Regents Review Spring Edition 2023

The Regents Review Spring 2023

Mathematics DEPARTMENTAL NEWS Further Maths We would like to wish the first Year 11 students to be entered for further maths GCSEs, the best of luck! After some amazing results in their recent mock exams, we believe in all of them! The Year 10 cohort have been set the following project as their current challenge, based on an A-Level coursework! Quadratic equations, and some cubic equations, can be solved simply through observation and algebra. Your project is to look at equations that cannot be solved this way because they do not have integer roots, and you will investigate how they can be solved using two, or three, different numerical methods. The numerical methods you need to research and use are: - Decimal search/change of sign - Newton Raphson Challenge #1 : Rearrangement/x=g(x) For each method, try to use a different equation and find at least one root of the equation, if not all of them. Some suggestions: x 3 - 2x 2 + 0.5 = 0 2x 4 - 3x 3 + 0.5 = 0 x 5 - 9x 2 + 3 = 0 Challenge #2 : Each of the equations below result in a failure for at least one of the methods - explain why. (2x 3 + 3x 2 - 4) 1/3 = 0 -5x 3 + 176x 2 - 9x + 0.1 = 0 x = (9x 2 - 3) 1/5 Challenge #3 : Use one of the equations which was used for a single method and find the same root using the remaining two methods. Compare how ‘quickly’ the three methods find the same root (how many iterations).

Maths Puzzle Move 3 matches to fix the equation.

Maths Mastery This term we teamed up with St Marks C of E School to develop our mastery teaching skills. We sent our mastery representatives to view each other’s lessons and discuss the mastery based techniques that are being used, and how to further improve. A concept discussed most was, using previously learnt skills to learn new content. For example, using negative number tiles to solve equations. Negative number tiles use the concept of ‘zero pairs’ as when together, they represent zero. Below is 4 pairs of negative number tiles. In total, they represent zero.

In the above example of solving equations with variables on both sides, the zero pairs have been used to explain how to rearrange to isolate the variable. As this concept is already familiar with students, it makes the idea of adding or subtracting on both sides easier to understand as we can see where the numbers ‘disappear’.

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