complete the quadrilateral

whereas normally e.g. a square is a kite (because it fulfills all of the properties), for this task it seems more interesting to insist on non-special cases of the various quadrilaterals
so, for this task:

• a parallelogram is not a rectangle or a square
• a kite is not a rhombus or an arrowhead
• a rhombus is not a square 
• a trapezium is not an isosceles trapezium 
• etc.

students must use the one given side as it is presented - you should not extend or shorten it

establishing that you have found the largest possible shape (in terms of area) is not that easy...

question 10 has an 'easy' answer that it is incorrect (with sides of length (root 5) and 2)!

many thanks to Fawn Nguyen for producing her own (neat and US-friendly) version of this task

see the related task from Math Pickle

my solutions have these areas
(questions 21, 22 and 24 have two congruent shapes that will work)

Schlegel diagrams

Victor Schlegel (1843 ~ 1905)

if you make one of the faces of a polyhedra 'see through' and peer in
what you see, distorted and flattened, is a 2-D representation of the solid

alternatively, you could view it as a projection:

what are these (common) 3D shapes?

which solid goes with which Schlegel diagram?
















for the 2-D (flat) representations, what is the relationship between the numbers of :

• faces (enclosed spaces)
• edges (lines)
• vertices (nodes)?

a square subtract 4

cylinder volume questions

a ppt is here

information from graphs

compare these two graphs
do they provide the same information?

sync

'sync' by Max Hattler

cumulative frequency questions

coordinates of quadrilaterals

drawing various quadrilaterals can be introduced without these resources - asking students to, for example, draw as many different parallelograms as they can with the corners on the (integer/whole) points of  a 6 by 6 grid

to gain an understanding of the relationships between corners of the various quadrilaterals might need some 'nudging' to consider the number of steps across and up from one corner (vertex) to another (i.e. a vectorial approach)

there are common relationships for all parallelograms
what distinguishes e.g. a rectangle from a parallelogram?
how can you see this from the coordinates?

central tendency

students are quickly (i.e. not given enough time to count them) shown three flocks of birds

a powerpoint is here

they record how many they think there are in each flock

they are told there are not a neat number of tens (otherwise they just guess decade numbers) and it is a competition to see who can guess the best...

student's guesses are recorded on the board (maybe they write these down as well)
then ask them to consider what an 'average' value might be for this set - a representative number, standing for the whole set
" if I wanted to tell someone one number that was, mostly, around what people guessed - what do you think I could do?"

these (student chosen) values can be compared with the actual numbers



there are several more 'averages' than are normally considered

there may be some value in introducing this wider variety before homing in on the more regularly used values

some discussion of which value is 'best' (advantages/disadvantages) might follow the calculations

the geometric mean, as with the median, is less affected by outlier values

for estimating values (e.g. the size of a crowd) it is supposedly helpful to multiply the lowest and highest estimates (that people guess for the size) and find the geometric mean of the two

for two numbers it can be established algebraically that the mean (arithmetical) is more than (or equal to) the geometric mean

start with (a - b)^2  >  0

physics in proportion

faster film rates

there is some interest in this since 'the Hobbit' has been released in versions that use 48 frames per second (fps) and 'Avatar 2' is likely to use an even faster film speed (of 60 fps)
we are used to films being at at 24 fps - the current standard 

there are opportunities to consider direct and inverse proportion relationships

basically a faster film speed allows the amount of motion blur to be reduced

from Wikipedia - showing how a shutter gate controls the amount of light allowed through to the film (or other sensor)

draw the shape