Develop understanding of fractions as numbers 


3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 

Sharing of a whole when partitioned including parts of a whole, models, and number lines.


Students will have an understanding that a fraction represents a part of a whole. A fraction is composed of pieces of a unit fraction, which has a numerator of 1. For example, 3/5 is composed of 3 equal pieces that each have a size of 1/5. These 3 pieces are the same size. 


Kansas Association of Teachers of Mathematics (KATM) Flipbooks.

Questions or to send feedback: Retrieved from Math Flipbooks.

Expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8

Parts of a whole


Identify and define the numerator and denominator. Given this information students should have plenty of practice identifying and reasoning with this vocabulary. For example, if I have a pie sliced into 6ths, and I have 4 friends. How much of the pie does each friend get? Each friend gets a piece of the whole which is 1/6. 


Understand that fractional parts are equal or “fair sharing”. 


Allow students to identify and represent fractions in a variety of context


Ex. - Choose the picture that shows ¼ shaded

Be sure to use a variety of models.

Start with circles (pizza and pies) and move on to other shapes partitioned differently.


How many friends can share this pizza equally? 8


How would you represent 3 pieces of this whole pizza? 3/8


The computer club has 4 people in it and the chess club has 8 people. Each club gets to order 1 pizza. Which club members get a bigger piece? Explain how you know. Computer club, less people to share equally with therefor the pieces are bigger


Circles, rectangles and squares

How many pieces is this whole broken up into? 9


What is the unit fraction? 1/9


How many one-ninths are in this model? 9

What fraction of the rectangle is shaded? 1/2


Can you draw the square a different way to show the shaded


Continue to build the understanding of a unit fraction.


Uncle Tony’s Pizza Place

½ of a 16 inch Pizza

½ of a 10 inch pizza

Both Pizza pictures represent 1/2 , does that mean they are the same size? Explain why or why not.


Importance of defining the whole


How could this picture represent 3/2 or ¾?

It is important to define the whole, numerators and denominators.


Number Lines

How many equal pieces are represented on this number line between 0 and 1? 6


Let’s say I had to fill a bag of candy almost to the top. Plot a point on the number line that would represent that situation? Ex. 5/6 plotted on a number line 

For additional information go to Achieve the Core

Coherence and Connections: Need to Know

Grade Below





Grade Level





Grade Above


Statement Key

Evidence Statement Text





Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b

i) Tasks do not involve the number line.




Understand a fraction 1/as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

i) Grade 3 expectations in this domation are limited to fractions with denominators 2, 3, 4, 6 and 8.  (Footnote in CCSS, p. 24)

ii) For fractions equal to a whole number, values are limited to 0, 1, 2, 3, 4, and 5.

3, 6, 5



Distinguish correct explanation/reasoning from that which is flawed, and - if there is a a flaw in the argument - present corrected reasoning.  (For example, some flawed 'student' reasoning is presented and the task is to correct and improve it.)

Content Scope: Knowledge and skills articulated in 3.NF.3b, 3.NF.3d

i) Tasks do not involve the number line.




In a contextual situation involving a whole number and two fractions not equal to a whole number, represent all three numbers on a number line diagram then choose the fraction closest in value to the whole number.

i) Whole numbers are limited to 0, 1, 2, 3, 4, 5.  Fraction denominators are limited to 2, 3, 4.

2, 4, 5

Illinois Assessment of Readiness Mathematics Evidence Tables. 

Retrieved from:


Grade 3 is the first time students are being introduced to fractions. In 3.NF.1 students are building the foundation of fraction sense and building on the idea that a fraction is part of a defined whole. 


Numbers and Operations- Fractions is a critical area of focus according to the Standards Document pg. 21


(2) Students develop an understanding of fractions, beginning with unit fractions.

Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in

a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve

comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.


Further clarification and discussion comes from the Progressions:


The meaning of fractions In Grades 1 and 2, students use fraction language to describe partitions of shapes into equal shares.2.G.3 I n Grade 3 they start to develop the idea of a fraction more formally, building on the idea of partitioning a whole into equal parts. The whole can be a shape such as a circle or rectangle, a line segment, or any one finite entity susceptible to subdivision and measurement. In Grade 4, this is extended to include wholes that are collections of objects.


Grade 3 students start with unit fractions (fractions with numerator 1), which are formed by partitioning a whole into equal parts and taking one part, e.g., if a whole is partitioned into 4 equal parts then each part is 1/4 of the whole, and 4 copies of that part make the whole. Next, students build fractions from unit fractions, seeing the

numerator 3 of 3/4 as saying that 3/4 is the quantity you get by putting 3 of the 1/4’s together.3.NF.1 They read any fraction this way, and in particular there is no need to introduce “proper fractions" and “improper fractions" initially; 5/3 is the quantity you get by combining 5 parts together when the whole is divided into 3 equal parts. Two

important aspects of fractions provide opportunities for the mathematical practice of attending to precision (MP6):

• Specifying the whole.

• Explaining what is meant by “equal parts.”


Initially, students can use an intuitive notion of congruence (“same size and same shape”) to explain why the parts are equal, e.g., when they divide a square into four equal squares or four equal rectangles.

Students come to understand a more precise meaning for “equal parts” as “parts with equal measurements.” For example, when a ruler is partitioned into halves or quarters of an inch, they see that each subdivision has the same length. In area models they reason about the area of a shaded region to decide what fraction of the whole it represents (MP3).


The goal is for students to see unit fractions as the basic building blocks of fractions, in the same sense that the number 1 is the basic building block of the whole numbers; just as every whole number is obtained by combining a sufficient number of 1s, every fraction is obtained by combining a sufficient number of unit fractions.

This scoop is for your 3’s 

Common Core Standards Writing Team. (2013, September 19).  

Progressions for the Common Core State Standards in Mathematics(draft). 3-5 Number and Operations - FractionsTucson, AZ: Institute for Mathematics and Educations, University of Arizona.

Also check out Student Achievement Partners Coherence Map

Classroom Resources

3.NF.1 Daily Discourse

HOT Questions

1.  Draw a non-example of a shape split into thirds

    Either 3 uneven parts or divided into more or less than three parts.

2.  Explain how a triangle can represent a half or a third

    It depends on how the whole is defined



3. The point marked with a star on the number line represents 1/6. Draw the rest of the number line up to 1 whole?


4. If you had a shape with a unit fraction of 18, how many equal parts are in the whole shape?    7


5. Draw a picture of five - thirds



    Higher level – connected to 3.NF.3 comparing the sizes of fractions


6.  A classroom ordered 3 Sheet Cakes, after the party there was some leftover. Below is a description of the leftover Cake. Draw a picture that represents the left over portions of the cake. Be prepared to share a statement about the pictures you drew.


Amounts of Cake leftover:

  • 1/8 of the Chocolate cake was left

  • 1/8 of the Yellow cake was left

  • 3/8 of the Marble cake was left


Example answers:

  • There was a total of 5/8 of a cake leftover

  • The Chocolate and Yellow cake was enjoyed the most because 1/8 is the smallest amount left over compared to the other cake

  • The Marble Cake was not liked very much because 3/8 is the biggest amount of cake left over




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