median
don steward
maths teaching 10 ~ 16

Sunday, 29 March 2015

squares nth term

for Fawn




















students form a growing sequence for each question and maybe describe it
(what will e.g. the 11th or 23rd shape in the pattern look like?)

they can then find an nth term rule
and hopefully justify this in relation to the diagram

can they make a rectangle out of the squares for each question?
and form an alternative generalisation?

how are the two generalisations the same?

Monday, 23 March 2015

Sunday, 22 March 2015

the stories of 6

what is the story of 6?
how do you undo it?

this says that 6
say it, backwards
then try to write it



















thanks to John Mason ( e.g. PM649 Supporting Primary Mathematics 1990)

Saturday, 21 March 2015

equation forming and solving

these questions are adapted versions of questions from the UK KS2 SATs (for age 10 to 11 year olds at the end of their primary school years)




doubling and halving

these questions are adapted versions of questions from the UK KS2 SATs (for age 10 to 11 year olds at the end of their primary school years)

I guess they could be called 'pre-algebra' (in that trial and improvement is just fine) but could involve algebraic considerations (e.g. a simplification of the problem and an ability to potentially solve any similar problem)






lengths

these are adapted versions of questions from the UK KS2 SATs (for age 10 to 11 year olds at the end of their primary school years)







equations with tables practice

practice equation solving, subtracting and a particular multiplication table
neighbours could be given different sheets






Thursday, 19 March 2015

sheds

estimate how many cubic metres would fit inside these sheds
then calculate their volumes



Saturday, 14 March 2015

directed number lines

I think all maths classrooms should have a directed number line in them - above the board preferably






so I was pleased to find this do-it-yourself version at Cleave books
provided by Frank Tapson

penguins on ice

life is now complete...


Thursday, 12 March 2015

'cover up' method

it seems helpful to begin work on solving equations informally - just by thinking about them



















equations involving trickier 'take away from' and 'divide into' operations, lend themselves to being solved by staging or simplifying a given equation - sometimes called the 'cover up' method

some students prefer this technique to one involving inverse operations
maybe unfortunately





Sunday, 8 March 2015

surface area cuboidal



(assuming that the surfaces are flat)

can a cuboid be found, with a volume of 12 cubes and a smaller surface area?

how many mints in each tube?

this idea is adapted from the (excellent) test questions produced by the national KS3 Maths assessment team in the UK

[these past papers can be found on a range of websites]





Wednesday, 4 March 2015

slanted squares

NRICH's tilted squares interactivity might be helpful

this work encourages students to draw squares where the edges are not parallel to the axes
and to find and maybe justify relationships between the corner coordinates

















Sunday, 1 March 2015

what's the question?

I very much like this idea
it is, I think, a fine example of how reversing the question can often lead to a more challenging task

I gather that the idea originates from an article by Alan Bell in Maths Teaching 118
(thanks to Jo Morgan for passing on the information from Mary Pardoe)

pythagorean quadratics




















without looking up pythagorean triples to see which work

division cycling

I recently revisited this work for a session (end of Feb 2015) in Huddersfield
it was offered as a task that made long division a bit more interesting
(a long divided by a short anyway)

I'm afraid that I misinformed the attendees... all divisors do actually work

here is the main task:

 what do you notice?
















dividing by 4 is the best place to start
can you create other numbers so that when you divide by 4 they 'cycle'
[i.e. the lead digit goes to the end]

as was found in the session, you can work backwards or forwards to create these numbers

with division by 4, all the lead digits will work
there are some families: those starting with 2, 5 and 8 for example

dividing by other numbers is also interesting:



































unfortunately the lengths of the numbers for other divisors are rather long:
  • dividing by 2 needs a number that is 18 digits long
  • 3 needs 28
  • 4 needs 6
  • 5 needs 42 apart from the one example above
  • 6 needs 58 (not for the faint hearted)
  • 7 needs 22
  • 8 all need 13
  • 9 needs 44

however, these are the best tables practice ever

it's interesting, if peculiar
that there is only one six long example for dividing by 5 and the division yields the repeating block for 1/7th as a decimal...

when dividing by 4
if you chop up the six digit numbers into two blocks of 3 
and add them e.g. 205 + 128 you get some interesting results

as you do if you chop them into three blocks of 2 and add them

all reminiscent of turning fractions into decimals with prime divisors

Ed Southall has kindly posted the slides from this session on his blog

and here's the T shirt: