1. Instructional Strategies
MAP2D
Quarter 1
Instructional Strategies
Grade 6

2. MAP2D Chapter 1 Algebraic Reasoning Chapter 2 Integers
Part of Chapter 3 Number Theory and
Fractions ( )

3. Instructional Strategies Chapter 1 Algebraic Reasoning
MAP2D
Instructional Strategies Chapter 1 Algebraic Reasoning

4. 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 4 2 = = 2 2 2 2 16
This is read as, “5 to the second power” or “5 squared.”
base 2 5 = = 25 5 5
SDAP 1.1 Mean, Median, Mode, and Range 7.1 2 2 2

5. Multiply or Divide from Left to Right
Order of Operations
Parentheses
Exponents
Multiply or Divide from Left to Right
Add or Subtract from Left to Right
Ch. 14 L 2

6. Order of Operations Parentheses Exponents Multiplication Division
in order from left to right
Addition
Subtraction or
in order from left to right

7. PROBLEM: Simplify 22 – 4 2 + 2  3
Order of Operations
PROBLEM: Simplify 22 – 4 2 + 2  3
Parentheses
22 – 4   3
(there are none here)
Exponents
4 – 4   3
(perform 2 squared first)
4 –
Multiply or Divide from Left to Right
(divide 42 and multiply 23)
Add or Subtract from Left to Right 8
(subtract 4-2, then add 6)

8. Properties Commutative Properties Addition 4 + 5 = 5 + 4 a + b = b + a
It’s like what you learned in All About the Facts!
Properties
Commutative Properties
Think of “commuting” from home to school…
Addition = 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

9. 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) + =

10. Distributive Property
and + 5 5 = +
Think of a teacher distributing something to every student in the class.

11. 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!
4 times x
4 times 3
 Multiply 4 times x
4(x + 3)
 Copy the operation sign 4x + 12
 Multiply 4 times 3
Ch. 3 Section # 1

12. It’s like looking in a mirror!
Identity Property
The sum of 0 and any number is the number. The product of 1 and any number is the number 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! 5
+ 0= 5

13. Writing Algebraic Expressions
Word Wall, Graphic Organizer or Foldable + -
add sum
plus more than
all together
total gain
rose
subtract minus
difference loss of take away drop
fewer than*
less than* =
equals is
divided by
quotient
every ratio
per fraction
parts into
multiply
product
multiplied by
of at by × ÷

14. Solving Equations by Subtracting
Step 1
Undo addition
Step 2
Simplify
Step 3
Check

15. Solve Addition Equations
Step 1
Add the opposite
Step 2
Simplify
Step 3
Check

16. Solving Equations by Adding
Step 1
Undo subtraction
Step 2
Simplify
Step 3
Check

17. Solving Equations by Adding
Undo addition or subtraction
Step 1
Step 2
Simplify
Step 3
Check

18. Solving Equations by Dividing
Step 1
Undo multiplication
Step 2
Simplify
Step 3
Check

19. Solving Equations by Dividing
Step 1
Undo multiplication
Step 2
Simplify
Step 3
Check

20. Solving Equations by Multiplying
Step 1
Multiply by the reciprocal
Step 2
Simplify
Step 3
Check

21. Solving Equations by Multiplying
Step 1
Undo division
Step 2
Simplify
Step 3
Check

22. Solving Equations by Multiplying
Rewrite
Step 1
Undo division
Step 2
Simplify
Step 3
Check

23. Instructional Strategies Chapter 2 Integers
MAP2D
Instructional Strategies Chapter 2 Integers

24. Adding Integers Song! Same Signs Add and Keep,
(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

25. Integers -3 -2 -1 1 2 3 4 5 All whole numbers and their opposites1 2 3 4 5
All whole numbers and their opposites
Zero is not positive or negative

26. Adding Integers -3 3 -2 2 -1 1 4 5 6 Same Signs, Add4 5 6
Same Signs, Add
Keep the same sign.
Different Signs, Subtract
Keep the sign of the number with the largest absolute value.

27. If integers have different signs. Subtract the numbers.
Adding Integers
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 the
number with the largest absolute value determines the sign that goes with the answer.

28. Adding Integers 2 + -3 = -1 2 + 3 = 5 -2 + 3 = 1 -2 + -3 = -5
If the signs are the same, add.
If the signs are different, subtract.
2 + -3
= -1
2 + 3
= 5
-2 + 3
= 1
= -5
The sign of the
number with the largest absolute value determines the sign of the answer.

29. Subtracting Integers
Subtraction is defined as adding the opposite of the number.
Rewrite subtraction as an addition expression.
Different Signs
Keep the sign of the +3
Use Addition Rules.

30. Subtracting Integers
Subtraction is defined as adding the opposite of the number.
Rewrite subtraction as an addition expression.
Different Signs
Keep the sign of the 4
Use Addition Rules.

31. Multiplying and Dividing Integers
Same Signs - POSITIVE
Different Signs - NEGATIVE
-9  -5 = 45
-9  5 = -45
Two negatives -
One negative
MAKE A POSITIVE
STAYS NEGATIVE

32. 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 
Try these:
-9  2 = ÷(-4)=-9

33. 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.

34. 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.

35. Instructional Strategies Part of Chapter 3
MAP2D
Instructional Strategies Part of Chapter 3
Number Theory
and Fractions
( )

36. 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.

37. Let’s Factor and Use Exponents!
PROBLEM: Write the prime factorization of 56.
 What are 2 factors with a product of 56? 56
Circle the PRIME FACTORS and… 7 8
 Continue to factor any COMPOSITE NUMBERS. 4 2
 Continue until only prime numbers remain. 2 2
 Write prime factorization in exponential form.
56 = 23•7

38. Let’s Use the Ladder for LCM, GCF and Simplifying Fractions!
 WRITE the two numbers on one line. 2 24 36 2 12 18
 DRAW THE L SHAPE
 DIVIDE out common prime numbers starting with the smallest 3 6 9 2 3
 LCM makes an L:
LCM = 2  2  3  2  3 = 72
GCF is down the left side:
GCF = 2  2  3 = 12 36 24 = 3 2
Simplified fraction is on the bottom

39. Let’s Use the Ladder for LCM and GCD with 3 or more numbers
 WRITE the two numbers on one line. 4 6 2 12 x
 DRAW THE L SHAPE 3 2 3 6
 DIVIDE out common prime numbers (at least 2 must be in common) x 2 2 1 2
*Numbers that can not be divided out, CIRCLE and bring STRAIGHT down 1 1 1
 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

40. 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