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Finding the relationship between the coordinates of reflected points.
Discussing the relationship between the x coordinates for points and the vertical mirror line.
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| Resources |
Vocabulary |
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Centimetre Pegboard symmetry teachers’ notesheet
Pegboards (one between two)
Coloured pegs
Labelled grid on board
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coordinates, mirror line, axis/axes,line of symmetry, reflection, points |
| Organisation |
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Near achievement pairs on mixed tables
When working on the board, stuck-on coloured counters are useful stand-ins for pegs
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| Whole Class Preparation: (about 5-10 mins) |
Give out the pegboards. We are going to do some thinking work with coordinates.
Remind children of the convention of labelling axes and coordinates (along the path and up the ladder). Draw a grid on the board to demonstrate
Put a green peg in (1, 3). Check with others on the table. Now put a blue peg in (7, 2).
What mistakes could people have made? Mixing up xs and ys, forgetting to count 0.
What things must we remember? Along the path and up the ladder.
Repeat with other colours in other positions.
Draw some coloured pegs on the grid on the board and get children to record the
coordinates.
Place pegs in (5, 1) (5, 7) (5, 9) (5, 4). What do you notice? They are in a line.
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| Paired Work: (about 5-10 mins) |
Place a variety of coloured pegs anywhere on your board to the left of your mirror line and
record their coordinates.
Reflect the pegs in the mirror line and record the coordinates after reflection. Keep reflected
pegs the same colour to avoid confusion. What do you notice about the numbers before
and after reflection?
After a few minutes, model a recording system on the board:
Colour Old Peg New Peg
Green (1, 3) (9, 3)
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| Class Sharing: (about 10 mins) |
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Invite individuals to draw their original and reflected coordinates on the board or pegboard OHT and record their coordinates on the class recording system.
What if an original coordinate was (4, 7)? What is the reflected coordinate?
What do you notice about the pairs of numbers? y coordinate stays the same, x coordinates add up to 10.
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| Paired Work: (about 10-15 mins) |
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Ask pupils to explore their ideas and work out answers to: What did you notice about the numbers with mirror line at x = 5? How would you express what you know as a written calculation? 5 – 1 + 5 + 1 = 10; 5 – 3 + 5 + 3 = 10, and so on.
What is happening here? 5 – (a number) + 5 + (the number) = 10 + 0 How is this 10 connected with x = 5? Double.
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| Class Sharing: (about 10-15 mins) |
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Discuss results from the paired work – looking for a general rule in words or symbols.
If time permits, follow with a ‘mental’ task without the pegboard: What would happen if the mirror line was at x=12? Without doing it, think about what would happen if we put a peg in at (10, 3). What is the reflection? What about (1, 5)? How would you express what you know as a written calculation? How does this relate to the case when the mirror line was at x= 5? 12 – (a number) + 12 + (the number) = ?
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