Category: Games

Maths Games mostly for 2-4 players

Game of Rectangles

 

If you know a student has rather problematic times tables, and/or is not confident working with areas, then this game will help you to assess what the scope and nature of the problem is. Please read the notes about what to say before each round – if you “teach” all the strategies in advance, the game won’t be fun any more!

You Will Need

  • 20180731_1125385404856147751014693.jpg3 or 4 sheets of printed hundred squares
  • a pen each
  • 2 dice (or even better, 2 each)
  • 5 reward counters (coins? buttons? toy dogs? be imaginative)
  • A page of pre-printed tables in the student’s favourite layout.

Before you start

“Here is your new game board – by the way how many small squares is it made up of?”

Most will count the first row with their finger. If they do it without a finger, they may get to 9 or 11. If that does happen, I suggest saying “oops, I think you need to check that”. Wait until they have “10”.

Do they then count the number of rows next? Or count each square in the next row? Or count down the rows saying 10, 20, 30?

Wait until they have 100.

“So the maximum score for you will be 100.”

This step will tell you what strategy your pupil is comfortable using to find areas.

  1. If they counted all the squares from one to 100, then they still need practice doing that, and they will be doing so for the rest of the game. Concentrate on accurate strategies for counting, and celebrating correct answers. Using a pen to “dot” each counted square is usually enough. Confirming that the answers at the end of each row are 10,20,30 will avoid some of the errors.
  2. Most students can chant “10,20,30” and will be confident to do so for this task.
  3. If they count to 10 then count 10 rows and say “100”, they are demonstating that they are confident with the link between areas, repeated counting, and tables.

Round 1

“Shall I start so you know what to do when it’s your turn?”. (This avoids the need for too many words!).

“Throw the dice, and use the 2 numbers to draw a rectangle. I’ve thrown 4 and 5. 4 and a 5 give you a 4×5 rectangle. Your score would be 20 for that, because it has 20 squares inside. That’s the area of the rectangle.” (You’ve explained it without putting them on a back foot by asking them for any of the information. You are only telling them how to play, not how to win.

Take turns to throw 2 dice and draw a rectangle. If a dice goes on the floor, say “Oh, it doesn’t count if it goes on the floor. You’ll have to roll it again”. This keeps the game calm!

How do they find the areas? Always count? Count correctly? Make mistakes with counting? Sometimes say “5,10,15,20”, sometimes say “5 5s are 25”?

This observation is *key* to what they may learn today. Choose the lowest level of skill (if they can’t confidently count, don’t worry about tables!!).

You should model at and just above their secure level of skill.

  • They count badly? You use dots.
  • They count well in ones? You count in 2s and 3s
  • They know some of the tables facts? You use others
  • They look up some facts on their chart? You look up all of them to reinforce this is a good strategy.

Once one of you has “blocked” most of the board, you will both need to draw 3 lives and each time you have a dice throw you cannot draw, you will lose a life. Once you are dead, the other player continues until they are dead.

Once both are dead, total up the scores you each have.

As they add their score, notice how they do it? Are they correct? Do they want you to do it? Can they add the numbers silently in their head? Do they want to jot the sum? do they want a calculator?

If they struggle and are unhappy, be helpful. Addition can be worked on with a different game on another occasion.

Round 2

Did they sensibly squeeze the rectangles onto the board? Or spread them out and waste space? Are they ready for a “nudge” on strategy, and start being more efficient? Or are they still overwhelmed by the skills needed for this game?

If you decide to nudge, give specific advice like “why not draw this one in the corner here, to leave room for big ones later?”. This is simpler than trying to explain in an abstract way.

If you decide not to nudge, then aim to lose by spreading your rectangles out. if they make a comment, you can say “I’m trying a different approach this time to see what happens”.

Aim for an understanding of some strategies work better than others rather than one being more “right” or “clever” than another.

Winning…

The winner of each round gets a counter. Play best of 5 games.

Extension ideas

If this whole game is too easy, then draw triangles instead. These may be all right angled or for very advanced version, allow scalene triangles. Discuss areas in either case. Use a ruler!

Right Angled Triangles game
Scalene Triangles Game

Skill or no skill? A Game for 2 or 3 players

Objective:

The winner is the player who has the highest total score at the end of a round

You Need:

  • A set of playing cards
  • A dice (or one each)
  • A spare piece of card or paper you can cut up

Before You start:

  • Agree how many score cards you will have, whether you are playing skill or no skill. Make enough score cards (about 2cm square is fine)

Example of working out your score:

If your dice says “3” and your playing card says “3d+1” then your score is 10, because 3×3+1=10

Playing “No Skill”

  • Suppose you have agreed to 5 score cards each. Deal the players 5 playing cards each, which they put in a line in front of them (no cheating!!)
  • Players take turns to roll the dice, and work out the score from the card, writing that score on the next small score card they own.
  • When everyone has finished using their cards, total up the score cards and see who won.

Playing “Skill”

  • Suppose you have 5 score cards. Agree a higher number of playing cards and deal those out.
  • Each time a player rolls their dice, they can choose which playing card to use this turn, to work out their score. Once a playing card is used it is turned over. You won’t be able to use it again.
  • You will find that some cards work well with large dice scores, some work well with smaller ones. Some cards (we called them “golden cards”) work brilliantly with sixes and can score as much as 49!!!

Making the playing cards:

It’s up to you how hard you make the algebra, but here are some ideas to get you started. You need about 20 cards.

  • 2d+1
  • d²-5
  • 4-d
  • d-3
  • (d-1)²
  • 3d+1
  • …

Game – Prime Number Recognition

You will need:

2 dice and a pen and paper.

Take in turns to:

  • Throw the dice
  • From the dice, construct 2 or perhaps 3 numbers. For example, if you throw a two and a three, you can make 5, 23 and 32 (3+2=5, two followed by three is 23 and three followed by two is 32)
  • Score one point for each prime number you have made (so this example scores one for the 5 and one for the 23, scoring two points in total).
  • If you need to use a calculator, then a Casio fx-83GT PLUS can tell you whether a number is prime. This is *not* cheating – students will soon start to recognise the primes they need, rather than having to check using the calculator!

The Winner Is:

The person who has the most points.

Things to discuss:

  • Why are two even numbers always such bad news? (even+even=even and the only even prime number is two)
  • Is it possible to score three points with one throw?
  • If there is a six in your throw, what happens?

This sample space diagram may help:

Sample Space Diagram for 2 Dice

1

2

3

4

5

6

1

(1,1)

(2,1)

(3,1)

(4,1)

(5,1)

(6,1)

2

(1,2)

(2,2)

(3,2)

(4,2)

(5,2)

(6,2)

3

(1,3)

(2,3)

(3,3)

(4,3)

(5,3)

(6,3)

4

(1,4)

(2,4)

(3,4)

(4,4)

(5,4)

(6,4)

5

(1,5)

(2,5)

(3,5)

(4,5)

(5,5)

(6,5)

6

(1,6)

(2,6)

(3,6)

(4,6)

(5,6)

(6,6)

 

 

 

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.

Death by Fractions – a game for 2 or 3 players

You will need 4 dice, 2 or 3 players, pen and paper each.

Start: You have 3 lives.

Each turn. Throw all 4 dice. Choose 2 of them and make the smallest fraction you can. For example, if you throw 3,3,4 and 6, the smallest fraction is 3/6 or 1/2. That is the number of lives you have to lose (by doing a subtraction).

You are dead: When the number of lives goes to zero, or goes negative. The winner is the last man standing….

Differentiation – one or all of the players may use a scientific calculator. It’s good practice in keying in fractions!

Questions to think about during the game:

  1. Who is winning? (Which is the bigger of 2 mixed numbers)
  2. How do “borrow” when you need to do so?
  3. You will need to think about common denominators. What is the largest one you may need?
  4. If you want to play a fast round, start with only 2 lives.

Getting used to negative numbers Part I – a simple game

IMG_0328The Philosophy of the Game

The learner will be more confident with negative numbers once they can sketch a number line like this in their heads. Helping to make one by numbering the chips is a great way to get to know how the line works. During play, the colour of the card will tell you whether to move towards the losers’ end (boo, red, negative) or the winners’ end (hooray, black, positive). This emotional response to the DIFFERENCE between plus and minus is really important later, especially in algebra when kids may not see the minus signs. Confidence subtracting EVEN WHEN THE ANSWER IS NEGATIVE takes time to learn, but this game is ideal, treating the minus numbers as just more places on the number line after you count 5,4,3,2,1,0….

You will need:

  • A pack of playing cards, use just the Ace,2,3,4,5 of all 4 suits.
  • A piece of A4 paper, scissors, a ruler, sellotape and a pen
  • 2 different small counters. A 1p coin and a 5p coin would do fine.

To prepare the game board

  • Cut the paper in half legthways and sellotape the two peices together to make a long thin shape. Rule a line across it and mark on it a number line with 0 in the centre, the negative numbers on the left, and the positive numbers going right. The scale must be regular (use the ruler to mark out 2cm-apart chips). It should look like this:negative number game
  • Place both the counters on the 0 (one below and one above, will avoid collsisions!

To Play:

  • The BLACK cards are positive values 1 to 5, and the reds are negative 1 to 5.
  • Shuffle the cards and take turns to choose one, moving either right (black) or left (red) the right number of chips.
  • The winner is the first one to go over the 11 (ie score 12), OR the loser is the one who falls off the left hand end by scoring -12.
  • If noone falls of the end, declare the winner after a timed period, say 5 minutes.
  • To make it more challenging, pick 1,2 or 3 cards each. The player decides how many cards to take and then takes them.

Next Time you play:

  • Can the child make the board? With a bit of help, perhaps?
  • Can they total their 2 or 3 cards before they move, or do they prefer to make the moves for each of their cards in turn?

Next Time:

  • Once the number line is a simple concept for them, you can play with all the cards from Ace to 10, and just keep a score on paper without counting any counters up and down the number line. Winner is the one with the highest (or maybe the least negative) score after say 15 rounds. Players can choose up to 10 cards in one round, and some interesting strategies develop for totalling their hands. More in the next post.