1. Problem Solving Resources for the NC New topics chris.olley@kcl.ac.uk chris@themathszone.co.uk www.themathszone.co.uk www.themathszone.com

2. What’s New KS3? (CJO) Aims: (i) fluent (ii) reason mathematically (iii) solve problems  appreciate the infinite nature of the sets of integers, real and rational numbers  expanding products of two or more binomials  model situations or procedures by translating them into algebraic expressions or formulae  … including piece-wise linear  recognise arithmetic sequences and … geometric sequences  interpret mathematical relationships both algebraically and geometrically  enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

3. What’s New KS4? (CJO) Aims: (i) fluent (ii) reason mathematically (iii) solve problems  set up appropriate algorithms and iterative procedures  understand and use algebraic arguments, relying on the multiplicative structure of number.  understand and use mathematical arguments  model simple contextual and subject-based problems algebraically  identify and interpret gradients, roots, intercepts, turning points graphically and numerically  solve velocity and acceleration problems … velocity/time graphs, and mechanics problems, such as those involving collisions and momentum.  solve growth and decay problems, such as financial mathematics problems with compound interest  use iterative methods to solve problems such as loan repayment  understand and use the concepts of instantaneous and average rate of change in graphical representations (chords and tangents), including with velocity and acceleration  calculate conditional probabilities … Venn diagrams  describe relationships in bivariate data … interpolate and extrapolate trends.

4. [finite to infinite, discrete to continuous]  appreciate the infinite nature of the sets of integers, real and rational numbers  recognise arithmetic sequences and … geometric sequences [Discrete numerical methods]  set up appropriate algorithms and iterative procedures  use iterative methods to solve problems such as loan repayment [Continuous functions]  expanding products of two or more binomials  identify and interpret gradients, roots, intercepts, turning points graphically and numerically [Discrete …]  enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams  calculate conditional probabilities … Venn diagrams [Modelling is …]  model simple contextual and subject-based problems algebraically  model situations or procedures by translating them into algebraic expressions or formulae  describe relationships in bivariate data … interpolate and extrapolate trends. [Modelling … precise]  solve growth and decay problems, such as financial mathematics problems with compound interest [Modelling … imprecise]  understand and use the concepts of instantaneous and average rate of change in graphical representations (chords and tangents), including with velocity and acceleration  … including piece-wise linear  solve velocity and acceleration problems … velocity/time graphs, and mechanics problems, such as those involving collisions and momentum. [Mathematics]  interpret mathematical relationships both algebraically and geometrically  understand and use algebraic arguments, relying on the multiplicative structure of number.  understand and use mathematical arguments

5. Venn Diagrams on the Floor Set theory Probability Venn Diagrams http://nrich.maths.org/public/leg.php?code=5 014&cl=3&cldcmpid=794

6. Topics 1.Functions with discrete variables (sets, sequences); (linear – arithmetic, exponential – geometric) 2.Continuous functions (polynomial – linear, product of monomials, exponential – compound interest) Forms 1.Values (sequence, table) 2.Algebraic description (sequence, function) 3.Geometric form (Venn diagram, graph) Applications 1.Examples of algebraic models (finance, mechanics) 2.Example of modelling (pizza)

7. Graphing Software How well can you manage any function as its parameters vary? http://nrich.maths.org/9005 http://nrich.maths.org/8742

8. Speed, distance, time Walking the function Average speed = distance over time [piecewise linear] Projectiles as a graph Momentum: https://www.youtube.c om/watch?v=4IYDb6K5 UF8 https://www.youtube.c om/watch?v=4IYDb6K5 UF8 Mechanics modelling assumptions http://nrich.maths.org/6528 http://nrich.maths.org/6528