Charlie in Fraction City: A Math-Infused Story about Understanding Fractions as Part of a Whole

Math MileMarker® MATH TALK

The following questions are offered to help launch rich math conversations and promote fractional

understanding.  Appropriate for both full class and small group discussions, these questions provide

an overview of the important content standards and vocabulary presented in the story.  Teachers may

want to review the full educational guide which outlines how the progression of knowledge surrounding

fractions evolves in the elementary years. The Math Mile Markers® questions offered at the conclusion

of the book will prove helpful for grade level specific follow-up surrounding this topic.  The conversation

starters below offer a broad view of the topics presented in the book.  Teachers should select questions

related to the specific standard requirements of the grade level being taught.

 Page 8 & 9

Welcome to Fraction City!  What do you see in the opening page illustration that lets you know that the story ahead will be about fractions? 

 The author establishes that Charlie, the red rectangular figure and the main character, is considered a “whole” in Fraction City.  What does it mean to be whole?  Why is the idea of identifying the whole so important when talking about fractions?

 Three of the main characters are present in the opening illustration, each of them wearing a sign identifying them as a President of a Whole Club.  What do these shapes have in common?  How are they different?

 In the story the author writes “Most of the other residents of Fraction City are smaller pieces that are just itching to be a part of a whole.”    Explain what it means for a fractional piece to be part of the whole. 

Pages 10-11

You may notice that throughout the book there are tents set up to welcome new fractional pieces.  The sign for each club represented at the fair is different in size and shape.  Take note of the whole represented on top of each UFA sign.  Can all the fractional pieces that you see at the fair be part of every whole club?  Why or why not? 

 Pages 12-13

There are three fractional pieces represented alongside Ralphie Ruler.  Note that Ralphie’s body measures from 0 to 1 inch (not drawn to scale).  Do you think these 3 rectangle pieces could become members in his club?  What fractional piece might each of these rectangular pieces represent on Ralphie’s scale?

 If Ralphie’s ruler was extended to 5 inches, what possible fractions might surface? How might they be different from the fractions found from 0-1?

What are your thoughts about the pie shaped figures near Sally?  Do you think they could be members of her club? 

 Pages 14-15

The author writes “. People on the street stop him, saying “Go Charlie! You are ONE great guy!” And they mean it! The Whole Club presidents are the real thing, 100%.” 

Explain how this statement applies to the various meters presented in this picture. 

 Discuss multiple ways to represent 1 whole. 

Pages 16-17

What does it mean to be a unit fraction? 

 Explain how unit fractions can be combined to make 1 whole.  

Pages 18-19

The author writes “Charlie’s whole was a finite space that could be subdivided into a multitude of different fractional variations. As long as each piece represented a part that was of equal measurement, and fit perfectly into his finite space, they were a match.”

Discuss what is meant by these statements (equal measurement, finite space). 

Ask students if they can identify the equivalent fractions in the illustration.  Based on what they see, can they write the definition of equivalent fractions? 


The author writes that no bells went off for this group of fractional pieces.  The blue triangle embedded in this rectangle is one piece out of six pieces.  Does this blue piece represent the unit fraction ?  Explain why or why not?


The author asks why the 4 fractional pieces were not given the unit fraction name 1/4 when clearly they all looked the same and there were in fact four of them?  Can you explain your thoughts using accurate math vocabulary?


How do the  want-to-bes help introduce the math terms denominator and numerator? 

28 -31

The final illustrations in the book offer the perfect opportunity to review the math content and vocabulary that surfaced throughout the story.  What visuals support what students learned. 



On My Way to Grandma's House:

A Math-Infused Story About the Number Line and the Concept of Rounding.

1. Teachers should draw students' attention to the number line that repeats itself throughout the story.  

It is important to refer back to this number line and utilize the image as a visual support of the rules of rounding.

2.  Lily's house #40, and Grandma's House is #50.  Why do you think the author purposely made them live

at either end of the block with so many houses in between.

3.  On pages 26 through 28, Olivia, Rosa and Caroline talk about where on the block their own house is located

and ask what Lily might do if it started to rain at various points.  These questions are intended for student response.  

There is not answer present in the story as that is intended for student to discuss.

3.  On page 30 the author writes " At house number 45 my friends joyfully giggled" ,  Why do you think the girls were so happy to pass house 45. 

4.  Students should retell the story using larger number or decimals.  Do the river rules still work?  What number house would Lily and Grandma live at now?  What number would the Kelly's house have on the sign post? Do the "river rules still apply?"

The Math MileMarkers® stories were designed to promote "math talk" in the classroom.  

The following questions/discussion points were created to help spark rich conversations about the important math content and vocabulary embedded in our stories.  We invite teachers to add to this list of suggested conversation starters by clicking on the  "math talk" button above.  We'd love to hear how Math MileMarkers® were used

in your classroom and welcome the chance to your great ideas!  


Calm, Command, and Conquer the Curriculum®