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# Investigate the difference between the products of the numbers in the opposite corner of any rectangles/squares that can be drawn.

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Introduction

INVESTIGATE THE DIFFERENCE BETWEEN THE PRODUCTS OF THE NUMBERS IN THE OPPOSITE CORNER OF ANY RECTANGLES/SQUARES THAT CAN BE DRAWN ON A 100 SQUARE Reflection of thought process An investigation was chosen to find a formula that would calculate the difference of products of four numbers in the opposite corners of any size of rectangles/squares when multiplied that can be drawn on a 'hundred square'. After deciding on investigation, my next step was to get hold of some books from the library, which would help me to carry out this investigation and further to complete the assignment appropriately. I also searched on the Internet for the materials related to the task and to get ideas for maths activities. To reach the desired level of investigation, many calculations were required, as well as the recordings of these calculations to form equations in order to finally obtain the formula. The investigation was time consuming, especially as I did not feel confident while carrying it out on my own. Being a mother of three children and living at a substantial distance from my friends, it was not easy to get together for any discussions related to the task. Though we exchanged views over lengthy telephone conversations, it would have been much easier if at least two of us were to work on the same investigation. It was realised during the investigation that my understanding and knowledge of algebra and number sequences needed further work. ...read more.

Middle

(See some activity ideas in the appendix) To calculate numbers for the investigation, it required me use a calculator. In KS1, children can be introduced to calculators to find number patterns, predict and discuss results. 'By the end of KS2, pupils should have the knowledge and competence to use a calculator to work out, say, (56+97) * (133-85) and round the answers to one decimal place' (NNS 1999, p. 8). During university sessions we were given lots of ideas and hands on practical activities which include: working with number lines, 100 squares, blank number lines, beads, number games, number songs &rhymes, cubes, picture stories, books, small investigations and lots more. I planned a series of maths lessons during my school practices and used different activities with confidence where children enjoyed and explored numbers in many ways. 'Millie's Maths' was popular software with children in the nursery to develop early maths skills and number recognition. Mathematics Educational Theories The dictionary definition of Numeracy is 'the ability to use numbers especially arithmetical operation' (Collins English Dictionary 1991). The system of numeration utilised currently was derived from an ancient Hindu system. However there have been many other systems developed by various cultures through the centuries. In recent years there has been a considerable discussion as to how children develop number concepts but it is generally agreed that they need experiences with counting, matching, grouping and comparing before reaching an understanding of number. There is now extensive evidence to show that the child's ability to master Piaget's tests of one-to-one correspondence does lay down some of the necessary foundations for counting, adding and subtracting. ...read more.

Conclusion

The children can predict the route; programme the Roamers and test out their predictions. Inexperienced children will need to put one or two instructions at a time, and then adjust the next accordingly, but later they can be challenged to write all the instructions in one go. They can also hold simple and complex sequences to solve problems that may require investigation, calculation and recording with groups of younger or older children accordingly Having collected data such as "Favourite colour" or "Favourite food" the children can enter the data into simple handling package (e.g. Graphers). Using 'click and drag' they can sort the data on screen and also produce pictogram/graphs/charts etc to support their conclusions. Using a drawing package the children can create geometrical shapes. By copying, pasting, reflecting and translating the shapes the children can produce images. LOGO is a computer programme based on a cursor in the shape of a turtle, moving around the screen. The children enter instructions to turn the turtle and move the turtle FD, BK, LT, RT to draw desired shapes and create patterns. The constructivist approach to using computers has shown that computers can support children's understanding particularly in problem solving. The implications are that teachers need to have a clear view of the aims and purposes of using ICT. When planning tasks teachers need to ensure that all activities will be accessible to all pupils, including pupils of different gender, ethnicity and ability (including children with special needs). ...read more.

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