Four Investigations and a Question

Enjoy our four consecutive days of investigation lessons, plus one BIG question: “Why the investigations? Are they worth the time invested?”

  1.  Party Seating. The PowerPoint is here , the worksheet is here, and  here  are answers and teacher feedback. A wonderful low-floor, high-ceiling activity. Everyone has access, since one method of solution is counting. Everyone began to see patterns quickly and found shortcuts, which is what math IS, we think!    Source:
  2. Knights of King Arthur’s Court.  The slidesworksheet and  answers   are here.  Again, the activity is accessible to all because students can draw circles of increasing sizes and count.  We started with 8 volunteer students standing in a circle, and counted them off – “Stay, Go, Stay, Go, …” until only one student is left. Then we tried it with 5 volunteers. After that, students can draw the circles and count off themselves. Again, most students noticed a pattern quickly, and had great questions about WHY that pattern occurs. Source:  Ask Dr. Math
  3. Four Fours. Here is the PowerPoint.           Source;  Youcubed.  “Soon after setting the challenge the board area becomes full of students putting up their solutions, then returning to their seat to look for more. For students, it is a very safe and non threatening activity. It builds number sense and is a fun challenge. This task is also a really nice way of helping students become comfortable sharing their work in front of the class.” (from YouCubed) Here are 3 photos
  4. Folding Fraction Strips.  Look at our post from last year about this activity:  WEEK ONE – Activity Three – Fraction Strips.   This activity always takes longer and is more difficult than we expect. The folding (especially of thirds) is inexact and challenging. We will use the strips next week for the game “Capture the Circle”.


And Now the Question:  Are Investigations Worth the Time?  If So, Why?

Over and over, through our combined decades of teaching, we have witnessed the  COLOSSAL importance of AFFECT in mathematics instruction. How students feel about their own abilities more closely predicts their learning outcomes than any other factor. We’re thrilled that university research is now backing up our own classroom observations.  Here  is a link from Stanford Medical School subtitled “A positive attitude toward math boosts the brain’s memory center and predicts math performance independent of factors such as a child’s IQ.”

We feel that a child who comes into our class thinking “I stink at math. I’m dumb. I can’t wait to get out of here. Can I get a bathroom pass? Can I copy? Can I hide? Can I become invisible?” might as well be outside at recess. At least they’d get exercise.

Any learning they do pick up half-willingly will usually be shallow, disconnected and fragile. Forgotten soon, misfiled, irretrievable.

Therefore, any time spent in September improving confidence is repaid tenfold later. So we choose investigations that build that confidence. Investigations that are accessible to all students. Investigations complex enough to make fifth graders feel smart.

We believe every human brain comes with 3 basic characteristics:

  • A love of patterns
  • A love of stories
  • A fascination with the mystery of the world around us

The MATH classroom can hold a WEALTH of all that which humans find most satisfying!  Let’s aim for that truth.





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