median
don steward
mathematics teaching 10 ~ 16

Thursday, 23 November 2017

multiplication find the gaps

Tony Gardiner has produced many such questions


















these problems involve consecutive digits






 with a clue
 with another clue
using the FACT key on a calculator to help

multiplication problems

all of these should have three ways of obtaining the result

later questions ask students to find a set of 5 numbers (different to those earlier)
17 has many sets of five numbers, one set giving 4 ways to obtain the result

23 also has many sets of five numbers

learning times tables by rote

this chart was introduced to me by Roy Lindsell

these are all the products that need to be learnt, starting off by learning the product that gives the particular result

a class chanting activity, someone taps on a number (maybe the teacher) and students call out the products
done a section at a time (initially)

it needs an enlarged version stuck to the wall


done a bit at a time
getting confidence with a line then going on to another one









powerpoints need to be downloaded for the animations to work:
once the results are all there someone can tap on them and a group of students/the class call out the multiplier e.g. if it's the 5 times table and 35 is tapped on, the multiplier (to be called out) is 7

2 times table
3 times table
4 times table
5 times table
6 times table
7 times table
8 times table
9 times table
mixture

the Number Gym table trainer app is a very helpful resource (£1.99 for an ipad)
note that you have to drag the sum to the result (not tap on the result)


















times tables problems




two tangents meet on the y-axis

these tasks are my versions of a five triangles tweet (July 19th 2017)




Monday, 20 November 2017

equable shapes

'equable shapes' can be an interesting study, in these resources to practice finding areas and perimeters of well known and compound shapes, leading (possibly) to solving equations

the powerpoint is here

for rectangles, it can be beneficial to appreciate the function/relationship by looking at a full range of values (not just integer values, as is usually a restriction for equable shapes)
the values for 'a' are selected so that the corresponding values for 'b' can be calculated, maybe without a calculator
and a graph of (a, b) values plotted - or at least considered



students can check that the area and perimeter values are the same



Thursday, 16 November 2017

arithmetic sequences meets equations

this task was devised by Martin Wilson, of Harrogate

students could substitute numbers (trial and improvement)
or, if they appreciate that there are equal 'steps' between adjacent (and other) pairs of terms,
they can set up and solve an equation

for the quadratic version there may appear to be two solutions
but checking will show that only one of these works





Wednesday, 15 November 2017

quadratic nth term using factors

this is an idea for working on quadratic sequences, developed with Martin Wilson in Harrogate

we hope that students will be able to make a link between factorising numbers and factorising a quadratic expression

the powerpoint is here

the technique involves
  • transforming a given sequence by adding or subtracting a number to/from all of the terms, this number chosen so that all of the resulting terms have factor pairs
  • seeing if this provides a regular growing (or decreasing) pattern
  • if not, looking at another option
this approach might precede an algebraic one (outlined here)

three GCSE exam board questions set this summer (2017) are explored, one that can be factored without transformation




the transformation can have various forms

 factorises straight away

Sunday, 12 November 2017

'cultivating curiosity' presentation

here are the two powerpoints from my presentation 'cultivating curiosity' on Friday 10th November 2017 in Leeds
the first was pitched mainly at KS3 (around 11 to 13 year olds)
the second continues (with some repeats) my interest in generalising or at least opening out some of the new GCSE questions

Leeds 1
Leeds 2

here is an example of a long multiplication sum presented in a loop
(it needs to be downloaded for the animations to work)
start it off and it should continue playing, until you press escape

I very much enjoyed the session and hope that some of it is useful
apologies for trying to jam in quite a lot of examples on a Friday afternoon...
thanks to Liz Smith and the Leeds team for inviting me



Sunday, 29 October 2017

cancelling fractions

maybe slightly too many questions....
(not using a calculator, especially a scientific one)

















the equivalent fractions below each involve all of the digits, 1 to 9
there are several more of these for some of the fractions
reference: ben vitalis at fun with num3ers
many thanks

practice at multiplying and dividing



there is another one for a third

Tuesday, 24 October 2017

from one percentage to another

this is my version of a very fine idea by Miss Konstantine (@GiftedBA)
clearly linking (as she says) percentages to ratio 
it will be interesting to see (and hear) how various students tackle these problems

she gives a description of her lesson sequence and her sheet here




Monday, 16 October 2017

algebra problems


equation of a circle

an introduction to the equation of a circle
which can later be generalised, using pythagoras