Visual Patterns and Functions: How Input/Output Tables Belong in 1st Grade

Two of Everything

The book that made kids think

As part of the #MTBoS 3rd mission we needed to choose a collaborative website and I want to give a huge shout out to @fawnpnguyen and  I have used her website in the past for developing k-2 lessons and if you haven’t visited to stretch your own thinking as an K-5 educator it might be time. What’s great about her website is the accessibility that students have towards generalizing a pattern because of its concrete”ness”. When patterns are built with materials and not on paper, students are able to fearlessly test a hypothesis or the extension of patterns (AND MAKE CHANGES) without the anxiety of being wrong.  I have found that using manipulatives when engaging students in patterns tends to break down the feelings of being mathematically incompetent….and that is wicked awesome!

Magic Pot Task Cards

Task Cards: What’s the rule?

CCSS asks that students in 1st grade to demonstrate fluency for addition and subtraction using multiple part-whole additive strategies CCSS.Math.Content.1.OA.C.6.  It would be really easy to “teach” students how to make a ten or the doubles  minus 1 strategy, but then we know they would forget the strategy by the time they got off the bus.  I always try to expose students to situations where they can visually see the relationships between numbers (and remember it).

We used the book Two of Everything by Lil Toy Hong to set the context which is a story about an old couple that finds a magic pot and everything that goes into the pot is doubled.  Although the book is about doubling in particular, this task asks students to focus on the number relationships between what goes in the pot, and what comes out.  Each task card had an underlying strategy that students had to identify and find the rule.

Doubles Minus 1

Doubles Minus 1

I’ve learned to never underestimate the power of the big brain in the little body!!!  I really like the way this task (not me) was able to engage students in the Standards for Mathematical Practice.  What worked extremely well was that as students created rules for the Magic Pot they immediately tested their generalization using manipulatives.  Now don’t get me wrong here, every student in the class was not an instant Rock Star when it came to input/output tables.  In fact, there were only 2 students that were able to find the rule for Task Card 4 (see above).  There was a group of students that REALLY struggled  when it came to identifying the rule but I was super stoked to see that every student was engaged for the entire lesson.  I didn’t expect students to write an expression to represent the pattern but I did expect students to verbalize and justify their rule and about a third of the students didn’t disappoint.  Was it the best lesson I’ve ever taught…heck no!!!!  Probably not even in the top 73 lessons!!! At times it was frustrating but I learned a lot about our students and their thinking and reasoning mathematically…because I went “there” with input /output tables for strategy development.

There is no “upper grades” or” lower grade” maths!!! I keep reminding myself that math is on a continuum of learning and depending on wherever our students are, it is our job to engage them on that continuum. So why not introduce input/out tables in 1st grade?  As @mattBgomez says “Be Brave!”

About gfletchy

K-8 math consumer trying to listen and learn each day. Stay thirsty my friends!
This entry was posted in Fact Fluency, Strategy Development and tagged , , . Bookmark the permalink.

8 Responses to Visual Patterns and Functions: How Input/Output Tables Belong in 1st Grade

  1. Cleargrace says:

    I love the idea of there being no upper or lower math! These cards would have engaged my 10th graders, and given them a new way of looking at number combinations!
    These are strategies every grade should consider using for those students in the gap between starting with common core lessons and already being in HS with common core assessments.

    • gfletchy says:

      Absolutely Cleargrace! Sadly we are a nation that are the masters of finger counting and counting on. Hopefully CCSS and its focus on computational fluency and strategy development makes numbers more accessible for students. I know this has been on MS and HS teachers wish list for years!!! We have been focusing on strategy development for the past 3 years in my county and the improvement is amazing (for both teaching and learning).
      Thanks for the comment!

  2. Jennifer says:

    While I am now in middle school (where students have trouble with input/output as well), I spent several years in first grade. I was always trying to expose them to “higher” math because I knew they could think just like older students and they always came up with insightful ideas involving patterns and connections. Thank you for recognizing that first graders can do math too!

  3. Fawn Nguyen says:

    Yay!!! Thank you so much, Graham, for writing this up. It’s always wonderful for me to learn how is used in the classroom, and it’s extra awesome that you’re using it with first graders!! Math is the study of patterns, after all. I have to check out “Two of Everything.”

    • gfletchy says:

      Thanks for the comment! I love taking what’s going on in big people math and making the connection to little people. Their thinking is so simple and unobstructed by rules and algorithms. Thanks for running the collaborative think tank ( and making us all a little smarter. Keep sharing your brain because it is very much appreciated!

  4. Interesting! I honestly have no idea what I would or wouldn’t do with first graders; I don’t know any, and teach high school. I do know that some students have more difficulty working a rule across a table, as opposed to patterning going down. I like the jump from 3 to 5, to subtly encourage the horizontal thinking. Also, make sure to give yourself some credit for doing the task, being observant, and pushing through frustration! Many ways to define a “top” lesson.
    Incidentally, speaking of being “Brave”, seen that song by Sara Bareilles? I rather like it.

  5. mathybeagle says:

    I used visual patterns with college algebra students. Reading your blog post solidified the awesomeness of this website in my mind. The fact that I can apply it with college algebra students and you can apply it with first graders is amazingly awesome. I’m fascinated, completely.

    • gfletchy says:

      @mathytans and mathybeagle,
      Thanks for the kind words!!!
      The brave one is my wife who teaches kindergarten. She has basically turned her class into a testing laboratory for ideas and concepts like this. We are always trying to come up with ways to push the boundaries and limits. She definitely doesn’t “run” the traditional kindergarten classroom. Many of her students can’t count in August but come May they are able to complete tasks such as the Magic Pot.

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