Topicmc2ef756c4efc425e_1528449000663_0Topic

Solving equations with one unknown

Levelmc2ef756c4efc425e_1528449084556_0Level

Second

Core curriculummc2ef756c4efc425e_1528449076687_0Core curriculum

VI. The elements of algebra. The student:

1) uses simple formulas with the letter marking, describes the formulas verbally;

2) uses the letter marking of unknownunknownunknown figures and writes down simple algebraic expressions on the basis of the information filled in with a practical contents, e.g. writes the perimeter of the triangle with the sides: a, a+2, b; solves linear equation in one unknownunknownunknown occurring in one side of the equation ( by guessing completing, or doing the opposite) e.g. $\frac{x-2}{3}=4$.

Timingmc2ef756c4efc425e_1528449068082_0Timing

45 minutes

General objectivemc2ef756c4efc425e_1528449523725_0General objective

Matching the mathematical model to a simple situation and using it in various contexts.

Specific objectivesmc2ef756c4efc425e_1528449552113_0Specific objectives

1. Checking if the number specifies the equation.

2. Solving the equations with one unknownunknownunknown.

3. Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Learning outcomesmc2ef756c4efc425e_1528450430307_0Learning outcomes

The student:

- checks if the number specifies the equation.

- solves the equations with one unknownunknownunknown.

Methodsmc2ef756c4efc425e_1528449534267_0Methods

1. Learning game.

2. Situational analysis.

Forms of workmc2ef756c4efc425e_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc2ef756c4efc425e_1528450127855_0Introduction

The teacher prepares a set of three cards including one of the following letters: A, B or C.

The students play learning game and revise the equations and calculation of the numerical value of the algebraic expressionalgebraic expressionalgebraic expression.

The students work in groups of three or four. They make up the name of their team and write it on the board. The teacher presents the questions in a form of the slideshow. The team which first gives the correct answer: A, B or C gets a point. The teacher writes the points to the appropriate team. The winner is the team with the greatest number of points.

Quiz

1. Select the expression, which is the equation:
A. 35 + 7 = 22 + 20
B. 35 + a = 47
C. 20x + 17

2. The equation with one unknown isn’t:
A. 2x + y = 15
B. 3x + 2x = 30
C. 7x = 77

3. The equation presented in the sentence: „The number larger by 37 than number m equals 78” is the equation:
A. m - 37 = 78
B. m + 37 = 78
C. 37m = 78

4. The algebraic expression of 5y + 12, for y = - 3 is:
A. 27
B. 14
C. - 3

5. The value of the algebraic expression (x + 4) : 2 is - 4 if:
A. x = - 8
B. x = - 10
C. x = - 6

The correct answers are the following:

1. A, 2. B, 3. B, 4. C, 5. A.

Proceduremc2ef756c4efc425e_1528446435040_0Procedure

The teacher introduces the topic of the lesson: solving the task with one unknownunknownunknown.

Discussion: What does it mean to solve the equationequationequation? How can we check if the number satisfies the equationequationequation?

The students can come up with the following conclusions:

- To solve the equationequationequation we should find all the numbers which satisfy it or prove there are no such numbers.

- The number satisfies the equationequationequation if after replacing the unknownunknownunknown with it, the left and the right sides of equationequationequation are equal.

Using the gained information the students solve the equationequationequation on their own. Then, in pairs they compare the results.

Task 1
Check if the number x satisfies the equationequationequation.

a. $120:x=30,x=4$

b. $7x+6=28,x=3$

c. $12x+12=48,x=3$

d. $(x-11)\cdot 4=76,x=30$

e. $(x+9):3=31,x=82.$

Task 2
Solve the equationequationequation.

a. $120-a=54$

b. $12·w=132$

c. $y+25=139$

d. $t-18=-13$

e. $7m=490.$

Task 3
Solve the equationequationequation.

a. $4y+8=40$

b. $15+2x=90$

c. $7a-23=61$

d. $5z-17=-47.$

The students work in pairs. They write and solve the equations depending on the drawings and the content of the tasks.

Task 4
Write the appropriate equationequationequation corresponding with the situation presented in the drawing and solve it. The scalesthe scalesThe scales are in balance.

[Interactive illustration]

Task 5
Write the appropriate equationequationequation and solve it.

a)The number fifteen times less by the number y equals 315. How much does the number y equal?

b) Eve is x years old and she is by 27 years younger than her mum who is 50. How old is Eve?

c) Marek weighs p kilos and he is by 17 kilos heavier than Tom whose weight is 48 kg. How much does Mark weigh?

An extra task:
Solve the equationequationequation:  $5x-5=16-2x.$

Lesson summarymc2ef756c4efc425e_1528450119332_0Lesson summary

The students do the summarising tasks.

Then they sum up the class drawing the conclusions to memorise:

- To solve the equation we should find all the numbers which satisfy it or prove there are no such numbers.mc2ef756c4efc425e_1527752263647_0To solve the equation we should find all the numbers which satisfy it or prove there are no such numbers.
- The number satisfies the equation if after replacing the unknown with it, the left and the right sides of equation are equal.mc2ef756c4efc425e_1527752256679_0The number satisfies the equation if after replacing the unknown with it, the left and the right sides of equation are equal.

Selected words and expressions used in the lesson plan

algebraic expressionalgebraic expressionalgebraic expression

assessingassessingassessing

equationequationequation

equation with one unknownequation with one unknownequation with one unknown

left side of the equationleft side of the equationleft side of the equation

right side of the equationright side of the equationright side of the equation

solution of the equationsolution of the equationsolution of the equation

the scalesthe scalesthe scales

unknownunknownunknown