Math Grade 3: Unit 6 for APS
Representing and Comparing Fractions
January - February Important Understandings and Concepts
“I Can” Help My Student!
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I can divide shapes into parts with equal areas and show
those areas as fractions (3.G.2)
I can show and understand that fractions are equal parts
of a whole (3.NF.1)
I can label fractions on a number line because I know the
space between any two numbers can be thought of as a
whole (3.NF.2)
I can explain in words or pictures how two fractions can
sometimes be equal (3.NF.3)
I can solve telling time word problems by adding and
subtracting minutes (3.MD.1)
I can measure liquids and solids with liters, grams and
kilograms (3.MD.2)
What should my student already know before I begin…..
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Able to use fraction to describe the equal parts of a shape
Able to divide shapes into equal parts
Learning at a Glance
Third grade students actively partitioning different models of wholes into equal parts (e.g., concrete
models, fraction strips, and drawn pictorial area models on paper). They identify and count equal parts
as 1 half, 1 fourth, 1 third, 1 sixth, and 1 eighth in unit form before an introduction to the unit fraction
1/b (3.NF.1).
Words to Know
fraction: A fraction is a part or portion of a whole. It is
represented by one number written over another.
partition: To partition means to divide into parts, portions,
or shares.
numerator: The top number of a fraction is called its
numerator. It represents the number of selected parts.
denominator: The bottom number of a fraction is called its
denominator. It represents the number of parts in all.
equivalent: Equivalent means having an equal value.
intervals: An interval is the distance between one number
and the next
Bar Graph: A bar graph displays data visually either
horizontally or vertically.
Picture Graph: A picture graph is a graph or chart
representing data in which symbols represent a certain
amount. Graphs should include a title, categories, category
label, key, and data.
Scale: The intervals with which the graph is measured. In 3rd
grade the scale for both a bar graph and a picture graph
should be greater than one.
Students will compare unit fractions and learn to build non-unit fractions with unit fractions as basic
building blocks (3.NF.3d). This parallels the understanding that the number 1 is the basic building block
of whole numbers. Students practice comparing unit fractions with fraction strips, specifying the whole
and labeling fractions in relation to the number of equal parts in that whole (3.NF.3d).
Students transfer their understandings to the number line as shown on the right above. They begin by
using the interval from 0 to 1 as the whole. Continuing beyond the first interval, they partition, place,
count, and compare fractions on the number line (3.NF.2a, 3.NF.2b, 3.NF.3d). They notice that some
fractions with different units are at the exact same point on the number line and therefore equivalent.
(3.NF.3a). For example, 1/2, 2/4, 3/6, and 4/8 are equivalent fractions (3.NF.3b). Students recognize
that whole numbers can be written as fractions, as exemplified on the number lines below (3.NF.3c
As they compare fractions by reasoning about their size, students understand that fractions with the
same numerator and a larger denominator are actually smaller pieces of the whole (3.NF.3d). Students
develop a conceptual understanding for partitioning a number line into unit fractions of any size
without using a ruler.
(adapted from EngageNY_G3_Module 5)
Revised 03-18-14
Math Grade 3: Unit 6 for APS
Representing and Comparing Fractions
How Can You Help Your Student?
Interactive Learning Lessons
Your student can watch the videos alone or with you. Have your
student take notes while watching. Allow them to watch as many
times as needed.
Sample Problems and other Resources
Andrew needs to cut a piece of paper into 8 equal parts. Draw at least three pictures to
show how Andrew can cut his paper so that all the parts are equal. (the same can be done
with halves, fourth, thirds, and sixths)
Learn Zillion – Writing fractions using objects
Learn Zillion – Equivalent fractions using a number line
Learn Zillion – Unit fractions as a number
Interactive Learning Games
Area Models of Fractions video on YouTube
Nalia, Pedro, and Sherri want to share a whole candy bar fairly. Which of your fraction strips
shows how they can each get an equal part? Draw the candy bar below. Label to show who
gets which part.
Basic Fraction practice for identifying parts
Equivalent Fractions – This is a link to an applet that allows
students the opportunity to explore dividing shapes into
fractional parts (resource: Illuminations – Equivalent
Fractions)
Playing games is a wonderful way to practice skills at home in
a fun environment. Stack-n-Pack books contain several math
games covering math concepts from Kindergarten through
High School. Stack-n-Pack card games may be checked out
from your school (contact your school’s Parent Liaison) or
purchased online: Stack-n-Pack Mathematics Card Games for
K-HS
Game:
Recommended Children’s Literature
The use of children’s literature is equally important as problems and deserves some
attention. Use these books to integrate and enhance both language literacy and
mathematical literacy for an interdisciplinary connection during story time. These
books can be checked out at your local Atlanta-Fulton Public Library System
www.afplweb.com
Equivalent Fractions
Give Me Half
By Stuart J. Murphy
(oral reading on YouTube.com)
The Hershey’s Milk Chocolate Fractions Book
by Jerry Pallata
(oral reading on YouTube.com)
Revised 03-18-14