A maths game using areas of rectangles

All my Primary-age pupils played this game this week. I originally created it three years ago but this week I made some pre-marked hundred squares just to save a bit of paper – by printing them smaller than 1cm squared, you can fit 6 on a page.

Screen Shot 2016-03-03 at 11.37.34You will need:

The winner will be the person who scores most small squares.

Do you remember how many small squares are in the 10×10 game board? That’s the same as saying “what’s the area in square centimetres”?

When it’s your turn, throw the 2 dice. I’m going to show you my moves in a particular game:

I could have drawn my rectangle anywhere, but it helps later if you try to keep things in the corners…..

I’ve drawn in two rectangles now and I must decide where to put this next throw of 1×5. Where would you put it?

Some of you preferred to count up every single square to decide the score after your turn, some of you counted them in lines (say, counting a 4×5 rectangle as 5…10….15…20 ) and some of you just said “4×5, that’s 20”. I think that depends how good your memory for tables is.

Here’s my board when I hit my first problem…

I can’t find anywhere to put this 5×6 throw, so it’s my first of three strikes…

I was lucky enough to throw a series of small numbers next, and build up my scores a bit…

But this throw was my second strike…

And this one was my third. I’m out, so I add up my score. What did I get? Here’s my opponent’s board. Who won?

Is there an easier way to work out your score?

What is the highest possible score for one rectangle?

Oh, and, what was the jam jar for? I got a bit fed up with some of you rolling the dice SO hard they rolled onto the floor, but one of you suggested we roll them INSIDE THE JAM JAR! Great idea! Well Done! A quick roll and it’s easy to see your score through the glass. Shake gently though….

PS for a whole class game, the teacher uses 2 big foam dice, and the winners are pupils who can place the rectangles in a logical way.

Chinese Multiplication, or how to multiply together VERY large numbers!

Chinese multiplication has been explained many times in many places on the Internet. This is a quick recap of the way I do it….

The kids I’ve taught, especially the more able ones, really like this way of multiplying numbers because it’s SOOOO easy to build up to very large numbers.

Within 20 minutes, a group of ambitious mathematicians has commandeered the class whiteboard and tried to do an ENORMOUS sum like 185936296722 x 15436796 and got an answer. This gives the teacher a problem. How can the sum be checked?  Calculators and EXCEL will round the answer to only 10 or so significant figures, which is pretty hopeless for checking the work.

Here is a link to an EXCEL spreadsheet  that will do these HUGE sums so you can check pupils’ (or your own) work.

The extra challenge that these interpid mathematicians give themselves, of course, is how to add together huge long lists of numbers. Here’s an example of one of the additions in the sum mentioned above:

One of the additions needed to do the sum...
One of the additions needed to do the sum…

The student has to add 4,1,7,5,2,1,2,5,7,1,4,2,5,1,2 and 0. It’s tough to add all that without errors, so encourage them to look for TENS, and cross them out, “carrying” them into the next column…

They could make ten from the 4,1 and 5, then another from 7,2 and 1, and anotherfrom 1,4 and 5. Cross them out neatly and there’s not really much more to add! The nice thing is you can tackly any column you like, in any order, which is great for mathematicians who don’t know their right from their left! (except of course the TENS have to move left!).

Most of the numbers made TENS! Each ten has been done in a distinct colour for clarity.
Most of the numbers made TENS! Each ten has been done in a distinct colour for clarity.
About half the adding done now...
About half the adding done now…

Once this TEN-hunting is complete, the final pass is to add up any digits that are left.

Most of the adding done now...
Most of the adding done now…
completed sum
Completed! The answer!

Finally, some thoughts about the process of learning Chinese Multiplication:

  • It’s great practice USING TABLES
  • It’s great practice at ADDING long lists of numbers
  • Pupils will normally self-differentiate and settle with the size of sum that suits them. For GCSE only a 2-digit by 3-digit sum is normally required (which seems a shame really!)
  • They take time to learn how to draw the grids, and need to practice regularly. Sadly this pus some schools off teaching the method as “THE” method of multiplication. It is the most powerful, and handles decimals really easily too:
Decimal points in Chinese Multiplication
Decimal points in Chinese Multiplication

Cancelling Fractions. A game for 2-4 players.


You will need:

Slow Rounds:

  • Play like this while they get used to the game.
  • Give out a card, read the fraction, ask them if they have it on their board? (Probably they will say no)
  • Ask which table both those numbers are found in? For example, if the card says 15/20, those two numbers are both in the 5 times table. Ask what position the 15 is in (answer, 3). What position is the 20 in (answer, 4). So, 15/20 is WORTH 3/4.
  • The pupil covers 3/4 with the card.
  • Take in turns until someone has 4 covered (or all covered, depending what pace you want).

Fast Rounds:

  • Play like this once they are really confident and getting bored with the pace…
  • Hand out one card each, fast, they grab it and place it on their board. Commiserate if it is a duplicate that they don’t need “Oh no, not another one EQUIVALENT to 3/4!”. If they are pleased, celebrate “Great, you needed 2/9”. This gets the correct terminology bedded in, and also they see that fractions that are equivalent to each other generally LOOK really different.
  • If 2 pupils draw (covering 4 fractions) have a tie break round with another card. At this pace, it works well to aim to cover all the factions up.
  • If someone goes “bingo” check their board to make sure all the cards are in the right place.

Super Fast Round:

  • Give each pupil 5 cards and see if anyone can go bingo.

Bonus level thinking:

  • “You need one more card. What do you want to get?” Suppose it is 2/5. Point out they need a fraction made up of a “position 2, position 5” pair. Placing one finger in each position explains this nicely. It’s very gratifying if they get what they want straight away!
  • Get the pupils to highlight the odd numbers before they start. Think about whether a fraction’s numbers are odd or even, or one of each, and which tables they should be looking in. Being hazy about the importance of odds and evens is common amongst struggling mathematicians.