what's gone wrong?

this problem posed by

jack frohlichstein (publ. dover, 1962)

mathematical fun, games and puzzles puzzle 153

free pdf version of book here

a ppt is here

oh, shouldn't they be the same answer?

decimal practice makes perfect (1)

a ppt is here

• addition and subtraction
• multiplication
• division

decimal scales

variations on a theme:

• locating points on a line
• finding end points
• generalising

what is a general rule for the end numbers?

why?

decimal multiplication targets

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

decimal multiplication and division practice

easy to check

multiplying decimals

what are

0.3 x 0.4
0.3 x 0.6
0.7 x 0.4
0.7 x 0.6 ?

and how does the diagram help?

such diagrams may well be helpful...

however, it seems that an attempt to explain decimal multiplication in terms of 'decimal places' might also benefit from an explanation involving fraction multiplication
[3 tenths x 4 tenths is 12 hundredths]

there are also possible anxieties about this model because the 'unit' shifts  from being in relation to a length (the side of the square) to a relationship with an area...

just as well that 1 x 1 is still 1...

decimal multiplication and division

what numbers go in the spaces to complete these multiplication tables?

(intended to be done without a calculator)

to extend/develop this task:
find the sum of the four numbers in the main part (not the outside) of the multiplication grid for each of the questions

and try to explain the result
or give further examples

smallish numbers