Lesson Plan - Simultaneous Equations With Different Coefficients 3d5e3f

Lesson Planning Sheet Title: Solve complex problems by derive and solving a pair of simultaneous equations Learning Objectives: By the end of the lesson: All students should be able to solve a pair of simultaneous equations with different coefficients using the elimination method  Most students should be able to derive and solve a pair of simultaneous equations by equating two unknowns.  Some students should be able to equate two unknowns from a diagram and solve using the method of elimination. Key words: Derive, Equate, Elimination, Coefficients, Simultaneous Equations 

Learning Activities

Resources:

Starter/Introduction Students are presented with different equations involving two unknowns and are asked to determine the odd one out using equivalences. At first, pose the problem as it is with no guidance. If a little help is required, pose a similar problem with simple equivalent fractions. This should recap their prior knowledge to look for equivalent coefficients. Students could attempt this in pairs so that they come to question each other’s method. Presenting solutions on mini-whiteboards to the teacher will enable an accurate assessment of their prior understanding to be made.

Mini-whiteboards Calculators

Development In order to progress on to deriving the equations the students will need to consolidate their ability to solve traditional problems at various levels of difficulty. Discuss how the problems on the second slide need to have unknowns with equal coefficients so that the method of elimination can be used. The starter activity will this. It is important to ensure that al students are proficient with solving these equations so that future energy is directed onto deriving the equations. Therefore, pose each problem for the students to do consecutively on mini-whiteboards and after each attempt. Discuss how the final problem has to be rearranged to line up the unknowns. Alternatively, the value for y can be substituted into the other equation. Once the problems on the second slide have been successfully completed the students should be encouraged to try the questions on the third slide independently. Encourage them to look for unknowns and assign appropriate symbols to represent them. Students should be encouraged to work in pairs or small groups so that they are able to question and extend each other’s thinking. This work can either be done on mini-whiteboards first or in their exercise books. the method and solutions progressively throughout the lesson in order to maintain pace and challenge. An extension to this could be to have students create their own problems for each other so that they have a deeper understanding of deriving and manipulating equations. Plenary The problem on the final slide is intended as a consolidation to the learning objective. Students should be simply posed the problem with no help provided. Ideally, they will be able to create the two shapes using combinations of x and y and therefore derive two equations. Should this be a problem the teacher could work through the first area, which will guide the students into making the second one. Students will need to use mini-whiteboards to construct the shapes so that individual x and y components can be seen.

Differentiation More able:  Students could use the method of substitution to solve the equations.  Creating their own problems will enable the students to gain a deeper understanding of how to derive and manipulate the equations into picture form. Less Able  Students may need extra time solving equations rather then deriving them.  Deriving equations which have equal coefficients will enable more energy to be spent on the derivation as opposed to solving them.