Topicmac8a211e033ec58b_1528449000663_0Topic

Transforming formulastransforming formulasTransforming formulas

Levelmac8a211e033ec58b_1528449084556_0Level

Second

Core curriculummac8a211e033ec58b_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).

Timingmac8a211e033ec58b_1528449068082_0Timing

45 minutes

General objectivemac8a211e033ec58b_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmac8a211e033ec58b_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 outcomesmac8a211e033ec58b_1528450430307_0Learning outcomes

The student:

- isolates given value from the formulaformulaformula.

Methodsmac8a211e033ec58b_1528449534267_0Methods

1) Situational analysis.

2) JIGSAW.

Forms of workmac8a211e033ec58b_1528449514617_0Forms of work

1) Individual work.

2) Group work.

Lesson stages

Introductionmac8a211e033ec58b_1528450127855_0Introduction

Students write down examples of formulas from physics, chemistry or geometry that they know. Discussion – do we always apply formulas in this form? Is it worth to transform them and why.

Students probably notice that very often there is a need to isolate unknowns from formulas and then we can use the ability to transform them.

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

Proceduremac8a211e033ec58b_1528446435040_0Procedure

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.mac8a211e033ec58b_1527752263647_0Transforming a formula is isolating the unknown in relation with other variables.

The teacher divides students into 4 persons groups that work using the JIGSAW method. Each member of the group gets different task from the tasks below. After solving the tasks, students gather in groups that were doing the same task. They discuss the solutions and clarify any doubts. Then, they return to the initial groups and present the solutions to other members.

Task
Insert such number in the dotted space that the sentence is true.

a) If y = 0,3x then x = ...y.

b) If $s=\frac{1}{2}t$ then t = ...s.

c) If z = 4v then v = ...z.

Task
Isolate the variable x from the formulaformulaformula.

a) $3x+2=x-a$,

b) $1-x=1-2a$,

c) $-4x+y+5=5y$.

Task
Isolate the given variable from the formulaformulaformula. Give necessary assumptions.

a) $I=\frac{U}{R},$ isolate R,

b) $F=m·a,$ isolate m,

c) $s=\frac{a\cdot t^2}{2},$ isolate a,

d) $\frac{T_1}{v_1}=\frac{T_2}{v_2},$ isolate TIndeks dolny 1₁.

Task
Area of a triangle whose base is 2a is equal to $\frac{1}{5}a$. Determine the altitude of this triangle.

Students discuss their work, the teacher evaluates their solutions and clarifies doubts.

Volunteers do the extra task on the board and get pluses for correct solutions.

An extra task
From the following formulas isolate given variable. All variables are positive numbers.

a) $\frac{x}{y}=\frac{z}{v},$ isolate z and v,

b) $\frac{2x}{y}=\frac{5z}{3},$ isolate x and z,

c) $\frac{x+2}{3y}=\frac{2}{3v},$ isolate y and z.

Lesson summarymac8a211e033ec58b_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

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

Selected words and expressions used in the lesson plan

formulaformulaformula

given quantitygiven quantitygiven quantity

isolating the variableisolating the variableisolating the variable

relativity theoryrelativity theoryrelativity theory

transforming formulastransforming formulastransforming formulas