Transcript 2. - My CCSD

1-1
1-1 Numbers
Numbersand
andPatterns
Patterns
Warm Up
Problem of the Day
Lesson Presentation
Course 2
1-1 Numbers and Patterns
Warm Up
Write a number in which no digit is
repeated for each description.
1. 4-digit number divisible by 5 and 10.
Possible answer 1,230
2. 4-digit number divisible by 3 and 5.
Possible answer 1,245
3. 4-digit number divisible by 2, 3 and 6.
Possible answer 1,356
Course 2
1-1 Numbers and Patterns
Problem of the Day
For each of the following, write the product
of three and the number.
–2, 3, 7, 12, 18
–6, 9, 21, 36, 54
Course 2
1-1 Numbers and Patterns
Learn to identify and extend patterns.
Course 2
1-1 Numbers and Patterns
Additional Example 1A: Identifying and Extending
Number Patterns
Identify a possible pattern. Use it to write the
next three numbers.
3, 12, 48,
,
,
3
,...
12
4
48
4
4
4
4
A pattern is to multiply each number by 4 to get
the next number.
48  4 = 192,
192  4 = 768,
768  4 = 3072
So the next numbers will be 192, 768, and 3072.
Course 2
1-1 Numbers and Patterns
Additional Example 1B: Identifying and Extending
Number Patterns
Identify a possible pattern. Use it to write the
next three numbers.
7, 12, 17,
,
,
7
,...
12
+5
17
+5 +5
+5
+5
A pattern is to add each number by 5 to get the
next number.
17 + 5 = 22,
22 + 5 = 27,
27 + 5 = 32
So the next numbers will be 22, 27, and 32.
Course 2
1-1 Numbers and Patterns
Additional Example 1C: Identifying and Extending
Number Patterns
Identify a possible pattern. Use it to write the
next three numbers.
20, 17, 14,
,
,
20
–3
,...
17
–3
14
–3
–3
–3
A pattern is to subtract each number by 3 to get
the next number.
14 – 3 = 11,
11 – 3 = 8,
8–3=5
So the next numbers will be 11, 8, and 5.
Course 2
1-1 Numbers and Patterns
Check It Out: Example 1A
Identify a possible pattern. Use it to write the
next three numbers.
18, 25, 32,
,
,
,...
18 25 32
+7
+7
+7
+7
+7
A pattern is to add each number by 7 to get the
next number.
32 + 7 = 39,
39 + 7 = 46,
46 + 7 = 53
So the next numbers will be 39, 46, and 53.
Course 2
1-1 Numbers and Patterns
Check It Out: Example 1B
Identify a possible pattern. Use it to write the
next three numbers.
45, 41, 37,
,
,
45
–4
,...
41
–4
37
–4
–4
–4
A pattern is to subtract each number by 4 to get
the next number.
37 – 4 = 33,
33 – 4 = 29,
29 – 4 = 25
So the next numbers will be 33, 29, and 25.
Course 2
1-1 Numbers and Patterns
Check It Out: Example 1C
Identify a possible pattern. Use it to write the
next three numbers.
2, 6, 18,
,
,
,...
2
3
6
18
3
3
3
3
A pattern is to multiply each number by 3 to get
the next number.
18  3 = 54,
54  3 = 162,
162  3 = 486
So the next numbers will be 54, 162, and 486.
Course 2
1-1 Numbers and Patterns
Additional Example 2: Identifying and Extending
Geometric Patterns
Identify a possible pattern. Use it to draw the
next three figures.
The pattern is to rotate the figure in a
counterclockwise direction.
So the next three figures will be
.
Course 2
1-1 Numbers and Patterns
Check It Out: Example 2
Identify a possible pattern. Use it to draw the
next three figures.
The pattern is three triangular objects that repeat,
while alternating between orange and green.
So the next three figures will be
.
Course 2
1-1 Numbers and Patterns
Additional Example 3: Using Tables to Identify and
Extend Patterns
Make a table that shows the number of
triangles in each figure. Then tell how many
triangles are in the seventh figure of the
pattern. Use drawings to justify your answer.
Figure 1
Figure 2
Figure 4
Course 2
Figure 3
Figure 5
1-1 Numbers and Patterns
Additional Example 3 Continued
Make a table that shows the number of
Triangles in each figure. Then tell how many
triangles are in the seventh figure of the
pattern. Use drawings to justify your answer.
The table shows the numbers of triangles in each figure.
Figure
1
2
3
4
5
6
7
Number of
Triangles
2
4
6
8
10
12
14
+2
+2
+2
+2
Figure 6 has 10 + 2 = 12 triangles
Figure 6
Course 2
+2
The pattern is to add
2 triangles each time.
+2
Figure 7 has 12 + 2 = 14 triangles
Figure 7
1-1 Numbers and Patterns
Check It Out: Additional Example 3
Make a table that shows the number of
squares in each figure. Then tell how many
squares are in the seventh figure of the
pattern. Use drawings to justify your answer.
Figure 1
Figure 2
Figure 4
Course 2
Figure 3
Figure 5
1-1 Numbers and Patterns
Check It Out: Example 3 Continued
Make a table that shows the number of Squares
in each figure. Then tell how many squares are
in the seventh figure of the pattern. Use
drawings to justify your answer.
The table shows the numbers of squares in each figure.
Figure
1
2
3
4
5
6
7
Number of
Triangles
4
8
12
16
20
24
28
+4
+4
+4 +4
Figure 6 has 20 + 4 = 24 squares
Figure 6
Course 2
The pattern is to add
4 squares each time.
+4 +4
Figure 7 has 24 + 4 = 28 squares
Figure 7
1-1 Numbers and Patterns
Lesson Quiz: Part I
Identify a possible pattern. Use the pattern to
write next three numbers.
1. –8, –6, –4,
,
,
,…
Add 2; -2, 0, 2
2. –3, 6, –12, 24, , , , …
Multiply by -2; -48, 96,-192
3. 0, 1, 3, 6, 10,
,
,
,…
Add 1 more than the number previously added;
15, 21, 28.
Course 2
1-1 Numbers and Patterns
Lesson Quiz: Part II
Identify a possible pattern. Use the
pattern to draw the next three figures.
4.
5. Make a table that shows the number
of dots in the figure. Then tell how
many dots are in the seventh figure of
the pattern. Use drawings to justify
your answer.
14
Course 2
1-1
and Patterns
1-2 Numbers
Exponents
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
1-1 Numbers and Patterns
Warm Up
Simplify.
1. 2 · 2 · 2
2. 3 · 3 · 3 · 3
8
81
3. 5 · 5 · 5
125
4. 4 · 4 · 4
64
5. 6 · 6 · 6 · 6 · 6
Course 2
7,776
1-1 Numbers and Patterns
Problem of the Day
You intend to place water lilies in the pond in
your backyard. A water lily doubles in size
every day. From the time you install the first
lily until the entire surface of the pond is
covered will take 20 days. how long will it
take for the pond to be half covered?
19 days
Course 2
1-1 Numbers and Patterns
Learn to represent numbers by using
exponents.
Course 2
1-1 Numbers and Patterns
Vocabulary
power
exponent
base
Course 2
1-1 Numbers and Patterns
A DNA molecule makes a copy of itself by
splitting in half. Each half becomes a molecule
that is identical to the original. The molecules
continue to split so that the two become four,
the four become eight, and so on.
Each time DNA copies itself, the number of
molecules doubles. After four copies, the
number of molecules is 2 · 2 · 2 · 2 = 16.
Course 2
1-1 Numbers and Patterns
This multiplication can also be written as a power,
using a base and an exponent. The exponent tells
how many times to use the base as a factor.
Base
Exponent
Reading Math
Read 24 as “the fourth power of 2” or “2 to
the fourth power.”
Course 2
1-1 Numbers and Patterns
Additional Example 1: Evaluating Powers
Find each value.
A. 44
44 = 4 · 4 · 4 · 4
= 256
Use 4 as a factor 4 times.
B. 73
73 = 7 · 7 · 7
= 343
Use 7 as a factor 3 times.
C. 191
191 = 19
Course 2
Use 19 as a factor 1 time.
1-1 Numbers and Patterns
Check It Out: Example 1
Find each value.
A. 33
33 = 3 · 3 · 3
= 27
Use 3 as a factor 3 times.
B. 62
62 = 6 · 6
= 36
Use 6 as a factor 2 times.
B. 141
141 = 14
Course 2
Use 14 as a factor 1 time.
1-1 Numbers and Patterns
Any number to the zero power, except zero
is equal to 1.
60 = 1
100 = 1
190 = 1
Zero to the zero power is undefined, meaning
that it does not exist.
Course 2
1-1 Numbers and Patterns
To express a whole number as a power, write
the number as a product of equal factors. Then
write the product using the base and an
exponent.
For example, 10,000 = 10 · 10 · 10 · 10 = 104.
Course 2
1-1 Numbers and Patterns
Additional Example 2: Expressing Whole Numbers as
Powers
Write each number using an exponent and the
given base.
A. 625, base 5
625 = 5 · 5 · 5 · 5
= 54
5 is used as a factor 4 times.
B. 64, base 2
64 = 2 · 2 · 2 · 2 · 2 · 2 2 is used as a factor 6
times.
= 26
Course 2
1-1 Numbers and Patterns
Check It Out: Example 2
Write each number as an exponent and the
given base.
A. 2,401, base 7
2,401 = 7 · 7 · 7 · 7
= 74
7 is used as a factor
4 times.
B. 243, base 3
243 = 3 · 3 · 3 · 3 · 3
= 35
Course 2
3 is used as a factor
5 times.
1-1 Numbers and Patterns
Additional Example 3: Application
On Monday, Erik tells 3 people a secret. The
next day each of them tells 3 more people. If
this pattern continues, how many people
besides Erik will know the secret on Friday?
On Monday, 3 people know the secret.
On Tuesday, 3 times as many people know as
those who knew on Monday.
On Wednesday, 3 times as many people know as
those who knew on Tuesday.
On Thursday, 3 times as many people know as
those who knew on Wednesday.
Course 2
1-1 Numbers and Patterns
Additional Example 3 Continued
On Friday, 3 times as many people know as
those who knew on Thursday.
Each day the number of people is 3 times
greater.
3 · 3 · 3 · 3 · 3 = 35 = 243
On Friday 243 people besides Erik will know the
secret.
Course 2
1-1 Numbers and Patterns
Check It Out: Example 3
In a game, a contestant had a starting score
of one point. She doubled her score every turn
for four turns. Write her score after four turns
as a power. Then find her score.
After the first turn, she had 2 points.
After the second turn, she would have 4 points.
After the third turn, she would have 8 points.
After each turn, her point total is 2 times greater.
2 · 2 · 2 · 2 = 24 = 16 points
Course 2
1-1 Numbers and Patterns
Lesson Quiz
Find each value.
1. 73
3. 34
343
2. 63
4. 85
81
216
32,768
Write each number using an exponent and
given base.
5. 125, base 5
6. 16, base 2
53
24
7. Find the volume of a cube if each side is 12
inches long. 1,728 in3
Course 2