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A piece of equations

In this UNIT we are going to see how a mathematical expression can be an useful tool for solving real-life problems. We have divided this UNIT into steps in order you to notice, understand, learn and apply this expression in solving problems.

Session 1: Dealing with real problems and converting them into mathematical expressions.
Session 2: Mathematical vocabulary. Parts of an equation. Standardizing equations.
Session 3: Solving first degree equations.
Session 4: Recap. Review of the concepts learned.
Session 5: Creating your own equations.

Before you start, notice that you have been provided with two explanatory sheets in order to carry out proposed activities:

Lan-sheet: It is a language sheet where grammar related to expressing opinions, moderating a debate, making conclusions,... However, if you need addittional help with grammar, it can be found in http://www.myenglishpages.com/site_php_files/grammar.php
Mat-sheet: It is a mathematical sheet where previous concepts related to the topic of this unit are recovered. However, if you need to explore more mathematical vocabulary, please go to http://www.amathsdictionaryforkids.com/dictionary.html

To get these sheets, please click on additional material, at the bottom of the page.

Then. Are you ready? Lets's start with session 1!

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SESSION 1

First of all I would want to ask you a question: Do you remember algebraic language? Moreover, how much algebraic language do you remember?

I think it is better for you to keep an eye to the following webpage before answering my question: remembering algebra

Now you're ready! Come on!

At the bottom of the page you can find a button "Let's start". Please, click on it and listen carefully what Daisy tells us.

Once you have listened to Daisy, how do you think you can solve her problem with additions, substractions, multiplications and divisions? Find a solution working with your full class:

choose a moderator
start a debate (remember explanatory sheets)
reach group consense
select one of you to write your solution in the blackboard
Check your solution by clicking on additional material, at the bottom of the page. You will find the solution file attached there. This is activity A.1.2.

Why don't we try with a more complicated problem? At the end of the page click on the button Still starting and listen to Mike's problem. After that:

choose a moderator
start a second debate (remember explanatory sheets)
reach again group consense
select one of you to write your solution in the blackboard
Check your solution by clicking on additional material, at the bottom of the page. You will find the solution file attached there. This is activity A.1.3.

Now you are aware of the process for converting real life problems into mathematical problems. Let's practice a bit!. Split your group of students into small ones, no more than 4 people in each one. Click on additional material and, once there, go to activity file and try to traslate the proposed daily problems into mathematical equations (activity A.1.4.). Control your time, as no more than 15 minutes will be needed.

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Have you finished? Are you sure of your answers? Then, click on additional material and, once there, move to the solution file and check them. It would be very interesting if you would share your errors and doubts with the rest of your class.

Before next session, please follow this link and see more examples in the following video (VIDEO 1):

See you in session 2!!

SESSION 2

Hello! Pleased to meet you again in this session 2. You might be dying with enthusiasm to continue with our lesson, so, let's start!

(Remember to look over explanatory sheets before coming to the substance)

In session 1 we learned how to convert a real life problem into a mathematical problem by getting a mathematical expression.

This expression is an equation and it conteins concepts that we don't know, numbers which we know and signs. We are going to deepen in equations. First of all we will see its elements. To this end, we will develop our first listening activity, so please, follow these instructions:

1. Please, click on activity A.2.1. at the bottom of the page and read carefully the statements, related to the parts of an equation.

2. You can find a video just bellow these lines (VIDEO 2). Please watch the following video, from the beginning to minute 9.00 and complete the activity A.2.1

3. Play the video a second time, but this time with the transcription, and correct you answers.

Have you performed well? Congratulations!

We would like you to add the concepts learned from the video to your mathematical glossary and to your maths notebook.

As you can be imagining now, it is possible to find several constants, variables, and coefficients in the same first degree equation. How can we deal with all of them?

To answer this question, please, play the previous video again (VIDEO 2), but this time please start on minute 9.00 and discover what "like terms" are, and the way for standardizing an equation, that is, the way for obtaining a 2-term equation able to be solved with Mathematics.

If you are not sure that you have completely understood how to standardize an equation, please watch the following video (VIDEO 3).

Note that in this course we deal with first degree equations, that is, equations with two terms, a constant and a unic variable, and in which the variable has exponent one.

Now you must be aware of the parts of an equation and of the standardizing process of a problem. It's high time for you to check if you have consolidated these concepts.

Please, click on activity A.2.2. at the bottom of the page and test what you have learned up to now.

If you want to practice standardization, please follow this link: standardizing equations

Do you fancy doing some cooperative work? Split your group of students into small ones, no more than 4 people in each one. Click on additional material and, once there, go to activity file and try to standardize the problems; These problems are the ones that you converted into equations in the previous session (activity A.2.3.). Control your time, as no more than 10 minutes will be needed.

_{tic...tac...tic...tac...}

Have you finished? Are you sure of your answers? Then, click on additional material and, once there, move to the solution file and check them.

How has it been? You are almost an expert in the equation's world. Congratulations. See you in session 3!!

SESSION 3

Hello! Pleased to meet you again in this session 3. You might be very keen on continuing with our lesson, so, let's start!

(Remember to look over explanatory sheets before coming to the substance)

In session 1 we learned how to convert a real life problem into a mathematical problem by geting a mathematical expression. And in session 2 we learned the parts of this expression and how to prepare this expression to be solved by geting a two-term equation. Then, it is a good moment to learn the solving process of an equation. At the end of this process, you will have found the solution to your real life problem. Are you ready?

We are going to develop our second listening activity, so please, follow these instructions:

1. Split your group of students into small ones, no more than 4 people in each one.

2. Please, click on activity A.3.1. at the bottom of the page and read carefully the statements, related to the steps of the solving process.

3. You can find a video just bellow these lines (VIDEO 3) explaining the solving process. Please watch the following video, from the beginning to minute 5.28.

4. Go back to activity A.3.1 and try to put your statements in the right order with your group.

5. Play the video a second time, but this time with the transcription, and correct you answers.

You have created a good methodology for solving first degree equations. Write it on your maths notebook, and remember to follow them every time you are solving an equation.

Let's go on with another video (VIDEO 4). You will find there 4 good exemples of real life problems solved with the previous methodology.

Now it is time for you to practice doing some cooperative work. Keep on with the same 4-people groups. Click on additional material and, once there, go to activity file and try to solve the real life problems explained (activity A.3.3.). Control your time, as no more than 20 minutes are needed.

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Once all the groups have finished it's a good moment to compare your answers:

Choose a member of your groups as the responsible for telling the rest of the students your solution to one of the problems of the activity A.3.1.
Take turns. Each time one of the groups will explain its solution to one of the problems until all the problems are explained.
If you disagree with any of the solutions given, please tell your opinion to the rest of the students, and try to reach consensus.

After you have gone over all the problems click on additional material and, once there, move to the solution file and check them. Were you right? I hope so, but, if not, don't worry about that! Try to understand the correct answer and find and correct your mistakes. I am sure that next time it will be better.

We have reached the end of session 3. Just in case you want to practice more, follow this link. There you can find on-line self-correcting exercises:more examples.

See you on next session!

SESSION 4

Hello! Pleased to meet you again in this session 4. We have almost reached the end of the lesson and I'm sure you want to see what we are going to do, so let's start!

(Remember to look over explanatory sheets before coming to the substance)

In session 1 we learned how to convert a real life problem into a mathematical problem by geting a mathematical expression. In session 2 we learned the parts of this expression and how to prepare this expression to be solved by geting a two-term equation. In session 3 we learned the solving process of an equation. Session 4 is devoted to recap and consolidate all the ideas explained. Are you ready?

Please, split your group of students into small ones, no more than 4 people in each one. Shuffling people between groups is advisable to learn how to work with different kinds of people. For each group, try to answer following questions and write notes in your maths notebook when necessary. Control your time, as no more than 20 minutes are needed.

What expression have we learned?
Which are its parts/elements?
How can you define each one?
What is the standardization process? Is it always necessary when solving equations?
Which are the steps for solving a first degree equation?
Give 5 examples of real life situations able to be solved with a first degree equation

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Once all the groups have finished, it is time to share answers with the rest of the class. To this end:

Choose a moderator.
Go through questions in order, one by one, until all the problems are explained.
Each group, choose a representative.
Take turns. For each question, the representative of one group will be responsible for telling the rest of the students the answer of his group.
If you disagree with any of the solutions given, please tell your opinion to the rest of the students, and try to reach consensus (remember explanatory sheets)
The moderator has to complete the poster of the equations unit with the answers.
When all the questions are analysed and the poster is fulfilled, please, hang it on the back wall of the class, and remember to see it each time you need.

After this recap of the content learned, please click on activity A.4.2. at the bottom of the page and test what you have learned.

Now, this session has ended. However, you are encouraged to practice more to consolidate the content learned, therefore, please, click on additional material and, once there, go the activity file and do activity A.4.3. You can self-correct your answers with the solution file.

Before the last session it is advisable for you to practice more. Therefore, follow this link and explore in "Part 1: Translating the problem into equations with variables" different kinds of related problems:different real problems

And if you want to become an expert in solving equations, please watch this video:

And see you in session5!!

SESSION 5

Hello! I'm sorry to say you that this is our last (but not least) session. What a pity!

(Remember to look over explanatory sheets before coming to the substance)

In session 1 we learned how to convert a real life problem into a mathematical problem by geting a mathematical expression. In session 2 we learned the parts of this expression and how to prepare this expression to be solved by geting a two-term equation. In session 3 we learned the solving process of an equation. Session 4 was devoted to recap and consolidate all the ideas explained. Finally, in session 5 you are encouraged to show your mates how can you apply equations to your daily life. Go on!

First stage: Chain of events

Please, split your group of students into small ones, no more than 4 people in each one. Like in previous sessions, shuffling people between groups is advisable to learn how to work with different kinds of people.

For each group:

Think about a situation from your daily life able to be solved with a first degree equation.
Analyse it, identifying: Problem, expression, parts of the equation, standardizing process, solving process, solution, interpretation.
Click on additional material at the bottom of the page and, once there, click on Chain, and complete it with the ideas merged in the previous step.

Control your time, as no more than 15 minutes are needed.

Second stage: Presentations

Now, once all the groups are ready, it would be great to share your problems and solutions with the rest of the class. So, please, start distributing tasks in your group:

One of the students presents the problem and explains how to convert it into a mathematical problem.
One defines the parts of the equation and the process of standardization.
One explains the solving process.
One interprets the solution and tells the rest the problems they have found during the development.

Each time one group has the word and has to explain previous questions to their mates. When listening to other group, if you disagree with anything, let them know and try to reach the correct answer

No time is advisable. Ii is up to you to discuss your equations during all the time you want.

Finally, when you finish, please, clilck on the "Bye, bye" button.