NVACS: Fractions, (4.NF)
Equivalency, Comparison, Addition, Subtraction, Multiplication
Concept Overview for 4th Graders
4.NF.1.2
Extend understand of fraction equivalence and ordering.
4.NF. 3.4
Build fractions from unit fractions by applying and extending previous understandings of operations
on whole numbers
4.NF.5.6.7
Understand decimal notation for fractions, and compare decimal fractions.
Critical Area of Focus:
Students develop understanding of fraction equivalence and operations with fractions. They recognize
that two different fractions can be equal (e.g. 15/9 = 5/3), and they develop methods for generating and
recognizing equivalent fractions. Students extend previous understandings about how fractions are built
from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions,
and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole
number.
Unit Fractions
Is a fraction with a numerator of a 1.
1 1 1 1
, , , ,
1
2 3 4 10 100
Equivalence
Equivalent fractions can be created by multiplying both the numerator and denominator by the same
number or by dividing a shaded region into various parts.
15
9
=
5
3
Ordering/Comparing of Fractions
Comparing fractions by creating visual fraction models or finding common denominators or numerators.
Student’s experiences should learn to draw fractions models to help them compare.
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 1
NVACS: Fractions, (4.NF)
Equivalency, Comparison, Addition, Subtraction, Multiplication
Concept Overview for 4th Graders
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 2
NVACS: Fractions, (4.NF)
Equivalency, Comparison, Addition, Subtraction, Multiplication
Concept Overview for 4th Graders
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 3
NVACS: Fractions, (4.NF)
Equivalency, Comparison, Addition, Subtraction, Multiplication
Concept Overview for 4th Graders
Build fractions from unit fractions
Students should be able to compose and decompose fractions from and into unit fractions.
Example:
2
3
1
1
1
3
3
3
= + and
1
2
3
3
+ =
Apply previous understandings of operations of whole numbers to fractions.
Word Problems can be used to help students understand adding and subtracting with fractions.
Fractions can be composed and decomposed just like whole numbers can.
Examples with whole numbers and fractions:
Decomposing:
127 = 100 +20 +7 = 60 + 60 + 5 +2
3
1
2
3
1
1
1
3=4+4+4+4+4+4+4
Composing:
50 + 50 +4 +12 = 100 + 16 = 116
1
3
1
2
+ 3= 3
Sample Word Problem:
3
1
Five Friends ordered 3 large sandwiches. John ate 4 of the sandwich. Kim ate 4. Ron ate
3
2
. Sam ate 4. How much of the sandwich is left? Explain your reasoning.
4
Answer:
3
4
of the sandwich is left.
Adding and Subtracting Mixed Numbers with Common Denominators Using Models
Susan and Maria needed 8
3
4
1
feet of ribbon to package gift baskets. Susan has 3 and Maria
8
3
has 5 feet of ribbon. How much ribbon do they have altogether? Explain why or why
8
not and use a model to explain the problem solving process and solution.
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 4
NVACS: Fractions, (4.NF)
Equivalency, Comparison, Addition, Subtraction, Multiplication
Concept Overview for 4th Graders
Multiplying a Fraction by a Whole Number Using Models
Students need to understand that the concept of repeated addition used to solve
multiplication problems of whole numbers also applies to the multiplication of a fraction by a
2
5
1
5
whole number. 3 x ( ) the value as 6 x ( )
Example Problem:
1
In a relay race, each runner runs 2of a lap. If there are 4 team members how long is the race?
Explain your answer by using a model to explain the problem solving process and solution.
______________________________________________________________________________
Decimals are introduced for the first time in fourth grade. Students should have ample opportunities to
explore and reason about the idea that a number can be represented as both a fraction and a decimal.
Decimal Notation
A fraction can be represented using decimal notation.
Example:
1
10
= .1
3
.03 = 100
Decimal Models
Circles and Rectangles partitioned into 10ths and 100ths can be used by the students to
represent decimal fractions.
90
100
=
9
47
9
10
100
100
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 5
NVACS: Fractions, (4.NF)
Equivalency, Comparison, Addition, Subtraction, Multiplication
Concept Overview for 4th Graders
Ordering/Comparing Decimals
Students need to realize that comparisons only work when they refer to the same whole. Students
should first develop the concept of fraction comparison through visual models. Some of the models
students can use are area models, decimal grids, decimal circles, number lines, and meter sticks.
Students use the symbols and words for equal to, greater than, less than, to compare while justifying
with a visual model.
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 6