Download Mental math

1-5
1-5 Mental
MentalMath
Math
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
1-5 Mental Math
Warm Up
Find each sum or product.
1. 17 + 15
32
2. 29 + 39 68
3. 8(24)
192
4. 7(12)
5. 3(91)
84
273
6. 6(15)
90
Course 1
1-5 Mental Math
Problem of the Day
Determine the secret number from the
following clues:
• The number is a multiple of 5.
• It is divisible by 3.
• It is less than 200.
• Its tens digit equals the sum of its
other two digits.
165
Course 1
1-5 Mental Math
Learn to use number properties to
compute mentally.
Course 1
1-5 Mental Math
Vocabulary
Commutative Property
Associative Property
Distributive Property
Course 1
1-5 Mental Math
Mental math means “doing math in
your head.”
Many mental math strategies use
number properties that you already
know.
Course 1
1-5 Mental Math
COMMUTATIVE PROPERTY (Ordering)
Words
You can add or
multiply numbers in
any order.
Course 1
Numbers
18 + 9 = 9 + 18
15  2 = 2  15
1-5 Mental Math
ASSOCIATIVE PROPERTY (Grouping)
Words
When you are only
adding or only
multiplying, you
can group any of
the numbers
together.
Course 1
Numbers
(17 + 2) + 9 = 17 + (2 + 9)
(12  2)  4 = 12  (2  4)
1-5 Mental Math
Additional Example 1A: Using Properties to
Add and Multiply Whole Numbers
Evaluate 17 + 5 + 3 + 15.
17 + 5 + 3 + 15
Look for sums that are
multiples of 10
17 + 3 + 5 + 15
Use the Commutative Property.
Use the Associative
(17 + 3) + (5 + 15) Property to make groups
of compatible numbers.
20 + 20
40
Course 1
Use mental math to add.
1-5 Mental Math
Additional Example 1B: Using Properties to
Add and Multiply Whole Numbers
Evaluate 4  13  5.
4  13  5
Look for products that are
multiples of 10
13  4  5
Use the Commutative Property.
13  (4  5)
Use the Associative Property to
group compatible numbers.
13  20
Use mental math to multiply.
260
Course 1
1-5 Mental Math
Check It Out: Example 1A
Evaluate 12 + 5 + 8 + 5.
12 + 5 + 8 + 5
Look for sums that are
multiples of 10
12 + 8 + 5 + 5
Use the Commutative Property.
(12 + 8) + (5 + 5)
Use the Associative Property to
make groups of compatible
numbers.
20 + 10
30
Course 1
Use mental math to add.
1-5 Mental Math
Check It Out: Example 1B
Evaluate 8  3  5.
835
Look for products that are
multiples of 10
385
Use the Commutative Property.
3  (8  5)
Use the Associative Property to
group compatible numbers.
3  40
Use mental math to multiply.
120
Course 1
1-5 Mental Math
DISTRIBUTIVE PROPERTY
Words
Numbers
When you multiply a
number times a sum, 6  (10 + 4) = 6  14
you can
= 84
• find the sum first
6  (10 + 4) = (6  10) + (6  4)
and then multiply, or
= 60
+
24
• multiply by each
=
84
number in the sum
and then add.
Course 1
1-5 Mental Math
When you multiply two numbers, you can
“break apart” one of the numbers into a sum
and then use the Distributive Property.
Helpful Hint
Break the greater factor into a sum that contains a
multiple of 10 and a one-digit number. You can add
and multiply these numbers mentally.
Course 1
1-5 Mental Math
Additional Example 2A: Using the Distributive
Property to Multiply
Use the Distributive Property to find the product.
6  35
6  35 = 6  (30 + 5)
“Break apart” 35 into 30 + 5.
= (6  30) + (6  5)
Use the Distributive Property.
=
Use mental math to multiply.
=
Course 1
180
+
210
30
Use mental math to add.
1-5 Mental Math
Additional Example 2B: Using the Distributive
Property to Multiply
Use the Distributive Property to find the product.
9  87
9  87 = 9  (80 + 7)
“Break apart” 87 into 80 + 7.
= (9  80) + (9  7)
Use the Distributive Property.
=
Use mental math to multiply.
=
Course 1
720
+
783
63
Use mental math to add.
1-5 Mental Math
Check It Out: Example 2A
Use the Distributive Property to find the
product.
4  27
4  27 = 4  (20 + 7)
“Break apart” 27 into 20 + 7.
= (4  20) + (4  7)
Use the Distributive Property.
=
Use mental math to multiply.
=
Course 1
80
+
108
28
Use mental math to add.
1-5 Mental Math
Check It Out: Example 2B
Use the Distributive Property to find the
product.
6  43
6  43 = 6  (40 + 3)
“Break apart” 43 into 40 + 3.
= (6  40) + (6  3)
Use the Distributive Property.
=
Use mental math to multiply.
=
Course 1
240
+
258
18
Use mental math to add.
1-5 Mental Math
Lesson Quiz
Evaluate.
1. 18 + 24 + 2 + 6 50
2. 10  5  3 150
3. 13 + 42 + 7 + 8 70
Use the Distributive Property to find each
product.
4. 8  12 96
5. 6  15
90
6. 5  34 170
7. 3  71
213
Course 1
1-5
Math
1-7 Mental
Patterns
and Sequences
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
1-5 Mental Math
Warm Up
Determine what could come next.
1.
2.
3.
4.
5.
Course 1
3, 4, 5, 6, ___
10, 9, 8, 7, 6, ___
1, 3, 5, 7, ___
2, 4, 6, 8, ___
5, 10, 15, 20, ___
7
5
9
10
25
1-5 Mental Math
Problem of the Day
How can you place the numbers 1
through 6 in the circles so that the
sums along each side are equal?
6
2
4
Course 1
1
3
5
1-5 Mental Math
Learn to find patterns and to recognize,
describe, and extend patterns in
sequences.
Course 1
1-5 Mental Math
Vocabulary
perfect square
term
arithmetic sequence
Course 1
1-5 Mental Math
Each month, Eva chooses 3 new DVDs from her
DVD club.
Eva’s DVDs
Position
Month
DVDs
1
2
3
4
3
6
9
12
Value
+3
+3
+3
The number of DVDs Eva has after each month
shows a pattern: Add 3. This pattern can be
written as a sequence.
3, 6, 9, 12, 15, 18, …
Course 1
1-5 Mental Math
A sequence is an ordered set of numbers. Each
number in the sequence is called a term. In this
sequence, the first term is 3, the second term is
6, and the third term is 9.
When the terms of a sequence change by the
same amount each time, the sequence is an
arithmetic sequence.
Course 1
1-5 Mental Math
Helpful Hint
Look for a relationship between the 1st term and
the 2nd term. Check if this relationship works
between the 2nd term and the 3rd term, and so
on.
Course 1
1-5 Mental Math
Additional Example 1A: Extending Arithmetic
Sequences
Identify a pattern in each sequence and then
find the missing terms.
48, 42, 36, 30,
–6
–6
–6
–6
,
–6
,
,...
–6
Look for a pattern. A pattern is to subtract 6
from each term to get the next term.
30 – 6 = 24
24 – 6 = 18
18 – 6 = 12
So 24, 18, and 12 will be the next three terms.
Course 1
1-5 Mental Math
Additional Example 1B: Extending Arithmetic
Sequences
Position
Value of Term
1
9
2
22
3
35
4
48
5
6
+13 +13 +13 +13 +13
A pattern is to add 13 to each term to get the next term.
48 + 13 = 61
61 + 13 = 74
So 61 and 74 will be the next terms in the arithmetic
sequence.
Course 1
1-5 Mental Math
Check It Out: Example 1A
Identify a pattern in each sequence and name
the next three terms.
39, 34, 29,
–5
–5
–5
24,
–5
,
–5
,
,...
–5
Look for a pattern. A pattern is to subtract 5
from each term to get the next term.
24 – 5 = 19
19 – 5 = 14
14 – 5 = 9
So 19, 14, and 9 will be the next three terms.
Course 1
1-5 Mental Math
Check It Out: Example 1B
Position
Value of Term
1
7
+9
2
16
+9
3
25
+9
4
34
+9
5
6
+9
A pattern is to add 9 to each term to get the next term.
34 + 9 = 43
43 + 9 = 52
So 43 and 52 will be the next terms in the arithmetic
sequence.
Course 1
1-5 Mental Math
Additional Example 2A: Completing Other
Sequences
Identify a pattern in the sequence. Name the
missing terms.
24,
34, 31,
+10 –3
41, 38, 48,
+10 –3 +10
,
,
,…
–3 +10 –3
A pattern is to add 10 to one term and
subtract 3 from the next.
48 – 3 = 45
45 + 10 = 55
55 – 3 = 52
So 45, 55, and 52 are the missing terms.
Course 1
1-5 Mental Math
Additional Example 2B: Completing Other Sequences
Position
1
2
3
4
Value of Term
1
4
2
8
4
÷2
5
6
16
7
8
32
 4 ÷2  4 ÷2  4
A pattern is to multiply one term by 4 and divide the
next by 2.
8 ÷ 2 = 4 4  4 = 16 16 ÷ 2 = 8
8  4 = 32
So 4 and 8 will be the missing terms in the sequence.
Course 1
1-5 Mental Math
Check It Out: Example 2A
Identify a pattern in each sequence and name
the missing terms.
6, 12, 14, 28 , 30,
2 +2 2 +2
2
,
,. . .
+2
A pattern is to multiply one term by 2 and add
2 from the next.
30  2 = 60
60 + 2 = 62
So 60 and 62 are the missing terms.
Course 1
1-5 Mental Math
Check It Out: Example 2B
Position
1
2
3
4
Value of Term
1
6
3
18
6
÷2
6
5
6
54
÷2
6
7
8
162
÷2  6
A pattern is to multiply one term by 6 and divide the
next by 2.
18 ÷ 2 = 9 9  6 = 54
54 ÷ 2 = 27
27  6 = 162
So 9 and 27 will be the missing terms in the sequence.
Course 1
1-5 Mental Math
Lesson Quiz
Identify a pattern in each sequence, and
then find the missing terms.
1. 12, 24, 36, 48,
,
,
, … add 12; 60, 72, 84
2. 75, 71, 67, 63,
,
,
,… subtract 4; 59, 55, 51
Identify a pattern in each sequence. Name
the missing terms.
3. 1000, 500,
4. 100, 50, 200,
Course 1
, 125,… divide by 2; 250
, 400,
,… divide by 2 then
multiply by 4; 100, 200