Using Rods

Editor's Notes

• #5: See NCETM progression document
• #7: Exploring a simple relationship between the rods.
• #10: Year 2 and 3This clip demonstrates the importance of comparison. When the first child says that the rod is 3, it could just be the third rod set out, when prompted he does say that it is three because three of the light green (named as 1) fit in. It is this same relationship which the second child now needs to label one third(?). After giving her time to think, the others prompt her by asking how many of the whites fit it and placing whites near the rod. This is enough to lead her to say “one third”. I recognize that it will be key when introducing fractions to the younger children for them to have an awareness that 3 means three of whatever is one. This awareness is allowing them to create names by comparison. The red is named as two thirds “because two of the third fit into it”. The green is named as three thirds. This is a start, but there seems to be a danger of them naming rods in succession using their length as measured by the white – pink as four thirds, yellow as five thirds, etc. But this will involve only limited comparison, so I try to “give the effort another twist and make another demand on the children” (Goutard 'Mathematics and Children<' p.7) by setting out an order of rods to be named for this next activity.
• #12: See NCETM progression document
• #15: Find them in this order….how many different names can you give them?
• #16: Years 2 and 3Children seem to like complexity which leads naturally to equivalent fraction names.  I notice they often add a new twist to the game themselves to satisfy their sense of fun at devising increasingly involved names. The first child starts to name the tan rod as eight fifths, but a ‘more interesting name” is suggested. He then responds with ‘four fifths plus four fifths’, this uses the labeling of the act of placing rods end to end as ‘plus’ to naturally lead to addition of fractions. He now needs to be encouraged to leave the name eight fifths. The children are comfortable with the idea of a fraction having two or more names. An opportunity has occurred for moving towards systematisation. These fraction names could be saved and studied later when more similar examples have been gathered.
• #17: Adding fractions
• #18: See NCETM progression document
• #23: See NCETM progression document
• #25: How old?Year 1 Partioning blue Free play with rods
• #26: Again, this clip seems to demonstrate the same value of this empirical activity for learning to use signs. The child writes y = g + r. When she reads this to the group she says ‘yellow plus green equals red’. When she asks the group if they agree they say ‘no’. She then tells them that she means ‘yellow on its own and green and red together’. She places the rods in this arrangement. When she reads her statement again she reads the = as ‘plus’ but quickly corrects herself. This shows she is clear about what she wants to say, but it not yet sure of how the signs relate to it. I notice that she writes y = g +, stops to look up at the pictures of the rods, then nods before writing ‘r’. She seems to be gathering empirical evidence.
• #33: What would you call this representation?
• #35: Play- “…one starts gleaning facts.  This is done by trial and error, the results being accepted or rejected according to the criterion imposed on oneself. These facts are gathered at random, everybody gleaning what he can… Nevertheless they will only have been able to gather material…The children have acquired more a technique than knowledge founded on reasons.” Goutard, 'Mathematics and Children' pg.6.Systemise- “… to organise experience, to clarify facts so as to fill gaps if some are found, to propose groupings of some significance, in a word to invent sure means with which a thorough study of the situation could be undertaken.” Goutard, Mathematics and Children pg.8Masterery- ‘’…It is therefore towards a deeper understanding of the structures involved in these situations that the above discoveries take us. Every element or group of elements is seen to potentially contain the infinite set of which it is part, as soon as the dynamic link between the elements has been noticed.” Goutard, 'Mathematics and Children' pg.18.