Mathematics Pacing Resource Document
4.NS.3
Standard: 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using
objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures.
Teacher Background Information:

The way we write fractions with a top and a bottom number and a par between is a convention- an arbitrary agreement for how to represent fractions.
However, understanding of the convention can be clarified by giving explicit attention to the meaning of the numerator and the denominator as part of
iterating activities. Include sets that are more than one, but write them as simple or “improper” fractions and not as mixed numbers. Include at least
two pairs of sets with the same numerators such as 4/8 and 4/3. Likewise, include sets with the same denominators. After the class has counted and you
have written the fraction for at least six sets of fractional parts, pose the following questions:
 What does the denominator in a fraction tell us?
 What does the numerator in a fraction tell us?
Too often, students aren’t exposed to numbers greater than 1 (e.g., 5/2 of 4 ¼), so they find them confusing.
13
13
If you have counted fractional parts beyond a whole, your students already know how to write or . Ask students to use a model to illustrate these values
6
5
and find equivalent representations using wholes and fractions (mixed numbers). Using connecting cubes was the most effective way to help students see both
forms for recording fractions greater than 1. (Multilink cubes could also be used.)
1
12
The figure illustrates how to use connecting cubes. Students identify one cube as the unit fraction (5) for the problem ( 5 ). They count out 12 fifths and build
wholes. Conversely, they could start with the mixed number, build it, and find out how many total cubes (or fifths) were used. This procedure is an example of a
length model. Repeated experiences in building and solving these tasks will lead students to see a pattern of multiplication and division that closely resembles
the algorithm for moving between these two forms. Context can help students understand the equivalence of these two ways to record a fraction. (Van De
Walle)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.NS.3
Standard: 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using
objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Unit 9

http://www.eduplace.com/kids/mw/swfs/manip/manipulative.swf?tm=/k
ids/mw/swfs/manip/fractions_int.swf good demo site

http://mrnussbaum.com/tony-fraction-lesson-plan/-Tony Fraction’s Pizza
Shop helps students understand equivalent fractions and add fractions
with unlike denominators to form a whole. Students will demonstrate
ability to divide a whole into parts, including parts with unlike
denominators.

http://www.visualfractions.com/MixedLines/mixedlines.html - Fraction
to Mixed with Number Line Models uses number lines to demonstrate
renaming fractions from fraction form to mixed form.

http://www.visualfractions.com/MixedtoFracC/mixedtofrCircles.html
Fraction to mixed number using area models.

http://illuminations.nctm.org/Lesson.aspx?id=3985 From NCTM
Illuminations – Fun with Fractions

http://illuminations.nctm.org/Lesson.aspx?id=1728 From NCTM
Illuminations – More Fun with Fractions

http://mathforum.org/paths/fractions/edible.fractions.html Edible
Fractions on Fraction Plates
Indianapolis Public Schools

http://www.visualfractions.com/MixedLines/mixedlines.html
Converting mixed numbers or whole numbers to improper
fractions with linear models

http://www.visualfractions.com/MixedCircles/imixedcircles.html
Converting mixed number or whole numbers to improper fractions
with area models

http://nlvm.usu.edu/en/nav/frames_asid_103_g_2_t_1.html?from
=category_g_2_t_1.html National Library of Virtual Manipulatives:
Fractions – Visualizing

http://www.eduplace.com/cgibin/template/kids/hmm/practice/templates/rules.thtml?ID=hmm0
7_ep/gr4/1907&GRADE=4&UNIT=7&CHAPTER=19&LESSON=7&UNI
T_TITLE=Fractions%20 Eduplace online quiz

http://www.eduplace.com/kids/mw/swfs/manip/manipulative.swf
?tm=/kids/mw/swfs/manip/fractions_int.swf Eduplace
eManipulatives: fraction circles

http://www.visualfractions.com/MixedLines/mixedlines.html
Fraction to Mixed with Number Line Models uses number lines to
demonstrate renaming fractions from fraction form to mixed form.
Curriculum and Instruction
Mathematics Pacing Resource Document

http://www.mathsisfun.com/improper-fractions.html Fractions using
Pizza
Indianapolis Public Schools

http://www.primaryresources.co.uk/maths/docs/impropermixed.d
oc Printable cards that may be used for matching or concentration
games

http://www.mathplayground.com/fractions_mixed.html Game
that practice conversion of mixed numbers to improper fractions

http://www.ixl.com/math/grade-4/convert-between-improperfractions-and-mixed-numbers convert mixed numbers to improper
fractions and improper fractions to mixed numbers

Houghton Mifflin Eduplace online quiz

Houghton Mifflin Eduplace eManipulatives: fraction circles

Fraction Cafe

Printable cards that may be used for matching or concentration
games

http://www.mathplayground.com/fractions_mixed.html Game
that practice conversion of mixed numbers to improper fractions
Curriculum and Instruction
Mathematics Pacing Resource Document
4.NS.3
Item Bank:
Which improper fraction does NOT equal a whole number? (Answer: D)
A.
4
2
6
3
B.
C.
8
4
D.
12
5
Which improper fraction does NOT equal a whole number? (Answer: D)
A.
14
2
B.
21
3
C.
28
4
D.
42
5
D.
18
6
How many thirds are in 4? (Answer: B)
A. 14 thirds = 4 whole
B. 12 thirds = 4 whole
C. 4 thirds = 4 whole
D. 3 thirds = 4 whole
Write 3
A.
13
6
4
as an improper fraction. (Answer: B)
6
B.
22
6
Indianapolis Public Schools
C.
36
6
Curriculum and Instruction
Mathematics Pacing Resource Document
Which number does NOT match the diagram shown? (Answer: C)
A.
7
4
B. 1
3
4
C.
Which of the following is equivalent to 2
A.
11
5
B.
5
7
Indianapolis Public Schools
3
2
D.
1+
3
4
1
? (Answer: A)
5
C.
5
11
D.
7
5
Curriculum and Instruction