Boxes in Boxes

When there are boxes inside other boxes empty the inner boxes into their containers and simplify, then empty the last boxes onto the board.

These two boxes are on the board.






Results in






Results in





Results in





Emptying these onto the board results in




In mathematics

2(8 + x + 3(2x – 1)) = 2(8 + x + 6x – 3) = 2(8 – 3 + 7x) = 2(5 + 7x) = 10 + 14x


Using cards




Gives the same results as




Gives the same results as




Gives the same results as



Gives the same results as




Gives the same results as




Gives the same results as

Parentheses Problems

In the UK I should say brackets problems but I lose the alliteration.

What hand would lead to this?

Record

Maths 5(4 - 3x)

A possible hand would be

Which gives the same result as

Which gives the same result as

Which gives the same result as

Which uses less pieces.

In some cases it is easier to play with the pieces on the game board.

On the game board the result would be







Removing the pieces from the boxes gives




This is twenty black counters and fifteen negative wildboxes

This is the result of playing the hand

5(4 – 3x) can also be written as 20 – 15x

Or in mathematics 5(4 – 3x) = 20 – 15x

NOTE

20 – 15x has been written as the product of two factors 5 and 4 – 3x

More on factorising with wildcards and wildboxes later.

Wildboxes and Other Boxes

Now we have introduced boxes into the game we need to make sure the rules for using them are clear.

A wildbox may contain any number of counters, including fractions of a counter.

Wildboxes are sealed and cannot be opened.

In any game

Wildboxes with the same label must contain the same number of counters.

The number of counters in a wildbox gives the declared value for any wildcard or wildholder using the same label.

The negative of a wildbox must contain the same number of counters as the wildbox but of the opposite colour.

A pair is Zero and can be removed from the board.

Wildboxes can be put inside other boxes, with our without other counters, for example



This is done usually when many boxes of the same type are needed.





Which is recorded as 3(2x – y + 3)