Lesson 31: Pairs of Lines

VocabularyIntersect

Intersecting linesOblique linesParallel lines

Perpendicular lines

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:

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.

Lesson 31

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

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 _____

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.

Lesson Activity: Your partner will check your work.

a. Draw two parallel segments.

b. Draw two perpendicular segments.

c. Draw two oblique segments.

Lesson 32: Angles and Polygons

VocabularyAcute Angle Polygon Straight AngleAngle Quadrilateral VertexCongruent Right AngleObtuse Angle SidePlane Similar

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 Angle Acute Angle Obtuse Angle

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:

Lesson 32

Ex. 1: Which of these angles appears to be a right angle?

Explain your answer: ____________________________________________________________________

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:

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.

Polygon # of Sides or Vertices

Example

triangle

quadrilateral

pentagon

6

heptagon 7

8

decagon 10

dodecagon

N-gon N “thirteen-gon” twenty-gon”, …

Lesson 32Ex. 2: Which of these shapes is not a

quadrilateral?

Ex. 3: Which of these shapes is not a polygon?

Lesson 32Ex. 4: Name each of these polygons.

_________ ___________ _________

Ex. 5: Which two rectangles are congruent?_______ and ________

A. B. C. D.

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.

Let’s Practice…Draw an example of each angle:

a. acute b. obtuse c. Right

Describe each angle as acute, obtuse, right, or straight.

d._______ e._______ f._______ g._______

Let’s Practice…h. Draw a triangle with two perpendicular lines.

i. A quadrilateral is a polygon with ____ sides.

j. Draw a quadrilateral that has one pair of parallel sides.

k. Draw a quadrilateral with two pairs of parallel sides.

Let’s Practice…l. Draw a quadrilateral that has NO parallel

sides. (Start by drawing two nonparallel segments, then connect

them with two more nonparallel segments.)

m. Name each shape.

________ __________ ________

Let’s Practice…

p. Draw a polygon shaped like the block letter F. What type of polygon did you draw?___________

q. Draw two triangles that are congruent.

Lesson 33: Rounding Numbers Using a Number Line

VocabularyExact number

RoundRound Number

Lesson 33Two 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.

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.

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.)

Lesson 33Round each number to the nearest ten. For each problem, you may draw a number line to help you round.

a. 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____

Lesson 34: Division with Zeroes in the Quotient

Vocabulary

No new, just review!

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

Lesson 34

Ex. 1: Divide.

Check by multiplying:

3656

Lesson 34

Ex. 2: Divide.

Check by multiplying:

6356

Let’s Practice…

316

1213

2426

16284

Let’s Practice…

1224 25.5$5

18.6$2 49816

Let’s Practice…

i. Show how to check this division answer.

Is the answer correct? ____________

21086506

R

Lesson 35: Problems About Comparing

Problems about Elapsed Time

Vocabulary

Elapsed Time

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.

Bigger Smaller

Difference

Names

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

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?_________

Let’s Practice…For each problem, write an equation

and solve the problem.a. There were 4 more boys than girls in the class.

If there were 17 boys in the class, how many girls were there? ________________________________

b. 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?

________________________________________

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? _____________________________________

d. How many years were there from 1066 to 1776? _____________________________________

e. How many years were there from 1776 to 1787? _____________________________________