Transcript Essential Question - Mr. Goodrich`s Class

Essential Question: Why are
and
both real numbers?
Estimating
Irrational
numbers… Prt 2
–Cube Roots and
Non-perfect cubes
Essential Question: Why are
and
both real numbers?
Vocabulary –Shoot For The Stars
30 seconds

I got this! I know this word AND I could even
teach it to somebody else.

I think I know this word, but I need more
practice.

I am clueless! I have no idea what this word
means.
Essential Question: Why are
and
both real numbers?
VOCABULARY
Perfect Cube:
The volume of a cube when the sides are whole numbers.
_________________________________
Cube Root:
The opposite of cubing a number. That means finding the
length of a cube’s side from it’s volume.
_________________________________
Essential Question: Why are
and
3
2
1
13 = 1
both real numbers?
23 = 8
33 = 27
The cube of an integer is a perfect
cube.
The opposite of cubing a number
is taking the cube root.
Essential Question: Why are

and
both real numbers?
For example 3 125
Means… if a cube has a volume of 125, then
how big is one of it’s sides?
In other words, what number multiplied by
itself three times in a row is
equal to 125?
That number is 5.
5
Essential Question: Why are
and
both real numbers?
Simplify each square root on your iPad
3
8
2
______
3
27
3
______
Essential Question: Why are
and
both real numbers?
But watch this…
3
-8
-2
______
Possible: Because any negative number multiplied
by itself three times in a row still equals a negative
answer.
3
- 8
-2
______
Possible: Since the negative sign is on the OUTSIDE
of the cube root sign, it just means “what number is
the opposite of the cube root of 8?”
Essential Question: Why are

and
both real numbers?
Do you see that cubes and cube roots
are inverses (opposites) of each other?
Essential Question: Why are
and
both real numbers?
Draw Number Line from board.
Essential Question: Why are
and
both real numbers?
Commercial Break

Quote of the Day:
“You always pass failure on the way to
success.”
Essential Question: Why are
and
both real numbers?
Estimating cube roots

Once we have memorized the perfect
cubes from 1 to 10 and their roots, we
can estimate irrational cube roots that
are not perfect cubes.

For example, what about
3
11 ?
Essential Question: Why are
and
both real numbers?
Estimating cube roots



We already know the two perfect cubes that are
before and after the cube root of 11. . .
3
8 and 3 27
Look at them on the number line on the board:
Essential Question: Why are
and
both real numbers?
Estimating cubre roots

3
We can see that 11 is between 2 and 3 but
is closer to 2. We would say that 3 11 is a little
more than 2, or approximately 2.1.
Essential Question: Why are
and
both real numbers?
TRY THIS:
What two perfect cube roots come before and
after the non-perfect cube roots below? Use your
iPad.
3
147
3
3
3
3
125 216
3
15
411
3
3
8 27
3
343 512
Essential Question: Why are
and
both real numbers?
TRY THIS:
What two whole numbers on the number line
come before and after the non-perfect cube roots
below? Use your iPad.
3
79
4 And 5
3
303
6 And 7
3
275
6 And 7
Essential Question: Why are
and
both real numbers?
THINK / PAIR / SHARE

Step 1 – Spend 20 seconds thinking silently about the
Essential Question.

Step 2 – Spend 30 seconds pairing up with your learning
partner.

Step 3 – Volunteer to share your answer with the class…
Volunteers will receive a Goodybuck.