Transcript 3. pattern blocks and fraction operations

Fraction Operations
Using Pattern Blocks
Fractions CCSS


4.NF.3c Add and subtract mixed
numbers with like denominators.
4.NF.4 Apply and extend previous
understandings of multiplication
to multiply a fraction by a whole
number
Fractions CCSS



5.NF.1 Add and subtract fractions with unlike
denominators (including mixed numbers) by
replacing given fractions with equivalent
fractions in such a way as to produce an
equivalent sum or difference of fractions with
like denominators.
5.NF.4 Apply and extend previous
understandings of multiplication to multiply a
fraction or whole number by a fraction.
5.NF.7 Apply and extend previous
understandings of division to divide unit
fractions by whole numbers and whole numbers
by unit fractions.
Fractions CCSS


6.NS.1 Interpret and compute quotients of
fractions, and solve word problems
involving division of fractions by fractions,
e.g., by using visual fraction models and
equations to represent the problem.
7.NS Apply and extend previous
understandings of operations with fractions
to add, subtract, multiply, and divide
rational numbers.
Adding Fractions
Using Pattern Blocks
Start Out Simple
1.
1 1
 
6 6
+
2

6
To simplify:
=

1
3
Start Out Simple
2.
1 1
 
4 4
+
2

4
To simplify:
=

1
2
Try
1 1 1
3.  
6 6 6
3 1
4.

12 12
2 4
5. 
6 6
Unlike fractions
1 1
1.  
4 2
+
=
Change to same denominator:
=
+
1

4
2

4
3

4
Cannot make
another shape
(Simplified)
1 2

2 4
Unlike fractions
1 1
2.  
6 3
+
=
+
1

6
2

6
1 2

3 6
=
Change to same denominator:
=
3

6

1
2
Try
1 1
3. 
6 4
5 1
4.

12 4
1 3
5. 
2 4
Subtracting Fractions
Using Pattern Blocks
Start Out Simple
1.
5 3
 
6 6
2

6
-
To simplify:
=

1
3
Try
11 5
2.

12 12
3 1
3. 
4 4
5 1
4. 
6 6
Unlike fractions
1 1
1.  
2 4
-
Change to same denominator:
-
=
=
1

4
Cannot make
another shape
(Simplified)
1 2

2 4
Simplifying
1.
5 2
 
6 6
3

6
-
To simplify:
=
=

1
2
Unlike fractions
1 1
2.  
3 6
-
Change to same denominator:
=
-
2

6
1

6
1

6
=
1 2

3 6
Try
10 1
3.

12 4
3 1
4. 
4 2
1 1
5. 
3 4
Multiplying Fractions
Using Pattern Blocks
Multiplying Fractions
½ X ½ means ½ of ½ which
means: one of two equal parts of
one-half.
Pictorially:
One-half
½ of one-half
1 1 1 1
of    ?
2 2 2 2
1
4
Multiplying Fractions
1/3 X ½ means 1/3 of ½ which
means: one of two equal parts of
one-half.
Pictorially:
One-half
1/3 of one-half
1 1 1 1
of    ?
3 2 3 2
1
6
Try
1 1
3. X
6 2
1 1
4. X
4 3
2 1
5. X
3 2
Dividing Fractions
Using Pattern Blocks
Dividing Fractions
6  2 can mean:
In 6, there are how many groups of 2?

There are 3 groups of 2 in 6,
so 6  2 = 3
This is important for us when
dividing fractions.
Dividing Fractions
1
1
means:
2
In one whole, there are how many halves?
Pictorially:
needs how many
Two
therefore 1 
cover a
1
2
2
to cover it?
Dividing Fractions
1 1

2 6
means:
In one-half, there are how many sixths?
Pictorially:
needs how many
Three
therefore
cover a
1 1
 3
2 6
to cover it?
Dividing Fractions
2 1

means:
3 6
In two-thirds, there are how many sixths?
Pictorially:
needs how many
Four
therefore
cover
2 1
 4
3 6
to cover it?
Try-- handout
Try-- handout
Try-- handout
Try-- handout
Dividing Fractions
1 1

2 3
means:
In one-half, there are how many thirds?
Pictorially:
needs how many
to cover it?
We need to think of this slightly differently because it is
more than 1 but less than 2
Dividing Fractions
Try
3 1
2. 
4 2
5 1
3. 
6 3