multiplication, long by a digit

these are intended to be done without a calculator

the powerpoint is here

arithmetic practice makes perfect

a ppt is here

connected results, opportunities for spin-off

multiplication find the gaps

Tony Gardiner has produced many questions like these
the powerpoint is here

these problems involve consecutive digits

with a clue

with another clue

multiplication of big numbers

no calculators
coping with the noughts

a ppt is here

largest product from 10

find some (two or more) numbers that sum to 10
then find their product
explore...

what is the largest product that can be obtained?

1 to 9 multiplied

the idea for this (and the first question) is from nrich 1134

thinking enables the (usually unique) solutions to be found

also see: NRICH multiplication equation sudoku

warp and weft multiplication and equations

the 'warp and weft' idea presents opportunities to use paterns to establish a solution method

extend a pattern in two directions, vertically and horizontally
these are some efforts to further use such an array
(there is another post with quadratic expansions)

these tasks use an idea from John Mason with Alan Graham and Sue Johnston-Wilder in their book 'developing thinking in algebra' published by the Open University in 2005
['going with and across the grain', developed further by Anne Watson and John Mason]

it is intended to be a pattern extending exercise, with equation solving

with multiplication sums, continuing the patterns might focus attention on how to adjust one sum to obtain results for a related sum

students are asked to complete the array i.e. to replace the gaps in the boxes:

reduction multiplication

some other questions:

• what is the largest number with an odd number root? 
• what is the common property of numbers that give an odd number root and why
• how nany numbers are there with an odd root?
• what happens to numbers with a 5 in them?
• by working backwards, find all of the 33 numbers that have a root of 5

this task is presented as 'Fossils' in 1000 problems (thanks to Puntmat for locating this for me - I had forgotten)

multiplication

olde measures

you can ask various questions
e.g.
how many twips in a barleycorn?

getting three

place four digits in the boxes
multiply across and add the two products
multiply down and add the two products
how can you get a difference of 3 between these two totals?









3 has been chosen as an initial target because any four consecutive numbers give this difference (but there are plenty of other ways to obtain 3)

proving that four consecutive numbers give a difference of 3 is good practice in expanding brackets

how can you get a difference of 0?

explore how you can predict the difference from the original chosen digits without doing too much work...

students might be able to appreciate what is going on from a numerical perspective:
6 x 5 - 6 x 2 = 6 x 3
7 x 5 - 7 x 2 = 7 x 3

the '3' is present from 5 - 2
the result is 1 x 3 because 6 and 7 differ by '1'

timestable

place the digits 2 to 7 (used once only) in the circles

multiply (in pairs) to get the nine products in the table

add these nine products

how do you place the six digits to get the highest possible total?

the maximum is 182
how is this maximum achieved?

all of the row (and column) totals divide by a certain number (other than 1)
what is it and why is this?

1 to 6 multiplication

use the digits 1 to 6, once only, in the six boxes to make the multiplication sum correct

how many ways can this be done?

four operations