Twenty Second of February Twenty Two - A lovely Palindrome

 This quote by Ian Stewart, author of many great mathematics Books sums Up what I feel is often missing in our classrooms.

Traditionally we have focused on skills and rules without seeing the patterns and connections that are there if we look, and our students laterally and beyond the numbers.

How many of our students have been encouraged to see the patterns of opposites?  Addition is the OPPOSITE to Subtraction and vice versa.  Multiplication and Division are Opposites (as I was explaining to my granddaughter last week to help her with division)

Using 22 2 22 (the twenty second of February Twenty two) as a starter would nt it be a great investigation to find other Numerical Palindromes? You know words and numbers that read the same forwards and backwards!

I would put 22 2 22 and ask my students what do they notice about it Probably using:

THINK  (on your own no discussion)

PAIR     (discus with a partner (or small group) your findings, observations)

SHARE (share with a larger group or the class) Perhaps list the findings on the board

It would surprise me if the idea of it reading the same forward and backwards was not on the list.

Using this idea, ask the students again(Think, Pair, Share) to come up with other Palindromic Numbers.

(11, 22, 33   121, 232 .....)

Pose the question:  I wonder if a Non- Palindromic Number can be converted into a Palindrome?

Again use Think Pair Share and if no one comes up with a response suggest something along the lines of, What would happen if we reversed the numbers and added (or subtracted)?  e.g. 23  -- 32  thus 23 + 32 = 55 wow a Palindrome!!!

Now we have the basis for a longer investigation: "Can all the numbers from 1-100 be converted into Palindromes?  and secondly How Many Steps for each one? 23 + 32 = 55 is one step 58 + 85 = 143;    143 + 341 = 484  thus 2 steps.    (Be aware there may be a couple which might not convert.)

A wall chart or student chart along the lines of this could be used to record the results of the investigation.

Now what will be the next set of Patterns to be investigated? Fibonacci Numbers? Kaprekars Constant? (these are other Blog Posts.

Patterns on a Calendar? ......

Check out this website NRich palindromes