2
MAP D
Quarter 2
Instructional Strategies
Grade 6
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
2
MAP D
Part of Chapter 3
Number Theory and Fractions (3.4-3.6)
Chapter 4
Operations with Rational Numbers
Chapter 5
Proportional Relationships
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
2
MAP D
Instructional Strategies
Part of Chapter 3
Number Theory
and Fractions
(3.4-3.6)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
How do you find equivalent
fractions with your fraction kit?
1
4
1
3
1
1
1
2
1
4
1
3
1
2
1
4
1
3
1
4
1
1
1
1
1
1
6
6
6
6
6
6
1
1
1
1
1
1
1
1
8
8
8
8
8
8
8
8
1 1 1 1 1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12 12 12 12 12
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
You can multiply both the numerator and denominator of a fraction
by any number except zero to find equivalent fractions.
2
5
4
10
2
5
Copyright ©, Long Beach Unified School District. All rights reserved.- Grade 5
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
6
15
You can divide both the numerator and denominator of a fraction
by any number except zero to find equivalent fractions.
8
12
Ch. 6 L 1
4
6
4
6
2
3
Copyright ©, Long Beach Unified School District. All rights reserved.- Grade 5
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Simplify Fractions!
10
PROBLEM: Simplify 12
 REWRITE both the
numerator and
denominator using prime
factors
 DIVIDE OUT common
factors (CANCEL)
 Multiply the remaining
numbers for the
simplified fraction
2 5
10 5

12 6
2
6
2 3
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Tips for Recognizing Simplified Fractions
 When the numerator and denominator
are CONSECUTIVE numbers the
fraction is in simplest form.
1
2
2
3
3
4
4
5
9
10
15
16
21
22
 When the denominator is PRIME the
fraction is in simplest form.
1
3
2
5
4
7
8
11
3
13
6
17
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
10
19
Tips for When to Simplify a Fraction
 You must simplify a fraction if both
numbers are EVEN.
6
8
6
10
4
10
14
18
8
14
10
12
20
28
 You must simplify a fraction if the
denominator is DIVISIBLE by the
numerator.
2
8
3
9
5 8
15 24
4
16
9
81
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
10
90
Let’s Convert Improper Fractions
to Mixed Numbers!
2
13
5
= 3 5
3
3
2
Improper
Fraction
2
=1
3
Divide
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Mixed
Number
Let’s Convert Mixed Numbers to
Improper Fractions!
2
4
3
+
x
FIRST multiply denominator
How many thirds are
in the whole number?
by the whole number
3 x 4 = 12
3 x 4
NEXT
12 + 2
2
4
3
+
add the product
to the numerator
PLUS how many thirds
are in the fraction?
12 + 2 = 14
x
LAST
The sum is the numerator
Keep the same denominator
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
14
3
Let’s Compare Fractions
COMMON DENOMINATORS

If the denominators
are the same,
compare numerators.
3 5

8 8
COMMON NUMERATORS

If the numerators are
the same, compare
denominators.
(Big denominators
make small fractions.)
1 1

6 2
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Compare Fractions
UNLIKE DENOMINATORS

Find a common denominator by
multiplying the denominators.
15 3

20 4
<
x
4 16

5 20

Find the numerators by multiplying
diagonally upwards.

Compare the new numerators.
SHORTCUT: Skip step 1, multiply diagonally and compare.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
ML Course 1 Section 2.6
Let’s Compare and Order Fractions!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
0.75
4 3.00
3
4
or
4
5
0.75 < 0.80
3 4

4 5
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
0.80
5 4.00
Comparing and Ordering Rational Numbers
ORIGINAL
List from least to greatest
1. Place the numbers in a grid
RANKING
DECIMAL
2. Convert fractions to decimals
Answer:
3. Add zero place holders so everything is
either in tenths, hundredths, or thousandths.
(Greatest)
(Least)
4. Think of money. What is the least amount
of money you would want? Place a 1. Then the
next amount you would not want. Place a 2….
etc.
5. Put the ORIGINAL numbers back in order
according to your rankings
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
2
MAP D
Instructional Strategies
Chapter 4
Operations with Rational Numbers
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
 PLACE the decimal point in
the sum
 ADD
 CHECK to see the answer is
close to the estimate
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
1 2.3 4
0 5.6 0
1 7.9 4
17.94 is close
to 18 
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
 SUBTRACT
 CHECK to see the answer is
close to the estimate
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
8 .9 5
 3 .2 0
5 .7 5
5.75 is close
to 6 
1 1
 
2 3
Add Fractions
 MULTIPLY
denominators to
find a common
denominator
 Multiply numerator
and denominator by
the same number
 REWRITE and ADD
 SIMPLIFY if possible
Can we simplify?
1x 3 1 x 2


2x 3 3 x 2
3 2 5
 
6 6 6
5 and 6 are consecutive
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Add Fractions
When the denominators are the same,
add the numerators
3 3
3
1
8
9



12 12 12 4
2
Can we simplify?
Use prime factors
6
2
3
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Add Fractions
1 2
 
PROBLEM:
12 3
 Can we add these as
they are?
1
2


12
3
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?
We will use 12 as the common denominator.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Adding/Subtracting Fractions
 Rewrite vertical (upside down T)
 Find the Least Common
Denominator (LCM)
1x 3
2x 3
 Make an equivalent fraction
for each fraction
1x 2
+ 3x 2
 ADD the numerators and
simplify if possible
5 and 6 are consecutive
Can we simplify?
*NS 2.4 Adding and Subtracting Fractions Section 4.2
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
1 1
 
2 3
3
6 5
2
6
5
6
Adding/Subtracting Mixed Numbers
 Rewrite vertical (upside down T)
12
 Find the Least Common
Denominator (LCM)
3x 3
12
4x 3
 Make an equivalent fraction for
each fraction
1x 2
3
6
x2
 Subtract the whole numbers,
then subtract the numerators
and simplify if possible
*NS 2.4 Adding and Subtracting Fractions Section 4.3
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
3
1
3 
4
6
9
12
2
12
7
9
12
7
Subtracting a Fraction from a Whole Number
2
PROBLEM: 5  
3
 Can we subtract the
fraction part as they are?
Why not?
We need to regroup the whole number
to HAVE a fraction.
 REGROUP
 REWRITE
the problem
 SUBTRACT
Regrouping
2
5 

3
5=4+1
3
2
4 
 5=4+3
3
3
3
1
43
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Subtracting Mixed Numbers with Regrouping
1
2
PROBLEM: 5  1 
3 3

1
2
5  1 
3
3
 Can we subtract the
fraction parts as
they are?
Why not? 2 is bigger than 1
 REGROUP
 REWRITE
the problem
 SUBTRACT
REGROUPING

1
53
=4+1
1
+3
4
2
4  1 
1
3 1
3
3
53 = 4 + 3 + 3

2
1
4
33
53 = 43
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Subtracting Mixed Numbers and RENAMING
 Rewrite vertical (upside down T)
4
 Find the Least Common Denominator
(LCM)
 Make an equivalent fraction
for each fraction
1x3
34
x3
Borrow from the WHOLE, carry the ONE 3
3x1
2
 Turn mixed number into an improper
x1
fraction
6
 Subtract the whole numbers, then
subtract the numerators and simplify if
possible
*NS 2.4 Adding and Subtracting Fractions Section 4.3
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
1
3
2 
3
6
2
16
3
6
5
1
6
8
6
3
6
Multiply Fractions
2 3

PROBLEM:
9 8
The Matching
Factors Method
 REWRITE the
expression
 FACTOR
composite numbers
23
23
1


98
33222
12
2
4
3 3
2 2
 DIVIDE OUT common
factors (CANCEL)
 MULTIPLY any
remaining factors
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Multiply Fractions
2 3

PROBLEM:
9 8
 REWRITE the
expression
1 1
23
98
3 4
The Canceling
Method
 Look for numbers with
common factors in the
numerator & denominator
2 goes into both 2 and 8
2 into 2 is?
2 into 8 is?
3 goes into both 3 and 9
3 into 3 is?
 DIVIDE OUT common
3 into 9 is?
factors (CANCEL)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Multiplying Fractions and Mixed Numbers
1
1
of
2 4
Multiply numerators
1
•
2
1
4
=
1
Multiply denominators
1
2
•
1
4
=
1 1
• =
2 4
Think: What is half
of a quarter?
1
8
Simplify if needed
*NS 2.4 Adding and Subtracting Fractions Section 4.4
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
1 1 1
• =
2 4 8
Multiply Decimals
PROBLEM: 12.3 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 55.35 is close
digit that was underlined
to 60 
 CHECK to see the answer is close to the estimate
1 2 .3
 4 .5
615
4920
5 5 35
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Divide Fractions
3 1

PROBLEM:
20 5

3 1

20 5
 CIRCLE the
the divisor

3 5

20 1
 and
 REWRITE as
multiplication by

the reciprocal
 REVERSE everything
in the circle!
 MULTIPLY
3
35
35


225 4
20
2 10
2 5
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Add Decimals!
PROBLEM: 12.34 + 5.6 =
 ESTIMATE as 12 + 6 = 18
 REWRITE the expression
vertically, line up by place
value and decimals
1 2.3 4
 05.6 0
1 7.9 4
 FILL IN the empty spaces 17.94 is close
with zeros
to 18 
 PLACE the decimal
CHECK to see
the answer is
point in the sum
close to the
estimate
 ADD
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Subtract Decimals!
PROBLEM: 8.95 – 3.2 =
 ESTIMATE as 9 – 3 = 6
8 .9 5
 REWRITE the expression

3
.
2
0
vertically, line up by place
value and decimals
5 .7 5
 FILL IN the empty spaces
5.75 is close
with zeros
to 6 
 PLACE the decimal
CHECK to see
point in the difference
the answer is
 SUBTRACT
close to the
estimate
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Multiply Decimals with ZEROS in the Product!
PROBLEM: 0.17 x 0.5 =
 ESTIMATE as 0 x 1 = 0
 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
0.085 is
 UNDERLINE the same number of digits
close to 0 
in the answer that were underlined in
the problem; fill in empty spaces with
zeros
 PLACE the decimal in front of the last
digit that was underlined
 CHECK to see the answer is close to the estimate
0 .1 7
 0.5
0 0 85
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Let’s Divide Decimals!
PROBLEM: 366
 12 =
30 5
12 366 .0
 REWRITE 12 into 366
 DIVIDE like regular whole
-36
numbers
6
 If there is a remainder,
-0
place a decimal and a zero in
60
the dividend
-6 0
 Bring up the decimal in the
quotient and continue to
0
x
divide
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Divide Decimals
PROBLEM: 4.48  0.08 =
 REWRITE 0.08 into 4.48
56
0.08 4.48
 MOVE decimals 2 places
right by multiplying divisor
and dividend by 100
 DIVIDE
 PLACE the decimal point in
the quotient
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
40
48
48
0
Let’s Divide Money!
PROBLEM: $9.80  4 =
 REWRITE
4 into $9.80
 WRITE the dollar
sign and decimal in
the quotient
 DIVIDE
$2 45
4 $9.80
-8
18
-16
20
- 20
0
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
2
MAP D
Instructional Strategies
Chapter 5
Proportional Relationships
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Writing Ratios
Write the ratio of girls to boys in
simplest form
A class has 20 girls to 16 boys.
Step 1
Identify the two quantities
being compared
Step 2
Write as a ratio
Step 3
Simplify
girls
boys
20 girls
4∙5 girls
5 girls
4 boys
=
=
16 boys 4∙4 boys
5 girls:4 boys
5 girls to 4 boys
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
5.1 Ratios
Writing Ratios
A car travels 360 miles and uses
15 gallons of gasoline. What is the
ratio of the distance traveled to
the gallons of gasoline used?
Step 1
Step 2
Step 3
Identify the two quantities
being compared
Write as a ratio
Simplify
miles
360 mi
gallons
15 gal
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
= 24 mi/gal
Unit Rates
PROBLEM: Anne ran 5 km in 50 min
Write the unit rate.
 Identify the two sets
of numbers and units.
 5 km and 50 min
 Write one on top of the
other, as a fraction.
 5 km
 Simplify and write
the units as a rate.
 1 km
50 min
10
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
min
Solving Real-life Problems Using Proportions
Jason can read 12 pages of a book in
15 minutes. How many pages can he read
in 25 minutes?
 Write
 Set
a ratio using words
up a proportion
 Multiply
 Solve
pages
the cross
for x
minutes
=
=
12 x
=
=
15 25
minutes
pages
15  x  25  12
products
15 x  300
1 15 x
300 20

1 15
15 1
X = 20 pages
*NS 1.3 Solving Proportions Section 5.4
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Customary Units of Length
Y = Yard
1 Yard = 3 feet
1 foot = 12 inches
12 inches
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
uart
int
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
allon
1.
Have students memorize the BIG G
2.
Students will be setting up proportions
3.
Example: How many cups are in 4 pints?

Identify what is being converted. In this
case, cups and pints

Write as a proportion:

Look back at the question and fill in the
number and variable in the appropriate
places:
cups
p ints
cups x

p ints 4
Practice Problems:

Look at the BIG G and fill in how many of
each that you see:
cups x 16
 
p ints 4 8

1. How many pints are in 3 quarts?
2. How many cups are in 2 gallons?
3. How many quarts are in 8 cups?
Solve the proportion!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Similar Polygons
8
11
16
22
6
12
Corresponding angles are congruent.
Corresponding sides are proportional.
11
6
8


22
12
16
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Missing Side in Similar Polygons
6
15
4
x
Write a proportion
small
large
6
15
4
x
Solve
6x = 4  15
6x = 60
6
6
x = 10
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Missing Side in Similar Polygons
Looks like I can
just add a semihorizontal line and
my proportion is
set up!
6
15
4
Write a proportion
Side
Base
6
4
15
x
x
Solve
6x = 4  15
6x = 60
6
6
x = 10
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Scale Drawings and Scale Models
The map below uses the scale of 1 inch equals 1,000 feet.
How many feet are represented by the 5 inches on this map?
•1 inch equals 1,000 feet
•The distance from each
star is 5 inches
•What is the distance in
feet from star to star?
inch
1
5


feet 1,000 x
x  5,000 feet
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6