Tag: Pythagoras

Pythagoras and Dyscalculia

This approach:

  • Uses a calculator.
  • Uses just one single approach for all problems (long side or short)
  • Reduces the number of steps by rooting and adding in the same step.
  • Keeps to an absolute minimum, the need to compare sizes, because Dyscalculia makes this challenging.
  • Uses a mnemonic to recall the steps.

Method:

Normally in a problem involving Pythagoras, you are given 2 of the sides of a right angled triangle and asked to find the third. You need to Root the Add of the Squares (R.A.S, end of PythagoRAS). Always key in the larger number first….wpid-20150422_133239.jpg

This will give the answer 8.0622..

but Perhaps You Takeaway (PYThagoras) so mouse back to the plus (+) and change it to a take away (-)… and this gives  5.7445..

Now it’s decision time – using the picture, which answer looks most sensible, 8.0622 or 5.7445? The length of the 3rd side in this example is clearly longer than 7 so the correct answer is 8.0622.

 

Once Upon a Time there were three squares

This is the sotry of 3 squares, Mummy Square, Daddy Square and Baby Square. They live on the edges of every right angled triangle in the whole wide universe, but you can’t usually see them. Daddy square’s real name is Hypotenuse, it’s Greek.

If you add together the areas of baby square and mummy square, you always get the area of Daddy square. If you know the sizes of two of the family, you can always work out the size of the third one.

Pythagoras - the story of the three squares.
Pythagoras – the story of the three squares

Once upon a time there was a right angled triangle. One side was 5cm, another was 7.3, and a donkey wanted to know how long the other side was. So, the donkey drew Mummy square, (area 25), Daddy square (area 53.29) and Baby Square (area unknown). The area of Baby Square must be 53.29 – 25 = 28.29. (Not easy to manage a calculator when all you’ve got is hooves). So, if the area of Baby SQuare is 28.29, the length of the baby side must be the sqaure root of 28.29. Donkey’s calculator says this is 5.318834459 but Donkey knows that that is TOO MUCH INFORMATION (TMI) and it’s enough to say 5.32 as the answer.

The problem
The problem
Mummy Square...
Mummy Square…
Daddy Square
Baby Square
Baby Square

Any Donkey who wants to get good at working with the Three Squares will need lots of practice.
First, have a go at these problems

Then, take your pick from this Google Search page, and practice! Look for websites where you are given the questions and the answers, so that you can check you are getting things right.