Lesson One:



Lesson – Mathematics

Topic: Pythagorean Theorem

Time: 1 – 2 class periods (45 minutes)

Materials: Dot paper, Note cards, Real Number Worksheet, Irrational Number Worksheet, The Wheel of Theodorus worksheet, The Number Devil

Objectives/ Goals:

Students will be able to categorize numbers by identifying and justifying their classification. (Rational vs. Irrational)

Students will use the Pythagorean Theorem to plot irrational numbers on a number line.

Students will use the placement of irrational number line to visually see the value of an irrational number by comparing it to rational numbers.

Common Core Standards:

CC.8.NS.1.Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0's or eventually repeat. Know that other numbers are call irrational.

CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Summary:

*after reading The Number Devil the fourth night

We will be using the Pythagorean Theorem to plot irrational numbers on a number line.

- using dot paper and an index card students plot irrational numbers on a number line.

- creating the Wheel of Theodorus to see all irrational numbers and plotting them on a number line.

Students should be able understand that irrational numbers are a subset of Real Numbers, and can be plotted on a number line.

Learning Activities & Procedure:

- Dot Paper Activity

• Are irrational numbers Real Numbers?

• Is there irrational number on the number line?

• Using information about right triangles to understand irrational numbers.

• Discovering how place irrational numbers on the number line.

- Guide line for Dot Paper Activity

Dot paper Activity- for this activity you will need dote paper and a note card or any separate sheet or paper. You will place irrational number on your number line using these materials. What do you notice about the dot paper? It has evenly space out dot making I unit from by connecting one dot with a dot that is above, besides, or below. This means that we could draw a number line using these dots since we could make equally spaced units. This also means that we could draw right triangles by connection dot to make the legs. Knowing all of this we could now carry out the activity. Create different right triangles that you know will give you irrational numbers as its hypotenuse. An example is a triangle that has two legs of 1 unit which will give you the hypotenuse of √2. You know this because of the Pythagorean Theorem. Using your note you can know take this measurement of √2 and transfer it to your number line. You have just plotted an irrational number on a number line. You should do some example with the students until they fully understand how to carry out this procedure and why it is that it works. You need to be organized with the different types of right triangles. Labeling everything as you go will make it easier to see relationships and avoid confusion.

* The reason for using this activity is so that students can visually see that irrational number can be plotted on a number line and that they are Real numbers.

The Wheel of Theodorus

• Using a note card as a tool –a ruler, and constructor of right angles

• Creating the lengths of square roots using the Pythagorean Theorem.

• Placing irrational numbers on our own number line or “ruler”.

• Home work: finish Wheel of Theodorus until reaching at least √15 and place square roots on self made number line/ “ruler”.

Guide line for Wheel of Thordorus

You will need to follow the “Wheel of Thordorus” worksheet. Make sure that all units on worksheet are the same for every student. This unit can be any measurement since our number line will be in the same units. In this case the unit was made one inch long. Again it can be any length as long as you keep that length the same throughout the whole activity. Make sure students are able to follow along creating the wheel. Students should understand that in order to get to the next triangle we will use the Pythagorean Theorem to get consecutive square roots as our hypotenuse as we continue with our wheel. Students need to be cautious of how they continue to draw their wheel. For example the right angle should always be in between the leg of the previous hypotenuse and our leg that we will draw in as one unit. Also make sure students understand how to use their index card to draw in their next leg and create their right angle. When wheel is finished, students will make a number line using the same units and fill in where the irrational numbers that are on the wheel corresponding them on the number line.

This is a creative active that has great history. Students are able to plot irrational numbers on a number line in a way that seem more like art than math.

Rational behind assignment: Students are to finish their wheel and use the length of the hypotenuse of their triangles to plot the real number on a number line. Students are then able to see how irrational number could be plotted on a number line.

Assessments

- Participation in Discussion

- Irrational Number and dot paper completion

- Wheel of Theodorus

- Journal Response

Lesson – Reading

Topic: Connections

Time: 1 – 2 classes (45 minutes)

Materials: The Number Devil, sticky notes, journal

Objectives/ Goals:

Students will make connections to their own lives to further understand the character in The Number Devil.

Students will relate claims in the text by finding examples in their real life.

Students will be able to pick out mathematics concepts and explanations from a realistic frictional context.

Students will prove claims made in the text by making connections to mathematical concepts learned previously.

Common Core Standards:

CC.8.R.I.8 Integration of Knowledge and Ideas: Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced.

CC.8.R.I.3 Key Ideas and Details: Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories).

Learning Activities & Procedure:

Teacher will read introduction to The Number Devil. After reading the short introduction, teacher will explain how mathematics plays a big part in our everyday lives. Teacher will then talk about the need to understand and use mathematics even though we may personally struggle to understand it. There will be a whole group discussion and as a class, we will make a chart- what do we know about how mathematics in our everyday life

- How have our experiences shaped how we view mathematics personally?

- Teacher will share personal stories about mathematics in her life in hopes that other will share as well.

We will read Chapter One in The Number Devil, as a whole group. Teacher will encourage students to make text-to-self and text-to-world connections while reading. Teacher will model a think out loud of a connection she has made on page 35. Ex. One of the reasons why I love mathematics is because there is always an answer. You maybe have to struggle to find that answer, but in the end there will always be an answer. I’m thinking back to what the number devil is saying about guessing in math. I disagree with him because you can always guess in math, but your guess needs to be an education guess. You can’t just guess, but you can think about certain situations where you can eliminate things and then guess. That’s the beauty about mathematics. On my sticky note, I am going to write about a time when I had to guess but it was an educational guess.

Students will use sticky note to write down their connections as we read the chapter. There will be a whole group or partner share about the connections they were able to make.

In small groups, students will work together to pick out mathematical concepts they are reading about. Once they have found one, they will work together to find a way to present the concepts to their classmates. The goal is to relate it to real life situations.

Assessments

- Journal Response

- Participation in Discussion

Lesson – Writing

Topic: Writing about a Mathematician

Time: 2 classes (45 minutes each)

Materials: Computer lab,

Objectives/ Goals:

Students will research and gather facts about a mathematic and their contribution to the mathematical world.

Students will analyze how that mathematical contribution has changed the mathematical world.

Students will determine how a world without that contribution would be to signify its importance.

Students will write about how they themselves are mathematics and the importance of their contribution.

Common Core Standards:

CC.8.W.7 Research to Build and Present Knowledge: Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

Learning Activities & Procedure:

Gathering facts

Students will research different mathematician using the book Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians. Students also have an opportunity to choose other self researched mathematician as long as it is approved by the teacher beforehand.

Teacher will model how to find facts on the internet and how to keep track of the facts by citing.

Students will have an opportunity to use the computer lab to research their mathematician in more depth (using teacher approved websites).

Key Information needed

• Name of mathematician

• Picture of mathematician

• Dates of birth and death of mathematician

• Childhood, struggles, family, education

• Most significant contribution(s), finding (s) to the field of mathematics

• How has their contribution(s) added to mathematics of today

• Citation!

After finding all required information, students will write a short report on their findings. The goal is to not overwhelm the audience with fact after fact. Teacher will model how to organize ideas and adding a personal touch to keep the audience interested. The personal touch will be making connections to how the students could relate to their mathematicians life. Teacher Ex. Mathematician Hypatia was a woman who understood the value of teaching mathematics. I can look up to her because even though she struggled to get acceptance of being an educated women in mathematics, she continued to strive and teach mathematics. My paper will focus on how I can relate her struggles to the struggles I have encounter that have gotten me here to teach you about mathematics as well.

Assessments

- Journal Response

- Participation in Discussion and Presentation

- Rubric

|Criteria |Pts Possible |Pts Earned |Comments |

|Birth Date/Birthplace |5 |  |  |

|Death Date/ Place of Death | | | |

|Picture | | | |

|Early Influences |10 |  |  |

|Ex. childhood, struggles, family | | | |

|Major Accomplishments |10 |  |  |

|Ex. education, discovery | | | |

|Significance (Must explain why their contribution is important to today’s field of |10 |  |  |

|mathematics.) | | | |

|Connections to self (Must include at least three individual connections to your |15 |  |  |

|mathematician) | | | |

Points Earned: ______________/ 50 Points

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