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MAP 2 D. Quarter 1 Instructional Strategies Grade 6. MAP 2 D. Chapter 1 Algebraic Reasoning Chapter 2 Integers Part of Chapter 3 Number Theory and Fractions (3.1-3.3). MAP 2 D. Instructional Strategies Chapter 1 Algebraic Reasoning. Exponents. Multiplication can be written as a power - PowerPoint PPT Presentation
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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
MAP2D
Quarter 1Instructional Strategies
Grade 6
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
MAP2D
Chapter 1Algebraic Reasoning
Chapter 2Integers
Part of Chapter 3Number Theory andFractions (3.1-3.3)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
MAP2D
Instructional Strategies
Chapter 1Algebraic Reasoning
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Exponents
SDAP 1.1 Mean, Median, Mode, and Range 7.1
•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
= =base
exponent
= =
This is read as, “5 to the
second power” or “5
squared.”
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
322422
Parentheses
Multiply or Divide from Left to RightExponents
Add or Subtract from Left to Right
Ch. 14 L 2
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Order of Operations
Exponents
Parentheses
Multiplication Division
SubtractionAdditionin order from left to right
in order from left to right
or
or
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
PParentheses
MMultiply or DDivide from Left to Right
EExponents
AAdd or SSubtract from Left to Right
Order of Operations
(there are none here)
(perform 2 squared first)
(divide 42 and multiply 23)
(subtract 4-2, then add 6)
PROBLEM: Simplify 22 – 4 2 + 2 3
22 – 4 2 + 2 3
4 – 4 2 + 2 3
4 – 2 + 6 2 +
68
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Multiplication3 ∙ 6 = 6 ∙ 3 ab = ba
Factors trade places
5(4 ∙ 8) = (4 ∙ 8)5
It’s like what you learned in All About the Facts!
Properties
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Think of a teacher distributing something to every student in the class.
cabacba )( cabacba )(and
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
The Distributive Property
Four is multiplying the quantity “x + 3”
That means four will multiply both the x and the 3!
Multiply 4 times x
PROBLEM: 4(x + 3)
Copy the operation sign Multiply 4 times 3
4(x + 3)
4 times x 4 times 3
4x + 12
Ch. 3 Section # 1
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Identity PropertyThe sum of 0 and any
number is the number. The product of 1 and
any number is the number
33x
1=
5 + 0=5Whenever 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 ExpressionsWord Wall, Graphic Organizer or Foldableadd sum
plus more thanall togethertotal gainrose
+ -
× ÷
=
subtract minusdifference loss of take away drop fewer than*
less than*equals ismultiplyproductmultiplied byof at by
divided by quotientevery ratioper fractionparts into
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
146x
80 x66
8x
Undo addition
1468
Step 1
Step 2
Step 3 Check
Simplify
Solving Equations by Subtracting
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
146 x
200 x66
20x
Add the opposite
14206
Step 1
Step 2
Step 3 Check
Simplify
Solve Addition Equations
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
146x
200 x
66
20x
Undo subtraction
14620
Step 1
Step 2
Step 3 Check
Simplify
Solving Equations by Adding
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
1923 n
n 19023nn
Undo addition or subtraction
19423
Step 1
Step 2
Step 3 Check
Simplify1919 n1923
n4
Solving Equations by Adding
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
427 k
742
77 k
61 k
Undo multiplication
4267
Step 1
Step 2
Step 3Check
Simplify
6k
Solving Equations by Dividing
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
n945
99
945 n
n5
5945
n15
Solving Equations by Dividing
Undo multiplication
Step 1
Step 2
Step 3Check
Simplify
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
2052 k
501 k
Multiply by the reciprocal
20 5052
Step 1
Step 2
Step 3Check
Simplify50 k
Solving Equations by Multiplying
25
2052
25
k
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
59
c
959
9 c
45c
5945
451 c
Solving Equations by Multiplying
Undo division
Step 1
Step 2
Step 3Check
Simplify
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
59c
959
9 c
45c
Undo division
5945
Step 1
Step 2
Step 3
Check
Simplify
59c
Rewrite
451 c
Solving Equations by Multiplying
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
MAP2D
Instructional Strategies
Chapter 2Integers
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
-3 -2 -1 0 1 2 3 4 5 All whole numbers and their opposites
Zero is not positive or negative
33
Integers
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213
413 413
213
Same Signs, Add
Different Signs, Subtract
Keep the same sign.
Keep the sign of the number with the largest absolute value.
Adding Integers
0 -1 1 -2 2 -3 3 4 5 6
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
15510
15510
5510 5510
If both integers are +, the sum is positive
If both integers are -, the sum is negative
If integers have different signs. Subtract the numbers.
Note: The sign of thenumber with the largest absolute value determines the sign that goes with the answer.
Adding Integers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
If the signs are the same, add.
The sign of thenumber with the largest
absolute value determines the sign of the answer.
Adding IntegersIf the signs are
different, subtract.
-2 + -3
2 + 3 = 5
= -5 -2 + 3
2 + -3 = -1
= 1
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
13
Subtraction is defined as adding the opposite of the number.
13 Rewrite subtraction as an addition expression.
Use Addition Rules.
213 Different Signs
Keep the sign of the +3
Subtracting Integers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
42
Subtraction is defined as adding the opposite of the number.
42 Rewrite subtraction as an addition expression.
Use Addition Rules.
242
Different Signs Keep the sign of the 4
Subtracting Integers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Multiplying and Dividing Integers
STAYS NEGATIVEOne negative
Different Signs - NEGATIVE
98
72
-9 5 = -45
MAKE A POSITIVETwo negatives -
Same Signs - POSITIVE
9872
-9 -5 =
45
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Multiplying and Dividing Integers
+
--
Cover up the signs that are being multiplied or divided
-9 -5 = 45In 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
-9 2 = -18 36÷(-4)=-9
Try these: 98
72
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solving Equations Containing Integers
Which operation needs to be undone?
Solve for X.
Undo the subtraction, by doing the inverse operation of adding. Remember to undo both sides.
Cancel out. Don’t forget the integer rules.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Solving Equations Containing Integers
Which operation needs to be undone?
Solve for X.
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.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
MAP2D
Instructional Strategies
Part of Chapter 3Number Theoryand 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 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.
2, 3, 5, 7, 11, 13, 17
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Factor and Use Exponents!
What are 2 factors with a product of 56?
② Circle the PRIME FACTORS and…
Continue to factor any COMPOSITE NUMBERS.
56
PROBLEM: Write the prime factorization of 56.
Continue until only prime numbers remain.
Write prime factorization in exponential form.
7 8
2 4
2 2
56 = 23•7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Use the Ladder for LCM, GCF and Simplifying Fractions!
WRITE the two numbers on one line. DRAW THE L SHAPE
DIVIDE out common prime numbers starting with the smallest
242 36122 18
63 92 3
LCM makes an L: LCM = 2 2 3 2 3 = 72
GCF = 2 2 3 = 12
3624
=32
GCF is down the left side:
Simplified fraction is on the bottom
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)
42 1233 612 2
1 1
LCM makes an L:LCM = 2 3 2 1 1 1 = 12
GCF = 2GCF* is down the left side:
62
*Numbers that can not be divided out, CIRCLE and bring STRAIGHT down
21
*If a number is circled, cross out the divisor that corresponds, and do not use it to find the GCD.
xx
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
GCD vs LCM: Problem Solving
• Are things being split into smaller sections?
• How many people can we invite?
• Are we arranging into rows or groups?
• Do we have to purchase multiple items?
• Are we trying to figure how soon an event will happen at the same time?
GCD LCM
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