the clever design of these sets of 6 'cards' is due to Adrian Pinel at Chichester

this set of resources practices substitution but also a with particular multiplication table

the 'cards' do not need to be cut out

students could just link the six expressions in a line

the number at the left is the input value

the arrow should connect with the correct output value

which will be the input value for the next card

and so on...

each student could be asked to work on one set of six 'cards' e.g. set 'c' this being a different set to their neighbour

then they could work with their neighbour e.g. with the two sets 'c' and 'f' etc.

the next set of loop card resources is intended to practice substitution with simple fractions of an amount

## Wednesday, 25 February 2015

### linear relationships

there is an argument for working with relationships before equations

the variables properly vary rather than being 'as-yet-unknown' numbers - that can be found

I'm told that in Hungary the maths curriculum starts from this more general appreciation before moving to the simpler, equation, cases (Paul Andrews' various articles with Gillian Hatch when he was at Manchester Metropolitan, Cambridge, now at Stockholm e.g. for BSRLM)

when one of the variables is fixed you then have a linear equation

the intention of these tasks is that students substitute numbers to find integer pairs that fit the rules, positive integers initially

they may well notice patterns that enable other pairs to be more easily found and lead this work into negative numbers

the Cuisenaire rod resources 'rod relationships' might be one way to begin such an exploration and you might choose to use a box and a triangle (or some other symbols) in place of x and y

the variables properly vary rather than being 'as-yet-unknown' numbers - that can be found

I'm told that in Hungary the maths curriculum starts from this more general appreciation before moving to the simpler, equation, cases (Paul Andrews' various articles with Gillian Hatch when he was at Manchester Metropolitan, Cambridge, now at Stockholm e.g. for BSRLM)

when one of the variables is fixed you then have a linear equation

the intention of these tasks is that students substitute numbers to find integer pairs that fit the rules, positive integers initially

they may well notice patterns that enable other pairs to be more easily found and lead this work into negative numbers

the Cuisenaire rod resources 'rod relationships' might be one way to begin such an exploration and you might choose to use a box and a triangle (or some other symbols) in place of x and y

Labels:
linear relationships

## Thursday, 19 February 2015

### decimal multiplication targets

question 20(c) is from the 'Mathematical Education on Merseyside Challenges' (Peter Giblin and Ian Porteous)

Labels:
decimal multiplication

## Tuesday, 17 February 2015

### 4 less than a square

having obtained the two solutions, by substituting values for 'n'

the two expressions could be equated and then rearranged to form a quadratic equation = 0

the two roots can then be related to the equations

Labels:
factorising quadratics,
substitution

### breeze blocks

sculpture by Sol LeWitt

how many breeze blocks are there?

each one has dimensions in the ratio 1 : 1 : 2 (as can be ascertained from the pictures)

how many breeze blocks are there?

each one has dimensions in the ratio 1 : 1 : 2 (as can be ascertained from the pictures)

Labels:
cube numbers,
volume cuboid

## Monday, 16 February 2015

### tapping

these resources are based on Dave Hewitt's erudite work

there are youtube videos demonstrating uses of his software Grid Algebra:

it can also be used for quick number and algebra practice and is simple enough to set up

some work needs to be done on analysing why a large expression can be reduced to a much simpler one

there are youtube videos demonstrating uses of his software Grid Algebra:

- grid algebra use with younger students
- grid algebra 1 getting to know the grid
- grid algebra 2 movements
- grid algebra 3 introducing and using letters
- grid algebra 4 inverse operations and solving equations

it can also be used for quick number and algebra practice and is simple enough to set up

some work needs to be done on analysing why a large expression can be reduced to a much simpler one

Labels:
expressions,
simplification

## Sunday, 15 February 2015

### il machina

what happens with the outcomes for various input pairs, (a, b)?

why does this work?

students could make up their own 'machinas' to have the same effect

consider what happens when a = b

when 'a' is less than 'b'

not just digits

with 'b' negative

Labels:
expressions,
symbols

## Wednesday, 4 February 2015

## Tuesday, 3 February 2015

## Friday, 30 January 2015

### jumping along a line

it can be helpful to start an nth term rule with n = 0 rather than n = 1

linking the 'n' number to time, in seconds, or the number of jumps might be helpful

linking the 'n' number to time, in seconds, or the number of jumps might be helpful

Labels:
nth term

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