Topicmdf22dc6bc48e4b8f_1528449000663_0Topic

Isolating given value from the formulaformulaformula

Levelmdf22dc6bc48e4b8f_1528449084556_0Level

Second

Core curriculummdf22dc6bc48e4b8f_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).

Timingmdf22dc6bc48e4b8f_1528449068082_0Timing

45 minutes

General objectivemdf22dc6bc48e4b8f_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmdf22dc6bc48e4b8f_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 outcomesmdf22dc6bc48e4b8f_1528450430307_0Learning outcomes

The student:

- isolates given value from the formulaformulaformula.

Methodsmdf22dc6bc48e4b8f_1528449534267_0Methods

1) Situational analysis.

2) Individual task contest.

Forms of workmdf22dc6bc48e4b8f_1528449514617_0Forms of work

1) Individual work.

2) Group work.

Lesson stages

Introductionmdf22dc6bc48e4b8f_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 formula.

Proceduremdf22dc6bc48e4b8f_1528446435040_0Procedure

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

[Slideshown]

Students analyse the example.

Example

From the formulaformulaformula $a=\frac{x}{x-1}$, where $a\ne 1$, we will isolate x.

On the right side of the equation there is a fraction. Because the denominator of the fraction needs to be different from zero, therefore $x-1\ne 0$, so $x\ne 1$.

We multiply both sides of the equation by $x-1$.

We write the left side of the equation without parentheses.

Expressions containing the variable need to be on the same side of the equation. We add a to both sides and subtract x.

We factor out x.

We divide both sides of the equation by $a-1,$ knowing that $a\ne 1$.

Conclusion

In order to isolate the given value from the formula 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).mdf22dc6bc48e4b8f_1527752263647_0In order to isolate the given value from the formula 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).

Task contest
Students isolate given values from formulas using rules they learnt. They do exercises from consecutive levels of the contest. They can go to the next level after verifying obtained results.

Three pairs with the best time score get the highest marks, next three – second highest marks.

Students do examples alternately. The other person verifies the solution.

Contest task
Write the formulaformulaformula for the area of:

a) equilateral triangle;

b) any triangle;

c) trapezoid;

d) parallelogram.

Isolate the altitude of each polygon from its formulaformulaformula.

Contest task
Isolate x from the formulaformulaformula.

a) $4bx+2a=c-cx$

b) $vx-5v=z(2x-v)$

Contest task
From the following formulas isolate given variable. All variables are positive numbers. In the Internet look for relations in geometric figures than this formulas describe.

a) $P=ab+ah+bh$, isolate h

b) $P=\frac{a^2\sqrt{3}}{4}+2ah$, isolate h

c) $V=\frac{1}{3}{a}^{2}H$, isolate a

d) $V=\frac{a^2\sqrt{3}}{4}H$, isolate a

Contest task
a) Isolate the length a of the longer base of a trapezoid whose area is 4p, if its altitude is 3x and the shorter base is z.

b) Isolate the length y of the shorter base of a trapezoid whose area is 2p is its altitude is 4h and the longer base is a.

An extra contest task
Isolate a from the formulaformulaformula

The teacher evaluates students’ work and clarifies doubts.

Lesson summarymdf22dc6bc48e4b8f_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 taskscontest taskscontest tasks

factoring outfactoring outfactoring out

formulaformulaformula

given quantitygiven quantitygiven quantity

isolating the variableisolating the variableisolating the variable

transforming formulastransforming formulastransforming formulas

uniformly accelerated movementuniformly accelerated movementuniformly accelerated movement