Topicm49bc5714a39f5a9a_1528449000663_0Topic

Solving the text tasks by using the equations

Levelm49bc5714a39f5a9a_1528449084556_0Level

Second

Core curriculumm49bc5714a39f5a9a_1528449076687_0Core curriculum

XIV. Text tasks. The student:

5) uses gained knowledge in the field of geometry and arithmetic, his accounting skills and appropriate methods to solve the tasks settled in the practical context.

Timingm49bc5714a39f5a9a_1528449068082_0Timing

45 minutes

General objectivem49bc5714a39f5a9a_1528449523725_0General objective

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

Specific objectivesm49bc5714a39f5a9a_1528449552113_0Specific objectives

1. Writing the information and data of the content of the task in a form of the equationequationequation.

2. Solving the equations with one unknownunknownunknown.

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

Learning outcomesm49bc5714a39f5a9a_1528450430307_0Learning outcomes

The student:

- writes the information and data of the content of the task in a form of the equationequationequation,

- solves the equations with one unknownunknownunknown.

Methodsm49bc5714a39f5a9a_1528449534267_0Methods

1. Snowball sampling.

2. Situational analysis.

Forms of workm49bc5714a39f5a9a_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm49bc5714a39f5a9a_1528450127855_0Introduction

The teacher prepares a set of six cards for each pair of students. There is one of the sentences written on each of the cards:

- Solve the equationequationequation.

- Write the answer given to the question.

- Specify the unknown of the task and mark it with the letter.

- Check, if the solution of the task specifies all the conditions of the task.

- Rearrange the equationequationequation describing the content of the task.

- Read the content of the task carefully.

The teacher also prepares 9 envelopes: three marked with number 1, three marked with number 2 and three marked with number 3.

The envelopes with number 1 contain the following task:

1. Darek and his father are 60 years altogether. Darek’s father is three years older than his son. How old is Darek?

The envelopes with number 2 contain the following task:

2. Marcin has raised the savings of 61 PLN. He has had only 2 PLN and 5 PLN coins in his money‑box . There were 8 coins of 2 PLN. How many coins of 5 PLN has Marcin got in his money box?

The envelopes with number 3 contains the following task:

3. The perimeterperimeterperimeter of the triangle is 24 dm. Calculate the length of its side knowing that the side of the middle length is longer by 2 cm than the shortest side and shorter by 2 cm than the longest side.

The student brings the cardboard and the colorful felt‑tips for the lesson.

The students revise solving of the equations and reducing the algebraic expressions to the simplest form.

Procedurem49bc5714a39f5a9a_1528446435040_0Procedure

The teacher introduces the topic of the lesson: solving the text tasks by using the equations.

The students work individually using their computers. They are going to analyse the slideshow about solving the text tasktext tasktext task by using the equations.

[SLIDESHOW]

The students work in pairs. Using the information they have gained they put the stages of the text tasks prepared by the teacher in the correct order. Next, one of the students reads the correct order aloud:

1. Read the content of the task carefully.
2. Specify the unknown of the task and mark it with the letter.
3. Rearrange the equation describing the content of the task.
4. Solve the equation.
5. Check, if the solution of the task specifies all the conditions of the task.
6. Write the answer given to the question.m49bc5714a39f5a9a_1527752263647_01. Read the content of the task carefully.
2. Specify the unknown of the task and mark it with the letter.
3. Rearrange the equation describing the content of the task.
4. Solve the equation.
5. Check, if the solution of the task specifies all the conditions of the task.
6. Write the answer given to the question.

The snowball sampling method. The students work in the groups of three or four. The receive the task prepared earlier by the teacher. They write on the cardboard the stages of solving the task. Next, the groups  which have solved the task 1 discuss gained results and complete their task descriptions, if necessary. The groups solving the task 2 and 3 act in the similar way. Finally the leaders of the groups present the solutions of the tasks 1, 2 and 3 in front of the class.

Using the gained information the students solve the text tasktext tasktext task by using the equations. Then, in pairs they compare the results.

Task 1
A x number was increased by 135 to receive the number of 271. What number was increased?

Task 2
The areaareaarea of the rectangle equals 104 cmIndeks górny 2². One of its side is 8 cm long. What is the length of the other side of the rectangle?

Task 3
There are 25 students in a class. The number of boys is lower by 6 than the number of girls. How many girls and how many boys are there in that class?

Task 4
Kate has paid 9,10 PLN for 2 kilos of apples and one kilo of pears. How much is 1 kilo of apples if one kilo of pears is 3,30 PLN?m49bc5714a39f5a9a_1527752256679_0Kate has paid 9,10 PLN for 2 kilos of apples and one kilo of pears. How much is 1 kilo of apples if one kilo of pears is 3,30 PLN?

An extra task:
Find three subsequent natural numbers whose sum equals 261.

Lesson summarym49bc5714a39f5a9a_1528450119332_0Lesson summary

The students do the summarising tasks.

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

To solve the text tasktext tasktext task by using the equationequationequation you should:

1. Read the content of the task carefully.
2. Specify the unknown of the task and mark it with the letter.
3. Rearrange the equatiodescribing the content of the task.
4. Solve the equation.
5. Check, if the solution of the task specifies all the conditions of the task.
6. Write the answer given to the question.m49bc5714a39f5a9a_1527752263647_01. Read the content of the task carefully.
2. Specify the unknown of the task and mark it with the letter.
3. Rearrange the equatiodescribing the content of the task.
4. Solve the equation.
5. Check, if the solution of the task specifies all the conditions of the task.
6. Write the answer given to the question.

Selected words and expressions used in the lesson plan

areaareaarea

conditions of taskconditions of taskconditions of task

equationequationequation

equation with one unknownequation with one unknownequation with one unknown

perimeterperimeterperimeter

solution of the equationsolution of the equationsolution of the equation

text tasktext tasktext task

unknownunknownunknown