Equations are useful to solve various daily life problems, especially the 1st degree equations which apply to everything, from your supermarket shopping to your future salary!

This WebQuest will help you learn to solve simple one and two step 1st degree equations, with many mathematical operations and a little… colouring!

**Your task is to find your way to the END of the maze.**

First, create teams of 3-4 persons. Then you will be given a maze with squares and numbers.

Each square is one of the following problems. The numbers are the possible answers. Solve the problems, find the solution, and follow the path from the START to the END. If you colour the path, it will be easier for you.

**P1**: Peter is eleven times the age of his daughter. In 6 years, Peter will be five times the age of his daughter. What is the current age of Peter?

**P2**: A gymnasium has 350 students. The 1^{st} grade has 20 students more than the 2^{nd} grade and the 3^{rd} grade has 32 less than the 1^{st} grade. How many students does the 3^{rd} grade have?

**P3**: If the students of a class sit in pairs on the desks, then 4 students remain standing. But if they sit in threes, then there will be 3 empty desks. How many students are there in the class?

**P4**: A cyclist travels a distance between two cities in 3 hours. If he increases his speed by 3 km / h, he will save half an hour. How long will the journey take if he drives at a speed of 3 km / h less than the first speed?

**P5**: The length and width of a rectangle are 10 cm and 6 cm, respectively. If its length increases by 5 cm, how much must its width be increased to double its area?

**P6**: One mother is 33 years old, and her daughter is 7 years old. After how many years will the mother be three times older than her daughter?

**P7**: There are 40 people at a party. If 8 boys leave and 2 girls come, then the number of boys is equal to the number of girls. How many girls were there in the beginning?

**P8**: Michael bought a painting giving a specific amount of money and bought a frame giving the same amount of money. If the frame cost 15€ less and the painting 10€ more, then the frame would cost half the painting. How much did the painting cost?

**P9**: A poultry farmer sold 1/3 of the eggs he had and 2 more, then he sold 4/5 of the rest and 2 more. So, he had 28 eggs left. How many eggs did he have in the beginning?

**P10**: One tap fills a tank in 12 minutes, another in 20 minutes and a third in 30 minutes. Find in how many minutes the tank will fill if all three taps run together.

**P11**: There are animals, chickens and goats, on a farm. If the animals have a total of 120 legs and 50 heads, how many goats are there?

**P12**: In a test with 10 questions each correct answer is scored with 5 points, while for each wrong answer 3 points are deducted. John got 26 points in the test. How many questions did he answer incorrectly?

**P13**: A theatrical performance was attended by a total of 100 parents and children. The receipts were € 590€. If each child paid 5€ and each parent 8€, how many parents were there?

**P14**: A pair of pants costs 125 € and we paid 95 €. How much per cent discount did they give us?

What you absolutely need to know are what is and how you can solve a 1st-degree equation.

- http://www.icoachmath.com/math_dictionary/first-degree-equations.html
- https://lexique.netmath.ca/en/first-degree-equation-in-two-variables/
- https://www.youtube.com/watch?v=jHsi_waT_9M
- https://www.youtube.com/watch?v=jtIIBBDjPK4
- http://www.sapiensman.com/matematicas/algebra8.php

The first step of your maze is PROBLEM 1 (P1). You need to solve this to start your path.

**P1: Peter is eleven times the age of his daughter. In 6 years, Peter will be five times the age of his daughter. What is the current age of Peter?**

So, this is a real-life problem. You have to translate the words into a 1st-degree equation, solve the equation and then you will know how to move.

Every box you come up with is a different problem. Every problem has one unique solution. Find this solution and continue your path to the END.

**Do not forget to colour the path. It will be easier for you to keep up with it!**

Choose one of the Following Mazes.

Maze no1 Maze no2

You have reached the END and now you have the path. Each path consists of equations. You need to deliver your teacher the equations’ solution.

You may try to solve all the other equations, which are not included in the path. All the problems are real-life situations you may come up in the future… Why don’t you give it a try?

- https://users.math.msu.edu/users/systeven/MTH1825/2.1B.pdf
- https://www.mathsteacher.com.au/year10/ch02_linear_equations/01_one_operation/solve.htm
- https://steemit.com/mathematics/@joseferrer/mathematical-explanation-first-degree-equation
- http://lsi.vc.ehu.eus/asignaturas/FdIvb/en/labs/lab04/FdI-Lab04en.pdf
- https://www.easycalculation.com/maths-dictionary/first_degree_equation.html
- https://www.mathsisfun.com/algebra/degree-expression.html

Game

This WebQuest aims at understanding the meaning of the first-degree equations, and how to use them to solve everyday problems.

Students are expected to develop their mathematical and logic skills. It is a necessary and highly beneficial course that can be used later in life to solve everyday problems.

In this section we will not dive very deep into the underlying educational theories about evaluation and testing: there’s too much out there than we could possibly cover in this small project report.

Instead, we want to concentrate on procedures that enable both students/pupils and their teachers to establish if the learning goals of the Webquest were achieved and, if so, to what extent. We recommend teachers make use of a combined evaluation procedure, that consists of:

- Statements by learners (after being asked to do so)
- telling what they learned about the subject (knowledge-oriented self-evaluation): now (after going through the Webquest) I know that …
- telling what he/she learned about herself/himself (formative evaluation, in this case, diagnostic self-evaluation): now (after going through the Webquest) I know about myself that I …

This pair of basic statements add up to a so-called__learner report__, in which the pupil/student reflects on what the Webquest brought him/her in terms of acquired knowledge and new personal views and attitudes concerning the subject.

For instance:

- ‘I learned that in medieval times the hygiene of people was hardly a concern which helped to let epidemic diseases like the Plague cause so many casualties’ Or:
- ‘I learned the facts and I know the earth is warming, but I cannot understand why people were so stupid to pollute the world and let it warm up so much.
- ‘I learned from the information about diseases that this subject is more appealing to me than I would expect in advance: maybe I should consider a medical career’. Or:

‘The Webquests confirms what I thought already: I could not care less about the climate and global warming. In fact, I thought it was all a hoax and I still do!’

This kind of assessment seems more subjective than it actually is: in his standard work on testing and evaluation (and much more), simply called Methodology (1974), Prof. A.D. de Groot described how consistent the student’s self-evaluations appeared to be: when asked again after 5 or 10 years, their evaluation would almost be the same. De Groot advised teachers to

__use the learner report as a start for joint evaluations__, striving for consensus between teacher and student/pupil about the learning outcomes and their value for the learner, but also__compared with the learning objectives as stated in the curriculum__. -
The learning achievements are visible in the output produced by the students: it is physical evidence: reports, answers to questions asked in the Webquest, presentations, and performance during presentations (preferably recorded). The teacher completes an evaluation grid stating clearly what the learning outcomes for the student/pupil are. The categories in the grid can be modified by the teacher to cover more precisely the content of a Webquest.

>We advise teachers to use the grid to start a joint evaluation discussion, aiming at consensus or at least understanding between the teacher and the student/pupil about the learning outcomes: were they achieved (as planned in the curriculum and communicated before the Webquest started) and to what extent? To communicate the learning goals clearly before any learning activity starts, is a__transparency requirement__that is widely acknowledged in the educational community. The history of making learning objectives explicit goes back to the evaluation ‘Bible’ by Bloom, Hastings and Madaus: ‘Handbook on formative and summative evaluation of student learning’ (1971), a standard work that also served as inspiration for the earlier mentioned Prof. De Groot.

The procedure also applies when students/pupils have worked together on a Webquest. The teacher will ask questions about individual contributions: ‘What did you find? What part did you write? How did you find the illustrations? Who made the final presentation?’

All the evidence (of learning efforts and outcomes plus joint evaluations) is preferably stored in the learning portfolio of the student, or in any other suitable storage system (folders with written or printed documents, online collection of files, etcetera ).

Changes in personal points of view and feelings are harder to value and here the consensus between teacher and student/pupil about experiences during the learning process provides essential insights.

The grid below gives an example of how the evaluation of the learning process and achievements can be shaped: what kind of reactions to the Webquest does the teacher expect and how valuable are they? Is the teacher capable to explain the value or score allocated to answers or presentations given by pupils? Does the pupil/student understand the evaluation outcomes, and does he/she agree? If an agreement (consensus is not possible, it is still the teacher who decides how to value the student’s work.

Please note that the text in the grid addresses the pupil/student directly: this is important and it is in fact a prerequisite for using such an evaluation grid: it is specifically meant to enable a discussion of learning results between teacher and student and not to communicate learning achievements of learners to others who had no direct role in the Webquest.

t: +357 2466 40 40

f: +357 2465 00 90

e: scool.it@scool-it.eu

t: +357 2466 40 40

f: +357 2465 00 90

e: scool.it@scool-it.eu

t: +357 2466 40 40

f: +357 2465 00 90

e: scool.it@scool-it.eu

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