Fraction Race

Age group
  • Junior/Intermediate (Age 9 to 12)

Curriculum Goal

Junior: Number Sense

  • Represent fractions from halves to tenths using drawings, tools, and standard fractional notation, and explain the meanings of the denominator and the numerator.
  • Compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts. 
Related Links
Context
  • Online only
  • Two to five students and the teacher on a video conference call.
  • Children should be familiar with representing fractions on a number line. 
Materials
  • Online game file (, )
  • Instructional slides ()
  • Video conference capabilities

Lesson

  • The objective is for children to accurately estimate the position of a fraction on a number line. 
  • The children with the closest estimations win a point. Children can also win points if their fraction is farthest along the number line (i.e., the largest fraction in the group).  
  • The instructor assigns each child a hashmark on the board and their own number line. The instructor distributes one fraction card to each child.
  • Children take turns and estimate where the fraction on their assigned card is located on the number line by moving their hashmark to that estimated position. 
    • E.g., if a child is dealt the fraction card 1/5, they move their hashmark to where they think 1/5 lies on the number line.
  • When all children estimate the position of their fraction on the number line, the instructor asks the children to use the fraction strips on the left to check their answer.
    • The fraction strips are visual models that represent different fractions on a number line (1/3, 1/4, 1/5, and 1/6). 
  • The children with the closest estimations (up to the instructors discretion) win a point. The child with the largest fraction also wins a point.
  • There are two different levels for this game.
    • Level 1: The denominators of the fraction cards all correspond to the denominators of the fraction strips.
    • Level 2: The card deck includes fractions that are not in their simplest form. For example, children might receive the fraction card 2/8. They will need to simplify 2/8 to 1/4 to check their estimate using the fraction strips because there are no fraction strips with a denominator of 8. 

Look Fors

  • Are children able to accurately estimate the locations of different fractions on the number line? What strategies do children use to make their estimates?
  • Do children compare the magnitudes of their fractions before plotting them on the number line? Can they determine which fraction is the largest without external tools like fraction strips? 

Specific Scenarios

Example 1: Difficulty estimating fraction on number line 

Child: My fraction is 2/3, and I dont know where to put my hashmark. 

Instructor: Try to imagine splitting the number line into three equal parts. We know that 2/3 refers to two parts of this divided number line. Can you put your hashmark where you think the end of the second part is? (substitute fractions where necessary) 

Example 2: Using the number line 

Child: "I don't get how to use the number line."  

Instructor: "This number line is between 0 and 1. These marks between 0 and 1 represent different numbers that are bigger than 0 and smaller than 1. The closer the fraction is to 1, the bigger it is. You can use the number line to help find your fraction. Can you help me find 1/2 on the number line? What strategy did you use to find 1/2 on the number line? Now, lets try it with your card! Do you think your card is bigger or smaller than 1/2? 

Example 3: Uncertainty with fraction magnitude 

Child: My 1/6 card is bigger than their 1/4 card since 6 is bigger than 4. 

Instructor: Lets break that down. The denominator in a fraction indicates the number of pieces that the whole is divided into. If the number line is the whole, the fraction 1/6 would mean that the line is divided into 6 pieces. Now lets think about the fraction 翹. What does the denominator represent? It means that the whole (or number line) is divided into 4 pieces. Which fraction divides the whole into smaller pieces? [instructor can share their screen and draw the example below on the whiteboard] (substitute fractions where needed) 

Example 4: Unsimplified fraction card 

Child: "How can I use the fraction strips if my fraction is 3/9, and there are no 1/9 fraction strips? 

Instructor: Lets think about what the fraction 3/9 means. What happens when you divide the number line into 9 pieces? What do you notice when you colour in 3 of those pieces? Does it resemble another fraction that you have seen before? (substitute fractions where necessary) 

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