## Posts Tagged ‘Pythagorean theorem’

The NCETM has a series of tools for analysing how confident you feel about various areas of mathematics. Part of the MaST programme requires me to complete each area over time. I also have to complete the sections for a range of Key Stages – 1, 2 and 3 – to demonstrate a broad knowledge of the subject.

Here are my results for the Understanding Shape/Geometry sections. (1 is not confident and 4 is very confident)

**Key Stage 1 – ****Understanding Shape**

- How confident are you that you understand the relationship between angle as a measure of turn?
- How confident are you that you can give relevant examples to illustrate the meaning of reflection?
- How confident are you that you can give relevant examples to illustrate the meaning of line or reflection symmetry?
- How confident are you that you know common side, angle and symmetry properties of polygons?
- How confident are you that you know common side, angle and symmetry properties of triangles?
- How confident are you that you know common side, angle and symmetry properties of squares and rectangles?

I answered 4 for each of these, giving me an outcome of **very confident**. I chose 4 for each of the answers as, reading through the examples given, I use the techniques described and go deeper too, being a Key Stage 2 teacher.

**Key Stage 2 – ****Understanding Shape**

- How confident are you that you understand through practical activity and the use of ICT the meaning of congruence?
- How confident are you that you understand through practical activity and the use of ICT the meaning of translation?
- How confident are you that you understand through practical activity and the use of ICT the meaning of reflection?
- How confident are you that you understand through practical activity and the use of ICT the meaning of rotation?
- How confident are you that you understand through practical activity and the use of ICT the meaning of Reflective (or line) symmetry?
- How confident are you that you understand through practical activity and the use of ICT the meaning of rotational symmetry?
- How confident are you that you can establish through practical activities the side, angle and symmetry properties of regular polygons?
- How confident are you that you can establish through practical activities the side, angle and symmetry properties of equilateral, isosceles, scalene and right-angled triangles?
- How confident are you that you can establish through practical activities the side, angle and symmetry properties of squares, oblongs, parallelograms, rhombuses, kites and trapeziums?
- How confident are you that you can establish through practical activities the nets of common 3D solids?
- How confident are you that you understand the terms right angle, acute angle, obtuse angle, reflex angle?
- How confident are you that you can show that the sum of the angles in a triangle is 180° in two different ways?

Again, I answered 4 for each of these questions, giving me an outcome of **very confident**. I chose 4 because of the ways I have used to teach shape over the years in Years 5 & 6. I use pull up nets to show how the 5 Platonic solids are made, regularly discuss the properties of shapes – especially the range of triangles – with my class. One minor concern was the use of ICT in the first 6 questions, but I consider my SMART Notebook slides to be using ICT and I rarely teach a maths lesson without one.

**Key Stage 3**** – ****Geometry**

- How confident are you that you are aware of a range of visualisation activities to help pupils to appreciate properties and transformations of shapes? (3)
- How confident are you that you understand through practical activity and the use of ICT the meaning of translation? (4)
- How confident are you that you understand through practical activity and the use of ICT the meaning of reflection? (4)
- How confident are you that you understand through practical activity and the use of ICT the meaning of rotation? (4)
- How confident are you that you understand through practical activity and the use of ICT the meaning of enlargement? (4)
- How confident are you that you know the meanings of alternate angles, corresponding angles, supplementary angles, complementary angles? (3)
- How confident are you that you can prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles, the sum of the angles in a triangle is 180° and the sum of the exterior angles of any polygon is 360°? (4)
- How confident are you that you can prove that the opposite angles of a parallelogram are equal? (3)
- How confident are you that you know the conditions for congruent triangles and can prove that the base angles of an isosceles triangle are equal? (3)
- How confident are you that you know how to establish through geometrical reasoning the side, angle and diagonal properties of quadrilaterals? (3)
- How confident are you that you know how to execute and prove the standard straight−edge and compass constructions? (3)
- How confident are you that you know how to describe simple loci? (2)
- How confident are you that you know how to explain and prove some circle theorems? (3)
- How confident are you that you understand Pythagoras’ theorem and its application to solving mathematical problems? (4)
- How confident are you that you can explain the conditions for similar triangles? (4)

This held some trepidation for me, as I haven’t ever really considered the Key Stage 3 curriculum before now for geometry while teaching. My answers are in brackets above and a mainly a mix of 3s and 4s with one 2. This gave me and outcome of **confident**. The 2 is for the question about simple loci – a choice made because I can’t remember having done any locus work in years! (The locus of a point is its path when it moves according to given rules or conditions. The plural is loci.) I think, having read the examples on the NCETM site, that I could certainly do the work for myself, but would probably struggle to teach it.

Where I chose 3, it is often because I felt I fully understood most of the content but there were areas where I may not have been able to give examples. In question 6, for instance, I would be fine with alternate angles, corresponding angles and complementary angles but may confuse supplementary angles.

Clearly from this, I need to develop my knowledge of some of the Key Stage 3 geometry material.