Starting the year: Logic, Fractions and Similes

Reminding ourselves of our goals:

  1. Higher achievement for all by slowing down the curriculum.
  2. Aiming for visualization and conceptual understanding over memorization.
  3. Providing challenge for fast learners, by going into more depth.
  4. Making math interesting and even fun.

1. Starting With Logic Puzzles

We started the year with several days of logic problems, much like last year  —  see our instructions from last Sept:  WEEK ONE  – A Logic Problem  and WEEK ONE – The Lady and the Tiger ,  and an early classwork/investigation: CW 9_4

Basically, you can use any logic problems – the internet is full of them. Liars and truth-tellers,  brain teasers, riddles. IMPORTANT: Try them yourself, first. They should be easy enough to do, after some head scratching. You’ll run into problems that are too hard or too easy, so caveat emptor. We use a think-pair-share approach to solving these, but other formats would work, too.

Our reasons for starting with logic:

  1. We want the kids to realize that math is about thinking, and puzzles are fun.
  2. Although we don’t require a logic table, hopefully students soon notice that these problems are easier to solve with a table of some kind. See slides 5 & 6 here. Isn’t that what math IS ? Using notes to make complex ideas easier?
  3. We look for problems in the “sweet spot” – not too easy, not too hard – that give a solid satisfaction when solved. Watch for kids saying things like  “I never knew I could do problems in math class”!

New this year: In the first week, we asked a “Simile” question:   “What is Math Like?” A few responses:

  • A rollercoaster. You’re finally starting to get  good at division, and then your teacher switches to multiplication…
  • Doing a crossword puzzle. You know it but you don’t. Your brain is scrambled. Sometimes it’s fun but sometimes it’s just hard.
  • Math is like when you have to close your eyes and eat something when you have no idea whether it’s going to be ice cream or broccoli
  • More responses here: CW 8_26


This week’s activities:

Making Fraction stripsCapture the Circle,  and Toblerone fractions.

And our first homework assignments: HW#1 ,   HW#2

After this intro, we’ll be going on to our unit on Patterns, but will keep working on fractions in the background!

What is a sandwich unit?

We  start our YEAR-LONG investigation of visual  fractions with the activities above.   We decided that – yes – fractions are the one NON-negotiable skill for graduating fifth graders. (see this post from last year). So we start drawing fractions in Sept, and then expand those models (STAYING VISUAL) to addition, subtraction and multiplication over the following months. We go on to other units as usual, but keep doing one visual fraction problem every day (like a vitamin!). More examples here and  here .  Then, finally, we transfer all that conceptual understanding to the algorithm in the late spring.  It works! Last year all our 5th graders left with at least a visual/conceptual understanding of fractions. Ask any middle school/ high school teacher —  this is huge!

Why Keep Our Fraction Work Visual For So Long??

What 9th grade teacher hasn’t heard a question like this: “Hmmm, fractions… um, is this the one where you like turn something upside down, and then just add the tops?”


Cue algebra teacher crying…

We all see that some children learn visually. We all see that some children need more time to transfer to abstract algorithms. Can’t we at least give them the vital skills around this one unit –  FRACTIONS –  that they’ll need so crucially? What would we gain by rushing through these skills?

Here an article by Jo Boaler:  Memorizers are the lowest achievers and other Common Core math surprises.  And a slide from her recent webinar, on the power of visual memory:



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