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Part 1 - Step by Step

  1. InstructInstruct each group that they are only going to use one side of the box that they’ve built.

    The box represents a “whole” (like the whole cupcake). Students will work to create as many whole equivalents as they can using the VEX GO Kit beams and plates that they collected earlier. As they fit each set of pieces into the box, students should draw and write the fraction on their graph paper or Blueprint Worksheet.

    Top down view of the fractions build showing a whole equivalent in the form of eight green beams on one side, and an empty box representing one whole on the other.
    Top down view of the fractions build showing a whole equivalent in the form of six red beams on one side, and an empty box representing one whole on the other.
    Top down view of the fractions build showing a whole equivalent in the form of four orange beams on one side, and an empty box representing one whole on the other.
  2. ModelModel using a group’s setup, how this process should work.

    Hold up a group’s base box, and explain that the inside of one side of the box represents the “whole.” Put in the large white plate first, and ask what fraction that would be. On the board, draw the rectangle and write 1/1 beneath it. (Repeat this process with the 2 black plates if needed.) Explain that the students will be following the same steps using their Blueprint Worksheet.

    Blueprint worksheet example showing a drawing of one whole on the left side, labeled one over one, and another whole on the right side, labeled two over two, to show how one whole is equal to two halves. The worksheet is labeled with the words "Whole Fractions" at the bottom.
    1 Whole = 2 Halves

     

  3. FacilitateFacilitate student thinking about the mathematical connections as well as the tangible ones with questions like:

    VEX GO Beams demonstrating whole equivalents. There is a white large beam at the far left, two black large beams in the middle showing two halves, and four green large beams at the far right showing four fourths.
    How can you make a Whole Equivalent? 
    • What do you notice about the size of the pieces and the number of pieces that fit in the whole?
    • What do you notice about the numerators and denominators of your whole fractions?
    • Why do you think it was important to build the walls on the outside of the bottom beams for this activity?
    • How do you know when pieces count as a whole?
  4. RemindRemind groups that it may take them a few tries to get the pieces in and the fractions drawn and written correctly.

    Offer the last steps of the Build Instructions as support if they need further guidance about how pieces can fit together.

  5. AskAsk students to think about the why pieces need to be flat in order to accurately represent the whole.

    Or ask about what students might add or change in this build to make the activity easier for them.

Mid-Play Break & Group Discussion

As soon as every group has created at least 5 equivalents, come together for a brief conversation.

  • Let’s see how many whole equivalents we’ve made so far. Have each group share one of theirs, and indicate them on the board as they are shared. There are eight total possibilities with materials provided.
  • Now, looking at all of these fractions, what do you notice about them? What about the numerators and denominators? Are there any patterns you see?
  • Besides looking at the numbers, what other pattern can I see with my VEX GO pieces?
  • What if I had two fractions with different numerators and denominators, how could I tell if they were equal?

Part 2 - Step by Step

  1. InstructInstruct students that this time, they will be using BOTH sides of their base box.
    Fractions Build with two green large beams side by side at the top of the left side box and a black large beam underneath. There are red boxes highlighting the two green beams and the black large beam. There is a red equals sign between the two boxes of the fractions build. On the right side there is one large white beam, with two red callout boxes around the top and bottom halves of the white beam, to show equivalence.

    Each side still represents 1 whole, but now, they are going to try to see how many equivalent fractions their groups can make, using the same sets of VEX GO pieces. They should draw and write their fractions on graph or Blueprint Worksheet, Play Part 1.

  2. ModelModel using a group’s setup, what this would look like.

    Place two green large beams into the right side of the base box and ask what fraction that represents. Then add one black large beam to the other side of the base box, and ask, are these equivalent? Lastly, model writing and drawing the fractions on the board (½ = 2/4).

    Blueprint worksheet with example drawing of a black large beam labeled with one-half and two green large beams labeled with two-fourths to show that one half equals two fourths. The bottom of the worksheet is labeled, "Equivalent fractions".
    1/2 = 2/4

     

  3. FacilitateFacilitate student thinking about the mathematical connections as well as the tangible ones with questions like:

    On the right, two large green beams with a red callout box around them are shown above one large black beam with a callout box around it. On the right, a large white beam is divided into two equal parts with red callout boxes that are identical to the ones on the left. A red equals sign is between the two sets of beams to show equivalent fractions Are equivalent sizes in the Fractions Build.
    Equivalent Fractions Are Equivalent Sizes
    • What do you notice about the size of the pieces and the fraction they represent?
    • What similarities are there between equivalent fractions?
    • Do you notice any patterns that might help you find the next set?
  4. RemindRemind groups that they may have to try multiple combinations of pieces in order to create equal fractions, and this trial and error is ok.

    Be sure that all members of the group are taking turns doing each part of the process to ensure that everyone understands the connections.

  5. AskAsk students questions to help them move from straight guessing and checking to more effective predictions, like:
    • What do you notice about how the pieces fit together?
    • What would happen if you doubled the denominator in the fraction ½?

    Encourage students to share these “tips and tricks” with their group as they find them.

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