T14 Using an Urdhu number grid
T14 Using an Urdhu number grid Henry Liebling (2013) Display an Urdhu counting grid from 0–99 or 1–100 on an OHP or computer screen, projector, IWB or visualiser (see p. 30 of The Really Useful Maths Book). You as the teacher will need to be able to point to it and cover and uncover it in some way. Use it with the whole class (see N3 Arabic and other number Systems pp. 26–31 and N4 Working with Grids pp 32–39 for a full description). Study it in silence on your own for a minute. Say what you see. What is important? What do you think it is? What do you notice? Any clues? Look carefully. Collect the responses and build on them. Ask someone to act as a scribe if you wish. I’m turning the image around clockwise through 90 degrees. Now what do you think? Just tell me what comes into your head. That way we can build up ideas together. Can anyone add to what X has just said? Who agrees? Who doesn’t? Who couldn’t care either way? Why not? Does it matter which way round it is? I’ll turn it clockwise through another 90 degrees. Any comments? And again. What now? What do you notice? How has it changed? Reinforce what has been observed. Try to highlight main points, strategies and insights. Where is the origin, where it starts? In which direction do the symbols go? An aside Tifinar is a script used by the Tuareg which can be written and viewed from any side. The writing was usually from the bottom to the top, although right-to-left, and even other orders, were also found.
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Imagine a group of children sitting around a teacher who is writing/drawing symbols in the sand. There is no front or back. Do you know any languages written from top to bottom or right to left? Why might that be? Do you know that there are some 23 scripts which have been found but not yet deciphered? (Here, you can talk about the Rosetta Stone).
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On the Urdhu Grid, can you see 1, 2, 3? Imagine making these marks on paper. Try skywriting now with me. Make 1 then 2, then 3 downward strokes from right to left. Can you see how the marks for 2 join up and the marks for 3 join up? When we look at them in this way we can see where the versions of 1, 2 and 3 that we use today have come from. The writing/mark making goes from right to left. What other numbers do you recognise? Are they false friends? One looks like a seven but isn’t. What of the number five? Try to find anchor points on the grid, symbols you feel sure of, then work out the symbols either side. I’ll point and you all say what you think each numeral is. (In Silent Way mode, go from 0 to 9 then down the tens, then wherever they direct you with the accuracy of their responses. Don’t be afraid to encourage any one individual who gets it right to carry on and the rest join in when they think they understand. Go back over some sequences if you wish (see N2 Saying and making numbers pp. 16–25). Cloud Put a paper cloud over one or more numerals and ask what is covered. Mask Cover the grid with a sheet of paper with a small hole in it which reveals only one number. Can they work out what it is? Slide the paper up and or down a number to give a clue or, easier, left and right. You are trying to get them to reveal the algebra within the grid. Finding X when you reveal X-10, X+10, X+1, X-1, etc. (see N4 pp. 34–35). Plenary Try to collect strategies used to work out where the origin is, what direction the numbers on the grid take, the value of the numerals, what helps and what doesn’t, etc. Will these strategies work with all the grids? Are they useful anywhere else? In other areas of maths, other subjects, outside school, at home? Any part of the above activity could be used as a starter activity and developed over a number of weeks with different number grids.
Opportunities for further work/bridging Repeat this lesson with a different number grid, and try two contrasting systems such as Chinese and Mayan. Try similar systems such as Urdhu and revise the following week with Arabic. Work on origins (the starting point) and frames of reference (which way round, orientation and direction), as concepts developed for pragmatic reasons, but in some sense arbitrary and changeable. Show grids with different origins such as the bottom left hand corner, or even ones that spiral from centre. Consider the nature of the four quadrants for an X, Y axis where values can be positive or negative. Explain and explore this notation for +ve and -ve values of X and Y. Extend this to grids other than counting grids, such as multiplication grids, addition grids, etc. (see pp. 37– 39). Jigsaws Print out any grid onto card and cut it up to make a jigsaw. Try to make them of different complexity from 4–10 pieces. Better still, get the pupils to make them. Try to do them yourself first. Put the pieces into a sturdy envelope, label them and use them as a short revision activity to use with pairs of pupils at the end or start of a session. Watch what happens and listen to the dialogue to assess pupils’ strategies and understanding (see p. 36).
©Routledge/Taylor & Francis 2014
Try making sets of dominoes with different number systems such as Mayan, Chinese or Korean (see pp. 28– 29). Create your own grids using a spreadsheet and different font sets for counting and multiplication. Discuss or ask them to research Indian number systems and how they evolved; the importance of zero; the acceptance and stability for 100 years of the Arabic number system which has now become international; or the burdensome nature of Roman numerals (using letters for numbers). Develop work on saying numbers in different languages (see p. 24). Develop target boards using different, combined number systems (see N5 Working with target boards pp. 40–45).
©Routledge/Taylor & Francis 2014
©Routledge/Taylor & Francis 2014
Imagine a group of children sitting around a teacher who is writing/drawing symbols in the sand. There is no front or back. Do you know any languages written from top to bottom or right to left? Why might that be? Do you know that there are some 23 scripts which have been found but not yet deciphered? (Here, you can talk about the Rosetta Stone).
©Routledge/Taylor & Francis 2014
On the Urdhu Grid, can you see 1, 2, 3? Imagine making these marks on paper. Try skywriting now with me. Make 1 then 2, then 3 downward strokes from right to left. Can you see how the marks for 2 join up and the marks for 3 join up? When we look at them in this way we can see where the versions of 1, 2 and 3 that we use today have come from. The writing/mark making goes from right to left. What other numbers do you recognise? Are they false friends? One looks like a seven but isn’t. What of the number five? Try to find anchor points on the grid, symbols you feel sure of, then work out the symbols either side. I’ll point and you all say what you think each numeral is. (In Silent Way mode, go from 0 to 9 then down the tens, then wherever they direct you with the accuracy of their responses. Don’t be afraid to encourage any one individual who gets it right to carry on and the rest join in when they think they understand. Go back over some sequences if you wish (see N2 Saying and making numbers pp. 16–25). Cloud Put a paper cloud over one or more numerals and ask what is covered. Mask Cover the grid with a sheet of paper with a small hole in it which reveals only one number. Can they work out what it is? Slide the paper up and or down a number to give a clue or, easier, left and right. You are trying to get them to reveal the algebra within the grid. Finding X when you reveal X-10, X+10, X+1, X-1, etc. (see N4 pp. 34–35). Plenary Try to collect strategies used to work out where the origin is, what direction the numbers on the grid take, the value of the numerals, what helps and what doesn’t, etc. Will these strategies work with all the grids? Are they useful anywhere else? In other areas of maths, other subjects, outside school, at home? Any part of the above activity could be used as a starter activity and developed over a number of weeks with different number grids.
Opportunities for further work/bridging Repeat this lesson with a different number grid, and try two contrasting systems such as Chinese and Mayan. Try similar systems such as Urdhu and revise the following week with Arabic. Work on origins (the starting point) and frames of reference (which way round, orientation and direction), as concepts developed for pragmatic reasons, but in some sense arbitrary and changeable. Show grids with different origins such as the bottom left hand corner, or even ones that spiral from centre. Consider the nature of the four quadrants for an X, Y axis where values can be positive or negative. Explain and explore this notation for +ve and -ve values of X and Y. Extend this to grids other than counting grids, such as multiplication grids, addition grids, etc. (see pp. 37– 39). Jigsaws Print out any grid onto card and cut it up to make a jigsaw. Try to make them of different complexity from 4–10 pieces. Better still, get the pupils to make them. Try to do them yourself first. Put the pieces into a sturdy envelope, label them and use them as a short revision activity to use with pairs of pupils at the end or start of a session. Watch what happens and listen to the dialogue to assess pupils’ strategies and understanding (see p. 36).
©Routledge/Taylor & Francis 2014
Try making sets of dominoes with different number systems such as Mayan, Chinese or Korean (see pp. 28– 29). Create your own grids using a spreadsheet and different font sets for counting and multiplication. Discuss or ask them to research Indian number systems and how they evolved; the importance of zero; the acceptance and stability for 100 years of the Arabic number system which has now become international; or the burdensome nature of Roman numerals (using letters for numbers). Develop work on saying numbers in different languages (see p. 24). Develop target boards using different, combined number systems (see N5 Working with target boards pp. 40–45).
©Routledge/Taylor & Francis 2014
