Investigations
= difficulty rating
Paper folding to the moon

"How many times would you need to fold a piece of paper to reach the moon?"

  • Metric conversions

  • Standard form

  • Exponential growth

   

PowerPoint                                               Handouts

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Tiling

Students investigate the number of each type of tile spacer they will need when tiling a floor. They start of looking at squares then move onto rectangles. They they "pattern sniff" or - if they are more competent with sequences - they can try and find  the nth term for the number of each type needed for any size floor!

  • Sequences

  • nth term

  • Square numbers

PowerPoint

Tiling.png
£10k a day or invest 1p?

Would you rather have £10,000 a day in for the next 31 days building up in your bank account or put 1p in the bank that turns into 2p the second day, then 4p, then 8p... etc for 31 days?

  • Geometric sequences

  

PowerPoint

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The fly vs the spider

What is the shortest distance that the spider must travel along the sides of the glass tank in order to reach the fly?

  • Pythagoras' theorem in 3D

  • Nets

 

PowerPoint

Castles

Students add two adjacent bricks to find the value of the brick on the top of them.

Using the numbers 1 to 5, which of the castles 50-59 is impossible? What is the smallest castle you can make? What is the largest? What do you notice about how the numbers on the bottom level are arranged? Create as many different castle 40's as you can.

 

  • Basic addition and subtraction

  • Commutativity

  • Negative numbers

  • Algebra

         

PowerPoint                                               Handouts

castles.png
Jumping Frogs

The classic puzzle! Students record the number of moves it takes to swap over the red and yellow frogs. They also record the number of slides and the number of jumps and find the nth term for these! But this takes it a step further! What if the number of yellow and red frogs wasn't the same?

  • Sequences

  • nth term

  • Square numbers

  

PowerPoint

jf.PNG
Pythagorean shoe laces

Which of these lace patterns would use the smallest length of lace?

What about when we vary the number of holes or the distance between the gaps?

Is there a general formula for each one?

  • Pythagoras' theorem

  • Forming formulae

PowerPoint

laces.png
fly.png
Peter Kay vs Peter Crouch

Which would you rather have:

Peter Kay's weight in pennies or Peter Crouch's height in pound coins?

  • Metric and imperial conversions

PowerPoint                                               Handouts

Cylindrical Soup

Which shape of container is the best to contain soup in?

  • Volume of prisms

  • Surface area of prisms

  • Finding missing side lengths when given volume of a prism

         

PowerPoint                                               Handouts

Coming soon

Pentominoes

Students have to find all 12 possible pentominoes first, considering that reflections and rotations are congruent pentominoes.

They then complete three puzzles with the pentominoes - fit them into a rectangle,fit them into a square and create the largest possible area with them!

  • Congruence

  • Area of shapes by counting squares

PowerPoint                                               Handouts

Coming soon

How dense is a Malteser?

We've seen the adverts of people blowing them into the air and there's actually a Guinness world record for it! So exactly how dense are they?

 

  • Volume of a sphere

  • Density, Mass and Volume

         

PowerPoint                                               Handouts

Coming soon

Up and down staircases

Investigate the relationship between the number of  cubes needed to make different staircases.

  • Sequences

  • Square numbers

  • Isometric drawing

PowerPoint                                               Handouts

Coming soon

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