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# Formulae and Equations for Problem Solving

## 20-23 December 2021

Bringing maths alive and learning programming in a fun and exciting way lie at the heart of what we do at LondonSMP.

This camp is for children interested in maths and programming who want to cement their existing knowledge, discover real life applications for it and learn much more, all online in small groups with like minded pupils.

In Maths, we will dive deep into the world of equations, looking at algebra and geometry, with complexity increasing by age group. We’ll study how practical problems or mathematical ideas can be transformed into formulae and how they can be manipulated and transformed back to provide practical results or mathematical theorems.

Here are more details of what will be studied by each Year group:

Years 3-4

Pupils will work on arithmetic and geometric puzzles moving on to using diagrams for solving word problems. In problem solving lessons, the pupils will work on past problems from the UK and international mathematics competitions for their age

Years 5-6

Introducing basic algebra to generalise the description of quantities and using equations as a powerful tool to answer questions about quantitative relationships. In problem solving, pupils will work on past problems from the UK and international mathematics competitions for their age

Years 7-9

Equations versus identities. How to set up an equation? Linear equations and simultaneous systems of linear equations. Typical mistakes. Working with parameters. The Greek world of Geometry and their handling of quadratic equations. In problem solving, pupils will study word problems and questions related to motion and geometry from UKMT Challenges.

Years 10-11

Different ways to look at an equation. Equivalent and nonequivalent steps. Typical mistakes. Why and how do we check our workings? The geometry of the simultaneous system of equations. In problem solving we will look at Diophantine equations: what if the solution is supposed to be a whole number? Number theory in action. Functional equations: what if the solution is supposed to be a function instead of a number? The gateway to modern science.

In Programming, depending on a child’s previous experience and knowledge, pupils will either learn the basics of programming in Scratch and Algorithmical Drawing or will go further and study Python, Processing or Python Blender 3D.

Format and fees for the senior online camp:

• class sizes are six pupils or fewer of similar age and ability
• each day runs for six hours with four one hour classes and strategic breaks from the screen between them
• class times are: 10.00-11.00, 11.30-12.30, 13.30-14.30, 15.00-16.00
• all classes are interactive, using Zoom, with pupils solving problems with the teacher and with each other
• pupils must have a PC or laptop (Windows or Mac OS) with a camera and mic and a stable internet connection.
• fees are £400 for four days.  Bookings of fewer days are not possible for this camp