cryptarithms

nought is not allowed for the far left-hand (most significant) digit

probability and words

a ppt is here

the letters of words are put into a hat and one is selected at random

you might point out to students that a probability scale is usually horizontal
but isn't for these resources so that lines can be drawn from the words to a point on the scale

you might also point out that the scale divisions can be any number you like - only the end points are fixed

it might be helpful to have dictionaries available

tables problems

triangular numbers

handshakes

a good task for the start of a new year
students can introduce themselves to each other by shaking hands (or a high five or a 'namaste')

maybe start with 5 or 6 students at the front of the room and get them to all shake hands with each other

then think about how this can be done (maybe more) systematically - to make sure everyone has shaken hands with everyone else

"and how many handshakes were there altogether?"

think of a way or ways to record or represent what they did (seeking some variety)

NCTM (USA) reflections on the 'handshake' problem

student recording

student recording

student recording

if 5 people shake hands with the 4 other people this suggests there would be 20 handshakes
why do you half this?

various methods for recording 'handshakes' can be compared

the 'handshake' numbers are triangular numbers
the rule for the number of handshakes for 'n' people is n(n - 1)/2
since for 1 person there are 0 handshakes

[note that the usually quoted rule for the nth triangular number 1, 3, 6, 10 ... is n(n + 1)/2]