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?

## Sunday, 29 March 2015

## Monday, 23 March 2015

## Sunday, 22 March 2015

### the stories of 6

what is the story of

how do you undo it?

this says that

say it, backwards

then try to write it

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

**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)

Labels:
linear equations,
rearrangement

## 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)

Labels:
linear equations,
pre-algebra

### 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)

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)

Labels:
pre-algebra

### 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)

Labels:
lengths,
pre-algebra

### equations with tables practice

practice equation solving, subtracting

neighbours could be given different sheets

*and*a particular multiplication tableneighbours could be given different sheets

Labels:
linear equations,
multiplication simple

## Thursday, 19 March 2015

## 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

so I was pleased to find this do-it-yourself version at Cleave books

provided by Frank Tapson

Labels:
directed number

## 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

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

Labels:
linear equations

## 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?

Labels:
surface area cuboidal

### 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]

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

Labels:
linear equations

## 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

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

Labels:
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)

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)

Labels:
ratio

### 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:

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:

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:

Labels:
division

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