Appreciation First of all, I would like to say Alhamdulillah, for giving me the strength and health to do this project work. Not forgotten my parents for providing everything, such as money, to buy anything that are related to this project work and their advise, which is the most needed for this project. Internet, books, computers and all that. They also supported me and encouraged me to complete this task so that I will not procrastinate in doing it. Then I would like to thank my teacher, Pn Hjh Ribuan bt Salleh for guiding me and my friends throughout this project.
We had some difficulties in doing this task, but he taught us patiently until we knew what to do. He tried and tried to teach us until we understand what we supposed to do with the project work. Last but not least, my friends who were doing this project with me and sharing our ideas. They were helpful that when we combined and discussed together, we had this task done. Objective The aims of carrying out this project work are: • To apply and adapt a variety of problem-solving strategies to solve problems • To improve thinking skills To promote effective mathematical communication • To develop mathematical knowledge through problem solving in a way that increases students’ interest and confidence • To use the language of mathematics to express mathematical ideas precisely • To provide learning environment that stimulates and enhances effective learning • To develop positive attitude towards mathematics Part One Introduction Cakes come in a variety of forms and flavors and are among favorites desserts served during special occasions such as birthday parties, Hari Raya, weddings and others.
Cakes are treasured not only because of their wonderful taste but also in the art of cake baking and cake decorating Baking a cake offers a tasty way to practice math skills, such as fractions and ratios, in a real-world context. Many steps of baking a cake, such as counting ingredients and setting the oven timer, provide basic math practice for young children. Older children and teenagers can use more sophisticated math to solve baking dilemmas, such as how to make a cake recipe larger or smaller or how to determine what size slices you should cut.
Practicing math while baking not only improves your math skills, it helps you become a more flexible and resourceful baker. MATHEMATICS IN CAKE BAKING AND CAKE DECORATING ( Geometry To determine suitable dimensions for the cake, to assist in designing and decorating cakes that comes in many attractive shapes and designs, to estimate volume of cake to be produced When making a batch of cake batter, you end up with a certain volume, determined by the recipe. The baker must then choose the appropriate size and shape of pan to achieve the desired result.
If the pan is too big, the cake becomes too short. If the pan is too small, the cake becomes too tall. This leads into the next situation. The ratio of the surface area to the volume determines how much crust a baked good will have. The more surface area there is, compared to the volume, the faster the item will bake, and the less “inside” there will be. For a very large, thick item, it will take a long time for the heat to penetrate to the center. To avoid having a rock-hard outside in this case, the baker will have to lower the temperature a little bit and bake for a longer time.
We mix ingredients in round bowls because cubes would have corners where unmixed ingredients would accumulate, and we would have a hard time scraping them into the batter. Calculus (Differentiation) To determine minimum or maximum amount of ingredients for cake-baking, to estimate min. or max. Amount of cream needed for decorating, to estimate min. or max. Size of cake produced. Progression To determine total weight/volume of multi-storey cakes with proportional dimensions, to estimate total ingredients needed for cake-baking, to estimate total amount of cream for decoration.
For example when we make a cake with many layers, we must fix the difference of diameter of the two layers. So we can say that it used arithmetic progression. When the diameter of the first layer of the cake is 8” and the diameter of second layer of the cake is 6”, then the diameter of the third layer should be 4”. In this case, we use arithmetic progression where the difference of the diameter is constant that is 2. When the diameter decreases, the weight also decreases.
That is the way how the cake is balance to prevent it from smooch. We can also use ratio, because when we prepare the ingredient for each layer of the cake, we need to decrease its ratio from lower layer to upper layer. When we cut the cake, we can use fraction to devide the cake according to the total people that will eat the cake. Part Two Best Bakery shop received an order from your school to bake a 5 kg of round cake as shown in Diagram 1 for the Teachers’ Day celebration. Diagram 1 ) If a kilogram of cake has a volume of 38000cm3, and the height of the cake is to be 7. 0 cm, the diameter of the baking tray to be used to fit the 5 kg cake ordered by your school 3800 is Volume of 5kg cake = Base area of cake x Height of cake 3800 x 5 = (3. 142)( )? x 7 (3. 142) = ( )? 863. 872 = ( )? = 29. 392 d = 58. 784 cm 2) The inner dimensions of oven: 80cm length, 60cm width, 45cm height a)The formula that formed for d in terms of h by using the formula for volume of cake, V = 19000 is: 19000 = (3. 142)( )? h = = d? d =