Unit 3Fifth Grade

Unit Goals• Determine angle measures bas

ed on relationships between angles.

• Estimate the measure of an angle.

• Measure an angle to within 2°.• Identify types of angles.• Identify types of triangles.• Identify place value in number

s to billions.• Know properties of polygons.• Define and create tessellations

.

Determine angle measures based on

relationships between angles.

• You can use your knowledge of angles to estimate angle measures.

• Remember- a circle is 360°, a straight line is 180°

For example:

• I know that this is a right triangle next to a square.

• The square’s corner measures 90°, and the angle of the triangle is about half that.

• Together, the angle should measure about 90 + 45, or 135°

What is the measure of this angle?

What is the measure of this angle?

180° 225° 240° 150°

Correct!This angle measures 240°. You can know

this because:- the angles in the equilateral triangles are

each 60° (60 + 60= 120) - the corner of the parallelogram could be

made up using two equilateral triangles (60 + 60 = 120)

- for a combined total of 240°.

60°

60°

Far Out!Click me to go

back to the goals page.

Keep Trying!This angle measures 240°. You can know

this because:- the angles in the equilateral triangles are

each 60° (60 + 60= 120) - the corner of the parallelogram could be

made up using two equilateral triangles (60 + 60 = 120)

- for a combined total of 240°.

60°

60°

Read through the description

carefully- click to go back to

the explanation page.

Estimate the measure of an angle.

Think about the angle in relationship to 90°

90°

90°

90°

90°

- A complete circle is 360°

- A half circle (or straight line) is 180°

- A quarter circle is 90°- If an angle is acute, it

will be less than 90°- If an angle is obtuse,

it will be between 91° -179°

- If the angle is a straight line, it will be equal to 180°

Estimate the measure of an angle.

Which of these angles is equal to about 175°?

A

B

C

D

Correct!A

This angle is closest to 175°.

- It is slightly less than 180° (which is a straight line)

Groovy!Click me to GO

for the GOALS.

Keep Trying!A

This angle is closest to 175°.

- It is slightly less than 180° (which is a straight line)

You might want to read the

description more carefully. Ask for

help if you still need it.

Measure an angle to within 2°

• For practice with this skill, visit:

http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html

• If you need a protractor, you can print one up at:

http://www.ossmann.com/protractor/conventional-protractor.pdf

* Make sure you line your protractor up carefully!Click me to go back to the goals

page.

Identify types of angles

A right angle is 90°. It looks like the corner of your paper or the letter L.

An acute angle is LESS THAN 90°. It is a cute little angle .

An obtuse angle is MORE THAN 90°

A reflex angle is MORE THAN 180°

Try One!

A B

C

D

E

F

Which of these is an obtuse angle?

<ABC

<ABE

<ABF

<FCD

CORRECT!

A B

C

D

E

F

<ABF is obtuse because it measures more than 90° but less than 180°.

Awesome Work! Click me to go

back to the goals.

Try Again!

A B

C

D

E

F

<ABF is obtuse because it measures more than 90° but less than 180°.

<ABE is a straight angle because it measures exactly 180°.

Stick with it- Click me to go back to

the explanatio

n.

Identify types of triangles

• Meet the triangle family

I’m Evelyn Equilateral, and

I’m always worried that everything

should be equal. I have three equal sides and three equal angles.

I’m Ivan Isosceles and while I’m not

as equal as an equilateral

triangle, I do still have two equal sides and two equal angles.

We’re Roger and Randy Right-

The Right Brothers! We

like to think that we’re always

right, but really we’re called

right triangles because we both have a

right angle that measures 90°.

That’s right, but one thing my brother Randy forgot to

mention is that I’m a special right triangle.

I take after the Isosceles side of the family because not

only do I have a right angle, I also have two

other equal angles and sides. That

makes me a Right Isosceles triangle.

I’m Salvador Scalene. I’m the oddball of the family- I

don’t have any equal sides or

angles.

Equilateral

Right Isosceles

Right

Isosceles

Scalene

Can you name us?

Try One!

Click on the scalene triangle.

Correct!That’s right, another

odd-ball. This triangle is scalene because it has no

equal sides or angles.

Click for the next problem.

Try Again!

This triangle is scalene because it

has no equal sides or angles.

Click for the next problem.

Try One!

Click on the right isosceles triangle.

Correct!That’s right, this is a

right isosceles triangle. This

triangle is isosceles because it has two

equal sides and angles. It is right

because it has a 90° angle.

Click for the next problem.

Try Again!This is a right

isosceles triangle. This triangle is

isosceles because it has two equal sides

and angles. It is right because it has a 90°

angle.

Click for the next problem.

Try One!

Click on the isosceles triangle.

Correct!That’s right, this is an

isosceles triangle. This triangle is

isosceles because it has two equal sides

and angles.

Click for the next problem.

Try Again!This is an isosceles

triangle. This triangle is isosceles because it has two

equal sides and angles.

Click for the next problem.

Try One!

Click on the equilateral triangle.

Correct!That’s right, this is an equilateral triangle.

This triangle is equilateral because it has all equal sides

and angles.

Click for the next problem.

Try Again!This is an equilateral

triangle. This triangle is

equilateral because it has all equal sides

and angles.

Click for the next problem.

Try One!

Click on the right triangle.

Correct!That’s right, this is a

right triangle. This triangle is right

because it has a 90° angle.

Click me to go to the

goals.

Try Again!That’s right, this is a

right triangle. This triangle is right

because it has a 90° angle.

Click me to go back to the

explanation.

Identify place value in numbers to billions

Billions Hundred millions

Ten millions

Millions

Hundred thousands

Ten thousands

Thousands Hundreds

Tens

Ones

1 3 5 4 2 0 6 5 9 9

For each set of three, there is a pattern of units, tens, and hundreds. Remember that when naming numbers, you name each group of three.

For example, the number above is one billion, three hundred fifty four million, two hundred six thousand, five hundred ninety nine.

Notice that when you name numbers, the only time you use the word “and” is when you are referring to a decimal point.

For example, 5.2 is five and two tenths. NOT five point two.

Try One!

1 3 5 4 2 0 6 7 8 9

Which digit is in the hundred thousands place?

3 2 7 0

Correct!

1 3 5 4 2 0 6 7 8 9

Billions Hundred millions

Ten millions

MillionsHundred thousands

Ten thousands

ThousandsHundreds

Tens

Ones

Which digit is in the hundred thousands place?

3 2 7 0

Click for the next problem

Try Again!

1 3 5 4 2 0 6 7 8 9

Billions Hundred millions

Ten millions

MillionsHundred thousands

Ten thousands

ThousandsHundreds

Tens

Ones

Which digit is in the hundred thousands place?

3 2 7 0

Click for the next problem

Try One!

1 3 5 4 2 0 6 7 8 9

Which digit is in the ten millions place?

5 8 4 0

Correct!

1 3 5 4 2 0 6 7 8 9

Billions Hundred millions

Ten millions

MillionsHundred thousands

Ten thousands

ThousandsHundreds

Tens

Ones

Which digit is in the ten millions place?

5 8 4 0

Click for the next problem

Try Again!

1 3 5 4 2 0 6 7 8 9

Billions Hundred millions

Ten millions

MillionsHundred thousands

Ten thousands

ThousandsHundreds

Tens

Ones

Which digit is in the ten millions place?

5 8 4 0

Click for the next problem

Try One!

1 3 5 4 2 0 6 7 8 9

Which digit is in the billions place?

3 5 4 1

Correct!

1 3 5 4 2 0 6 7 8 9

Billions Hundred millions

Ten millions

MillionsHundred thousands

Ten thousands

ThousandsHundreds

Tens

Ones

Which digit is in the billions place?

3 5 4 1

Click me to go to the goals.

Try Again!

1 3 5 4 2 0 6 7 8 9

Billions Hundred millions

Ten millions

MillionsHundred thousands

Ten thousands

ThousandsHundreds

Tens

Ones

Which digit is in the billions place?

3 5 4 1

Click me to go back to the explanation.

Know properties of polygons

• A polygonpolygon is a plane shape having 3 or more sides.

• The number of degrees in a polygon depends upon the number of sides it has.

• The name of a polygon depends upon the number of sides it has and the relationship of those sides to one another.

Some examples of polygons…

How many can you name?

pentagon

rectangle

rhombus

trapezoid

square

octagon

hexagon

Right triangle

Equilateral triangle

Some polygon terms…• A regular polygon has equal sides

and angles.

• A quadrilateral describes any four-sided polygon.

• A parallelogram describes any quadrilateral with two sets of parallel sides of equal length with equal angles.

Naming Polygons• The prefix in the

name of a polygon indicates the number of sides it has.

tri quad pent

hex oct

Sides prefix7 hept9 non10 dec12 dode

c20 icosa

Explore Polygons

• Check out the polygon playground!

• Learn more about figures and polygons.

Click me to go back to the

goals.

Define and create tessellations

• A tessellation is a pattern of shapes that has no gaps or overlaps

• A regular tessellation is made up of regular polygons (polygons with equal sides and angles)

• Tessellations are described by listing the number of sides of the polygons around each vertex.

Examples of Tessellations

To The Unit Goals Page

Click HERE To Go Back

• Learn more about tessellations

• Try a think quest on tessellations

• Try making some tessellations!

• Tessellations can be a form of art. Check out some galleries!