Lesson Title: Mathematics of the Middle Ages. (made up of 3 lesson plans)
Lesson plan 1 : Pythagorean Theorem
Lesson Length: 45 minutes
Grade: 8
Subject: Math
Rationale: 1. To show the connection between mathematics and medieval history. Especially with respect to
the past and how it shaped the future.
2. The goal of these lessons is to integrate mathematics, medieval history (specifically knights and
catapults), art, and ESL pedagogy.
3. Math is a universal subject and the origins of math were not in the English language but in other
languages. Some of which the students in our classes speak.
Prescribed Learning Outcome(s):
C1 develop and apply the Pythagorean theorem to solve problems
A1 demonstrate an understanding of perfect squares and square roots, concretely, pictorially, and
symbolically (limited to whole numbers)
A2 determine the approximate square root of numbers that are not perfect squares (limited to whole
numbers)
Materials and Resources:
- computer for youtube vidoes with speakers
- colored markers
- large poster paper
- cloze handouts
Hook: 5 min
History of Pythagorean Theorem Power Point
BODY: Direct Instruction 20 minutes
During Power Point:
Start with the history of the Pythagorean Theorem and why it was such an important event in history.
- The theorem was named after Pythagoras of Samos but he was not the first one to
discover the theorem.
This shows how important other cultures and languages were to mathematics. Hopefully this will show students from other countries how we appreciate their contributions to what we know today.
- The Babylonians discovered it 1000 years before Pythagoras.
- Show the students where Samos is and ask them if any of them were from or have
visited any place close to Samos.
This would give students from other countries around Greece an opportunity to share
where they are from and what it is like there. Making a more inclusive classroom.
- Pythagoras had a school where he believed that all things in life were related to
numbers and all things could be reduced to a fraction. Or in other words all numbers
were rational numbers.
-Only a triangle? Explain how the discovery of an irrational number devastated the belief
system of Pythagoras.
-Have them work in groups of 3.
Group work will allow them to discuss the concepts in a safe environment and allow
them to form their thoughts before discussing them with the class.
- I will number them off as obtuse,right or acute and they will work together with the
people beside them. So one obtuse, one right and one acute.
This will allow the ESL students to hear and use mathematical terms over and over so
they become familiar with the vocabulary.
- Ask them to discuss with their group what is a rational number and what is an
irrational number. Tell them that someone in their group will explain or give an example
of each.
-Group work allows the ESL learner to hear more language, allows them to interact with
other student. Also would allow ESL students to hear different ways to say the same
idea.
-Show them the slide and explain the difference
- Next they will discuss within the same group and then share their thoughts
with the class. (2 minutes to discuss 30 sec to share = total 7 minutes)
-Get students to think about other events in the world that changed the way we think or
act. Ex. the world is round not flat, Bill Gates, Internet, world war, catapult, guns etc.
Group work that demands participation of all groups so they will actually talk instead of just sitting there. For example they will have to share with the class there is no choice.
*Remember to wait for the kids to listen and give them more time to respond to questions.
- Define what the sides of a triangle are and what is the hypotenuse.
- Discuss what makes a right angle triangle special. - What is the Pythagorean Theorem?
- Go to link below called Pythagorean Triangle.
Discuss obtuse (one angle greater than 90 degrees) and acute (where all the angles are less than 90 degrees) triangles.
Pythagorean theorem only works with right triangles!!
Discuss what makes up a Pythagorean triple. All whole numbers!
Demo the different types of triangles with the links below.
Closure (approximate time): 2 min
- Understand the steps for determining if a triangle is a right triangle.
- Make clear what is for homework and that I will be checking that it is done.
Organizational and management strategies:
- Make the groups for the students
- Use the randomizer.It is a program that randomly picks names from the list you input.
This holds all students accountable because they might be called on to answer the question.
Link : (http://www.superteachertools.com/instantclassroom/random-name-generator.php)
Assessment and Evaluation:
- Formative assessment. I will walk around as they discuss changes of the world and give them hints and listen for understanding.
- The cloze worksheet to start in there groups and then finish for homework.
This allows the students to discuss the questions and answers. The next day we will have a discussion and make poster boards using this vocabulary.
Universal Design for Learning: (How can the lesson be inclusive for all student abilities and cultural backgrounds?)
- It includes some group work so ESL students can have some discussion about the math terms and also concepts that they will be familiar with. For example events that changed ESL students lives could be very different from events that changed English as first language students lives.
-Group work that demands participation of all groups so they will actually talk instead of just sitting there. For example they will have to share with the class there is no choice.
- Formative assessment. I will walk around as they discuss changes of the world and give them hints and listen for understanding.
- The cloze worksheet to start in there groups and then finish for homework.
This allows the students to discuss the questions and answers. The next day we will have a discussion and make poster boards using this vocabulary.
Universal Design for Learning: (How can the lesson be inclusive for all student abilities and cultural backgrounds?)
- It includes some group work so ESL students can have some discussion about the math terms and also concepts that they will be familiar with. For example events that changed ESL students lives could be very different from events that changed English as first language students lives.
-Group work that demands participation of all groups so they will actually talk instead of just sitting there. For example they will have to share with the class there is no choice.