Investigation lessons
= difficulty rating

Students add numbers at the bottom of the "castle" to find the number at the top! Different levels of challenge:

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


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Palindromic numbers

Students investigate what palindromic words and numbers are. How many are there up to 500?

What happens when we double a palindromic number?     Does this always work? What about when I take a number, reverse the digits and add them together?                                Does this always

work? What year

was the last

palindromic year?

When is the next

one? What date

will next be a


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Paper folding to the moon

Students must investigate to answer the question - how many times would you need to fold a piece of paper to reach the moon?

All resources are provided and you will need to make sure certain posters/equipment is available in the room (see first slide).

  Great to use


  metric conversions

  or standard form

   or exponential


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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!

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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?


 Highly recommend

getting the students

 sat on chairs at the

 front of the class

 and trialing it as a

 class to start off.

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I've used this with low attaining year 7s and they enjoyed it - definitely get the multilink cubes out for this one!.

They investigate the relationship between the number of  cubes needed to

 make different



   sequences or

  even isometric


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Up and down staircases
£10k a day or invest 1p?

Students must investigate to answer the question - 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

Great way to introduce the idea of exponential/geometric sequences and

 really gets

 students to



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Geometry and Measures

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?

This lesson does need you to give at least one malteser to each   group of students (and some spare may be a good idea).

   To make it more challenging, ask your students to consider at         least 3 different ways

    of finding the radius

    and pick the one they

     think is the most

       accurate. They will

        also need to weigh

         their malteser.

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The fly vs. the spider

This lesson requires knowledge of 3D pythagoras.

I did this with top set year 10 and nobody got the perfect answer! Although some got very close through trial and error.

Students start by finding the distance between two flies in a box. They then

have to find the

shortest possible

path a spider

must travel to

reach a fly!

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

They then complete three puzzless with the pentominoes -

Fit them into a


fit them into a

square and

create the largest

possible area

with them!

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I did this with my top set year 9s and it worked really well. They were all engaged. All of them managed the challenge.  
Vast majority did extension 1.  A lot did extension 2.  
About 5 did extension 3. And 2 girls got scarily close to

"Quit school now"!
Impressive for

1 hours work!!!  
  I would say the

  class needs to be

  fairly high ability

    to begin with.

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Pythagorean shoe laces
Cylindrical soup

An investigation lesson into what shape container is best to contain soup - comparing volumes and surface areas.

This lesson requires students to be confident with calculating the volume and surface area of cuboids and cylinders, including working backwards.
The lesson does

end with showing

the students the

answer for a sphere

   but they are not

    required to

     calculate it.

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Peter Kay vs. Peter Crouch

Students are asked: Which would you rather have?

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

They can ask questions before they begin their task - but you shouldn't need to answer any! All the information they need to solve the

problem is on

posters around the

room. Great for

converting between

metric and imperial


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How dense is a malteser?
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