Transcript MAP2D - Long Beach Unified School District

2
MAP D
Quarter 1
Instructional Strategies
Grade 6
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
2
MAP D
Chapter 1
Algebraic Reasoning
Chapter 2
Integers
Part of Chapter 3
Number Theory and
Fractions (3.1-3.3)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
2
MAP D
Instructional Strategies
Chapter 1
Algebraic Reasoning
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Exponents
•Multiplication can be written as a power
•There is a base and an exponent
•The exponent tells how many times to use the base as a factor
exponent
=
=
base
=
This is read as,
“5 to the
second power”
or “5 squared.”
=
SDAP 1.1 Mean, Median, Mode, and Range 7.1
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Parentheses
Exponents
Multiply or Divide from Left to Right
Add or Subtract from Left to Right
2  4 2  2 3
2
Ch. 14 L 2
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Order of Operations
Parentheses
Exponents
Multiplication
or
Division
in order from left to right
Addition
or
Subtraction
in order from left to right
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Order of Operations
PROBLEM: Simplify 22 – 4 2 + 2  3
Parentheses
(there are none here)
Exponents
(perform 2 squared first)
Multiply or Divide
from Left to Right
22 – 4  2 + 2  3
4 – 42+23
4 – 2
(divide 42 and multiply 23)
2
Add or Subtract
from Left to Right
(subtract 4-2, then add 6)
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+
+
8
6
6
It’s like what
you learned in
All About the
Facts!
Properties
Commutative Properties
Think of “commuting” from home to school…
Addition
4+5=5+4
a + b = b + a
Addends trade places
3 + (7 + 6) = (7 + 6) + 3
Multiplication 3 ∙ 6 = 6 ∙ 3
ab = ba
Factors trade places
5(4 ∙ 8) = (4 ∙ 8)5
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Associative Properties
Groups change, Numbers stay in same order
Addition
(7 + 5) + 6 = 7 + (5 + 6)
a + (b + c) = (a + b) + c
You are just regrouping the numbers so “friends” can be together.
Multiplication
4(3 ∙ 7) = (4 ∙ 3)7
(a ∙ b)c = a(b ∙ c)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Distributive Property
a (b  c )  a  b  a c
and
a (b  c )  a  b  a c
Think of a teacher distributing something to
every student in the class.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
The Distributive Property
PROBLEM: 4(x + 3)
Four is multiplying the quantity “x + 3”
That means four will multiply both the x
and the 3!
 Multiply 4 times x
 Copy the operation sign
 Multiply 4 times 3
4 times x
4 times 3
4(x + 3)
4x + 12
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Ch. 3 Section # 1
Identity Property
The sum of 0 and any
number is the number.
The product of 1 and any
number is the number
5
+ 0= 5
3
x 1= 3
Whenever you add zero and
multiply by 1, the answer will
ALWAYS be the original
number.
It’s like looking in a mirror!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Writing Algebraic Expressions
Word Wall, Graphic Organizer or Foldable
+
×
add sum
plus more than
all together
total gain
rose
equals
multiply
product
multiplied by
of at by
-
subtract minus
difference loss of
take away drop
fewer than*
less than*
is
divided by
quotient
every ratio
per fraction
parts into
=
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÷
Solving Equations by Subtracting
Step 1
Step 2
Step 3
x  6 14
 6  6
x 0  8
x 8
8  6  14
Undo addition
Simplify
Check
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solve Addition Equations
Step 1
Step 2
 6  x  14
 6  6
0  x  20
Add the
opposite
Simplify
x  20
Step 3
 6  20  14
Check
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solving Equations by Adding
Step 1
x  6  14 Undo subtraction
 6  6
Step 2
x  0  20
Simplify
x  20
Step 3
20  6  14
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Check
Solving Equations by Adding
Step 1
Step 2
Step 3
23 n  19
n n
23  0  19  n
23  19  n
 19   19
4 n
Undo addition
or subtraction
23  4  19
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Simplify
Check
Solving Equations by Dividing
Step 1
Undo
multiplication
Step 2
Simplify
Step 3
Check
7k  42
7k 42

7 7
1k  6
k 6
7  6  42
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Solving Equations by Dividing
Step 1
Undo
multiplication
Step 2
Simplify
Step 3
Check
45 9n
45 9n

9 9
5  1n
5 n
45  9  5
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solving Equations by Multiplying
Step 1
Multiply by the
reciprocal
Step 2
Simplify
Step 3
Check
2
k  20
5
 5  2 k  20  5 
 
 
25
2
1k  50
k  50
 2 50  20
 
5
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solving Equations by Multiplying
c
5
Step 1
9
Undo division
c
9 5  9
9
1c  45
Step 2
Simplify
Step 3
Check
c  45
45
5
9
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solving Equations by Multiplying
Rewrite
Step 1
Undo division
Step 2
Simplify
Step 3
Check
c  9 5
c
5
9
c
9  59
9
1c  45
c  45
45
5
9
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2
MAP D
Instructional Strategies
Chapter 2
Integers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Adding Integers Song!
Adding Integers
(to the tune of Row, Row, Row Your Boat)
Same Signs Add and Keep,
Different Signs Subtract,
Take the Sign of the Higher Number,
Then it’ll be Exact!
Ch 15 L 4
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Integers
-3 -2 -1 0 1 2 3 4 5
All whole numbers and their opposites
Zero is not positive or negative

3 3
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Adding Integers

-3 -2 -1 0


3  1 4



3  1 4



3  1 2



3  1 2
1 2 3 4 5 6
Same Signs, Add
Keep the same sign.
Different Signs, Subtract
Keep the sign of the number with
the largest absolute value.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Adding Integers
If both integers are +, the sum is positive



10  5  15
If both integers are -, the sum is negative



10  5  15
If integers have different signs. Subtract the numbers.



10  5  5



10 5  5
Note: The sign of the
number with the largest absolute
value determines the sign that
goes with the answer.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Adding Integers
If the signs are the
same, add.
2+3
=5
-2 + -3 = -5
If the signs are
different, subtract.
2 + -3 = -1
-2 + 3
=1
The sign of the
number with the largest
absolute value determines
the sign of the answer.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Subtracting Integers
Subtraction is defined as adding the
opposite of the number.


3 1
Rewrite subtraction as an addition expression.


 3 1
Use Addition Rules.



3  1 2
Different Signs
Keep the sign of the +3
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Subtracting Integers
Subtraction is defined as adding the
opposite of the number.


2 4
Rewrite subtraction as an addition expression.


 2 4
Use Addition Rules.


Different Signs
Keep the sign of the 4

2 4 2
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Multiplying and Dividing Integers
Same Signs POSITIVE
Different Signs NEGATIVE
-9  -5 = 45
 72
9
8
-9  5 = -45
72
 9
8
Two negatives MAKE A POSITIVE
One negative
STAYS NEGATIVE
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Multiplying and Dividing Integers
 Cover up the signs that are being
+
multiplied or divided
-9  -5 = 45
 In the example, since 9 is
negative and so is 5,
with two fingers cover
the two negative signs
 Since, the sign that isn’t
-
covered is POSITIVE, the
answer is POSITIVE 45
-
72
 Try these: -9  2 = -18 36÷(-4)=-9  8  9
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solving Equations Containing Integers


Which operation needs
to be undone?


Undo the subtraction, by
doing the inverse operation
of adding. Remember to
undo both sides.


Cancel out. Don’t forget the
integer rules.

 Solve for X.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solving Equations Containing Integers


Which operation needs
to be undone?


Undo the division, by doing
the inverse operation of
multiplication. Remember to
undo both sides.


Cancel out. Don’t forget to
show all of your work.

 Solve for X.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
2
MAP D
Instructional Strategies
Part of Chapter 3
Number Theory
and Fractions
(3.1-3.3)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Prime Numbers
 What are the first seven prime numbers?
2, 3, 5, 7, 11, 13, 17
 One is NOT PRIME because it does not
have exactly two factors.
 One is NOT COMPOSITE because it does
not have more than two factors.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Factor and Use Exponents!
PROBLEM: Write the prime factorization of 56.
 What are 2 factors with
a product of 56?
 Circle the PRIME FACTORS
and…
56
7
 Continue to factor any
COMPOSITE NUMBERS.
4
2
2
2
 Continue until only prime
numbers remain.
 Write prime factorization
in exponential form.
8
56 = 2 •7
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3
Let’s Use the Ladder for LCM, GCF
and Simplifying Fractions!
 WRITE the two
2 24 36
numbers on one line.
 DRAW THE L SHAPE
2 12 18
 DIVIDE out common
3 6
9
prime numbers
starting with the
2
3
smallest
LCM = 2  2  3  2  3 = 72
 LCM makes an L:
GCF = 2  2  3 = 12
24
2
=
Simplified fraction is on the bottom
36
3
GCF is down the left side:
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Use the Ladder for LCM and
GCD with 3 or more numbers
 WRITE the two
numbers on one line.
 DRAW THE L SHAPE
 DIVIDE out common
prime numbers (at least 2
must be in common)
*Numbers that can not be
divided out, CIRCLE and
bring STRAIGHT down
6 12
2 4
3 2 3 6
2 2 1 2
1 1 1
x
x
 LCM makes an L: LCM = 2  3  2  1  1  1 = 12
*If a number is circled, cross out the divisor that
corresponds, and do not use it to find the GCD.
GCF* is down the left side: GCF = 2
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
GCD vs LCM:
Problem Solving
• Are things being split into
smaller sections?
• Do we have to purchase
multiple items?
• How many people can we
invite?
• Are we arranging into rows
or groups?
GCD
• Are we trying to figure how
soon an event will happen at
the same time?
LCM
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6