = m C = Saxon Math Course 1 L105-419 Adaptations Lesson 105

Written Practice (continued) (page 552) 21. 1 qt is just less than 1 L 22. Multiply the probabilities. qt = 1 gal 1 gal is just less than L 23. perimeter = 18 cm 24. area 25.? = 0 12 = 5 5 26. Write the answer as a decimal. 27. perimeter 28. x 1_ 2 1 1_ 2 2 y 1 1_ 2 3 41_ 2 6 Rule: Multiply x by to find. 29. yd ft yd ft 1 1? 15? 12 15 ft 12 ft 30. The probability is because the past outcome does affect the future o. by Saxon Math Course 1 L105-420 Adaptations Lesson 105

LESSON 106 Two-Step Equations (page 553) Name Always do the same thing to both sides of an equation. To solve two-step equations: 1. Change the sign. 2. Move to the other side. 3. Then multiply or divide. 4. Check the answer. + Example: 3n 1 = 20 Changed minus to plus. 3n = 21 Added 1 to both sides of the equation. n = 7 Divided both sides of the equation by 3. 3(7) 1 = 20 Replaced n with 7. Practice Set (page 554) + 3n + 1 = 16 2x 1 = 9 3n = 2x = n = x = + c. 3y 2 = 22 d. 5m + 3 = 33 3y = 5m = y = m = e. 4w 1 = 35 f. 7a + 4 = 25 4w = 7a = w = a = Saxon Math Course 1 L106-421 Adaptations Lesson 106

Written Practice (page 555) 1. (28 + 15 + ) 3 = 20 2. 2 1 2 = 2.5 in. mi 10 2.5? 3. is of 4. nickel quarter = 100 5. Numbers from 1 30 that have a 1 in them.,,,,,,,,,,, 6. 8x + 1 = 25 8x = x = Write the probability as a fraction and a decimal. x = 7. 3w 5 = 25 3w = 8. 15 + +20 = 15 +20 = 9. tons pounds w = w = c. ( 3) + ( 2) ( 1) =? 10. 1 gal = qt 1 qt c. = pt Saxon Math Course 1 L106-422 Adaptations Lesson 106

Written Practice (continued) (page 555) 11. 12. 13. 14. 15. 8 1 3 = 3 1 2 = 16. 2 1 2 100 17. 0.014 0.5 ) 18. (6 10 4 ) + (9 10 2 ) + (7 10 0 ) 19. 100 2 2 5 2 1000 2 3 5 3 20. 1,000,000 Saxon Math Course 1 L106-423 Adaptations Lesson 106

Written Practice (continued) (page 556) 21. 6 + 3 2 (5 4 ) = 22. volume 23. inches foot 3 = 100 24. area c. 25. perimeter 26. circumference (Use 3.14 for π.) A 6 ft B 6 ft 3 in. C 6 ft 8 in. D 7 ft 27. area 28. List the miles in order. 3,,,,,, 10 29. average 30. How many miles did Celina ride on Thursday then on? Answer: Saxon Math Course 1 L106-424 Adaptations Lesson 106

LESSON 107 Area of Complex Name Shapes (page 557) Perimeter of complex shapes Area of complex shapes Add all sides. 1. Divide the shape into two or more parts. 2. Find the area of each part. 3. Add the parts. Formulas to remember: Area of a rectangle A = lw Area of a triangle A = bh 2 (Be sure to label area in square units.) Teacher Note: Review Hint #61, Perimeter of Complex Shapes. 28 cm 2 + 6 cm 2 34 cm 2 Practice Set (page 558) The same figure has been divided two different ways. Find the length of the unknown side in each figure and find the total area of each figure. The trapezoid is divided into a rectangle and a triangle. Find the area of the trapezoid. Saxon Math Course 1 L107-425 Adaptations Lesson 107

Written Practice (page 558) 1. ) 2. in. ft 1 2? 3. tulips roses 4. A pentagon has how many sides? 1 = 100 5. kg g 1 6. +15 + 10 = 15 10 = c. (+3) + ( 5) ( 2) (+4) = c. 7. 10 3 (10 2 100 ) 10 3 100 = 8. 6 u = 8 1.2 9. 10. u = Saxon Math Course 1 L107-426 Adaptations Lesson 107

Written Practice (continued) (page 559) 11. 12. 5 3 8 = 4 1 4 = + 3 1 2 = 13. 8 3 5 12 9 10 = 14. 64.8.. 15. The sum of the angles in a triangle is 180. 16. See the Student Reference Guide. pt oz 1 17. 3m + 8 = 44 = 18. Use exponents. 110,000,000 m = m = 19. GCF of 30 and 45 1,,,,,,, 30 20. ( ) + ( ) Saxon Math Course 1 L107-427 Adaptations Lesson 107

Written Practice (continued) (page 559) 21. 1 yd = ft 22. 0.3n = $6.39 1 layer all layers n = 23. perimeter 24. area 25. 26. Arrange in order.,,,,,,,, most frequent: middle age: c. average rounded: d. m, m, m 27. Complete the line plot to display the dat See Investigation 4. 28. 12 lb 3 oz 8 lb 7 oz 29. 30. 10 gallons 1 31.5 miles 1 gallon = Saxon Math Course 1 L107-428 Adaptations Lesson 107

LESSON 108 Transformations (page 561) Name Figures that have the same shape and size are congruent. One will fit exactly on top of the other. The matching parts are equal in measure. To position triangle ABC on triangle XYZ, make three different kinds of moves (transformations). Teacher Note: The activity in the Student Edition is optional. Transformations Name Rotation Movement turning a figure about a certain point Translation Reflection sliding a figure in one direction without turning the figure reflecting a figure as in a mirror or flipping a figure over a certain line Practice Set (page 563) Name the transformation(s) necessary to position triangle I on triangle II in each exercise. c. d. e. and and Saxon Math Course 1 L108-429 Adaptations Lesson 108

Practice Set (continued) (page 563) f. Triangle ABC is reflected across the y-axis to become triangle A B C. List the coordinates of the vertices of triangle ABC and its image, triangle A B C. A ( 2, 4) A (2, 4) B ( 1, 1) B (, ) C (, ) C (, ) Written Practice (page 563) 1. sum of the first five positive even numbers 2. 3. 4. area 5. is of 6. LCM of 6, 8, 12 7. 8. 0.7 20 = n 100 Rotate triangle I until its orientation matches t II. Then translate t I until it is positioned on t II. n = 9. 10. Saxon Math Course 1 L108-430 Adaptations Lesson 108

Written Practice (continued) (page 564) 11. 12. 4 3 4 + ( 2 1 4 7 8 ) = 2 1 4 = 7 8 = 4 3 4 = + = 13. 1 1 5 ( 2 1 2 3 ) = 14. 6.2 + (9 2.79) = 9. 2.79 6.2 +. 15. 3 + +7 + 8 1 = 16. Round the answer to the nearest cent. $2.89 $2.89 17. m mm 18. least to greatest 0.3, 0.31, 0.305 19. volume = lwh 20. 2 5 5 2 + 25 2 =,, Saxon Math Course 1 L108-431 Adaptations Lesson 108

Written Practice (continued) (page 564) 21. 8a 4 = 60 = 60 = 60 22. A right angle is. 1 (right angle) = 3 a = 23. perimeter 24. area 25. 2 gal = pt 26. total area pt lb 27. 1 liter = milliliters 28. Multiply the probabilities. first second draw draw 10 9 = 29. 1 1 2 = 1.5 km m 1 1.5? 30. R( 1, 4), S( 3, 1), T( 1, 1) Reflect across the y-axis. R (1, 4), S (, ), T (, ) Saxon Math Course 1 L108-432 Adaptations Lesson 108

LESSON Name 109 Corresponding Parts Similar Figures (page 566) If two figures are congruent, their corresponding parts (angles and sides) match exactly. Example: Triangle ABC and triangle XYZ are congruent. A corresponds to X. AB corresponds to XY. Teacher Note: Refer students to Similar and Congruent Triangles on page 28 and Scale Factor on page 31 in the Student Reference Guide. If two figures are similar, they have the same shape but not necessarily the same size. Similar figures have equal matching angles. In all similar polygons the ratios of corresponding sides are equal. The lengths of corresponding sides are related by a ratio called the scale factor. scale factor from smaller figure to larger figure = scale factor from larger figure to smaller figure = Make sure you use corresponding sides. larger side smaller side smaller side larger side To find an unknown corresponding side length, multiply by the scale factor. Triangles I, II, and III are similar. Triangles I and II are congruent. Practice Set (page 569) All squares are similar. True or false? All similar triangles are congruent. True or false? c. If two polygons are similar, then their corresponding angles are equal in measure. True or false? d. These two triangles are congruent. Which side of triangle PQR is the same length as AB? Saxon Math Course 1 L109-433 Adaptations Lesson 109

Practice Set (continued) (page 569) e. Which two of these triangles appear to be similar? and f. These two pentagons are similar. The scale factor for corresponding sides is 3. How long is segment AE? How long is segment IJ? AE = IJ = Written Practice (page 569) 1. prime numbers See the Student Reference Guide. 2. cm km 2 10? 3. commercial minutes program minutes 8 = 4. 5. 6. Write the probability as a fraction and a decimal. Pacific states total states 7. 7w 3 = 60 = 8. 8 n = 4 2.5 9. = w = n = Saxon Math Course 1 L109-434 Adaptations Lesson 109

Written Practice (continued) (page 570) 10. 11. 12. numbers less than 4 total numbers 13. 200 cm 1 1 m 100 cm = prime numbers total numbers 100 14. (6.2 + 9) 2.79 = 15. 10 3 10 2 10 1 = 6.2 + 9.. 2.79 16. y = 2x x 2 3 5 10 17. ) 18. y 19.. 20. 0.12m = $4.20 scale factor from small to large scale factor from large to small m = Saxon Math Course 1 L109-435 Adaptations Lesson 109

Written Practice (continued) (page 571) 21. +7 + 8 = 7 + +8 = 22. The triangles are congruent. A = 1 2 bh c. 7 +8 = d. 7 8 = 23. 24. area of triangle = 1 2 bh r and t 25. 26. similar triangles 27. 28. 29. 6 2 3 ( 100 30. 1 2 10 ) 0.01 Saxon Math Course 1 L109-436 Adaptations Lesson 109

LESSON 110 Symmetry (page 573) Name A line of symmetry divides a figure in half so that the halves are mirror images of each other. Example : An equilateral triangle has three lines of symmetry. Rotational symmetry is when the image of a figure reappears in the same position as it turns less than one full turn. Example: A square reappears in its original position as it is turned 90, 180, and 270. Practice Set (page 575) Sketch a different line of symmetry for each square. Which of these letters does not have a line of symmetry? A B C D E F c. Which two of these letters have rotational symmetry? (Hint: Rotating your paper might help you find the answer.), L M N O P Q Saxon Math Course 1 L110-437 Adaptations Lesson 110

Written Practice (page 575) 1. 2. ) 3. volume 4. is of 360 5. The equilateral triangle has lines of symmetry. 6. perimeter It rotational symmetry. 7. area 8. 9. 10. Saxon Math Course 1 L110-438 Adaptations Lesson 110

Written Practice (continued) (page 576) 11. 12. 24 1 6 = 23 1 3 = + 22 1 2 = 13. ( 1 1 5 2 ) 1 2 3 = 14. 9 (6.2 + 2.79) 6.2 + 2.79 9.. 15. 0.36m = $63.00 16. Round to the nearest cent. $24.89 0.065 m = 17. Round to the nearest thousandth. 0.065 4 18. ) ) ) ) ) ) 1000 19. All squares are similar. True are false? 20. 3 3 3 2 3 3 3 = Saxon Math Course 1 L110-439 Adaptations Lesson 110

Written Practice (continued) (page 577) 21. perimeter 22. area 23. 24. The triangles are congruent. perimeter = 24 cm length of shortest side = r, r, and t 25. circumference to the nearest hundred feet 26. Label point M at the midpoint of AB. 27. center on origin radius 5 units 28. area of the circle in problem 27 (Use 3.14 for π.) 29. 3 + 4 5 +7 = 30. = (, ), (, ) Saxon Math Course 1 L110-440 Adaptations Lesson 110