Calendars
and Hundred Squares
Thanks
S
Froggatt
.
Effect :
Find a page
from a calendar.
Ask a participant to circle a square of 9 dates.
Here is an example:





1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

Now ask the participant to reveal the total of
the smallest and the largest numbers.
The participant says 26. Immediately call out all
nine dates in his square.
Ask
another participant to
choose a different set of nine dates.
This time ask the participant for
the centre date in her square.
Immediately tell her the total of all the
dates she selected!
Next
task : the
hundred square
Ask each pupil to choose a 4
x 4 square of numbers.
Ask them to call out the total of their
smallest and biggest.
Respond by telling them their first
row.
How can you do this?
Method
Do mental
algebra to start off.
If I am thinking of a number d,
what is the number
after mine?
Answer
: d
+ 1.
We
draw three grids, one for
each
trick:
d

d
+ 1

d
2d + 16. Just
divide by 2 and subtract 8 to get the first number, then count on.
+ 2

d
+ 7

d
+ 8

d
+ 9

d
+ 14

d
+ 15

d
+ 16

d
 8

d
7

d
The total is
just 9d
since all those + and
– numbers cancel out. IJust multiply the number by 9.
 6

d
1

d

d
+ 1

d
+ 6

d
+ 7

d
+ 8

d

d
+ 1

d
+ 2

d
Subtract 30,
then 3, from 2d
+ 33, then
halve the result. Once you know the first number, the first
row is
easy.
+ 3

d
+ 10

d
+ 11

d
+ 12

d
+ 13

d
+ 20

d
+ 21

d
+ 22

d
+ 23

d
+ 30

d
+ 31

d
+ 32

d
+ 33

