in two nth term sequences with venn diagrams

a ppt is here

equations with arithmetic and quadratic sequences

these resources are from Jason Steele, Barnsley
they are based on Martin Wilson's idea

arithmetic sequences meets equations

this task was devised by Martin Wilson, of Harrogate
the powerpoint is here

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 linear equations with the unknown on both sides

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

fraction sequences

starts by counting on
fraction sequences with their 'simplest' (cancelled) form on the powerpoint
this could be done orally, with some explanations sought

then finding three missing terms and a general rule (nth term) for a fraction sequence
with (assumed) regular increases on the first resource
and a regular pattern (nth term) for the numerators and the denominators on the second resource

students might need nudging to consider equivalent fractions - hopefully not...

in the limit

puntmat posted an interesting idea (7th August 2014) involving various functions and exploring their limit as n gets very large indeed (tends to infinity)

these resources involve two of their functions plus another one

what fractions are shaded with a colour (out of the whole rectangle) at each stage?
what happens to this fraction as the shape (n) grows bigger and bigger?

all give rise to a common set (or subset) of fractions
with the same limit...
why?

the puntmat post helpfully included some animated gifs for two of these sequences:

getting a positive whole number

largely a substitution exercise
involving trial and perseverance, with some thought maybe

script:
"I'm thinking of a number and you don't know what it is (or do you...?)
here it is [write b]
whatever it is, I'll multiply it by 2 [put a 2 in front of the b]
then I'll add 5 to that
then I'll divide all this by 3 [maybe emphasise by drawing the line slowly, making sure that students are looking at the board]

what does this expression say happened to my number?

OK, all of this here [putting a hand over the expression] is 9
so what was my number?

good, now I'm interested in what other positive whole numbers that this expression could be..."

find a general form for the letters
possibly explaining why these work

find the linear rule

given 7 points that fit a (linear) rule
but 2 of them are incorrect

from an idea by David Wells

plotting them as points seems to be cheating...

however, putting them in order is eminently sensible

the powerpoint goes through a couple of examples

bike stand algebra

students can find general rules and possibly find the value for the next bike stand in the sequence
fairly realistic data - only tweaked slightly...

all are the same width and height

straight line graphs and nth terms

maths GCSE questions (mostly based on WJEC past papers)

amount of blood

the following tables are from the Welsh government numeracy sample materials (2013)

assume a linear sequence (constant difference)

cupcakes

a cupcake context for nth terms and equation solving

from the 2015 sample KS2 sample assessments