# LESSON PLAN 2

- Least common multiples and greatest common divisors (LCM & GCD)

- Arts (includes music, architecture ...), Languages (includes English), Mathematics (includes geometry, proportionality, finances ...), Science (includes physics, biology ...)

- ISCED 2 = Lower Secondary Education

## Duration

4 Learning Units / 4 hours / 45 minutes each

## Topic

To factor means to express a number – or an algebraic expression – as a product of its factors, i.e. its divisors.

## Synopsis

This lesson contains LCM & GCD examples and exercises for students in the first year of secondary school or students aged 12.

## Contributors

Teachers form other related subjects

## Framework

**Action plan formulation:**

There are 4 activities involved.

**Teacher’s cooperation and division of work:**

Teacher 1 – Mathematics

Activity number 1: this activity, the teacher will take class time to explain the theory of the LCM and the GCD. At the end of the class, there will be time for questions.

Teacher 2 – Science

Activity number 4: this activity, students become familiar with the primate family through a prime factor decomposition activity.(Annex 4)

Teacher 3 – Arts

Activity number 2: Through this manipulative activity, students continue to learn the basic concepts of LCM and GCD. (Annex 2)

Teacher 4 – English

Activity number 3: Students go through reading comprehension to be able to do mathematical problems. (Annex 3)

## Material / Equipment

Material needs for students:

- Photocopies
- Pens

Material needs for teachers:

- Laminator
- Photocopying
- Base ten cubes
- Blocks

## Previous knowledge and skills

The student must know how to make divisions to carry out the activities in this lesson plan.

## Learning Objectives

**Learning Objectives: **

Upon completion of the class students should **know****:**

- Know and calculate mcm and LCD by factorial decomposition of numbers.
- Understand and apply the GCD by common multiples of numbers.
- Understand and apply the LCD by common divisors of numbers.

Develop strategies for mental calculation of LCM and GCD of simple numbers.

**Learning Outcomes and Expected Results:**

__Learning____O____utcomes__:- The student uses the principles of computational thinking by organising data, decomposing it to parts, recognising patterns, interpreting, modifying and creating algorithms, to model situations and solve problems effectively.
- The student is interested in formulating and testing simple conjectures or posing problems autonomously, recognising the value of reasoning and argumentation, to generate new knowledge.
- The student represents, individually and collectively, mathematical concepts, procedures, formation and results, using different technologies, to visualise ideas and structure mathematical processes.
- The student communicates individually and collectively mathematical concepts, procedures and arguments, usg oral, written or graphic language, using appropriate mathematical terminology, to give meaning and coherence to mathematical ideas.

## Methodology

Connections with e-platform ( general ideas):

**Methodology**

Cooperative learning

**Teaching Method(s): **A methodology in which students are grouped to heterogeneous groups and work a coordinated and interactive way to solve a task. The distribution of roles is fundamental: coordinator, secretary, spokesperson and assistant.

The objectives of this methodology are as follows:

- To favour the learning of all.
- Favours socialisation and interdependence.
- Stimulates peer support.
- Develops dialogue and cooperation skills.
- creases motivation for the task.
- Allows content to be adapted to the level of the students.

**Motivation strategy:** Students will have the opportunity to present a fall portfolio to the class. In the end, a vote will be taken and the best of all will be voted on. The winner will get a prize and the rest of the groups will get another reward for their participation.

__The general strategy to be followed by the teacher__: The teacher will assign roles to the participants each day. If the class is 20 students, groups of 4 will be formed. In this case, 5 groups of 4 people will be formed. This lesson plan is distributed to 4 activities, so each activity, each student will have a role. For example:

Activity 1/student 1: Coordinator

Activity 2/student 1: Secretary

Activity 3/ student 1: Spokesperson

Activity 4/ Student 1: Assistant

## Preparation & Resources

Before you start you have to think about whether the class is yours, or whether you have to move to another class stead. If you have a classroom, make sure you leave all the material in the same place so that the students can have it at any time. If you don’t have your own classroom, make sure you take all your materials with you before the class starts and make sure the students are distributed as they should be for about 3 minutes.

Tables will be arranged in groups of 4 people. If there are odd numbers of students, it does not matter if there is one more or one group less. It is always possible to take on repeated roles and divide up the tasks, or one less role (such as assistant).

**Troubleshooting Tips**:

Some necessary tips to keep md are as follows:

- Make the class rules and the rules for each activity clear to the students.
- Keep in mind that the groups should be heterogeneous.
- Remember that at the end of this lesson plan, the students will have a reward (positive reinforcement).
- Keep in mind that not all activities are equally difficult.
- Consider that students do not come motivated every day and that some activities will be more difficult for them.
- If some of the students do not cooperate, you can give them time to think again. Spend ten minutes with that student. You can ask them to help by suggesting that they be the observer/helper that day. If the student is the observer/helper, this means that he/she will have to be aware if there is any discussion with any group and try to help or if there is any doubt, try to solve it.

**Optional resources**:

I Do Maths · GCD and LCM: Theory for teachers

Least common multiple (practice) | Khan Academy: Website with theory and activities

Least Common Denomator – Worksheets (superteacherworksheets.com): Calculation activities

## Implementation

Lesson plan duration: 180 minutes. Each activity will last a maximum of 45 minutes.

As mentioned above, each student will have a role in each group. However, each day will follow a collaborative learning technique.

- First activity (mathematics): Numbered heads

This is a cooperative learning strategy, everybody gets ready to answer. Each student numbers himself/herself with a number from one to four. And only the student who has the number that the teacher says answers. The teacher will go group by group, asking questions at the end of the class to find out if there are any doubts.

- Second activity (arts): Dynamics 1-2-4

This dynamic consists of the following:

- The question to be developed is posed to the students.
- We hand out a sheet of paper divided into three Each column corresponds to a number: 1 for individual work, 2 for pair work and 4 for group work.
- We give each student five minutes to respond individually to column
- After this time they are given five minutes again. This time they will work in pairs column 2, sharing their answers.
- Fally, column 4, they will work in groups. They will have to agree on all their answers so that they can write one that unifies everything they have worked on. At this pot, we can give them a little more time.

- Third activity (English): Pencils to the centre

This technique consists of 3 steps:

- Students put the pencils on the table. Students read the exercise to be done individually and together.
- The pencils are on the table. Question time. Students ask questions and, among themselves, clarify them or ask the teacher for help.
- Students take pencils and can no longer speak. They can only write.

- Activity four (Science): The 4 Wise Men

The steps to follow are:

- On the day of the exhibition, the teacher chooses four students from the class who have mastered a certain topic, skill or procedure. They become “savants” in certain things. He asks them to prepare well, as they will have to teach what they know to their classmates.
- During the session, the spokesperson from each core team goes to one of the “four wise men ” to explain their topic, skill or procedure.

The spokesperson returns to their team to explain what they have learned to the rest of their teammates

## Outline of the Lesson

The main focus of the activities is the explanation of the theory of the least common multiple and greatest common factors.

From this point on, all the activities are related. Following the cooperative methodology class, all students will be involved in each activity to a greater or lesser extent.

We hope that no one will feel lost during each lesson.

## Extension Activities

If we find ourselves in a class in which there is more than one student with learning difficulties the teacher must take into account, on the one hand, the distribution of the groups. On the other hand, manipulative material (such as base ten cubes, Annex1, blocks or the pocket key rg) can also be used to support this type of student. If there is an exam, the student can use this material to do it, as it is more visual and manipulative.

For more advanced learners, some materials can also be adapted. For example, for the explanation of the theory (activity 1), advanced learners can look up, for example, quantification of who invented this method and in which period. For activity 4, on the other hand, the teacher can adapt the worksheet and choose larger, three-digit numbers.

## Assessmement

The assessment will be done through the portfolio that the students will present in class. The portfolio can be done online (through the Google Sites tool). This portfolio, an image/video of each activity carried out in class must be uploaded every day, adding a description.

The portfolio should be reviewed every day and will be graded at the end of this lesson plan through a rubric (Annex 5).

## References

*Máximo común divisor Y mínimo común múltiplo – unidad de … – UNAM*. (n.d.). Retrieved from https://uapas2.bunam.unam.mx/matematicas/mcd_y_mcm