Bigger or Smaller

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

Curriculum Goal

Junior: Number Sense

  • Compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts.
  • Represent fractions from halves to tenths using drawings, tools, and standard fractional notation, and explain the meanings of the denominator and the numerator.
Related Links
Context
  • Two to five students and the dealer (either a designated student or the instructor) sitting on the carpet, around a table, or on a video conference call.
  • Children should be familiar with fractions and recognize the parts of a fraction. 
Materials

In-person:

  • Fraction cards ()
  • Two sticky notes for each student: one with the word “Bigger” and one with “Smaller”
  • For levels 1, 2, 4, 5, a number line from 0 to 1 (drawn on a whiteboard or marked with tape) with fractions marked between.
  • Students are challenged to play levels 3 and 6 without using the number line.

Online:

  • Game file
  • Instructional Slides ()

Lesson

  • Children practice comparing fractions based on magnitude. The objective is for children to correctly predict whether their fraction is bigger or smaller than the dealer’s fraction.
  • The card deck consists of fraction cards ranging from zero to one.
  • The instructor or a designated student plays the role of the dealer. 
  • The dealer gives one card face-up to each child.
  • Then the dealer gives themself one card face-down. 
  • Children take turns predicting whether their card is bigger or smaller than the dealer’s card. 
  • Prompt the children to explain their reasoning by asking: How confident are you in your prediction? Can you explain your reasoning?
    • Encourage the children to use the number line available to them.
  • Once every child has made their decision and explained their reasoning, the dealer reveals their card.
  • Ask the children to determine whether they were correct. 
  • The children can use the number line to determine if their fraction is bigger or smaller than the dealer’s fraction.
  • Every child who made the correct prediction receives one point. 
  • There are six levels of difficulty.
  • Instructors start at Level 1 and progress to higher levels based on the children’s understanding.
    • Level 1: Fraction cards with denominators of 4. 
    • Level 2: Fraction cards with denominators of 4 and 8. 
    • Level 3: Fraction cards with denominators of 4 and 8. 
    • Level 4: Fraction cards with denominators of 4, 6, and 8
    • Level 5: Fraction cards with denominators of 2, 3, 4, 6, and 8
    • Level 6: Fraction cards with denominators of 2, 3, 4, 6, and 8
  • Reminder: For levels 1, 2, 4, and 5, the number line from 0 to 1 used to help students compare fraction magnitudes. Levels 3 and 6 do not include a number line. 

Look Fors

  • How often do the children correctly predict whether their card will be bigger or smaller than the dealer's card? What strategies do the children use to make their predictions?
  • Are the children considering various factors, such as the magnitude of their own card, before making their decision?
    • E.g., “My card is 1/8 so I think that the dealer’s card will be bigger, because 1/8 is a low card.”
  • Are the children able to accurately use the number line as a visual tool to make comparisons?
  • Are the children able to compare fractions of different denominators? 

Specific Scenarios

Example 1: Child confuses fractions  

Child: “I think 1/4 is bigger than 3/4.” 

Instructor: “Let's use the number line to compare 1/4 and 3/4. See how 1/4 is a quarter of the whole and 3/4 is 3 quarters of the whole? Which one is bigger?” (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 fractions. The closer the fraction is to 1, the bigger it is. You can use the number line to help find your fraction. Let’s try it with your card!” 

Example 3: Lack of confidence in guesses 

Child: "I’m not sure if 3/4 is smaller than your card, which is 1/2.” 

Instructor: "Let's find 1/2 on the number line first. It goes here in the middle. Now, where would 3/4 go? Right, it's closer to 1. See how 3/4 is bigger than 1/2?" (substitute fractions where necessary) 

Example 4: Unsure with how to guess  

Child: "I don’t know whether my card is going to be bigger or smaller.” 

Instructor: "Let’s take a look at your card. I see you have a 1/4 card. Is this bigger or smaller compared to the rest of the deck? Remember, in the deck, the possible bigger cards are 2/4, 3/4, and 1. The only card that could be smaller is the 0 card. Knowing that information, where do you think your card lies in comparison to the rest of the deck?” (substitute fractions where necessary) 

Example 5: Uncertainty with fraction magnitude 

Child: "Why is 1/8 smaller than 1/4 if 8 is bigger than 4?" 

Instructor: “Because when the denominator is larger, the pieces are smaller. Imagine sharing a chocolate bar with 8 people versus 4 people. Each piece of the chocolate bar is smaller when you share it with more people, because you need to make sure you have enough for everyone. When you share the same chocolate bar with 4 people, each person gets more chocolate than they would if they had to share with more people!” [use a whiteboard to draw example with explanation] (substitute fractions where necessary) 

 

 

Example 6: Equivalent fraction card 

Child: "My card is the same as yours.” 

Instructor: “Your card is the same! How do you know they are the same?” (prompt them to explain why they are equivalent, e.g., 2/4 and 1/2)  

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