Transcript Fourth Grade Fractions

4.NF.1 4.NF.2 4.NF.3 4.NF.4
4.NF.5 4.NF.6 4.NF.7


Extend understanding of fraction
equivalence & ordering
Build fractions from unit fractions by
applying & extending previous
understandings of operations on whole
numbers


Multiplying the numerator & denominator by
the same number changes the size of the
pieces, & how many pieces, but not the total
amount given.
You still get the same amount!
3rd Grade
Develop understanding
of fractions as
numbers
 Parts
of a set
 Parts of a whole
 Partitioning
 Fractions as numbers
5th Grade
Use equivalent
fractions as a strategy
to add & subtract
fractions
 Concrete
models
 Grid models
 Meaning +/ +/- fractions &
mixed numbers
Task #1
Jan needs ¾ of a cup of brown sugar. She only has
a 1/3 measuring cup & an ⅛ measuring cup. Which
should she use, and why?
4.NF.1
Equivalent Fractions: Recognize & Generate
Equivalent Fractions
Task #1 Answer
Jan should use the ⅛ cup because she can
make an equivalent fraction that has a
denominator of 8 by multiplying both the
numerator & denominator of ¾ by 2.
4.NF.2 Compare two fractions with different numerators
& different denominators by creating common
denominators or numerators, or by comparing to a
benchmark fraction such as ½. Recognize that
comparisons are valid only when the two fractions refer to
the same whole. Record the results of comparisons with
symbols >, <, =, and justify the conclusions, by using a
visual fraction model.





Common denominators
Common numerators
Benchmark fraction
Number lines
Use <, >, =
3rd Grade
Understand a
fraction as a
number on the
number line;
represent fractions
on a number line
diagram.
5th Grade
Solve word
problems involving
addition and
subtraction of
fractions referring
to the same whole
including cases of
unlike
denominators.
4.NF.2 Benchmark Fractions
4/4
¼
¾
1/3
2/3
½
4.NF.2 Common Denominators
Compare 4/5 & 5/6
4/5
<
5/6
24/30 < 25/30
4.NF.2 Common Numerators
Compare 4/5 & 5/6
4/5
20/25
<
<
5/6
20/24
4.NF.2 Number lines
Compare 4/5 & 5/6
0
0
1/5
1/6
2/5
2/6
3/5
3/6
4/6
4/5
5/6
5/5
1
1
6/6
4.NF.2
Comparing Fractions
Task #2
Savannah & Mia are selling boxes of fruit as a
fundraiser. Savannah has sold 9/10 of her
boxes of fruit & Mia has sold 5/8 of her boxes.
Which girl has sold a greater fraction of her
boxes of fruit?
4.NF.2
Comparing Fractions
Task #2 Answer
9/10
5/8
Savannah sold more boxes of fruit than Mia
because 9/10 > 5/8. Nine tenths has a larger
shaded portion of the whole than 5/8.
4.NF.3
Understand a fraction a/b with a >1as a sum of
fractions 1/b.
a.) Understand addition and subtraction of fractions as joining
and separating parts referring to the same whole.
b.) Decompose a fraction into a sum of fractions with the same
denominator in more than one way, recording each
decomposition by an equation. Justify decomposition, by using
a visual fraction model.
c.) Add & subtract mixed numbers with like denominators, by
replacing each mixed number with an equivalent fraction, & by
using properties of operations and the relationship between
addition and subtraction.
d.) Solve word problems involving +/- of fraction referring to
the same whole & having like denominators, by using visual
fraction models & equations to represent the problem.
3rd Grade
Explain
equivalence of
fractions in special
cases, and
compare fractions
by reasoning
about their size.
5th Grade
Interpret a fraction
as division of the
numerator by the
denominator.
4.NF.3
a.) Understand addition and subtraction of fractions as
joining and separating parts referring to the same whole.
b.) Decompose a fraction into a sum of fractions in more
than one way and writing an equation for them.
0
1/8
2/8
3/8
4/8
5/8
5/8 = 1/8 + 1/8 + 3/8
5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8
5/8 = 2/8 + 3/8
Or
5/8 - 4/8 = 1/8
5/8 – 1/8 -1/8 -1/8 -1/8 = 1/8
6/8
7/8
8/8
Numbers and Operations - Fractions
4.NF.3 Understand addition and subtraction of fractions as joining
and separating parts referring to the same whole. Decompose a
fraction. Add and subtract mixed numbers. Solve word problems
involving addition and subtraction of fractions.
4
I can add and subtract fractions and
6 mixed numbers with like
denominators and unlike denominators.
3
I can easily add and subtract fractions and mixed numbers
with like denominators.
2
Most of the time, I can add and subtract fractions and mixed
numbers with like denominators.
1
I am beginning to add and subtract fractions and mixed
numbers with like denominators.
0
I am unable to add and subtract fractions and mixed numbers
with like denominators.
4.NF.3
C.) Add & subtract mixed numbers with like
denominators, renaming the mixed number.
2 ¼ = 4/4 + 4/4 + ¼ = 9/4
0
1
0
¼
2
3
2/4
¾
4
5
6
7
8
9
10
4/4
5/4
6/4
7/4
8/4
9/4
10/4
11 12
11/4
12/4
4.NF.3.a.b.c.d
Operations with Fractions
Task #3
1. Vaughn used 4 2/3 cups of cereal & 3 1/3 cups of
marshmallows to make cereal bars. How many
more cups of cereal did Vaughn use than
marshmallows?
2. Madison ran the first part of a relay in 4 4/6
minutes. Noah ran the next part in 3 5/6 minutes.
How long did they take to run both parts of the
relay?
4.NF.3.a.b.c.d
Operations with Fractions
Task #3 Answers
1. Vaughn used 1 1/3 more cups of cereal than
marshmallows.
cereal
marshmallows
1
2
3
4
5
4.NF.3.a.b.c.d
Operations with Fractions
Task #3 Answers
2. It took Madison & Noah 8 3/6 or 8 ½ minutes to
run both parts of the relay.
Madison
Noah
4NF.4 Apply & extend previous understandings of
multiplication to multiply a fraction by a whole
number.
a.) Understand a fraction a/b as a multiple of 1/b.
Use fraction models to represent the product, record
the conclusion as an equation.
Example: 5/4 is the product of 5 x 1/4.
b.) Understand a multiple of a/b as a multiple of
1/b, and use this understanding to multiply a
fraction by a whole number. Use fraction models to
show the equation and the product.
c.) Solve word problems involving multiplication of a
fraction by a whole number. Use visual fraction
models and equations to represent the problem.
3rd Grade
5th Grade
Apply and extend
previous
understandings of
multiplication to
multiply a fraction or
whole number by a
fraction.
4.NF.4 Multiplying fractions by whole numbers.
4/1 ‘vs’ 4/4
‘VS’
4.NF.4 Multiplying fractions by whole numbers.
5x¼
Multiplication is repeated addition.
1/4 +1/4 + 1/4 + 1/4 +1/4 = 5/4
Using a number line:
0
¼
¼
¼
0
¼
2/4
¾
1
¼
¼
¼
¼
2
¼
4/4
5/4
6/4
7/4
8/4
Using Models:
One fourth
two fourths
three fourths
four fourths
five fourths
4.NF.4 Multiplying fractions by whole numbers.
Task #4
Claire is starting to run a little each day. She ran 1/5 of
a mile on all 7 days last week. Tessa and Claire each
wanted to run at least 2 miles during the week.
Did they?
4.NF.4 Multiplying fractions by whole numbers.
Task #4 Answer
Claire did not run 2 miles her first week. She ran 1 2/5
miles that week.