Rational and Irrational numbers | mhorley

I only recently properly considered why all fractions are either terminating or recurring decimals.  Fundamentally, this is because there are a finite number of options for the remainder, which is a maximum of 1 less than the divisor.  This is most easily seen when dividing by 7.  All six potential remainders are used and the 7th division goes back to the beginning of the sequence as shown on this task from Don Steward.

Maybe this is an important thing to establish before talking about irrational numbers. With irrational numbers, we are effectively trying to convince students that there…

Continue reading at:

http://ift.tt/2tjllvL

Rational and Irrational numbers | mhorley

I only recently properly considered why all fractions are either terminating or recurring decimals.  Fundamentally, this is because there are a finite number of options for the remainder, which is a maximum of 1 less than the divisor.  This is most easily seen when dividing by 7.  All six potential remainders are used and the 7th division goes back to the beginning of the sequence as shown on this task from Don Steward.

Maybe this is an important thing to establish before talking about irrational numbers. With irrational numbers, we are effectively trying to convince students that there…

Continue reading at:

http://ift.tt/2tjllvL

Generalising Surface area | mhorley

What is the surface area of a cube of side length 1?
If we then cut this cube in half, and throw one of the halves away, what is surface area of the remaining cuboid?
Repeat the process, cut the shape in half along the same plane. What pattern can you see?

What is the general formula for the surface of a cuboid of width 1, depth 1 and height h?

What is the general formula for a cuboid of width 1, depth d and height h?

What is the general formula for a cuboid of width w, depth d and height h?

What other 3D shapes can you find the general formula for the surface area? Try:
A…

Continue reading at:

http://ift.tt/2uYJC6L

Generalising Surface area | mhorley

What is the surface area of a cube of side length 1?
If we then cut this cube in half, and throw one of the halves away, what is surface area of the remaining cuboid?
Repeat the process, cut the shape in half along the same plane. What pattern can you see?

What is the general formula for the surface of a cuboid of width 1, depth 1 and height h?

What is the general formula for a cuboid of width 1, depth d and height h?

What is the general formula for a cuboid of width w, depth d and height h?

What other 3D shapes can you find the general formula for the surface area? Try:
A…

Continue reading at:

http://ift.tt/2uYJC6L

Student generated data | mhorley

I know many teachers find teaching Statistics at KS3 & 4 a bit dry.  One way to make it a bit more interesting is to make the data somehow relevant to the students.  I’m not talking about football scores or download charts here. I’ve gone to great lengths to source that kind of data and create beautiful resources with it only to find that, while it engages some students, it has the opposite effect on others if it is something they are definitely not into.

So, having given up trying to get down with the kids, here is another approach which involves them generating data so they feel they…

Continue reading at:

http://ift.tt/2uu6MSY

Student generated data | mhorley

I know many teachers find teaching Statistics at KS3 & 4 a bit dry.  One way to make it a bit more interesting is to make the data somehow relevant to the students.  I’m not talking about football scores or download charts here. I’ve gone to great lengths to source that kind of data and create beautiful resources with it only to find that, while it engages some students, it has the opposite effect on others if it is something they are definitely not into.

So, having given up trying to get down with the kids, here is another approach which involves them generating data so they feel they…

Continue reading at:

http://ift.tt/2uu6MSY