Grade 4: Happy Numbers Investigation
Think of a number. Any number.  Square each digit and sum the squares.  Follow the same process with each answer and if the resulting number chain resolves to 1, then the number you started with is Happy!  E.g: 31 ..... (3 x 3) + (1 x 1) = 9 + 1 = 10....... (1 x 1) + (0 x 0) = 1.  31 is a happy number!
So, we will need to be able to square all digits up to 9.  Here is a representation of the first seven square numbers:

1,4,9,16,25,36,49,......... so, what are the 8th, 9th and 10th square numbers?
Task #1:  When will your next 5 Happy Number birthdays be?
Task #2:  What are the first two consecutive Happy Numbers?

Recording is important here because any chain leading to 1 will contain other happy numbers.  Chains that do not resolve to 1 will contain other unhappy numbers!

Grade 4 inquiry into number patterns/sequences: The Collatz Conjecture

Here is a representation of numbers 1 to 10 and their iterations following the rule (even n)/2, 

(odd n)x 3 +1

Solving word problems in Grade 2.
The following example is from a research project, 'How old is the captain?', by Christoph Selter, Vol.5 No 1, October 1984

What will the Grade 2 students make of this first question?  This totally redundant question illustrates a common problem with word problems: children often just look at the numbers and calculate.  A further issue is that publishers of maths text books presume the number ranges that are appropriate for a particular grade which can lead to assumptions being made by students as to what operation(s) should be used.  A grade 5 once said to me: 'word problems are easy! If there are single digits you always multiply; if there's a big number and a little number you always do division; if there are two big numbers it's nearly always an adding; If there are two big numbers that are close together in size it's always a subtraction; if there are two 2-digit numbers it's always multiplying.....!
Check out the textbooks!  Is this student correct?

Parents' session, December 6th

Grade 3 example:

The cube model shows the dimensions of the box, aids visualizing and points the way to the generalization/formula.  Earlier learning about arrays and area helped students make connections and have their own eureka moments when they were able to construct a rule and explain it.