Of mice and maths
This is the story of a group of quiet, clever creatures called the Maths Mice. They hide in different classrooms, coming out at night when the children have gone home. The mice head straight for the maths equipment, which they love to eat. They nibble the edges of number cards and 100 squares, making them look as if the children have handled them carelessly.
Sometimes they take some things away for a feast. Being a Maths Mouse is hard. They have to make sure they are not seen and have enough to eat.
You will need:
Cone mice (see instructions below)
How to make a Maths Mouse (or Cone Mouse)
A square of card will make two mice.
Draw a circle and cut it out.
Cut the circle in half.
Roll up the semi-circle to make a cone.
Cut out ears and add tail, whiskers and eyes. (Alternatively, you can make ears and eyes out of other materials and add them.) Fold along area shown by dotted line and stick with glue or tape.
One summer Monday evening, the Maths Mice moved into Miss Count's classroom. All the children had gone. The maths equipment was packed tidily in a large box. The mice looked at it carefully, thinking it must contain something to eat. They found some interesting things. First they found number cards, good for nibbling, but not really filling. They dug deeper, looking for more. Soon, they found a pot of small wooden cubes. These were needed for their food supply and they started to carry them to their hiding place. But they didn't take all the cubes: some were left on the floor for the teacher and children to find the next morning. Miss Count could not understand why the cubes were on the floor. She was even more puzzled because some were missing. She wondered what had happened and how many were gone.
The cube problem
On Monday afternoon there were 10 cubes in the maths box.
On Tuesday morning there were only 4 left.
How many cubes did the Maths Mice borrow?
* Instead of giving the number, show the remaining cubes.
* Change the total number of cubes andor the number left.
* Demonstrate with a "cone" mouse. Hide some cubes under the mouse. The children see the other cubes and have to work out how many the mouse has taken.
On Tuesday afternoon, everyone carefully packed the maths equipment away.
In the top of the box were some games. When darkness fell and the school was quiet, the Maths Mice came out, ready for another feast. They headed straight for the maths box, and discovered other boxes inside it. These contained special objects. They were bigger than the wooden cubes they had borrowed the day before, but the same shape. The mice wondered what they were. One mouse went up to one object, which seemed to have a face. "It's got two dots on it," he said. "No it hasn't," said the mouse opposite him.
"It's got five dots." Each mouse then moved round the corner. "Ah," said the first mouse. "I've gained a dot. Now there are three." The other mouse had lost a dot and had only four.
The mice were puzzled by the different numbers of dots on each face of the mystery objects, but they had a bigger problem. They had to get the objects back to their hiding place. Slowly, they rolled the first one over on to another face. Each time they rolled it over, one of them called out the number on the top. Soon, everyone could guess which number would come next.
They chanted the numbers like a song all the way home. Then they returned for the other object, for their food supply. Their leader said: "These will feed us for the rest of the week. We will call them 'Dinner for Mice' or 'Dice' for short."
* Ask the children to add the opposite numbers of the dice in the story or a real one and see what they notice. Once they realise that the dots on opposite faces always total seven, this can be extended to a game.
* One child holds up a large dice with one face towards the class. They have to work out the number of spots on the face nearest the child. First to answer has the next turn. How are the children working it out?
Ask the children to roll a dice along one face at a time and call out or write down the number on the top.
* Can they predict the next number?
* How many different sequences can you get by rolling a dice in this way?
On Wednesday morning, Miss Count had a mystery to solve. Why were there no dice in the games boxes when the children had put them away properly the day before? When she went to the staffroom at break, she told the other teachers about the missing dice. Her friends Miss Take, Mrs Turn and Mr Point said it had happened to them too. Little did they know the Maths Mice had moved from class to class. Miss Count was pleased that she had planned some work that did not use the dice. They were going to use a large 100 square that was pinned to the wall. At the end of the day, she took the square down and laid it on the table. It would be safe there, as it was too big to lose. The next day, the children could use it to move counters around.
The 100 square was used more than the teacher planned. That night, the mice came out and ran across the table. They were surprised to find something under their feet. The younger mice enjoyed running up and down the square.
The older mice had trouble keeping track of where they all were.
One of the mice started on square number 3 and moved up to 13, then 23. Her mother was trying to work out where she would go next. Some mice were starting from the top of the square. One started on 98 then moved down to 88. No one was sure where he went next. To add to the confusion, some mice moved across the square, forwards or backwards. One even tried to go from corner to corner but it was hard to work out where she was in the middle of her journey. After so much running, everyone was exhausted. They went home and nibbled the dice before falling asleep.
100 square problems
As you read the story, ask the children to say which square each mouse will be on next.
* Alternatively, after reading the story aloud, get children to work on problems: give them the first two numbers and tell them the mouse moves in a straight line. Which number will she land on next? Which number will she be on after three steps? Which number will she be on when she gets to the other side of the square? Ask children to make up problems like this for each other.
* Mouse steps can be demonstrated by using a cone mouse to move across a 100 square. Can your children tell you which square the mouse is on even when the number has been covered up?
When Miss Count came to school next morning, she was delighted to see that the 100 square was still there. She did not know that it had been used as a running track for the Maths Mice.
During the lesson, the children moved counters around the 100 square looking for patterns. Little did they know that they were playing the same game the mice had played late at night. Miss Count decided they would have one last day working with the square on Friday, so it was left out again on Thursday night. The mice were so pleased to see the square again that they got excited and ran across the square in different directions. This nearly led to an accident, so they decided to take turns, with only one mouse using it at a time. There was a large clock in the classroom. The big hand was on 12 and the small hand on 9. The first mouse ran around the square till she was exhausted. She was surprised to see when she stopped that the big hand was still on 12. Her friend said that the small hand was on 10.
She wondered how long she had been running. All her friends wanted turns lasting as long as hers did and 10 mice took turns before it was time to hide. They wondered where the hands on the clock were now and when the children would arrive.
* Ask someone to use a large clock to show the times mentioned in the story.
* Ask the children what time they are showing.
* How long is it between those times?
* What time will the clock say when all 10 mice have finished running?
Suppose each mouse is allowed only half an hour, or 10 minutes, in which to play on the 100 square. Fix the start and finish time then work out how long each mouse will be allowed. Change the starting time, or the number of mice.
Friday was a good day for everyone. The mice slept soundly after their night's exercise. The children were now experts at using the 100 square.
They asked their teacher what they would be doing next week. Miss Count said they would be using number cards and number fans. As she made her plans, she hoped that nobody would lose or damage the number cards. The children promised that they would look after them. She didn't think to ask the mice. The mice had had a brilliant week too. They had feasted on cubes and dice. They had run around the 100 square till they were exhausted. Now they had the weekend to investigate the cards and fans that Miss Count had got ready for next week. It would be a good weekend for them.
Number fan problems
Suppose the maths mice have eaten one of the numbers from a number fan.
* Show the children what is left of the fan (hold it by the missing number) and ask them which number has been eaten.
* Ask one child to select a number to be "eaten", but not tell the others.
They have to find out the number by asking questions such as "Is it even?"
or "Is it greater than five?"
* Agree on one or more numbers which are missing from a fan. Ask the children to come up with calculations that can still be answered using it.
They can be left open, or narrowed down to particular types of calculation.
For example: suppose 1 and 2 are missing. Ask the children for additions of single-digit numbers that can be answered with the broken fan.
* Suppose 0 is missing. Ask the children for calculations from the 5x table that can be answered with the broken fan.
Jenny Houssart works at the Centre for Mathematics Education at the Open University