Number properties and transformations of shape SCITT Jan 2014

Objectives (students will): gain a better understanding of the structure and special properties of the number system; be able to teach further aspects of 2d shape, including transformations; understand the relationship between 2d nets and associated 3d solids; continue work on the mathematics subject audit.

Associated issues for teaching Developing understanding of the complete number line. Using number properties to set challenging problems.

Maths Observations Spring 2014 Group 1 Fran Johnson Lucy B Rebecca B Candice Louise D Tamsin D Emma D David F Daniel H Stacey L Tom LeM Hannah TC Katie W Danielle W Gill Haysham Rose B Stuart C Stefanie C Tracey C Adam H Krystal H Emma K Isabel L Rachel M Tony Sarah P Alison P Tacita S Peter S Martin W Expectations

Maths Observations Spring 2014 Group 2 Debbie S Sophie A Katie B Cath B Jessica B John C Tom C Hannah E Emma F Tash H Chelsey K Laura K Hollie M Roxanne M Joanne P Amy W Gill Haysham Kimberley M Rebecca S Caroline S Fran Johnson Matt B Tom D Bobby K Sarah M Cora N Clare S Richard W Luke W Expectations

Properties of Number Gain a better understanding of the structure and special properties of the number system; Developing understanding of the complete number line; Using number properties to set challenging problems.

Provide an example for each… palindromic Square number factor integer digit consecutive Triangular number fraction decimal real multiple odd irrational even complex imaginary Fibonacci recurring decimal whole prime rational natural square root root digit (or digital root) Mixed number

A Number ‘Schematic’ complex imaginary real irrational rational integer fraction whole integer natural

Properties of Number Choose a number between 1-100 (inclusive) Talk about what ‘families’ it belongs to… What makes it ‘special’?

Tests of divisibility – 5472, 3564, 4215, 2340, 72432 100 The last two digits are 00. 25 The last two digits are 00, 25, 50 or 75 10 The last digit is 0 2 The last digit is 0,2,4,6,8 3 The sum of the digits is divisible by 3 4 The last 2 digits are divisible by 4 5 The last digit is 0 or 5 6 The number is even AND divisible by 3 8 The last 3 digits are divisible by 8 9 The sum of the digits is divisible by 9

Prime Numbers Which numbers between 1 and 30 are prime numbers? ‘Number Grid ITP’

Prime factors - Year 6 “Find all the prime factors of any number to 100” e.g. the prime factors of 60 are 2,2,3 and 5 because: 60 6 10 3 2 2 5

A Happy Number A happy number… follows the rule: “Add the square of each digit” …creating a number chain that ends in ‘1’

Is your ‘special’ number happy? 2 3 23 is happy! 2² 3² 4 + 9 = 1 3 1² 3² 1 + 9 = 1 0 1² 0² 1 + 0 = 1

Shape be able to teach aspects of 2d shape, including transformations; understand the relationship between 2d nets and associated 3d solids;

Polygons Poly comes from the Greek word meaning ‘many’; gon comes from the Greek word for ‘angles’. A polygon is a flat shape with ‘many angles’. When we talk about polygons we are talking about shapes with 3 or more straight sides. (Polyhedrons: a solid shape with ‘many faces’)

Regular and Irregular If all the angles AND sides are equal it is called a regular polygon. Examples?

Triangles A 3-sided polygon is called a triangle. Can you sketch them all? Right angled Isoceles Equilateral Scalene Congruent – shapes which are exactly the same size and shape are called congruent.

Area of a triangle… ½ b x h 4cm 6cm 5cm 8cm

Glossary Definitions What vocabulary would you use to define these quadrilaterals: Parallelogram Rhombus Rectangle Square Oblong Kite and inverted kite (delta) Trapezium How do we compare to www.amathsdictionaryforkids.com ?

2 piece tangram Start with a square. Draw a straight line from one corner of the shape to bisect one of the opposite sides. Use this 2-piece tangram to investigate what different 2D shapes you can make by joining the pieces ‘full side’-to- ‘full side’. (No overlapping) How many different shapes can you make? Can you identify their properties?

Gnome Homes The King of the Gnomes needs your help! Triominoes  Tetrominoes  Pentominoes Use a systematic approach to find all the possibilities How will you know you have found them all?

Research: ‘Tangrams’/ ‘Tesselations’/ ‘MC Escher’/ ‘Origami’/ ‘Transformations’/ ‘Platonic Solids’ 2D challenges Tarsia Jigsaw ITT website: Keith Ws ‘Cutting up quadrilaterals’ Investigate ITP's - Isogrid, Polygon, Area, Coordinates What different shapes can you make by folding A4 paper? Isogrid ‘Dot to Dot’ - use a triangular array of 15 dots to draw different triangles. How many are there? 3D challenges The 12 Pentominoes – Which make the net of an open cube? Nets... what are the minimum number of 'flaps‘ required to secure a cube? Nets Challenge - What 3D closed shapes can you construct using up to 6 squares and 8 equilateral triangles? Building Nets from card – cube, tetrahedron, others… You will feedback!

Task 3 given out on Day 6 (Hand in Day 8 – 27/28 Feb 2014) Prepare 15 maths questions with explanation, working at your own level. This will give an indication of your progress with the subject knowledge audit. In your reflection – identify any areas for future study. WILF OUTCOMES: Access materials to revise/ revisit some identified aspects of subject knowledge, show evidence of research in identified areas