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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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