Geometric Formulas (page 474) Name


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1 LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note: Review Geometric Formulas on page 29 in the Student Reference Guide. Practice Set (page 476) a. Write the formula for the area of a rectangle. Then substitute 8 cm for the length and 5 cm for the width. Solve the equation to find the area of the rectangle. formula: A = substitute: A = ( cm)( cm) solved: A = Write the formula for the perimeter of a parallelogram. Then substitute 10 cm for the base and 6 cm for the side. Solve the equation to find the perimeter of the parallelogram. formula: P = substitute: P = ( cm) + ( cm) solved: P = c. Write a formula for the area of this piece of paper. Substitute numbers. Solve the equation to find the area of this paper. formula: A = substitute: A = ( in.)( in.) solved: A = Saxon Math Course 1 L Adaptations Lesson 91
2 Written Practice (page 476) 1. 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 prime composite = 2. 6:15 a.m. 5:15 p.m. hr 5:15 p.m. 5:45 p.m. min rectangular triangular 5. b = 15 cm h = 4 cm formula: A = 6. Each minute is 6 of a circle. 45 min = substitute: A = solved: A = Use work area parallelogram a. P = 2b + 2s a. A = bh a. 9. a = 7 20 = c. a. 10. Saxon Math Course 1 L Adaptations Lesson 91
3 Written Practice (continued) (page 477) = = = = % a of 300 sprouted 6 of 300 did not sprout y = 10 is of? y = Saxon Math Course 1 L Adaptations Lesson 91
4 Written Practice (continued) (page 477) 21. w 20 = area w = 23. volume in cubic inches (2, 0), (0, 2), ( 2, 0), (0, 2) 26. See the times table in the Student Reference Guide. and = 29. a. whole squares half squares c. area a. 30. Write the probability as a fraction and as a decimal. = Use work area. c. units 2 Saxon Math Course 1 L Adaptations Lesson 91
5 LESSON Name 92 Expanded Notation with Exponents Order of Operations with Exponents Powers of Fractions (page 479) To write numbers in expanded notation, we may also show whole number place values with powers of 10. Teacher Notes: Refer students to Expanded Notation Using Exponents on page 21 in the Student Reference Guide. Review Order of Operations on page 22 in the Student Reference Guide. Notice the exponent and the number of zeros it takes = 10, = = 10 1 = = 1 Example: Show 186,000 in expanded notation using exponents. 186,000 (1,000) + (8 10,000) + (6 0) ( ) + ( ) + ( ) The exponent after the 10 is equal to the number of digits to the right of the number. In the order of operations, simplify exponents before multiplying or dividing. 1. Simplify parentheses. Some students remember the order of operations 2. Simplify exponents (powers) and roots. by memorizing this phrase: 3. Multiply and divide left to right. Please P is for parentheses. 4. Add and subtract left to right. Excuse E is for exponents. My Dear M is for multiplication; D is for division. Aunt Sally A is for addition; S is for subtraction. Exponents may be used with fractions and with decimals. Convert a mixed number to an improper fraction before you multiply. Practice Set (page 481) a. Write 2,500,000 in expanded notation using exponents. ( ) + ( ) ( ) 2 ( 3 2 ) 2 Write this number in standard notation: ( ) + ( ),,, Saxon Math Course 1 L Adaptations Lesson 92
6 Practice Set (continued) (page 481) c (7 + 2) 9 = d. ( 1 2 ) 3 e. (0.1) 2 = f. ( ) 2 Written Practice (page 481) ( ) = g. (2 + 3) 2 ( ) = (2 + 3) 2 ( ) = 1. If the chance of rain is %, then the chance that it will not rain is %. So the chance that it will not rain is g 2. Write the probability as a fraction and a decimal. square total cards than the c that it will r. It is more likely that it rain. 3. average ) 4. All quadrilaterals are polygons. True or false? See the Student Reference Guide = (3 1) 3 7. formula: P = substitute: P = 8. least to greatest 1, 0, 0.1, of 30 present 6 of 30 absent 6 solved: P = Use work area.,,, 10. Reduce before multiplying. (24)(36) 48 = is of Saxon Math Course 1 L Adaptations Lesson 92
7 Written Practice (continued) (page 482) = = = = w $ w = 17. A = πr 2 Round the answer A, B, C, D, E, F, G, H, I, J 20. Saxon Math Course 1 L Adaptations Lesson 92
8 Written Practice (continued) (page 482) = w 23. area w = Reduce where possible. 1 16, 1 8, 3 16, 1 4,,,,,... a ,,, 26. perimeter 27. area 28. (4, 3), ( 2, 3), (0, 2), ( 6, 2) area 29. a. (12 cm)(8 cm) = 36 ft2 4 ft = 30. gal pt 1 3? a. square units Saxon Math Course 1 L Adaptations Lesson 92
9 LESSON 93 Classifying Triangles (page 484) Name Teacher Notes: Refer students to Classifying Triangles on page 28 in the Student Reference Guide. Review Types of Angles on page 18 in the Student Reference Guide. Practice Set (page 485) a. One side of an equilateral triangle measures 15 cm. What is the perimeter of the triangle? An equilateral triangle is also an acute triangle. True or false? c. All acute triangles are equilateral triangles. True of false? d. Two sides of a triangle measure 3 inches and 4 inches. If the perimeter is 10 inches, what type of triangle is it? e. Every right triangle is a scalene triangle. True or false? Saxon Math Course 1 L Adaptations Lesson 93
10 Written Practice (page 485) = 3. average 4. volume ) bottom layer all layers 5. Write 9 as a decimal and a percent % = 8. (0.3) 3 = is of 9. ( ) ( ) 2 = Saxon Math Course 1 L Adaptations Lesson 93
11 Written Practice (continued) (page 486) dozen = voted yes total = 12. yes + no total no yes = 13. w = = = = m 30 w = m = 15. In what type of triangle are all three sides the same length? of 8 is of triangle gal qt 1 2 1_ 2? 20. Saxon Math Course 1 L Adaptations Lesson 93
12 Written Practice (continued) (page 486) 21. Round one hundred twentyfive thousandths to the nearest tenth n = $1.20 n = 23. area of one triangle = 25. A 1 B 2 C 3 D ( ) + ( ) + ( ),,, 27. a. 6 s total numbers less than 6 total numbers c. The event is 6 and its c is not rolling 6. The sum of their probabilities is. 28. ( 3, 2), (0, 2), (3, 2), (5, 2) 29. A = bh 2 b = 20 cm h = 15 cm Use work area , 1 8, , 1 4, , 3 8,,,,, The rule is a to the preceding term.,,, Saxon Math Course 1 L Adaptations Lesson 93
13 LESSON Name 94 Writing Fractions and Decimals as Percents, Part 2 (page 488) To write a fraction as a percent: Set up a proportion with a denominator of. Multiply the loop and divide by the outside number. Teacher Note: Review FractionDecimalPercent Equivalents and Fraction Decimal Percent on page 13 in the Student Reference Guide. 6 5 =? 1 3 =? = 120% 3 = % or, multiply the number by %: 3 5 % = 300% = 60% 1 5 To write a decimal as a percent: Shift the decimal point two places to the right = 12.5% or 12 1_ 2 % Practice Set (page 490) Change each number to a percent. a. 0.5 = 0.06 = c = d = e. 1.3 = f = g = h = i = j. 2 3 =? k. 1 6 =? l. 1 8 =? m = 4 = o = = n = = p. What percent of the rectangle is shaded? = q. What percent of a yard is a foot? yd ft 1 = Saxon Math Course 1 L Adaptations Lesson 94
14 Written Practice (page 491) 1. = 2. halfway boil C freeze 0 C AC = 12 cm AB = 1 of AC 3 BC = of AC 3 is of is of 5. Convert =? 6. shift % is of circumference Use 3.14 for π. Saxon Math Course 1 L Adaptations Lesson 94
15 Written Practice (continued) (page 491) 11. A = π r = = = = ,000 ( ) + ( ) 15. $ = = 21 x = 19. x = 20. one hundred twenty and three hundredths Saxon Math Course 1 L Adaptations Lesson 94
16 = = Written Practice (continued) (page 491) 21. least to greatest 2.5, Change to decimals. 2 5, 5 2, ,,, 23. area 24. A acute B right C obtuse (0, 0), (0, 4), ( 4, 0) square units , 25, 22, 19, 22, 24, 20, 22, 24 First write the scores in order. a.,,,,,,,, qt gal 1 24? 30. Write the probability as a fraction and as a decimal rounded to the nearest hundredth. A tiles total tiles = Saxon Math Course 1 L Adaptations Lesson 94
17 LESSON Name 95 Reducing Rates Before Multiplying (page 493) Cancel numbers in fractions before multiplying. Also cancel units in measures before multiplying. 4 miles 1hour 2 hours 1 = 8 miles Convert units using the loop method: 1. State the words you are talking about. 2. Fill in the equivalent values. Examples: 1 week = 7 days 1 foot = 12 inches 1 meter = centimeters 3. Put the known factor in the correct place. 4. Multiply the diagonal loop. 5. Divide by the number outside the loop. Example: Change 56 days to weeks. weeks days0 1 7? 56 (56 1) 7 = 8 weeks Practice Set (page 494) Cancel numbers and units when possible before multiplying: a. 3 dollars 1 hour 6 baskets 10 shots 8 hours 1 shots 1 = dollars = baskets c. 10 cents 1 kwh 26.3 kwh 1 = d. 160 km 2 hours 10 hours 1 = e. 29 students 1 teacher 18 teachers 1 = students f. 2.3 m 1 cm 1 m = g. How far will the train travel in 6 hours at 45 miles per hour? mi hr = hr Saxon Math Course 1 L Adaptations Lesson 95
18 Written Practice (page 494) 1. $ $ m cm 1? 3. 5 of 40 sprouted 8 4. (5 ) + (6 10) + ( ) + ( 3 1 ) 8 of 40 did not sprout is of =? shift 2.5 = 7. 30% is of 8. 1 minute = 6 degrees minutes? 9. turns feet 1? volume bottom layer all layers Saxon Math Course 1 L Adaptations Lesson 95
19 Written Practice (continued) (page 495) = = = = = (1.5) 2 = ) Round 6 1 to 4, 4.95 to, and 8.21 to. Then a. 20. a. radius A = π r 2 a. Saxon Math Course 1 L Adaptations Lesson 95
20 Written Practice (continued) (page 495) 21. least to greatest 22. y = 5 Change to decimals. 1, 4%, ,, y = = x a. x = c = 42 mm 27. pint quart 28. b = 1.2 m h = 0.9 m A = bh Round 1.2 to and 0.9 to. Then m liters 1 0 milliliters 1 liter = 30. Write the probability as a fraction and a decimal. even numbers total numbers = Saxon Math Course 1 L Adaptations Lesson 95
21 LESSON Name 96 Functions Graphing Functions (page 497) A function is a rule that changes an input number to an output number. If you know the rule, you can make a function table with pairs of input and output numbers. Example: The side length of a square (s) is the input number. The perimeter of the square (P) is the output number. The function (or rule) is P = 4s. s P Teacher Note: Review Hint #55, Rectangular Coordinates. If you have a function table but do not know the rule, ask yourself, What is done to the input number to make the output number? Make sure the rule works for every number in the function table! Graphing a function is a way to show all the input and output numbers: 1. Make a function table with at least four input and output numbers. 2. Plot each pair of input/output numbers on a coordinate plane. The input number is the xcoordinate, and the output number is the ycoordinate. 3. Draw a ray through the dots. Example: The function for side length and perimeter of a square is graphed below. Practice Set (page 501) Find the missing number in each function table: a. x y a b c. x d x x x Saxon Math Course 1 L Adaptations Lesson 96
22 Practice Set (continued) (page 501) e. The alchemist mixed a vat of solution that weighed 2 pounds per quart. Complete the function table, then graph the ordered pairs. Would it be appropriate to draw a ray through the points? Why or why not? Any part of a q may be weighed, so it Q P appropriate to draw a ray. Written Practice (page 501) 1. ( ) ( ) = ? = Find the missing sum. 4. See the Student Reference Guide. 5. shift a = 1.5 = a = 7. Which one is not equivalent to the others? = 9. is of A 1 B % C 0.1 D 10. See the times table in the Student Reference Guide. and Saxon Math Course 1 L Adaptations Lesson 96
23 Written Practice (continued) (page 502) 11. completely around = 360 average of three turns 12. x x Use work area. 13. Factor and reduce. (45)(54) 81 ) ) ) 45 = ) ) ) ) 54 ) ) ) ) 81 = ) = = = is of 19. $ Saxon Math Course 1 L Adaptations Lesson 96
24 Written Practice (continued) (page 502) 21. dime quarter = 22. 4n = 6 14 n = n = Mark point S at the midpoint of RT n = = 36 w hours 1 6 dollars 1 hour = w = 27. (0, 0), (6, 0), (4, 4), ( 2, 4) 28. pints = 1 gallon area pints pounds units Write the probability as a fraction and as a decimal. prime numbers total numbers Saxon Math Course 1 L Adaptations Lesson 96
25 LESSON 97 Transversals (page 503) Name A line that intersects two or more other lines is a transversal. When a transversal intersects two parallel lines, the eight angles formed have special relationships. Teacher Note: Refer students to Transversals on page 32 in the Student Reference Guide. Corresponding angles ( 1 and 5; 2 and 6; 3 and 7; 4 and 8) have the same measure. Corresponding angles lie on the same side of the transversal in matching positions along parallel lines. Alternate exterior angles ( 1 and 7; 2 and 8) have the same measure. Alternate exterior angles lie on opposite sides of the transversal and outside parallel lines. Alternate interior angles ( 3 and 6; 4 and 5) have the same measure. Alternate interior angles lie on opposite sides of the transversal and inside parallel lines. All four acute angles in the figure have the same measure, and all four obtuse angles in the figure have the same measure. Practice Set (page 505) a. Which line in the figure is a transversal? Which angle is an alternate interior angle to 3? c. Which angle corresponds to 8? d. Which angle is an alternate exterior angle to 7? e. If the measure of 1 is 105, what is the measure of each of the other angles in the figure? 3, 5, and 7 each measure. 2, 4, 6, and 8 each measure. Saxon Math Course 1 L Adaptations Lesson 97
26 Written Practice (page 505) 1. hamburgers pounds 4 1? 2. halfway 212 F 32 F When C =, the result is These are the b p of water. Use work area. 5. Convert Convert = = 7. shift 0.7 = = 9. Use exponents. ) ) ) ) ) ) ) degrees minutes 60? Saxon Math Course 1 L Adaptations Lesson 97
27 Written Practice (continued) (page 506) 11. completely around = 360 average of four turns = = = = (1 0.1)(1 0.1) 1.. ) = = 19. part part whole % is of 30 Saxon Math Course 1 L Adaptations Lesson 97
28 Written Practice (continued) (page 506) , 0,, 10, 1,, a = a = = w perimeter each side w = 25. area (square) area (triangle) A = 1 2 bh 26. About how long would it take Mark to run 2 miles? He won t speed up. miles time 1 + 1_ 2? = A 9:30 B 11:00 C 15:00 : 27. If Mark kept up his 1_ mile record pace for a full 4 mile, about how long would it take him to run the mile? a (10 + 8) : m 5 = ; m 8 = composite numbers total numbers Saxon Math Course 1 L Adaptations Lesson 97
29 LESSON Name 98 Sum of the Angle Measures of Triangles and Quadrilaterals (page 508) Polygons have exterior angles (outside; 1) and interior angles (inside; 2). The sum of all exterior angles of a polygon is one full turn or 360. The sum of the interior angles of a triangle is 180. Teacher Notes: Review Angles on page 27 in the Student Reference Guide. Refer students to Finding the Degree of Exterior and Interior Angles of a Regular Polygon on page 33 in the Student Reference Guide. The sum of the interior angles of a quadrilateral is 360. Practice Set (page 510) Quadrilateral ABCD is divided into two triangles by segment AC. Use for a c. a. What is the sum of m 1, m 2, and m 3? What is the sum of m 4, m 5, and m 6? c. What is the sum of the measures of the four interior angles of the quadrilateral? d. What is m P in PQR? e. What is the measure of each interior angle of a regular quadrilateral? average of four angles f. Elizabeth made five left turns as she ran around the park. Find the average number of degrees in each turn. Saxon Math Course 1 L Adaptations Lesson 98
30 Written Practice (page 510) 1. ( ) ( ) = 2. (5 ) ft = 1 ft =? in of 200 finished 5 5 is of of 200 did not finish 4. a. m 6 = ; m 7 = 5. 25,000 miles 6. Divide by to find the r. Multiply by to find the c. ( ) + ( ) 7. circumference A spoke B axle C tire 8. 1, 1, 2, 3, 5, 8, 13,, , , , Write the answer as a decimal. part part whole % = Saxon Math Course 1 L Adaptations Lesson 98
31 Written Practice (continued) (page 511) w = $ w = _ volume bottom layer all layers = = 17. $ $ R $19.79 to $. 6% is ft = in. 3 = 6 cents per dollar, so tax is about $ m = cm = a Saxon Math Course 1 L Adaptations Lesson 98
32 Written Practice (continued) (page 512) 21. least to greatest 22. See the Student Reference Guide. 1, 1, 0, 1 2, 1 2,,,, 23. Congruent means the same shape and the same size. 24. The sum of the angles in a triangle is 180. a % 26. area a ( 1 2 ) in. 1 1 ft 12 in. = 29. a. red blue blue total 30. Classify by sides. See the Student Reference Guide. 20 red + 15 blue total a. Saxon Math Course 1 L Adaptations Lesson 98
33 LESSON Name 99 FractionDecimalPercent Equivalents (page 513) Teacher Note: Review FractionDecimalPercent Equivalents and Fraction Decimal Percent on page 13 in the Student Reference Guide. Practice Set (page 514) Complete this table. Fraction Decimal Percent c. 3 5 a. 0.8 d. e. f. 20% i. 3 4 g. h j. k. l. 5% Saxon Math Course 1 L Adaptations Lesson 99
34 Written Practice (page 514) 1. 1 ft = in. 2. See the Student Reference Guide year = months a. 5. volume bottom layer all layers 6. Every 90 is a 1 4 turn was eaten 5 5 was not eaten 5 = 8. = = Saxon Math Course 1 L Adaptations Lesson 99
35 Written Practice (continued) (page 514) = = (2 + 3) = 24 n n = ( ) $ $ a. mode First, put the percents in order.,,,,,, middlescore countries: and c. The middle score is called the m. It 19. ) ) ) ) ) ) 900 always be the same as the mode. Use work area. 20. Write two prime numbers:, Find their GCF. Saxon Math Course 1 L Adaptations Lesson 99
36 Written Practice (continued) (page 515) 21. m cm 2? perimeter cm 22. each side a. 23. The sum of the angles in a quadrilateral is Fraction Decimal Percent a. 0.6 a a. 15% 3 10 a. Use work area. 27. Mark point B at the midpoint of AC. 28. Write the answer as a percent in. letter card total cards quart < 1 liter 4 quarts = 1 gallon 1 gallon 4 liters 30. r d To find d, m r by. Use work area. Saxon Math Course 1 L Adaptations Lesson 99
37 LESSON Algebraic Addition of Name Integers (page 517) To add integers as illustrated on a number line: 1. Begin at zero. 2. Move right or left as indicated by the sign of the first number. If the number is positive, move right. If the number is negative, move left. Teacher Note: Refer students to Adding Two Signed Numbers and Subtracting Signed Numbers on page 26 in the Student Reference Guide. 3. From the point of the first number, move right or left as indicated by the second number (and third number...). 4. After every number has been added, the answer is the sum. Example: = +3 To add signed numbers: If the signs are the same, add the absolute values and keep the same sign. If the signs are different, subtract the absolute values; keep the sign of the greater number. Examples: ( 5) + ( 3) = 8 (+8) + ( 5) = +3 Opposites are numbers that have the same digits but opposite signs. If opposites are added, the sum is zero. ( 3) (+3) = 0 In algebraic addition, instead of subtracting, add the opposite. Instead of subtracting a positive, add a negative. Instead of subtracting a negative, add a positive. 1. Rewrite like an addition problem, and change the second number to its opposite. 2. Solve like an addition problem. ( 3) (+5) 10 6 ( 3) + ( 5) = = ( 3) + ( 5) = = 4 Saxon Math Course 1 L397 Adaptations Lesson
38 Practice Set (page 521) Illustrate a and b on a number line. Solve the rest mentally. a = = c = d = e. (+3) + ( 4) = f. (+10) + ( 5) = g. ( 10) + ( 5) = h. ( 10) + (+5) = Find the opposite of each number: i. 8 j. 4 k. 0 Solve each subtraction problem by using algebraic addition: l. 3 4 m ( ) = 4 ( ) = n. (+3) ( 6) o. ( 2) ( 4) 3 = = Written Practice (page 521) 1. The dividend is missing ) average a = = c = d = Use work area. Use work area. Saxon Math Course 1 L398 Adaptations Lesson
39 Written Practice (continued) (page 522) 6. a = 3 = 7. equilateral triangle The sum of the angles in a triangle is 180. c d = 2 = Use work area. 8. The sum of the angles in a quadrilateral is 360. m B = 9. a. 6 = 6 of 30 m C = a. m D = 10. volume 11. boys + girls total girls boys (5 2 11) = 14. Write the answer as a fraction. part part = = = whole % Saxon Math Course 1 L399 Adaptations Lesson
40 Written Practice (continued) (page 522) ( ) 19. area rounded to the nearest square foot V is a measure of space. To measure space, we use u that take up space (c ). S do not take up space = 15 x Use work area. x = 22. area of ABC 23. perimeter of ABC circumference rounded to the nearest millimeter 26. Write the probability as a fraction and a decimal rounded to the nearest hundredth. blue total Fraction Decimal Percent 9 10 a. a gallon = quarts 2 pints = quart 29. a. 4% Use work area. Saxon Math Course 1 L400 Adaptations Lesson
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