NATURE BY NUMBERS FIBONACCI SEQUENCE HOW TO

Branches must wait one spring before sprouting other branches, and male bees must wait one generation before they have another female male ancestor. They might also observe that there is a delay of one spring or generation. Students might note that extra branches or ancestors are added by splitting into two. Students should note that the same sequence of numbers 1, 2, 3, 5, 8, 13, 21,…, occurs in the tree branching pattern and the bee’s ancestor patterns. The next layers of the table are: Generation

There will be a female ancestor for each bee in the layer below, but a male ancestor only for each female bee.

Each female ancestor will have both a mother and father.

Each male ancestor will have only a mother.

GenerationĪsk the students to consider what will happen in the next two generations: Create a table of values for the numbers of ancestors and their genders. How many ancestors are in the family tree after five generations?Īsk students to draw the family tree to five generations. Comment that some plants sprout in this manner, though often conditions like weather and animals mean that branches get lost. Watch the animation until three generations are past. Female bees have two parents, a father (male) and a mother (female). Male bees have only one parent, a mother (female). Progress to Slide Two which shows the growing family tree of a male bee.

How many branches will the tree have after next spring?Ĭlick on the mouse to reveal that the tree has 21 branches next spring.ĭo students notice that each new branch does not sprout another branch until its second spring?ĭo they notice that each new number of branches is the sum of the two springs before it? Watch carefully how the tree grows new branches each spring. After the first sequence, show the tree growing until it has 13 branches. Show the students Slide One of PowerPoint One.

NATURE BY NUMBERS FIBONACCI SEQUENCE HOW TO

In this lesson we explore how to generate the Fibonacci sequence. Te reo Māori kupu such as raupapa (sequence) and ture (rule, formula) could be introduced in this unit and used throughout other mathematical learning. Students might investigate Fibonacci in real life situations and apply the sequence to a situation in their life. Investigate related situations that are of interest to your students, such as Fibonacci in human proportion, in spirals (fern fronds), in nautilus shells, and in the construction of famous buildings. The Fibonacci sequence is found in a variety of natural and human-made phenomena, which is reflected throughout this unit. The contexts for this unit are, and can be, varied.

directly and explicitly instructing students on key foundational concepts, such as square numbers, consecutive numbers, the golden ratio.

providing opportunities for students to demonstrate their learning, and scaffold the learning of others, through the creation and sharing of presentations that reflect their understanding (e.g.

This will allow them to benefit from the sharing and justification of ideas, collaboration (mahi tahi) and peer learning (tuakana teina)

providing opportunities for students to work in mixed groupings, pairs, as individuals, and with the whole class.

using calculators to ease the cognitive load associated with making calculations with larger whole numbers, so students can focus more on pattern and less on finding answers.

pacing the sequencing of patterns appropriately allowing time for students to discuss their predictions with others.

using recording tools such as tables and branch diagrams (featured in the PowerPoints, and of your own creation in response to students’ needs) to support students’ search for patterns.

This could include creating a family tree of direct relatives with class members

physically acting out scenarios using people or materials.The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:

Nature by numbers fibonacci sequence