The Journey Begins

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“Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.”  ~Paul Lockhart, “A Mathematician’s Lament”


Our Goals in Teaching Math


1. Concrete  −> Pictorial −> Abstract. This is perhaps Singapore’s greatest contribution to math pedagogy. Based on research that goes back over a hundred years (Dewey, Bruner, Piaget, Vygotsky, Montessori, and others), Singapore validated the strength of this approach by using it to achieve top scores internationally. 

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WEEK ONE – Activity One – A Logic Problem

Activities in the first couple weeks need to draw the children in. Even (especially!) those who think they dislike math. We avoid computation, instead looking for activities that involve ambiguity, head-scratching patterns, puzzles and stories.



A puzzle has the ability to pull children into the subject of math. It appeals to a wide range of learners and can generate small feelings of success….

…read more >>a WEEK ONE act 1



WEEK ONE – Activity Two – The Lady and the Tiger


(~60 minutes)

A puzzle has the ability to pull children into the subject of math. A story even more so. Let’s combine the two.

1. The Story

We start this activity by reading a condensed version of Frank Stockton’s classic tale “The Lady or the Tiger”. 

After the story, we discuss the word “Ambiguity”, since the children are fascinated and frustrated by the fact that the author does not give an answer to the question “Did …

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WEEK TWO – Activity One – Capture the Fraction Circle

1. WARM UP –  The Fraction Template

Project the fraction template below.  Click for pdf:  fraction template

Photocopy it for students if at all possible. Our 5th graders keep one in their binder for weeks.

Ask simply : “WHAT DO YOU SEE? You can’t give a wrong answer – whatever you see is true.” Early answers might refer to colors and numbers. Accept all as true. Gradually ….

… read more… e WEEK ONE act 3

WEEK THREE – Activity One; Word Problems, + a Note on Differentiation

Our first unit is a twin unit of Fractions (mostly visual) and Word problems. We begin working with both these topics very early in the year, so that we have all year to incorporate them into every unit.  We find that word problems are an excellent way to teach fractions, too. Our next two units will be place value, patterns and multiplication, after which we will return to fractions in more depth.

This introduction to 5th grade word problems starts at the concrete, as it should.



  1. Pass out a handful of rainbow cubes (smallest base-10 blocks) or similar per child.
  2. Have each child count out 11 blocks, and set the others aside.
  3. Project or write up Problem 1.
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