Lesson 31: Pairs of Lines

1. Lesson 31: Pairs of Lines Vocabulary Intersect Intersecting lines Oblique lines Parallel lines Perpendicular lines

2. Lesson 31 • When lines cross we say they intersect. If we draw two lines on the same flat surface, those lines will intersect at some point, or they won’t intersect at all. Remember that lines keep going in both directions. You many need to extend the lines to decide if they will intersect. • Lines that never intersect are called parallel lines. Draw an example below:

3. Lesson 31 • Lines on the same surface that are NOT parallel called intersecting lines. This is because they will intersect (or cross) eventually. • Draw 3 pairs of intersecting lines below.

4. Lesson 31 • Perpendicular lines form 4 right angles. Draw 2 pairs of perpendicular lines below.

5. Let’s Practice… • Ex. 1: Draw a pair of oblique lines. • Ex. 2: Look at page 152 of your book. Copy figures A-D below. • Which figure does not appear to contain perpendicular segments? Figure _____

6. Lesson Activity: You will work with a Partner. • 1. Draw a line segment. • 2. Your partner will draw two line segments, one parallel to your line segment and the other perpendicular to your line segment. • 3. Repeat the activity, but switch roles. • 4. This activity should take you about 3 minutes total.

7. Lesson Activity: Your partner will check your work. • Draw two parallel segments. • Draw two perpendicular segments. • Draw two oblique segments.

8. Lesson 32: Angles and Polygons Vocabulary Acute Angle Polygon Straight Angle Angle Quadrilateral Vertex Congruent Right Angle Obtuse Angle Side Plane Similar

9. Lesson 32 • When lines or segments intersect, they form angles. An angle is an “opening” between intersecting lines. This opening may be very wide or very narrow. Show an example of each type of angle below. Right AngleAcute AngleObtuse Angle

10. Lesson 32 • Remember that a right angle forms a square corner. We usually mark these angles with a box. • An acute angle is “a cute” little angle. It is more narrow than a right angle. • An obtuse angle is a wider angle than a right angle. • A straight angle is exactly what it sounds like, a straight line. Show one below:

11. Lesson 32 Ex. 1: Which of these angles appears to be a right angle? Explain your answer: ____________________________________________________________________

12. Lesson 32 • A plane is a flat surface that extends without end. The classroom floor is a part of a plane that extends beyond the walls. The walls are part of other plane because they go in a different directions. A cube is a 3D shape made up of six flat “faces” or “planes.” • A polygon is a flat shape formed by line segments that close in an area. Remember that polygons do not have any curves or parts left open. “Don’t let the cows get out!” Here are some familiar polygons:

13. Lesson 32 • Remember that a vertex is where two sides of a polygon meet. A polygon’s number of vertices = the polygon’s number of sides. • Complete the chart on the next slide.

15. Lesson 32 Ex. 2: Which of these shapes is not a quadrilateral? Ex. 3: Which of these shapes is not a polygon?

16. Lesson 32 Ex. 4: Name each of these polygons. _________ ___________ _________ Ex. 5: Which two rectangles are congruent?_______ and ________ A. B. C. D. L T E

17. Lesson 32 • Congruent shapes are also similar.Similar figures have the same exact shape, but may not be the same size. Similar shapes look like a ‘magnified version’ and a ‘mini-version’ of the same shape. • Which two triangles are similar? ____ and ____ A. B. C. D.

18. Let’s Practice… Draw an example of each angle: • acute b. obtuse c. Right Describe each angle as acute, obtuse, right, or straight. d._______ e._______ f._______ g._______

19. Let’s Practice… • Draw a triangle with two perpendicular lines. • A quadrilateral is a polygon with ____ sides. • Draw a quadrilateral that has one pair of parallel sides. • Draw a quadrilateral with two pairs of parallel sides.

20. Let’s Practice… • Draw a quadrilateral that has NO parallel sides. (Start by drawing two nonparallel segments, then connect them with two more nonparallel segments.) • Name each shape. ________ __________ ________

21. Let’s Practice… • Draw a polygon shaped like the block letter F. What type of polygon did you draw?___________ • Draw two triangles that are congruent.

22. Lesson 33: Rounding Numbers Using a Number Line Vocabulary Exact number Round Round Number

23. Lesson 33 Two of the following statements use exact numbers, while the other two statements use round numbers. Can you underline the statements that use round numbers? About 600 people attended the homecoming game. The attendance at the game was 614. The price of the shoes was $48.97. The shoes cost about $50.

24. Lesson 33 • The first and last segments use round numbers. Round numbers end with one or more zeroes. • Round numbers are often used in place of exact numbers because they are good estimates to work with. • When we round a number, we find another number to which the number is near. One way to do this is to use, or think of, a number line.

25. Lesson 33 • Ex 1: Round 67 to the nearest ten. (Show this on a number line below.) • Ex. 2: Round 523 to the nearest hundred. (Show this on a number line below.)

26. Lesson 33 Round each number to the nearest ten. For each problem, you may draw a number line to help you round. • 72 ____ b. 87 ____ c. 49 ____ d.95____ Round each number to the nearest hundred. You many draw a number line to help you round. e. 685____ f.420____ g.776____ h.350____

27. Lesson 34: Division with Zeroes in the Quotient Vocabulary No new, just review! 

28. Lesson 34 • Remember that the answer to a division problem is called a quotient. Sometimes one or more of the digits in the quotient is zero. Today you will learn how to divide with zeroes in the quotient. • You will still follow the pattern: D.M.S.B. • “Does McDonalds Serve Burgers?” can help you remember the four steps: Divide, Multiply, Subtract, Bring Down

29. Lesson 34 Ex. 1: Divide. Check by multiplying:

30. Lesson 34 Ex. 2: Divide. Check by multiplying:

31. Let’s Practice…

32. Let’s Practice…

33. Let’s Practice… • Show how to check this division answer. Is the answer correct? ____________

34. Lesson 35: Problems About ComparingProblems about Elapsed Time Vocabulary Elapsed Time

35. Lesson 35 • Some stories compare numbers of objects or sizes of object. The biggest player weighed 245 pounds. The smallest player weighed 160 pounds. The biggest player weighed how much more than the smallest player? We can use these rectangles to find the answer.  Difference Bigger   Smaller Names

36. Lesson 35 Ex 1: Abe is 6 years younger than his brother Gabe. Abe is 11 years old. How old is Gabe? _______________ Larger – Smaller = Difference

37. Lesson 35 • Elapsed time is the amount of time between two points in time. • You can use this equation to help you with an elapsed time problem. • Later – Earlier = Difference (Elapsed Time) Ex. 2: How many years were there from 1492 to 1620?_________

38. Let’s Practice…For each problem, write an equation and solve the problem. • There were 4 more boys than girls in the class. If there were 17 boys in the class, how many girls were there? ________________________________ • The Mackinac Bridge spans 3800 feet, which is 400 feet less than the span of the Golden Gate Bridge. What is the span of the Golden Gate Bridge? ________________________________________

39. Let’s Practice… c. From Rome to Paris is 1120 kilometers. From Rome to London is 1448 kilometers. The distance from Rome to London is how much greater than the distance from Rome to Paris? _____________________________________ • How many years were there from 1066 to 1776? _____________________________________ • How many years were there from 1776 to 1787? _____________________________________