Tag Archives: Triangles

268. Monkeying with Pythagoras

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My (not so little) monkeys in KS3 have been discovering and using Pythagoras’ Theorem. They usually deal with open questions quite well, however this one took a fair bit of discussion. This challenge requires no worksheets or fancy resources, just write it on the board. The context is modified, but the essential question remains the same.

Challenge

Zookeepers have attached eight bolts in a cuboid formation (sides 3m, 4m and 5m) to the trees in a chimpanzee enclosure. The keepers attach taut ropes between the bolts for the chimps to climb on. Each length of rope is individually cut. No length is lost in knots.

  • What is the maximum length of any one piece of rope?
  • What is the total amount used, if every corner is joined without duplication?

 

Solution

The first step to solving it is a good diagram of the problem. Students then need to break it down into triangles. The solution has several levels of difficulty:

  • Total of the edges of the cuboid
  • Total of the diagonals on the faces
  • Total of the diagonals across the inside of the cuboid

This diagram demonstrates the levels of the problem – have fun!
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230. Resource of the week

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I came across this splendid resource on Similar Triangles, by cturner16, on the TES website:
Similar triangles matching activity

The cards start with a standard diagram of overlapping triangles and you match it up with the individual triangles. The final step is to work out the scale factor and the missing side. It follows the exact steps you would want students to follow when working on these problems.

Now, I know my class well and to avoid the standard bickering, mess and ‘I didn’t think you meant pick up every sheet when you said pick up every sheet’, I copied every set on a different colour:

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The colour made it so much easier to manage and discuss. There are six problems, so if your students work in 2’s or 3’s, they each get 3 or 2 sets to stick in their book. The problems are full of misconceptions and interesting scale factors. I’m really glad I used it!

Thank you cturner16!

18. Similar triangles

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This quick activity shows that although the sides change in similar triangles, the angles stay the same. It can also be used with enlargement.

Equipment
Two pieces of different coloured card (A5 or A6 is fine)
Ruler
Pencil
Scissors
Sticky tape

Step by step instructions
Two Lines
Draw a line parallel to the long sides of one piece of card (min 2cm from the edge)

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Wrap
Place the two pieces of card at 90 degrees to make a cross.

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Wrap the lined card around the unlined card

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Cut
Mark out a triangle using the pencil lines as a guide.
Cut along two sides as shown. It’s okay to tidy up a messy cut, so long as the line remains straight.

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Stick
Turn over the card and refold in the opposite direction. Stick the bottom edge of the folded card in place, as shown.

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Slide
Slot the second piece in place.

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Turn over.

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As the slider moves up and down a contrasting triangle appears and disappears.

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You can measure the sides & angles of every triangle you make.

This can be stuck into books by gluing along the folded edges, which still allows the slider to move.