1. Instructional Strategies
MAP2D
Quarter 1
Instructional Strategies
Grade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

2. 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)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
1.1 Pre-Requisite Skill

3. Evaluating Algebraic Expressions
Evaluate x + 5 for x = 11
Step 1:
Substitute 11 for x.
11 + 5
Step 2: 16
Add.
Section 1.1 Evaluating Algebraic Expressions
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

4. Evaluating Algebraic Expressions
Evaluate 2y + 3 for y = 4
Step 1:
Substitute 4 for y.
2(4) + 3
Step 2:
8 + 3
Multiply.
Step 3: 11
Add.
Section 1.1 Evaluating Algebraic Expressions
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

5. Evaluating Algebraic Expressions
Evaluate 5x + 2y for x = 13 and y = 11
Step 1:
5(13) + 2(11)
Substitute 13 for x and 11 for y.
Step 2:
Multiply.
Step 3: 11
Add.
Section 1.1 Evaluating Algebraic Expressions
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

6. 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 × ÷
Section 1.2 Writing Algebraic Expressions
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

7. Section 1.3 Integers & Absolute Value-3 -2 -1 1 2 3 4 5
All whole numbers and their opposites
Zero is not positive or negative
Section 1.3 Integers & Absolute Value
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

8. Opposite numbers are the same
Opposites 4 -4 -3 3 -2 2 -1 1
Opposite numbers are the same
distance from zero.
The opposite of -2 is 2.
The sum of opposites is 0.
Section 1.3 Integers & Absolute Value
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

9. Absolute Value Absolute value is the distance of a number from zero.
The absolute value of -3 is 3. -3
= 3 -1 1 -2 2 -3 3 4 5 6
The absolute value of 2 is 2. 2
= 2 -1 1 -2 2 -3 3 4 5 6
Hint: Count the spaces from zero to the number.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Section 1.3 Integers & Absolute Value

10. 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.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Section 1.4 Adding Integers

11. 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.
Section 1.4 Adding Integers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

12. Adding Integers 2 + -3 = -1 2 + 3 = 5 -2 + 3 = 1 -2 + -3 = -5
If the signs are different, subtract.
If the signs are the same, add.
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.
Section 1.4 Adding Integers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

13. 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.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Section 1.5 Subtracting Integers

14. 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.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Section 1.5 Subtracting Integers

15. 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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Section 1.6 Multiplying Integers & Dividing Integers

16. Solving Equations by Subtracting
Step 1
Undo addition
Step 2
Simplify
Step 3
Check
Section 1.7 Solving Equations by Adding or Subtracting
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

17. Solve Addition Equations
Step 1
Add the opposite
Step 2
Simplify
Step 3
Check
Section 1.7 Solving Equations by Adding or Subtracting
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

18. Solving Equations by Adding
Step 1
Undo subtraction
Step 2
Simplify
Step 3
Check
Section 1.7 Solving Equations by Adding or Subtracting
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

19. Solving Equations by Adding
Step 1
Undo addition or subtraction
Step 2
Simplify
Step 3
Check
Section 1.7 Solving Equations by Adding or Subtracting
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

20. Solving Equations by Dividing
Step 1
Undo multiplication
Step 2
Simplify
Step 3
Check
Section 1.8 Solving Equations by Multiplying or Dividing
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

21. Solving Equations by Dividing
Step 1
Undo multiplication
Step 2
Simplify
Step 3
Check
Section 1.8 Solving Equations by Multiplying or Dividing
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

22. Solving Equations by Multiplying
Step 1
Multiply by the reciprocal
Step 2
Simplify
Step 3
Check
Section 1.8 Solving Equations by Multiplying or Dividing
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

23. Solving Equations by Multiplying
Step 1
Undo division
Step 2
Simplify
Step 3
Check
Section 1.8 Solving Equations by Multiplying or Dividing
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

24. Solving Equations by Multiplying
Rewrite
Step 1
Undo division
Step 2
Simplify
Step 3
Check
Section 1.8 Solving Equations by Multiplying or Dividing
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

25. Solving Two-Step Equations
6x – 2 = 10
Step 1
+ 2
+ 2
Add 2 to both sides of the equation
Step 2
6x = 12
Then divide both sides by 6 2 2
Step 3
x = 2
Simplify
Section 1.9 Solving Two-Step Equations
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

26. Solving Two-Step Equations
Subtract 5 from both sides of the equation -5 -5
Step 2
Then multiply both sides by 6
Step 3
x = 48
Simplify
Section 1.9 Solving Two-Step Equations
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

27. Compare Fractions
COMMON DENOMINATORS
If the denominators are the same, compare numerators.
COMMON NUMERATORS
If the numerators are the same, compare denominators (Big denominators make small fractions.)
Section 2.2 Ordering Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

28. SHORTCUT: Skip step 1, multiply diagonally and compare.
Compare Fractions
UNLIKE DENOMINATORS
Find a common denominator by multiplying the denominators. 15 16
< x
Find the numerators by multiplying diagonally upwards.
Compare the new numerators.
SHORTCUT: Skip step 1, multiply diagonally and compare.
Section 2.2 Ordering Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

29. Add Decimals PROBLEM: 12.34 + 5.6 =  ESTIMATE as 12 + 6 = 18
 REWRITE the expression vertically, line up decimals
 FILL IN the empty spaces with zeros
17.94 is close to 18 
 PLACE the decimal point in the sum
 ADD
 CHECK to see the answer is close to the estimate
Section 2.3 Adding and Subtracting Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

30. Subtract Decimals PROBLEM: 8.95 – 3.2 =  ESTIMATE as 9 – 3 = 6
 REWRITE the expression vertically, line up decimals
 FILL IN the empty spaces with zeros
 PLACE the decimal point in the difference
5.75 is close to 6 
 SUBTRACT
 CHECK to see the answer is close to the estimate
Section 2.3 Adding and Subtracting Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

31. Add Fractions 3 3 2 6 2 3 Yes When the denominators are the same,
add the numerators 3 3 2 6 2 3
Can we simplify?
Yes
Use prime factors
Section 2.3 Adding & Subtracting Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

32. The Matching Factors Method
Multiply Fractions
The Matching Factors Method
PROBLEM:
 REWRITE the expression
 FACTOR composite numbers
 DIVIDE OUT common factors (CANCEL) 2 4 3 3
 MULTIPLY any remaining factors 2 2
Section 2.4 Multiplying Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

33. 1 1 3 4 Multiply Fractions PROBLEM:  REWRITE the expression
The Canceling Method
PROBLEM:
 REWRITE the expression
 Look for numbers with common factors in the numerator & denominator 1 1
2 goes into both 2 and 8
2 into 2 is?
2 into 8 is? 3 4
3 goes into both 3 and 9
3 into 3 is?
 DIVIDE OUT common factors (CANCEL)
3 into 9 is?
Section 2.4 Multiplying Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

34. 1 1 3 4 Multiply Fractions PROBLEM:  REWRITE the expression
Section 2.4 Multiplying Rational Numbers
The Canceling Method
PROBLEM:
 REWRITE the expression
 Look for numbers with common factors in the numerator & denominator 1 1 3 4
 DIVIDE OUT common factors (CANCEL)
 MULTIPLY any remaining factors
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

35. Multiply Decimals PROBLEM: 12.3 x 4.5 =  ESTIMATE as 12 x 5 = 60
Section 2.4 Multiplying Rational Numbers
PROBLEM: x 4.5 =
 ESTIMATE as 12 x 5 = 60
 REWRITE the expression vertically
 MULTIPLY the numbers as if they were whole numbers
 UNDERLINE the digits to the right of the decimal in the multiplication problem
 UNDERLINE the same number of digits in the answer that were underlined in the problem
 PLACE the decimal in front of the last digit that was underlined
55.35 is close to 60 
 CHECK to see the answer is close to the estimate
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

36. 2 10 2 5 Divide Fractions  PROBLEM:  
 CIRCLE the  and the divisor 
 REWRITE as multiplication by the reciprocal 
 REVERSE everything in the circle! 2 10 2 5
 MULTIPLY
Section 2.5 Dividing Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

37. 5 6 40 4 8 4 8 Divide Decimals PROBLEM: 4.48  0.08 =
 REWRITE into 4.48 40
 MOVE decimals 2 places right by multiplying divisor and dividend by 100 4 8
4 8
 DIVIDE
 PLACE the decimal point in the quotient
Section 2.5 Dividing Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

38. Add Fractions No Yes PROBLEM:  Can we add these as they are?
Why not?
They have unlike denominators.
TO FIND A COMMON DENOMINATOR:
 First ask if one denominator goes into the other.
Does 3 go into 12 evenly?
Yes
We will use 12 as the common denominator.
Section 2.6 Adding & Subtracting with Unlike Denominators
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

39. Add Fractions No  MULTIPLY denominators to find a common denominator
Section 2.6 Adding & Subtracting with Unlike Denominators
PROBLEM:
 MULTIPLY denominators to find a common denominator
x 3
x 2
x 3
x 2
 Multiply numerator and denominator by the same number
 REWRITE and ADD
 SIMPLIFY if possible No
Can we simplify?
5 and 6 are consecutive
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

40. Add Fractions 18 + 8 48 Here is a shortcut: Multiply along the arrows
Simplify
Section 2.6 Adding & Subtracting with Unlike Denominators
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

41. Subtracting a Fraction from a Whole Number
Regrouping
PROBLEM:
 Can we subtract the fraction part as they are? No
Why not?
We need to regroup the whole number to HAVE a fraction.
5 = 4 + 1
 REGROUP 4
 REWRITE the problem
5 = 4 + 4
 SUBTRACT
Section 2.6 Adding & Subtracting with Unlike Denominators
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

42. Subtracting Mixed Numbers with Regrouping
PROBLEM:
 Can we subtract the fraction parts as they are? No
Why not?
2 is bigger than 1 
5 =
 REGROUP
 REWRITE the problem
5 =  3
5 = 4
 SUBTRACT
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

43. 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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

44. Convert Improper Fractions to
Mixed Numbers 2 1 5 3 = = 5 3 3 3 1 2 1
Improper Fraction
Mixed Number
Divide
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

45. Convert Mixed Numbers to Improper Fractions
FIRST multiply denominator
by the whole number
FIRST
3 x 4
How many thirds are in the whole number?
3 x 4 = 12 1 2 3 4 5 6 7 8 9 10 11 12
NEXT
PLUS how many thirds are in the fraction?
NEXT
12 + 2
= 14 14
TOTAL THIRDS =
add the product
to the numerator 13 14 =
LAST
The sum is the numerator 3
Keep the same denominator
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7