# Triangles, Rectangles, Squares, and Circles

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1 LESSON Name 2 Teacher Notes: page 27 Triangles, Rectangles, Squares, and Circles Refer students to Circle on page 4 in the Student Reference Guide. Post Reference Chart Circle. Use the compasses from the manipulative kit to illustrate concepts in this lesson. New Concept Triangle 3 sides Rectangle 4 sides width length Square 4 equal sides (special kind of rectangle) Circle Radius = of diameter 2 A compass is a tool used to draw circles. radius cm in Diameter = 2 radius diameter Saxon Math Intermediate 4 33 Adaptations Lesson 2

2 New Concept, continued Activity page 29 Drawing a Circle Use your textbook to complete this activity. Lesson Practice a. Draw a TRIANGLE with two sides that are the same length. b. Draw a RECTANGLE that is about twice as long as it is wide. c. Use a compass to draw a CIRCLE with a radius of inch. d. What is the diameter of a circle that has a 3-cm radius? 3 cm e. What is another name for a rectangle whose length is equal to its width? s Saxon Math Intermediate 4 34 Adaptations Lesson 2

3 Written Practice page Hiroshi Harry in all Tisha n Jane total n = 3. The ones digit is 5. The number is greater than 640. It is less than seven hundred fifty-three expanded form: 5. x 0 y 6. average daily high and low temperatures x + y Use a centimeter ruler. a. length b. width c. perimeter Perimeter Add all sides. a. b. c. Saxon Math Intermediate 4 35 Adaptations Lesson 2

4 Written Practice, continued page \$486 + \$ \$524 + \$ Perimeter Add all sides. 3. bottom missing 7 a bottom missing 5 b 6 a = b = d bottom missing 4 b 2 d = b = Saxon Math Intermediate 4 36 Adaptations Lesson 2

5 Written Practice, continued page 3 9. top missing y bottom missing 75 p y = p = a., 28, 35, 42,,,, b., 40, 30, 20,,,, 26. Add the two l 27. d = 2r plus the two w 4 cm to fine the p. A 8 in. B 2 in. C 8 cm D 2 cm Saxon Math Intermediate 4 37 Adaptations Lesson 2

6 Written Practice, continued page Use your student clock. Count forward minutes 7:35 a.m. = minutes start time end time 29. Round to the nearest ten: a. 7 6 b. 7 3 c. 7 5 a. b c. 30. Round to the nearest 25 cents: a. \$6.77 \$6.77 \$6.75 \$7.00 b. \$7.97 \$7.97 \$7.75 \$8.00 Saxon Math Intermediate 4 38 Adaptations Lesson 2

8 Lesson Practice What fraction of each shape is shaded? (Name the number shaded out of the total number of parts.) a. b. Order from least to greatest. c. 3, 2 0, 4,, d. 2 5, 3 8, 2,, e. Order from greatest to least. f. Order from greatest to least. Act it out using fraction manipulatives. Act it out using fraction manipulatives. 3 4, 5, 2 3,, 6 0, 4 5, 2,, g. Three dimes are what fraction of a h. \$ \$2.75 dollar? \$ i. \$ \$4.28 j. Estimate. Use compatible numbers. \$.49 + \$.49 \$ + \$ \$ Saxon Math Intermediate 4 40 Adaptations Lesson 22

9 Written Practice page l in. beginning grew end l = 3. Less than , 80, 72, 64,,,, odd 5., 60, 54, 48,, 6.,, Perimeter add all sides 7. See page in the Student Reference Guide. 8. What place? 89 Saxon Math Intermediate 4 4 Adaptations Lesson 22

10 Written Practice, continued page expanded form: words: + +. Eighteen is greater than negative twenty. 2. a. 2 8 b. \$5.95 a. b. 3. Estimate. Desk = meters high cm d = 2r 6. Saxon Math Intermediate 4 42 Adaptations Lesson 22

11 Written Practice, continued page meter = cm 2 meters = \$ \$ \$ \$ n x p 4 n = x = p = If the equation 20 + n = 60 is true, then which of the following equations is not true? a = n b. 60 n = n c. n 20 = 60 d. n + 20 = 60 Saxon Math Intermediate 4 43 Adaptations Lesson 22

12 Written Practice, continued page Estimate. compatible numbers \$.26 \$ + \$ \$ \$,26 can be rounded to, and \$3.73 can be rounded to. It s easier to estimate the sum using c n. 29. Waterfalls Name Location Height (ft) Multnomah Oregon 620 Maletsunyane Lesotho, Africa 630 Wentworth Australia 64 Reichenbach Switzerland 656 Least to greatest. Look at the hundreds. Look at the tens. Wentworth,,, 30. tenth number 4, 8, 2, 6, 20,,,,, Saxon Math Intermediate 4 44 Adaptations Lesson 22

13 LESSON Name 23 Teacher Notes: page 40 Lines, Segments, Rays, and Angles Introduce Hint #5 Geometry Vocabulary. Refer students to Types of Lines and Types of Angles on pages 5 6 in the Student Reference Guide. New Concept Lines and Segments Math Language Parallel lines never cross. When lines cross, they intersect. Intersecting lines that form square corners are perpendicular. line A B ray F G segment D E parallel lines intersecting lines intersecting and perpendicular Math Language A vertex is where 2 sides of an angle meet. Angles are formed where lines or segments intersect or where two or more rays begin. Angles side vertex side Straight Obtuse Acute Right Activity page 43 Real-World Segments and Angles This activity is optional. Saxon Math Intermediate 4 45 Adaptations Lesson 23

14 Lesson Practice a. Draw two SEGMENTS that intersect b. Draw two LINES that are but are not perpendicular. perpendicular. c. Draw a RAY. d. Are the rails of a train track parallel or perpendicular? Train track rails are p because they never i. Locate and describe the angles of items in or around your classroom. item type of angle item type of angle item type of angle e. A triangle has how many angles? f. Which of these angles does not look like a right angle? A B C D Saxon Math Intermediate 4 46 Adaptations Lesson 23

15 Written Practice page first second both 2. 2 first n second both 3. Greater than a., 40, 36, 32,,,, odd b., 30, 27, 24,,,, a. b Six hundred thirty-eight is less than six hundred eighty-three a. 9 2 b. \$9.67 a. b. Saxon Math Intermediate 4 47 Adaptations Lesson 23

16 Written Practice, continued page If a nickel s radius is cm, its diameter is cm. Ten nickels in a row is cm, or cm Which of these shapes has four right angles? a. Length A B b. Width c. Perimeter Perimeter Add all sides. C D. 2. Use your student clock. Count forward minutes. = start time end time minutes 3. \$83 \$27 Check: \$27 + \$ Check: Saxon Math Intermediate 4 48 Adaptations Lesson 23

17 Written Practice, continued page Check: \$ \$ \$ \$ k b 6 k = b = 20. k k = = 25. a. \$ = nickels b. nickel = of a dollar c. 7 nickels = of a dollar Saxon Math Intermediate 4 49 Adaptations Lesson 23

18 Written Practice, continued page If 26 + m = 63, then which of these equations is not true? m A m + 26 = 63 B m 63 = 26 C 63 m = 26 D = m 27. Which of these figures illustrates a ray? A B C D 28. \$.99 \$ A reasonable estimate would be \$ = \$. 29. Look at the hundreds. Look at the tens. Look at the ones v a b c v = Saxon Math Intermediate 4 50 Adaptations Lesson 23

19 LESSON Name 24 Teacher Note: page 47 Review Missing Numbers on page 7 in the Student Reference Guide. Inverse Operations New Concept ADDITION: to find missing addend 5 + a a = 3 x SUBTRACTION: to find missing top t t = 8 SUBTRACTION: to find missing bottom 8 b b = 6 subtract 7 3 x = 4 add subtract Lesson Practice Find each missing number: a m 42 b. q c. 53 w 28 m = q = w = d. n e y 63 f. 62 a 26 n = y = a = Saxon Math Intermediate 4 5 Adaptations Lesson 24

20 Written Practice page 49. in in ft = in. 2 ft = 2. 2 commercials p not commercials 3. Does equal mean odd or even? So which is not? total A 36 B 45 C 60 D 24 p = 4., 9, 8,,, 45,, 5. 7, 4, 2,,,, Saxon Math Intermediate 4 52 Adaptations Lesson 24

21 Written Practice, continued page a. 7 7 b. \$29.39 c. \$9.9 \$9.9 a. \$9.00 \$9.25 b. c. 8. meter is a little more than 3 feet Use your student clock. Count forward hours: 8:0 p.m. = hours start time end time Count forward minutes: 8:0 p.m. 9:05 p.m. = minutes Add. start time end time hours + minutes = hours and minutes Saxon Math Intermediate 4 53 Adaptations Lesson 24

22 Written Practice, continued page Which street is parallel to Elm? Parallel looks like railroad tracks. Elm Oak Broadway W N S E. a. \$ = dimes 2. 5 cm long 2 cm wide b. dime = of a dollar c. 9 dimes = of a dollar a. b. c. 3. Name each type of angle shown below. 4. \$3 \$4 a. b. c. a. b. c. Saxon Math Intermediate 4 54 Adaptations Lesson 24

23 Written Practice, continued page 5 5. \$468 + \$ \$ \$ c 9 9. b d 93 c = b = d = 2. n n = See page 5. Saxon Math Intermediate 4 55 Adaptations Lesson 24

24 Written Practice, continued page A segment has two e and is part of a l. A has no e. 28. Round to nearest dollar. \$4.25 \$ + \$ \$ + \$ one ticket two tickets One ticket costs about \$ A reasonable estimate of the cost of two tickets is \$ + \$, or \$ = Jasmine found found seashells. Then she more seashells. How many F did she find in all? Saxon Math Intermediate 4 56 Adaptations Lesson 24

25 LESSON Name 25 Teacher Note: page 52 Subtraction Word Problems Review Missing Numbers on page 7 in the Student Reference Guide. New Concept Lesson Practice Subtraction word problems have a missing number. If the top number is missing Add. Some Some went away What is left p pencils 5 pencils 22 pencils p = 37 If the bottom number is missing Subtract. Some 42 seashells Some went away s seashells s = 3 What is left 29 seashells If the difference is missing Subtract as usual. Some 65 beads Some went away What is left 3 beads b beads b = 52 a. 42 had n mailed now b. n beginning donated now n = n = c. 75 \ c had spent n \ c now n = Saxon Math Intermediate 4 57 Adaptations Lesson 25

26 Written Practice page had had gave gave now now 3. n had 4. Half Divide by 2. used now 5. a., 5, 0,,, 25,, b., 5, 0,,, 5,, a. b. 6. Seven hundred sixty-two is less than eight hundred twenty-six. Saxon Math Intermediate 4 58 Adaptations Lesson 25

27 Written Practice, continued page a. 7 8 b. \$7.80 c. \$7.80 \$7.80 \$7.75 \$8.00 a. b. c in. d = 2r Use your student clock. Count forward minutes: :35 p.m. = minutes start time end time Saxon Math Intermediate 4 59 Adaptations Lesson 25

28 Written Practice, continued page Which street is perpendicular to Elm? Perpendicular looks like this:. Elm Oak Broadway W N S E 2. 4 cm Find the pattern. Try ones. Try twos. 4. \$52 \$ \$ \$2.03 Saxon Math Intermediate 4 60 Adaptations Lesson 25

29 Written Practice, continued page g b d g = b = d = 2. y y = Which of these is not equivalent to one meter? A 000 mm B 00 cm C 000 km D m meter = mm meter = cm km = m Saxon Math Intermediate 4 6 Adaptations Lesson 25

30 Written Practice, continued page A ray has one e. A segment has t endpoints Illinois Potomac total 29. Round to nearest 0 cents. \$ \$0.59 \$ + \$ To get a reasonable estimate, I used com numbers. \$3.39 is close to \$, and \$0.59 is close to \$. Adding these together gives a sum of \$. 30. from F 0 F = from 0 F 2 F = Saxon Math Intermediate 4 62 Adaptations Lesson 25

31 LESSON Name 26 Teacher Notes: page 58 Drawing Pictures of Fractions Introduce Hint #6 Drawing Fractional Parts. For additional practice, students may complete Fraction Activity 26. New Concept Example To draw a picture of a fraction:. Draw the figure. 2. Divide into equal parts (bottom number). 3. Shade the correct number of parts (top number). Draw a rectangle, and shade 2 of it. 3 Rectangle 3 equal parts 2 parts shaded Here are some pictures of other fractions: Example To divide a circle into thirds:. Draw a dot in the center. 2. Make a Y from the dot. 3. There are 3 equal parts. These are NOT equal parts: Saxon Math Intermediate 4 63 Adaptations Lesson 26

33 Written Practice, continued page Less than cm 6 cm 8 cm even Perimeter Add all sides. 7. Negative twenty is less than negative twelve. 8. a. 9 b. \$0.90 a. b. 9. meter = cm See page in the Student Reference Guide. 0. Before noon Which street makes a right angle with Oak? A right angle looks like this: Elm Oak Broadway W N S E Saxon Math Intermediate 4 65 Adaptations Lesson 26

34 Written Practice, continued page F 4. y \$486 + \$277 y = 6. \$68 \$39 7. \$ \$ n n 65 n = n = Saxon Math Intermediate 4 66 Adaptations Lesson 26

35 Written Practice, continued page c e c = e = In which figure is 2 not shaded? A B C D 27. Is the largest angle of this triangle acute, right, or obtuse? Saxon Math Intermediate 4 67 Adaptations Lesson 26

36 Written Practice, continued page How many three-digit numbers can you write with 0, 7, and 3? Write even or odd. Act it out. 3 7 odd can t be 0 7 different numbers. 29. Round to nearest fifty cents. \$ \$8.59 \$ + \$ Yes, \$4 is reasonable because \$5.45 is about \$ and \$8.59 is about \$, and the sum of these is \$ Saxon Math Intermediate 4 68 Adaptations Lesson 26

37 LESSON Name 27 Teacher Notes: page 62 Review Hint # Elapsed Time. Review Hint #0 Reading Clocks. Multiplication as Repeated Addition Elapsed Time New Concept Multiplication as Repeated Addition Change + problems to problems : = = 20 Use multiplication to show repeated addition. 4 5 = 20 or 5 4 Four groups of five equals twenty. 20 Elapsed Time Example Elapsed time: will it be ago forward backward It is afternoon. What time will it be in hour and 50 minutes?. The time now is :45 p.m. 2. Count forward hour to 2:45 p.m. 3. Count forward 50 minutes to 3:35 p.m Saxon Math Intermediate 4 69 Adaptations Lesson 27

38 New Concept, continued Activity page 64 Finding Time Use your textbook to complete this activity. Lesson Practice a. 3 b. 9 c. 7 d. 5 How many times? Remember to write a.m. or p.m. e. If it is morning, what time will it be in 2 hours and 25 minutes? Time now: Count forward 2 hours. Count forward 25 minutes. f. If it is morning, what time was it 6 hours and 30 minutes ago? Time now: Count back 6 hours. Count back 30 minutes. Saxon Math Intermediate 4 70 Adaptations Lesson 27

39 Written Practice page before noon 2. ft a. ft = left at noon b. Perimeter Perimeter Add all sides. a. b. 3. Even numbers between 3 and 39 4., 2, 5, 8,,,,,,, 5., 2, 24, 36,,, , expanded form: a. 6 3 words: b. \$6.30 a. b. Saxon Math Intermediate 4 7 Adaptations Lesson 27

40 Written Practice, continued page Look at hundreds. Look at tens. 0. a b Find the pattern. Try fifties a. b.. Shade one fourth of the square. 2. out of parts are shaded, so is the num and is the den. 3. afternoon What time will it be 3 hours from now? Time now: Count forward 3 hours Saxon Math Intermediate 4 72 Adaptations Lesson 27

41 Written Practice, continued page \$67 \$ \$5.88 \$ d d = f bottom missing 87 r top missing b 4 27 f = r = b = Change to multiplication: a. \$ = pennies b. penny = of a dollar c. pennies = of a dollar a. b. c. Saxon Math Intermediate 4 73 Adaptations Lesson 27

42 Written Practice, continued page If 3 and 4, then what does equal? A 343 B 7 C 0 D 27. Draw 2 perpendicular rays from the dot. 28. v total 29. Round to nearest dollar. \$ \$5.95 \$ + \$ No, \$40 is reasonable because \$5.95 is close to \$, and the sum of \$ plus \$ is \$. 30. Show six different ways to add 2, 4, and Saxon Math Intermediate 4 74 Adaptations Lesson 27

43 LESSON Name 28 Teacher Notes: page 68 Introduce Hint #7 Multiplication/ Division Fact Families. Refer students to Multiplication Multiplication Table Table on page 5 in the Student Reference Guide. Review Properties of Operations on page 22 in the Student Reference Guide. New Concept One fact family four facts ) ) 2 Properties of Multiplication Commutative Property m n = n m Identity Property n = n Zero Property 0 n = 0 2s facts 5s facts double the other number count by 5s Lesson Practice a. 9 3 b. 3 9 c. 6 4 d. 4 6 e. 7 8 f. 8 7 g. 5 8 h. 8 5 i. 0 0 j. 0 8 k. 9 l. 2 2 Saxon Math Intermediate 4 75 Adaptations Lesson 28

44 Lesson Practice, continued m. Which property of multiplication is shown below? 2 = 2 C Property of Multiplication n. Use the Zero Property of Multiplication to find the product: 0 25 = o. Use the Identity Property of Multiplication to find the product: 25 = Written Practice page morning afternoon in all 2. \$8 saved + n more needs 3. Perimeter Add all sides. 4 cm 4., 2,,, 30, 36,, 5., 36,,, 24, 20,, 6. Change to multiplication: = Saxon Math Intermediate 4 76 Adaptations Lesson 28

45 Written Practice, continued page a. 2 8 b. \$2.29 c. \$2.29 \$2.29 \$2.25 \$2.50 a. b. c. 8. Finish drawing the right triangle (one right angle). The two perpendicular sides should be 3 cm long and 4 cm long. 4 cm 9. Morning. What time will it be 90 minutes from now? Time now: Count forward 90 minutes Saxon Math Intermediate 4 77 Adaptations Lesson 28

46 Written Practice, continued page expanded form: words: a. temperature b. increase by 0 degrees Count by twos. 0 C a. b \$286 + \$ \$73 \$39 6. \$ \$ c 9 8. n c = n = Saxon Math Intermediate 4 78 Adaptations Lesson 28

47 Written Practice, continued page y d y = d = a. 8 b. 0 7 c yard meter a. b. c. 26. Which of the following shows 3 ones and 4 hundreds? A 304 B 403 C 4003 D 3400 Saxon Math Intermediate 4 79 Adaptations Lesson 28

48 Written Practice, continued page See the multiplication table on page 70. How many times? Property: C 28. cheetah elk s difference Property of Multiplication 29. Round to the nearest five. \$37 \$ + \$54 + \$ \$ is a reasonable e because \$37 is close to, \$54 is close to \$, and the sum of these is \$ , 80, 70, 60, 50,,,,,, Saxon Math Intermediate 4 80 Adaptations Lesson 28

49 LESSON 29 page 75 Name Multiplication Facts: 0s, s, 2s, 5s New Concept Lesson Practice 0 any number = 0. any number = the same number. 2 any number = double the number. 5 any number = a number that ends in 0 or in 5. Instead of completing Power Up C, complete the multiplication facts below. a. 0 3 = b. 4 0 = c. 7 0 = d. 5 = e. 6 = f. 4 = g. 5 9 = h. 5 4 = i. 5 6 = j. 2 5 = k. 7 5 = l. 3 5 = m. 2 3 = n. 5 5 = o. 7 2 = p. 6 2 = q. 2 8 = r. 2 2 = Saxon Math Intermediate 4 8 Adaptations Lesson 29

50 Written Practice page made Rochelle + n Zuri sold remained in all 3. a. radius in feet b. diameter in feet d = 2r 4. Subtract to find the pattern., 8,,, 32, 40,, 2 yd a. b. 5., 4,,, 35, 42, 6. Less than Two hundred nine is greater than one hundred ninety. odd Saxon Math Intermediate 4 82 Adaptations Lesson 29

51 Written Practice, continued page Afternoon. Time now: 9. Shade two thirds of the 3-cm-by-- cm rectangle. 3 cm Count forward 5 minutes. Count forward 35 minutes a. 2 8 =. A B b. 5 7 = c. 2 7 = D C d. 5 8 = It is it is b r angle. because than a a. b. c. d. Saxon Math Intermediate 4 83 Adaptations Lesson 29

52 Written Practice, continued page Find the pattern See page 2 in the Student Reference Guide. At what temperature does water freeze a. on the Fahrenheit scale? b. on the Celsius scale? a. b. 4. \$83 \$9 5. \$286 + \$ \$ \$ q n 37 q = n = Saxon Math Intermediate 4 84 Adaptations Lesson 29

53 Written Practice, continued page m g m = g = Change to multiplication: = 25. sets of ten = 26. Which of these does not equal 24? A 3 8 B 4 6 C 2 2 D Use Properties of Operations table on page 22 in the Student Reference Guide. a. Z Property of Multiplication b. C Property of Multiplication c. I Property of Multiplication Saxon Math Intermediate 4 85 Adaptations Lesson 29

54 Written Practice, continued page a. \$3.49 b. \$3.49 \$3.49 \$3.25 \$3.50 a. b. 29. equation with product of 8 = z x y x + y z + Saxon Math Intermediate 4 86 Adaptations Lesson 29

55 LESSON 30 page 79 Name Subtracting Three-Digit Numbers with Regrouping New Concept To subtract three-digit numbers: \$365 \$87? 5 \$36 5 \$ \$3 6 5 \$ \$3 6 5 \$ 8 7 \$ 7 8 Line up last digits. Exchange ten for 0 ones; subtract ones. Exchange hundred for 0 tens; subtract tens. Subtract hundreds. To subtract three-digit decimal numbers: \$4.0 \$.2 0 \$4. 0 \$ \$4. 0 \$ \$4. 0 \$. 2 \$2.98 Line up the decimal points. Subtract pennies. Subtract dimes. Subtract dollars. Lesson Practice Subtract. a. \$365 \$287 b. \$4.30 \$.8 c d. 240 e. 459 f. 57 Saxon Math Intermediate 4 87 Adaptations Lesson 30

56 Lesson Practice, continued g. Round to nearest 25 cents before adding. \$ \$2.27 \$ + \$ \$ is a reasonable e because \$8.24 is about \$ and 2.27 is about \$. The dif between the rounded numbers is \$. page 82 Written Practice. n bell rang left black shoes n no black shoes 73 altogether 73 remained 3. A nickel is worth morning Gilbert has an even number of nickels. Which could not be the value of his nickels? Any even number 5 will end in. Time now: Count forward 5 minutes. A 45 B 70 C 20 D Saxon Math Intermediate 4 88 Adaptations Lesson 30

57 Written Practice, continued page , 2, 8,,,, 6. Find the pattern expanded form: words: 9. a. 6 8 = b. 4 2 = c. 4 5 = d. 6 0 = a. b. c. d. Saxon Math Intermediate 4 89 Adaptations Lesson 30

58 Written Practice, continued page Use a centimeter ruler to find the: 2. a. length. b. width. c. perimeter. Perimeter Add all sides. a. b. c \$3.86 +\$ \$4.86 \$ m a 43 m = a = Saxon Math Intermediate 4 90 Adaptations Lesson 30

59 Written Practice, continued page y q y = q = 2. Since 89 is g than 85, = it is closer to than to. 23. Find half of Change to multiplication: = = 26. Which of these sets of numbers is not an addition/subtraction fact family? A, 2, 3 B 2, 3, 5 C 2, 4, 6 D 3, 4, Saxon Math Intermediate 4 9 Adaptations Lesson 30

60 Written Practice, continued page See Multiplication Table on page 5 in the Student Reference Guide. a. 0 0 = b. = c. 2 2 = 28. Tabitha bought a package of pencils. She sharpened them. of How many were not s? a. = b. c. 29. Round to the nearest 50. \$500 is r because \$749 is about \$, \$259 is about \$, and \$ \$ = \$. 30. c a b a + b = c c = + = = Saxon Math Intermediate 4 92 Adaptations Lesson 30

61 INVESTIGATION 3 Name Teacher Notes: page 85 Focus on Multiplication Patterns Area Squares and Square Roots Introduce Hint #8 Area and Perimeter Vocabulary and Hint #9, Square Roots. Review Perimeter, Area, Volume on page 7 in the Student Reference Guide. Students will need copies of Lesson Activity 20. Multiplication Patterns An array is a rectangular model of multiplication. 3 rows and 5 columns 3 5 = 5 3 and 5 are factors of 5 5 columns 3 rows Refer to this array of Xs to answer problems 4 below.. How many rows are in the array? 2. How many columns are in the array? 3. How many Xs are in the array? 4. What multiplication fact is illustrated by the array? = Saxon Math Intermediate 4 93 Adaptations Investigation 3

62 INVESTIGATION 3 continued 5. Represent Draw an array of 2 Xs in 2 rows. 2 2 =? 6. How many columns of Xs are in the array you drew? 7. What multiplication fact is illustrated by the array you drew? = Here is an array of 0 Xs. 8. Which two factors of 0 are shown by this array? and 9. Can you draw a rectangular array of ten Xs with three rows? Act it out. 0. Can you draw a rectangular array of ten Xs with four rows? Act it out.. Can you draw a rectangular array of ten Xs with five rows? Act it out. 2. Represent Draw an array of Xs in 3 rows and 6 columns. Write the multiplication fact. = Saxon Math Intermediate 4 94 Adaptations Investigation 3

63 INVESTIGATION 3 continued 3. Represent The chairs in a room were arranged in 6 rows, with 4 chairs in each row. Draw an array. Write the multiplication fact. = Area An area model is an array of connected squares. 4 6 = 24 6 squares on this side 4 squares on this side 4. How many small squares are in the rectangle above? Represent Use Lesson Activity 20 for problems 5 and Outline a 3-cm-by-8-cm rectangle. How many small squares are in the rectangle? What multiplication fact is illustrated by the rectangle? = 6. Outline a rectangle that is made up of 24 squares. Make the rectangle 2 cm wide. How long is the rectangle? What multiplication fact is illustrated by the rectangle? = Saxon Math Intermediate 4 95 Adaptations Investigation 3

64 INVESTIGATION 3 continued Math Language Area is the space inside the perimeter of a flat figure. Trace the edge of this paper with your finger. You are tracing the paper s perimeter. Rub the surface of this paper with your palm. You are rubbing the paper s area. 7. Use your finger to trace the perimeter of your desktop. 8. Use the palm of your hand to sweep over the area of your desktop. To measure the area of a shape cover its surface. count how many squares cm in. cm one square centimeter ( sq. cm) in. one square inch ( sq. in.) 9. How many square centimeters cover the area of this rectangle? 3 cm 2 cm square centimeters 20. Represent On Lesson Activity 20, outline a 4 cm by 3 cm rectangle. Area Perimeter Problems 2 23 are optional. Saxon Math Intermediate 4 96 Adaptations Investigation 3

65 INVESTIGATION 3 continued Activity page 88 Finding Perimeter and Area This activity is optional. Activity page 89 Estimating Perimeter and Area Use your textbook to complete this activity. Squares and Square Roots Use Lesson Activity 20 for problems Represent Outline these four squares and write the multiplication fact for each square. by Multiplication fact: 2 by 2 Multiplication fact: 3 by 3 Multiplication fact: 4 by 4 Multiplication fact: When we square a number, we multiply a number by itself: 3 squared = = Outline a 6 by 6 square. 6 squared = 26. Outline a 7 by 7 square. 7 squared = Problems 27 and 28 are optional. Saxon Math Intermediate 4 97 Adaptations Investigation 3

66 INVESTIGATION 3 continued To find the square root of a number, ask: What factor multiplied by itself equals the original number? The square root of 25 equals 5 because 5 5 = = 5 25 squares in all 5 squares on each side 29. a. 9 squared = b. What is the square root of 9? 30. Find each square root: a. 4 = b. 6 = c. 64 = 3. If the area of a square is 49 square centimeters, how long is each side of the square? Saxon Math Intermediate 4 98 Adaptations Investigation 3

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