Naburn Church of England
Primary School
| Solving Mr Kenwright's Problems |
| If you like, you can record your answers and bring them into school. |
1 Odd Operations |
In class, I gave you a Theory (an idea to test): |
| This is my Theory, it is mine: |
| odd whole numbers X even numbers = even numbers |
| even X even = even |
| odd X odd = odd |
| No-one has given me a sum that breaks these rules. Can you? |
| Stephen thought of a Theory: |
| odd + even = odd |
| even + even = even |
| odd + odd = even |
| Can you find sums that fit his theory? Can you find any that don't fit? |
| Challenge: |
| Can you come up with a similar theory for subtraction (take away)? |
| - beware, it works a little differently |
| Can you come up with a similar theory for division? |
| Can you prove they are right? |
2 Dice Combinations |
| If you throw a pair of dice, you could get totals as low as (1 + 1 =) 2 or as large as (6 + 6 = ) 12. If you throw a pair of dice twenty times, you could get totals as low as (20 X 2 =) 40 or as large as (20 X 12 = ) 240. But when we did it in class, each group got between 116 and 155. Why? |
| Here are the possible throws: |
 |
| If it worked like times tables, you could get 21 combinations, but each die is different (try it with different coloured dice). |
We investigated and found that: There is only one way to score two (1 and 1) and one way to score twelve (6 and 6). There are two ways to score three: (2 and 1) and (1 and 2). There are two ways to make the three and eleven. |
| Here is another way to look at it: |
 |
or:  or:  |
| So how many possible throws are there really and what chance do you have of throwing a 7? |
| 3 Time Flies |
You start with a fly in a jar and the next day have two. Each day the number doubles. How many will you have in a week?Two weeks? After a month? |