Topicm91786e98a261032e_1528449000663_0Topic

Transforming formulastransforming formulasTransforming formulas

Levelm91786e98a261032e_1528449084556_0Level

Second

Core curriculumm91786e98a261032e_1528449076687_0Core curriculum

VI. Equations with one unknown. The student:

5) transforms simple formulas to isolate a given value in geometric formulas (for example areas of figures) or physical formulas (for example about velocity, distance and time).

Timingm91786e98a261032e_1528449068082_0Timing

45 minutes

General objectivem91786e98a261032e_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm91786e98a261032e_1528449552113_0Specific objectives

1. Isolating given value from the formulaformulaformula.

2. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm91786e98a261032e_1528450430307_0Learning outcomes

The student:

- isolates given value from the formulaformulaformula.

Methodsm91786e98a261032e_1528449534267_0Methods

1. Situational analysis.

2. Individual task contest.

Forms of workm91786e98a261032e_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm91786e98a261032e_1528450127855_0Introduction

The teacher introduces the subject of the lesson – isolating the given value from the formulaformulaformula.

The class starts with a short pair contest. Each students gives a simple chemical or physical formulaformulaformula. The other person from the pair isolates the given value from this formulaformulaformula.

Procedurem91786e98a261032e_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to observe the way of isolating the given value from the formulaformulaformula.

[Slideshow]

Conclusion:

Transforming a formula is isolating the unknown in relation with other variables.m91786e98a261032e_1527752263647_0Transforming a formula is isolating the unknown in relation with other variables.

In order to isolate the given value from the formulaformulaformula we need to:

- Add (subtract) the same expression to (from) both sides of the equation.

- Multiply (divide) both sides of the equation by the same expression (while remembering about the assumption that the value of this expression needs to be different than zero).

Inidividual task contest.
Students isolate given values from formulas, using learn rules.

They can go to the next level after verifying results from the previous level.

Three students with the best time score get the highest marks, three following – second highest marks.

Contest taskcontest taskContest task 
Write the formulaformulaformula for the longer diagonal of a deltoid whose area is P, in which one diagonal is three times longer than the other.

Contest taskcontest taskContest task 
Isolate the variable $c$ from the following formulaformulaformula. All variables are positive numbers.

a) $\frac{a+4^0}{3b}=\frac{\sqrt{5^2}}{c}$

b) $\frac{a}{b+3}=\frac{2c}{d+\sqrt{25}}$

Contest taskcontest taskContest task 
Isolate the given variable from the following formulaformulaformula. All variables are positive numbers.

a) $W=a^2+\frac{ah}{5}$, isolate $h$

b) $Z=\frac{{\displaystyle a^2\sqrt{3}}}{3}+4a·h$, isolate $h$

c) $G=\frac{1}{4}{a}^2·s$, isolate $a$

d) $E=\frac{a^2\sqrt{2}}{5}·t+1$, isolate $a$

Contest taskcontest taskContest task 
The altitude of an equilateral triangle is equal to h. Calculate the perimeter of this triangle.

Contest extra task:
Search the internet for the formulaformulaformula for the harmonic mean of two positive numbers a and b. Isolate a from this formula.

Lesson summarym91786e98a261032e_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

In order to isolate the given value from the formulaformulaformula we need to:

- Add (subtract) the same expression to (from) both sides of the equation.

- Multiply (divide) both sides of the equation by the same expression (while remembering about the assumption that the value of this expression needs to be different than zero).

Selected words and expressions used in the lesson plan

contest taskcontest taskcontest task

formulaformulaformula

given quantitygiven quantitygiven quantity

isolating the variableisolating the variableisolating the variable

kinetic energykinetic energykinetic energy

potential energypotential energypotential energy

transforming formulastransforming formulastransforming formulas