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To be systematic.
To find and express a rule.
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| Resources |
Vocabulary |
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Square dotty paper
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grid, square numbers, steps, systematic, rule, pattern, horizontally, vertically, path |
| Organisation |
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Small groups on mixed achievement tables.
Have copies of square dotty paper or dots drawn onto the board.
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| Whole class Preparation: (about 5-10 mins) |
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There is a new Olympic sport called Beanbag Pick Up.
Draw a 3 x 3 grid of dots on the board. Do not describe this as a 3 by 3 grid at this stage.
This is level three of the competition.
The beanbags are laid out on the dots. Going horizontally and vertically only, you must pick up all the beanbags in the shortest time possible.
Draw quite a long path onto the board to show one possibility.
Ask the children to demonstrate a different or quicker path. The line representing the run or walk must be continuous. You may need to put some arrows onto the diagram to show when a particular path has been retraced.
How could we describe how far we have walked or run? Be careful here to emphasise the steps and not the dots.
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| Group work : (about 5-10 mins) |
Children work in pairs to find different paths for level three. They draw the lines on the grid
and record the number of steps taken.
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| Class sharing: (about 5-10 mins) |
Get some children to draw their paths, with arrows to show path taken, and to record the
distance travelled. Start with some of the longer distances that you have observed in the
group work.
What is the shortest distance that you have found? Invite children to demonstrate any
mistakes that have been made, such as miscounting, leaving a dot out and so on. Show
several paths that are all eight steps long.
Describe the shortest path. Draw out starting points, zigzag or spiral pattern and no retracing
of steps.
Now let’s look at the next level of the competition.
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| Paired Work: (about 15 mins) |
Ask children to find the shortest possible paths for levels four and five of the competition.
You will need to show them the layout – 4 x 4 and 5 x 5 grids.
Look to see if there is a pattern to your numbers.
Try to predict the length of the route for level six of the Beanbag Pick Up.
When you have lots of beanbags, how can you be sure that you haven’t missed any out? Spiral
or zig-zag pattern.
Write down any rules that you have noticed and check them for an even higher level.
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| Class Sharing: (about 10 mins) |
Ask the children to share ideas for the shortest Beanbag Pick Up.
What rules have you noticed?
Why is the shortest walk or run one less than the number of beanbags?
How can you express this for any level? n squared – 1. Some children may think that the rule is
(n – 1) squared.
What would happen if the layout of the beanbags were rectangular and not a square?
Ask the children to comment on other similar real-life situations where steps and stops are related, such as fences and bus routes.
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