Maths Kitchen. Horrible Recipes COUNT ON US MATHS CLUB ACTIVITIES SESSION. Upper Key Stage 2. Resources. Hints and Tips

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1 COUNT ON US MATHS CLUB ACTIVITIES SESSION 07 Maths Kitchen Horrible Recipes Upper Key Stage 2 Resources Two nonsense recipes, copy of the legend of the rice and the chessboard Salt spoon/teaspoon, ladle, saucepan Measuring jugs, mass measurers Picture of salt and teaspoon (see resources) Paper folding and recording table resource for task 1 Hints and Tips You could consider some other equivalents, such as cups in bottles, smaller and larger bottles or even the number of litre bottles of water in a swimming pool (25m x 15m x 1.5m over half a million litres). MATHEMATICAL FOCUS Equivalent and comparative volumes/capacity Doubling (and its link to powers of two) Large numbers SESSION OUTLINE To Start Show the Amblongus pie recipe. Edward Lear was a poet famous for his nonsense poetry in particular. What do the children think an Amblongus is? Can they draw one? Do they think they would like Amblongus pie? Main Activity Show the class the Crumbobblious Cutlets recipe. What do they think Crumbobblious is? You might want to pick either task 1 or task 2 in the main activity so you can go into more detail with the concepts. Task 1 The recipe starts by cutting up slices of beef. Imagine you took a slice of beef and cut it in half; you would have 2 pieces. If you cut each of those pieces in half again you would have 4 pieces, and again would be 8 pieces. If you did this nine more times, how many pieces would you have? You might like to show this by folding a piece of paper and recording in a table. Please see the resources for an example. If you keep halving each piece, how far can you go? (first to pass a million). See the doubling table in the resources. Task 2 The recipe asks you to stir the mixture with a salt spoon or a soup ladle. What do you think? Are they a similar size and shape and will they be as easy as each other to use? How many salt spoons (use a teaspoon if you do not have a salt spoon) do you think you would need to fill a ladle? How many ladles might be needed to fill a saucepan? How could we work these out? Discuss some strategies as a class, considering an efficient method. Divide the class into groups and share the two tasks so that there are at least two groups working on each one to enable cross-checking. Write the results on the board. How good were our estimates?

2 COUNT ON US MATHS CLUB ACTIVITIES SESSION 07 Maths Kitchen Round-up Use the story of the Ruler (King) and the game of chess to demonstrate how continued doubling (which is the same as finding powers of 2) leads to numbers getting very big very quickly. This is called exponential growth and is a very important idea that affects our everyday lives. For example, people who borrow money and do not pay back the interest regularly end up with massive debts because what they owe grows exponentially.

3 TO MAKE AN AMBLONGUS PIE By Edward Lear Take 4 pounds (say 4 1/2 pounds) of fresh Amblongusses, and put them in a small pipkin. Cover them with water and boil them for 8 hours incessantly, after which add 2 pints of new milk, and proceed to boil for 4 hours more. When you have ascertained that the Amblongusses are quite soft, take them out and place them in a wide pan, taking care to shake them well previously. Grate some nutmeg over the surface, and cover them carefully with powdered gingerbread, curry-powder, and a sufficient quantity of Cayenne pepper. Remove the pan into the next room, and place it on the floor. Bring it back again, and let it simmer for three-quarters of an hour. Shake the pan violently till all the Amblongusses have become a pale purple colour. Then, having prepared a paste, insert the whole carefully, adding at the same time a small pigeon, 2 slices of beef, 4 cauliflowers, and any number of oysters. Watch patiently till the crust begins to rise, and add a pinch of salt from time to time. Serve up in a clean dish, and throw the whole out of the window as fast as possible.

4 TO MAKE CRUMBOBBLIOUS CUTLETS By Edward Lear Procure some strips of beef, and having cut them into the smallest possible slices, proceed to cut them still smaller, eight or perhaps nine times. When the whole is thus minced, brush it up hastily with a new clothes-brush, and stir round rapidly and capriciously with a salt-spoon or a soup ladle. Place the whole in a saucepan, and remove it to a sunny place, -- say the roof of the house if free from sparrows or other birds, -- and leave it there for about a week. At the end of that time add a little lavender, some oil of almonds, and a few herring-bones; and cover the whole with 4 gallons of clarified crumbobblious sauce, when it will be ready for use. Cut it into the shape of ordinary cutlets, and serve it up in a clean tablecloth or dinner-napkin.

5 Task 1 Support information: The recipe starts by cutting up slices of beef. Imagine you took a slice of beef and cut it in half you would have 2 pieces. If you cut each of those pieces in half again you would have 4 pieces, and again would be 8 pieces... If you did this nine more times, how many pieces would you have? o You might like to show this by folding a piece of paper and recording in a table. Please see below for an example. If you keep halving each piece, how far can you go? (First to pass a million!) See the doubling table in the resources. The children might like to draw a diagram to help them. This might be a difficult concept for your children to understand. We suggest that you begin by folding paper to represent the cuts. This can be done as shown below: 1. Cut in half (fold) creates 2 pieces. 2. Cut each piece in half again (2 folds) creates 4 pieces. 3. Cut each of the 4 pieces in half again (3 folds) creates 8 pieces. 4. Cut each of the 8 pieces in half again (4 folds) creates 16 pieces. Before you fold, ask the children to imagine where they could cut each piece in half and predict how many pieces they will have. Use the recording table provided to record the cuts and number of pieces. Eventually, it will become difficult to fold the paper to represent the cuts; the children will need to have recognised the doubling pattern by then to be able to carry on.

6 Task 1 Recording Table Number of Cuts in Half Number of Pieces Prediction Actual

7 (For teacher s eyes only) Doubling Table Written as a power of x x2x x2x2x x2x2x2x x2x2x2x2x x2x2x2x2x2x x2x2x2x2x2x2x x2x2x2x2x2x2x2x x2x2x2x2x2x2x2x2x x2x2x2x2x2x2x2x2x2x x2x2x2x2x2x2x2x2x2x2x x2x2x2x2x2x2x2x2x2x2x2x x2x2x2x2x2x2x2x2x2x2x2x2x x2x2x2x2x2x2x2x2x2x2x2x2x2x

8 The Story of Rice on the Chessboard This is a very ancient story which was first recorded in 1256 by Ibn Khallikan (an Arab scholar). The version I am going to tell you today is from India. The story goes that the ruler was so pleased with one of his wise men who invented the game of chess, which the ruler loved to play, that he offered this wise man a reward of his own choosing. The wise man, who was also a clever mathematician, told the ruler that he would like his reward in the form of rice. If the ruler would please place just one grain of rice on the first square of the chess board, double that number of grains of rice on the second square, and so on, doubling the number of grains of rice on each of the next 62 squares. This seemed to the ruler to be a very reasonable request, so he called for his servants to bring the rice. The servants brought in one sack of rice and started to pile the grains on the chessboard, but it did not take long before they would not fit on a square so the servants had to start to make small piles of rice around the room. They soon had to go and get another sack of rice and they had to keep going to get more sacks of rice as they moved into the next room and the next and the next and then, when no room was left in the palace they moved into the palace garden.

9 The ruler ran out of rice in his stores and was very shocked and dismayed. The number of grains of rice on the last square would have been: 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2... or 2 times itself 63 times. In mathematics we have a short way of writing this number. It is: 2 63 (two to the power of 63) This is roughly 18,446,744,070,000,000,000. A grain of rice is approximately 2.5mm long. The length of this number of grains of rice, placed end-to-end, is about 60,000,000,000,000 miles. It is about a quarter of a million miles to the moon so the grains of rice would go round the moon and back 240 million times. It is approximately 150 million miles to the sun so the grains of rice would go out to the sun and back 400,000 times. In fact, the grains of rice laid end to end would go as far as the nearest star (apart from our sun), Alpha Centauri, and back. It is unclear what happened to the wise man. In some stories he was beheaded because the ruler was so angry but in others the ruler promised that he and his descendants would give rice to the poor and needy. What do you think happened?

10 Tablespoon and salt spoon Tablespoon, dessert spoon, teaspoon and salt spoon