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Alike or Different Game


Alignments to Content Standards: K.G.B.4

Task

Materials:

This game uses the 16 cards below.

Task_1_7b8f936cd8d764fa088ef0427c384d69

Actions:

Students in pairs take turns drawing two cards. They should name something that is the ALIKE or DIFFERENT between the two cards. Then the next two cards are drawn and the process repeats until no cards remain.

In a cooperative game, the students work together to name a property for each pair.

In a competitive game, the student who can name a property first gets to keep the cards and the student with the most cards at the end of the game wins. Since the properties may depend on the orientation of the cards, students should sit side-by-side in this version.

IM Commentary

If a more difficult game is desired the students can name two things that are alike or different.

Including blank cards allows students to draw their own shapes to add to the game.

The language students use will be informal, as is appropriate for kindergartners (ex: “This one is curvy and this one isn’t”; “This one has more corners”; “Both of them are pointy”).

Submitted to Jason Dyer to the fourth Illustrative Mathematics task writing contest.

The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. Possible secondary practice connections may be discussed but not in the same degree of detail.

This particular task is linked very intentionally to the first part of Mathematical Practice Standard 3, construct viable arguments. Students work in pairs and take turns drawing two cards. These cards have pictures of different shapes. The students are asked to describe what is similar or different between the two shapes. This type of task lays the foundation for the art of explanation leading to “critiquing the reasoning of others.” Before students can critique the reasoning of others, they must feel comfortable in supporting their own thinking with evidence.  For instance, a kindergartner might offer the explanation, “I know that the shape has straight sides and the second shape has one curvy.” The teacher can easily promote a classroom discussion on this argument by asking, “Do you agree and why?” This type of math talk in the classroom is built through collaborative problem solving and dialog.

 

Attached Resources

  • Black line master (png)
  • Solution

    Sol_1_5d114c9e28cab473e3ffb96054d3cdd4
    ALIKE: “They both have four sides.”
    Sol_2_e21c7d7352c2954d35b2e89fe185b979
    DIFFERENT: “Only one is round.”
    Sol_3_f19222c15df2cf4263699ed2a2cb5023
    DIFFERENT: “There are fewer sides on the triangle.”
    Sol_4_b7caef58bc43067a622d85d57dd50cef
    ALIKE: “They are narrower at the top.”
    (This depends on the orientation when students place the cards down.)

    There are many possible solutions for this game. Each solution a child produces should be evaluated based on their reasoning, such as "these are the alike because..." or "these are different because....".

    alyce mcmenimen says:

    almost 6 years

    Again, it is about that mathematical language. I like that you changed it to "alike", "same" would not have worked for me either. Thank you Jeff. Exposing the K students to the word "similar" is not a bad idea either. alycemac48

    Jeff Meyer says:

    over 6 years

    Is "SAME" a good term to use here, rather than "SIMILAR"?

    "SAME" is a specific term that seems to imply later geometric concepts, such as "equal" or "congruent" or "equivalent." In addition, the exercises encourage an identification that is "different" from the formal English definition of "same."

    "SIMILAR" on the other hand, while possibly too complex for a K student, is consistent with the geometry concept of "SIMILAR."

    "ALIKE" and "UNALIKE" might be another set of alternatives.

    Kristin says:

    over 6 years

    I agree that "similar" is better than "same" and changed the wording throughout the task. I'll ask one of the kindergarten teachers who contributes to the project whether we need to add anything to the commentary about supporting students who might be unfamiliar with the word "similar," although my guess is that most kindergarten teachers know how to support students in learning new words since vocabulary development is so huge at that age. It's always good to get the opinion of an expert.

    Heather_Brown says:

    about 6 years

    I disagree. I think the term "same" is less mathematical than "similar". Since this is a more informal task (kindergarten), I think "same" is better. In higher grades, "similar" is a mathematical word that has a little different meaning than it does outside math. This is something that already requires a certain amount of "unlearning" to see that "similar" means proportional figures. Encouraging this non-mathematical definition in a MATH classroom is going to make unlearning more difficult.
    The standard uses the word "similarity" maybe this is better. Say "List a similarity or a difference in the two shapes." Or "alike" and "different" is fine.

    Kristin says:

    about 6 years

    Heather--that is a great point. I changed it to "alike." Let's see what others think!