triangle differences

for this task it can be helpful to use a spreadsheet

as rules are found, these can be checked by building in formulas for the cells
and then the rules can be established algebraically

positive differences

there is an Excel file for this task (called 'Deduce'), prepared by Graeme Brown, at nrich 5512

(you need to search for nrich 5512 generally, rather than on the nrich site)

percentages KS3 SATs questions

some of (what were the) KS3 maths SAT questions in England

percent 'of'

a ppt is here

it's a historical quirk that we have percentages
but they appear to have been around for a while

Wikipedia claims that they were evident in Ancient Rome,
emperor Augustus levied a tax of 1/100 on goods sold at auction

as denominations of money grew in the Middle Ages, computations with a denominator of 100 became more standard and from the late 15th century it became common for arithmetic texts to include such computations
many of these texts applied these methods to profit and loss and by the 17th century it was standard to quote interest rates in hundredths

as '% of' operators, maybe it is simplest if percentages are turned into decimals from the outset, and ongoingly...

see who can get nearest

to be done mainly mentally, with jottings

questions quite often relate to another one

percent spiders

a ppt is here

this lesson development has been advocated by Dave Hewitt  (at Loughborough University) in his 'lot for a little' considerations

maybe better done without these resources, initially at least
"given that 100% is £12
what else do we know?"

and build up a 'spider' progressively, from student suggestions

fractions as a percentage

a ppt is here

some justification for the existence of percentages
when you have different denominators it's handy to have a common measure
per cent
per one
per mille
per dozen
etc

writing gradients of hills as a percent, as they do on some road signs

the Wrekin is a landmark hill in Shropshire

this task is from Dan Walker - many thanks to him
it can take students a while to find all the options:

giving students a start on question 3

















Dan Walker's resource (different ways)
hints:
question 1
there is an obvious percentage to look at (with three options)
question 2
there is a 'common' percentage to look at

for the other sheet (question 3)
I think the answers are:
(1) 78.05%
(2) 82.69%
(3) 83.87%
(4) 80.64%

fractions to percentages

a ppt is here

for tapping on, whole class chanting (ideally in unison)
you tap on a fraction, the class calls out the equivalent percentage

given one percentage equivalent find (related) others

practice changing fractions into a percentage to do some sums

percentages to simplest fractions

a ppt is here

an opportunity to look at the difference of two squares

which looks like it might be 50%?

intended as a trial and improvement (with a calculator) exercise

with some estimation