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Mathematics Age 7-8: Let’s make a straight line Introduction: This lesson is about multiplication, factors and multiples. It is based around a number grid that displays multiples of a given number. This lesson uses the Number Grid program from the DCSF Standards site. It can be downloaded from: http://nationalstrategies.standards.dcsf.gov.uk/node/47785 Resources One computer and a data projector for whole class work Children may need paper and pencil to record the inputs and outcomes – this will help them to discover the relationship between the inputs and the resulting patterns. To access the program go to: http://nationalstrategies.standards.dcsf.gov.uk/node/47785 and then choose the option that says Download as Windows executable file. Previous learning Children will need a basic knowledge of their multiplication tables. Children should have the ability to look for, and recognise, pattern in numbers. Learning Objectives Children will learn: how to perform calculations (multiplication) and to reinforce their knowledge of multiplication tables, factors and multiples how to change variables and to understand the effect of doing so. What to do This lesson uses the Number Grid program from the Standards site. This is a teacher led session with the children gathered round an interactive whiteboard (if available), offering suggestions as to how to achieve particular outcomes. There are a number of control buttons on this program (which makes it a very versatile piece of software that could be used by children at all ages in KS1/2). This lesson only uses 3 of the controls: Start – will allow the teacher to set the number in the top left hand corner cell Columns – will display anything up to 13 columns Multiples – will display in colour all the multiples of a particular number (use the up and down arrow keys to adjust the number and then click on the number itself to colour the appropriate cells). Begin by setting the grid to the usual 100 number square and then, for example, colouring in multiples of 3. The challenge might be to line up numbers in 4 straight lines (vertically). How can we achieve this? Some children will suggest changing the start number. What happens? Others might suggest changing the number of columns. If the columns are reduced to 9 then these numbers do line up in straight lines (but there are only three lines and the challenge requires 4). Once the children have the basic idea, it is then possible to explore this idea in more depth. However, we need to define the term ‘straight line’. This implies a set of coloured numbers that are all on the same vertical line, but the coloured cells do not have to be adjacent squares. For example, a ‘straight line’ may be any of these:
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Maths Age 7-8: Let’s make a straight line 2009
a) If we go back to the traditional number square (1 – 100), what can I set the multiples to in order that I can get two straight lines immediately (without adjusting ‘start’ or ‘columns’)? b) How can I get the multiples of 4 lining up in two straight lines? c) How do I get the multiples of 6 lining up in three straight lines? d) How do I get the multiples of 2 lining up in four straight lines? e) Can I get the multiples of 7 lining up in two straight lines? f) Can I get the multiples of 3 lining up in three straight lines, one on the left hand side of the grid, one on the right hand side and one down the middle? If not, why not? g) Is it possible to set a grid size so that no multiples line up? h) Starting at 1, how can we set up the columns and multiples to give a pattern similar to the middle column in the table above? Some other extension activities are explained below. However there are numerous others based upon introducing diagonal lines and looking at numbers that are multiples of two given numbers (i.e. in order to achieve this, don’t use the ‘reset’ button and any existing pattern will remain on display, together with the new pattern in a different colour) Differentiation As discussed above the concept is extendable to challenge even the most able children. In the case of weaker children, they could start with a 10 x 10 number grid drawn on centimetre squared paper and then shade in, for example, all the multiples of 3. They could then take a 10 x 12 blank grid and cut up the rows of their 10 x 10 table and paste them onto the new grid. They will then see the multiples of 3 realigning themselves into vertical columns. The role of ICT The computer allows for numerous displays in a very short period of time. The children can concentrate on the problem and are not distracted by drawing and colouring. The program allows the children to work iteratively, refining their answers to try and achieve the desired display. Follow-up suggestions There are a number of ways of extending this problem. One challenge is to consider a range of problems similar to those shown below. The children either have to predict their answers (because the computer software is limited in the range of numbers that it handles) or they have to work backwards from knowing the outcomes. Start number 3 3 1 1 1 2 4
Number of columns 8 ? 9 ? 15 15 16
Multiples of …..? 6 6 ? 4 5 6 6
Number of straight lines ? 1 3 5 ? ? ?
Number of cells coloured in ? ? ? ? ? ? ?
Assessment The children should consider the difference between a random approach and an approach based around a systematic method. Each time that the children suggest changing one of the variables, they should provide a justification as to why. They could debate which questions were easy to answer and which were the hardest and why. They could create further questions for each other or even ‘test the teacher’. This lesson idea was first published as part of the Becta Direct2U subscription service for teachers, (c) Becta, 2005-2006 € ictopus ltd
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Maths Age 7-8: Let’s make a straight line 2009