LESSON 21 • Triangles, Rectangles, Squares, and Circles Power Up multiples Power Up K The multiples of 7 are 7, 14, 21, and so on. On your hundred number chart, circle the numbers that are multiples of seven. Which of the circled numbers is an even number as well as a multiple of five? 70 mental a. Number Sense: 44 + 32 76 math b. Number Sense: 57 + 19 76 c. Number Sense: 32 + 43 + 100 175 d. Number Sense: What number should be added to 6 to get a total of 9? 3 e. Money: What is the total value of 2 quarters, 3 dimes, and 1 nickel? 85¢ f. Money: What is the total cost of a $200 bicycle and a $24 helmet? $224 g. Estimation: Round $13.89 to the nearest dollar. $14 h. Estimation: Round 73 yards to the nearest ten yards. 70 yd problem Choose an appropriate problem-solving strategy to solve solving this problem. The P.E. instructor divided the 21 students into four teams. If the P.E. instructor divided the class as evenly as possible, how many students were on each of the four teams? one team of 6 students and three teams of 5 students New Concept In this lesson we will practice drawing triangles, rectangles, squares, and circles. Lesson 21 127 Example 1 Represent Draw a triangle whose sides all have the same length. You may need to practice on a separate sheet of paper to Math Language understand how to draw this triangle. A triangle has three sides, but A triangle whose sides are all equal those sides can be positioned many different ways. If you start with in length is called a “square corner,” the third side will be too long. an equilateral triangle. This side is longer than the other two sides. square corner A triangle whose sides are the same length looks like this: Example 2 Represent Draw a rectangle whose sides all have the same length. A rectangle has four sides and square corners. It does not have to be longer than it is wide. A rectangle whose sides are the same length looks like this: This figure looks like a square. We know that it is a square because it has 4 sides with the same length. It is also a rectangle. A square is a special kind of rectangle. Example 3 Represent Draw a rectangle that is 3 cm long and 2 cm wide. Thinking Skill We use a centimeter ruler to help us make the drawing. Analyze What is the cm perimeter of this rectangle? 12 10 cm cm 123 128 Saxon Math Intermediate 4 A circle is a closed, curved shape in which all points on the shape are the same distance from the center. To draw circles, we can use a tool called a compass. Below we show two types of compasses: Math Language When we talk cm 1 234567891011 about one radius, we say “radius.” When we talk in. 1 234 about more than one radius, we say “radii.” The plural of radius is radii. There are two points on a compass: a pivot point and a pencil point. We swing the pencil point around the pivot point to draw a circle. The distance between the two points is the radius of the circle. The radius of a circle is the distance from the center of the circle to the edge of the circle. The diameter of a circle is the distance across the circle through the center. As the diagram below illustrates, the diameter of a circle equals two radii. Math Language The circumference of a circle is the radius radius distance around— or the perimeter of—a circle. diameter Activity Drawing a Circle Material needed: • compass Represent Use a compass to draw a circle with a radius of 2 cm. Label the diameter and the radius. Example 4 If the radius of a circle is 2 cm, then what is the diameter of the circle? Since the diameter of a circle equals two radii, the diameter of a circle with a 2-cm radius is 4 cm. Lesson 21 129 Lesson Practice a. Draw a triangle with two sides that are the same length. See student work. b. Draw a rectangle that is about twice as long as it is wide. c. See student work. 1 in. c. Use a compass to draw a circle with a radius of 1 inch. See student work. d. What is the diameter of a circle that has a 3-cm radius? 6 cm e. What is another name for a rectangle whose length is equal to its width? square Written Practice Distributed and Integrated Write and solve equations for problems 1 and 2. 1. Hiroshi had four hundred seventeen marbles. Harry had two hundred (1, 13) twenty-two marbles. How many marbles did Hiroshi and Harry have in all? 417 + 222 = t; 639 marbles * 2 . Tisha put forty pennies into a pile. After Jane added all of her pennies, (11, 14) there were seventy-two pennies in the pile. How many pennies did Jane add to the pile? 40 + j = 72; 32 pennies 3. The ones digit is 5. The number is greater than 640 and less than 650. (4) What is the number? 645 * 4 . Represent Write seven hundred fifty-three in expanded form. (16) 700 + 50 + 3 * 5 . Connect If x + y = 10, then what is the other addition fact for x, y, (6) and 10? What are the two subtraction facts for x, y, and 10? y + x = 10; 10 − x = y, 10 − y = x * 6 . These thermometers show the average daily low and high (18) temperatures in San Juan, Puerto Rico, during the month of January. What are those temperatures? 71°F and 82°F & & 130 Saxon Math Intermediate 4 * 7. Model Use a centimeter ruler to measure the rectangle below. (Inv. 2) a. What is the length? 4 cm b. What is the width? 2 cm c. What is the perimeter? 12 cm 8. 493 9. $486 10. $524 (13) (13) (13) + 278 + $378 + $109 771 $864 $633 * 11. Represent Draw a triangle. Make each side 2 cm long. What is the 2 cm (Inv. 2, 21) perimeter of the triangle? 6 cm 2 cm 2 cm * 12 . Represent Draw a square with sides 2 inches long. What is the (Inv. 2, 2 in. 21) perimeter of the square? 8 in. 2 in. 13. 17 8 14. 45 15. 15 9 16. 62 (12) (15) (12) (15) − a − 29 − b − 45 9 16 6 17 17. 24 21 18. 14 12 * 19 . y 89 * 2 0 . 75 30 (14) (16) (16) (16) + d − b − 36 − p 45 2 53 45 21. 46 22. 14 23. 14 24. 15 (17) (17) (17) (17) 35 28 23 24 27 77 38 36 + 39 + 23 + 64 + 99 147 142 139 174 * 2 5 . Conclude Write the next three numbers in each counting sequence: (3, Inv. 1) a. , 28, 35, 42, 49 , 56, 63 , . b. , 40, 30, 20, 10 , 0, −10, . Lesson 21 131 * 2 6 . Explain If you know the length and the width of a rectangle, how (Inv. 2) can you find its perimeter? Sample: Add 2 lengths plus 2 widths to find the perimeter. * 2 7. Multiple Choice Alba drew a circle with a radius of 4 cm. What was (21) the diameter of the circle? C A 8 in. B 2 in. C 8 cm D 2 cm * 2 8 . Each school morning, Christopher wakes up at the time shown on the left (19) and leaves for school at the time shown on the right. What amount of time does Christopher spend each morning getting ready for school? 45 minutes * 2 9 . Round each number to the nearest ten. You may draw a number line. (20) a. 76 80 b. 73 70 c. 75 80 * 3 0 . Round each amount of money to the nearest 25 cents. (20) a. $6.77 $6.75 b. $7.97 $8.00 Early Erin and Bethany both drew circles on their paper. The radius of Finishers Erin’s circle is 14 cm. The diameter of Bethany’s circle is 26 cm. Real-World Bethany said that her circle is bigger. Was Bethany correct? Explain Connection your answer. Bethany is not correct. Since the diameter is equal to two radii, Erin’s circle would have a diameter of 28 cm and would be the larger of the two circles. 132 Saxon Math Intermediate 4 LESSON 22 • Naming Fractions • Adding Dollars and Cents Power Up facts Power Up A count aloud As a class, count by sevens from 7 to 35. mental a. Number Sense: 63 + 21 84 math b. Number Sense: 36 + 29 + 30 95 c. Number Sense: 130 + 200 + 300 630 d. Geometry: If a triangle measures 1 centimeter on each side, what is the perimeter? 3 cm e. Time: What time is 2 hours after 1:00 p.m.? 3:00 p.m. f. Money: What is the total cost of two pens that are $1 each and one pair of scissors that is $4? $6 g. Estimation: Round $2.22 to the nearest 25 cents. $2.25 h. Measurement: How many centimeters are equal to 1 meter? 100 cm problem Seven days after Tuesday is Tuesday. Fourteen days after solving Tuesday is Tuesday. Twenty-one days after Tuesday is Tuesday. What day of the week is 70 days after Tuesday? Focus Strategy: Find/Extend a Pattern Understand We are asked to find which day of the week is 70 days after Tuesday.