A math lesson for Grade 5, Grade 6, Grade 7 or Grade 8
Lesson title: Fibonacci Sequence in poetry - Fibs
Free to use math lessons. Thank you for posting a comment.
Brief lesson summary/general objectives
The objectives of Math Magic lessons are: expanding students’ knowledge beyond the curriculum, learning math without being concerned about grades, and thus developing love for math --- all as early as possible.
In this lesson, students are recognizing a mathematical pattern in nature and poetry. Students are introduced to Fibs; these are poems in which the number of syllables in the individual lines follow the Fibonacci pattern. Creating kebabs with the same pattern will help students to remember its rule. Students will enjoy an activity that involves all the senses --- sight, hearing, touch, taste and smell. This learning experience is further enhanced by strong cross-curriculum connections.
Connections to the British Columbia (K-7) curriculum
The lesson is connected to the Patterns and Relationships unit in the BC curriculum for grades 4 and 5 math.
Additional Connections and Enrichment Opportunities
There are also curriculum connections are with:
· Language Arts, through learning about Haiku and Fibs poetry;
· Art, by coloring representations of the Fibonacci sequence in nature, and seeing the Golden Ratio in paintings and architecture;
· Life Science, based on seeing the connection between the Golden Ratio and proportions of the human body; and
· Technology, by using the presentation tools of modern technology to support individual learning.
Manipulatives/Supplies Needed
• Kebab sticks (number of students x 2 and some extras),
• Edible ingredients (fruits, vegetables or other snack foods) of a least five different types. From each type, there should be enough to make 20-30 bite size pieces of each type for x number of students.
• Access to the Internet, for each student, with computers / tablets, in order that they can see Youtube videos and on-line presentations.
• Access to the Internet, for each student, with computers / tablets, in order that they can see Youtube videos and on-line presentations.
Grouping Strategies
A teacher keeps to his/her usual grouping strategies, except for the Main activity. For that activity, the grouping is based on students’ preferences. For every unconnected lesson, students shall choose to work either individually, or in groups of up to 4 students, organized by themselves.
OR
A teacher follows the same strategy for all Math Magic lessons. Hook/Warm–up and Debrief /Consolidation activities are done as a full class body. Then, the end-of-class reflection write-up is done as individual journal entry by each student. The Main Activity grouping is done as explained above, and all participants from it will exchange learning points by way of shared activities during classes or in virtual reality.
Assessment
Math Magic lessons are envisaged to be an evaluation-free zone, in order to enhance the students’ creativity and enjoyment of learning mathematics, free from the stress of achieving good grades.
Warm-Up (10 to 15 min)
1st: A teacher presents an example of a Haiku poem. He/she may take the poems from Richard Wright’s collection of Haiku poems, published in the book This Other World (Arcade Publishing, 1998).
A sample poem is:
Whitecaps on the bay
A broken signboard banging
In the April wind
2nd: Teacher and students talk about this form of poetry. The focus and depth of the discussion will depend on what the teacher wants to accomplish from Haiku. For example, the discussion might focus only on the 5-7-5 syllables pattern, if the goal is recognition of syllables. What could be accomplished by having a precise rule about number of syllables? An answer could be: to extend our vocabulary and/or build talent for choosing the right word, or an apt word.
3rd: A teacher presents an example of Fibs. These are poems in which the number of syllables in the individual lines follow the Fibonacci sequence:1/1/2/3/5/8/13/…
It could be the following:
One
Small
Precise
Poetic
Spiraling mixture:
Math plus poetry yields the Fib.
Teacher and students recognize the number of syllables in each line as 1/1/2/3/5/8 and look for the Fibonacci principle/rule. It is: 1+1=2, 2+3=5, 3+5=8.
So, continuing with the above example, the following line will have 5+8=13 syllables.
At this point the teacher will tell students that this sequence is named the “Fibonacci sequence,” after its inventor, Leonardo Fibonacci, and that is how the name Fibs came about.
Alternate Warm-Up
If a teacher does not like the idea of Haiku, s/he could replace the 1st and 2nd steps with the following Donald Duck mathemagic video, which introduces the Fibonacci sequence, and then move on to the 3rd step.
Main Activity (20 to 25 min)
The tables in the classroom are set up so as to seat up to 5 students per table. There should be at least two types of edible ingredients on each table.
1st: Each student will get one kebab stick, and s/he will walk around in order to access the edible ingredients located on different tables. The finished ready-to-eat kebabs will be made up along this pattern: 1st one piece of one ingredient, 2nd one piece of another ingredient, 3rd two pieces of yet another ingredient, and so on, with 3, 5,8,13,21, … ingredients.
Students would make their own choices when organizing ingredients, based on what is available, and will aim to reach bigger Fibonacci numbers. A second round of kebab-making will give all an opportunity for a different organization of ingredients.
2nd: The students eat snacks, write more elements of the sequence, such as 21, 34, 55, 89, 144,... and explore ratios: 144/89, 89/55, 55/34, … This will serve as background for and prelude to information on the Golden Ratio. The Golden Ratio will be introduced by way of a Youtube video about the Fibonacci sequence and the Golden Ratio. My suggestion is the video titled “Fibonacci Sequence: Nature's Code.”
Alternate Activity
For exploration of mathematics, a teacher shall provide additional resources and/or give opportunities for Internet research and coloring. Students may also organize learning points into a storyboard for a future presentation.
Consolidation and Reflection (10 to 15 minutes)
A teacher shares “Where to Go from Here” with the students. They then write journals. If appropriate, they may use the following guiding questions:
1) Write the first 12 numbers from the Fibonacci sequence.
2) Could you write all the Fibonacci numbers? Why or why not?
3) Write three examples of Fibonacci numbers from situations in nature.
Where to go from here
1st : After introducing the Fibonacci sequence and the Golden Ratio, a teacher could let students run with it, using their own imagination.
2nd : S/he could devote more class time to learning about this topic, either through LdL (see below) or presentations prepared and made by students.
Additional Resources and Notes
If a teacher should opt to go even further with Haiku, s/he may use:
LdL is short for “Learning by Teaching” (based on the German expression “Lernen durch Lehren.”) For this to work, one or more students must be capable of, and willing to, prepare a lesson and to teach it to the class. This is a priceless experience for the student who is willing to accept this challenge. The student will not merely master a new lesson, but will also acquire preparation skills, public speaking experience, and other abilities that are just as valuable as the actual lesson material. In this case, with light guidance from the teacher, the student(s) will have wide freedom in deciding how to teach the lesson, and what the focus of the lesson shall be. A teacher could provide suggestions for resources.
“The Murderous Math’s- Numbers: the Key to the Universe” by Karat Poskit
“Eat Your Math – Homework Recipes for Hungry Minds” by Ann MacCallum
”The Man of Numbers --- Fibonacci’s Arithmetic Revolution” by Keith Devlin
Golden Ratio in Human Body (Golden Mean in Mankind)
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