Math in Art and Nature

Background Information

Indigenous Art

Mi’kmaq people create art that is practical, meaningful and aesthetically pleasing, often using resources provided by the land. Mi’kmaq people are well known for their basket making and quill work. To create baskets and other forms of art different woods are used including the bark and the branches of the tree. Quill work uses porcupine quills, for more information about quill work click here.

Mi’kmaq artist Loretta Gould is a quilter and painter who loves bright, beautiful colours. She is also the author of the book “Counting in Mi’kmaw” which introduces counting in both Mi’kmaq and English up to 10. To view some of her art click here.

Well known Mi’kmaq artist Alan Syliboy’s work is based on Indigenous Mi’kmaq rock drawing and quill work traditions. His themes include family, spirituality, struggle and strength. To visit his website for further information click here.

African Nova Scotian Art 

African art began as images carved into rock known as petroglyphs and sculptures made of terracotta. This art has influenced many well known artists and evolved throughout time. African art is created in many different modes including sculptures, painting, pottery, rock art, textiles, masks, personal decoration and jewelry. African art is not limited to collectibles as it can be found on human skin, on houses and on rock faces.

The Black Artists’ Network of Nova Scotia (BANNS) is a non-profit organization that seeks to develop the African Nova Scotian arts community. Click here to visit their website.

How do these types of art connect to math?

Check out the following link to learn about how math is connected to famous art https://study.com/academy/lesson/how-mathematical-models-are-used-in-art.html

Math Connections to Art and Nature 

Try the following activities to learn the connections math has to our everyday lives.

Activity 1) Tessellations 

Tessellations are a pattern of shapes that fit together perfectly without any overlaps or gaps. The only classic polygons that can make up tessellations are triangles, squares and hexagons as they are the only geometric 2-D shapes that will fit together without any gaps or overlaps. However, you can make tessellations with irregular shapes that do not fit the category of a triangle, square or hexagon. 

Option 1: Make your own tessellation on a piece of blank paper! Click here to learn some Tips and Tricks to create your own Tessellation.  Some of the tips outlined in the video are; 

  • Use sticky notes or tape to make your shapes to keep them from moving as you are making you tessellation 
  • Choose the right size shape for your tessellation to be able to fit enough on your paper to make a pattern

Option 2: Create an account on GeoGebra and use the Geometry application to create virtual tessellations. 

Tessellations can also be found in nature on animals (snakes, dragonflies and giraffes), on honeycombs and on pineapples! 

Activity 2) Spirolaterals

Spirolaterals are a spiraled design of repeated commands using length and angles.  In order to create a spirolateral a number is chosen and its multiplication sequence is written out.

To learn how to make your own spirolateral click here! 

OR follow these steps;

Step 1) Choose a number from 2-9 and write out its multiplication sequence. For this example we will use the number 5. Multiplication sequence: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55

Step 2) Next you will need to turn the sequence into single digits by adding the two digits of each number together. 10 becomes 1+0=1, 15 becomes 1+5=6. Added digits: 5, 1, 6, 2, 7, 3, 8, 4, 9 (Once you see a pattern you can stop)

Step 3) Using graph paper these digits will turn into art. Use your first number from step 2 and draw a line that is __ (5 in this case) many squares long. Make a 90-degree turn to the right, and draw a line that is the second digit long (1 in this case). Make a 90-degree turn and draw a line that is the third digit long (6 in this case), etc.

Step 4) When you complete the final line of the sequence (use the final digit) start over with the first number and continue until the spiral connects back to the very first line.

Step 5) Color in your spirolateral!

Activity 3) Fibonacci Numbers in Nature 

The Fibonacci numbers are; 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 133 and onto infinity. Each number is the sum of the previous 2 numbers. The Fibonacci numbers often appear in nature and can be seen on flowers and even the human body. 

The Fibonacci spiral is a connection of quarter-circles drawn inside squares that use the Fibonacci numbers for dimensions. The squares fit perfectly together because of the nature of the sequence; the next number is equal to the sum of the two before it.

 

Step 1) Draw your own Fibonacci spiral on graph paper and decorate it how you want (seen above).

Step 2) Watch this video to learn how the Fibonacci spiral and the Fibonacci numbers are found in nature: 

Step 3) Go for a walk outside and see if you can find the Fibonacci numbers in any plants around your neighborhood. If you find a pine cone laying on the ground take it home and decorate it with any materials you have available to emphasize the Fibonacci spirals on the pine cone as seen in the above video. This can be done with glitter glue, tape, markers or any other materials that you have.

Activity 4) Nature Walk 

This activity is a great for younger students. Watch this video to learn how walking around your neighbourhood you can find math in many places.

Try going for a walk around your neighbourhood and find some of the items that were pointed out in this video or think of your own math connections that can be found outside in nature! Look for; bee hives, pine cones, sunflowers, reflections on the water and any other patterns that you may find! 

While outside on your nature walk, create patterns using pinecones, rocks, fallen leaves, etc. Create the core of the pattern and have a friend or family member determine what the pattern is and extend the pattern. Additionally, notice sounds that you can hear in nature. Are there any birds that are creating a pattern with their chirping? 

Desmos

Check out the following links to learn more about the connections between math, art and nature.

Des-Pet: Get creative while reviewing function inequalities and domain and range restrictions. https://teacher.desmos.com/activitybuilder/custom/573cfb11023d1d8f0b0a09c9

Math in Nature: https://teacher.desmos.com/activitybuilder/custom/5ecbbf62c002ff2d8b0262fb

Materials Needed

  • Paper
  • Coloured pencils/markers
  • Tape
  • Scissors
  • Graph Paper
  • Pine cones (found on nature walk)
  • Glitter glue, paint and paint Brushes (optional)

Nova Scotia Curriculum Connections

Note: Younger students can complete activities 1 and 4. 

Grade Primary 

Mathematics: Patterns and Relations (PR): Students can build patterns with objects they have found in nature.  They can also identify the patterns they see in tessellations and nature. 

PR01 Students will be expected to demonstrate an understanding of repeating patterns (two or three elements) by identifying, reproducing, extending, and creating patterns using manipulatives, sounds, and actions.

Science: Have discussion while on the nature walk. Outcome: Learners will compare living things through the senses. 

Social Studies: Explore the resources in the background information section relating to Mi’kmaq and African Nova Scotian Art. Outcome: Students will investigate how local people, including Acadians, African Nova Scotians, Gaels, Mi’kmaq including Treaty Education, and various cultural groups, have varied traditions, rituals, and celebrations. 

Grade One 

Mathematics: Patterns and Relations (PR): Students can build patterns with objects they have found in nature.  They can also identify the patterns they see in tessellations and nature. 

PR01 Students will be expected to demonstrate an understanding of repeating patterns (two to four elements) by describing, reproducing, extending, and creating patterns using manipulatives, diagrams, sounds, and actions.

Science: Have discussion while on the nature walk. Outcome: Learners will analyze interconnectedness of living things and the environment.

Social Studies: Explore the resources in the background information section relating to Mi’kmaq and African Nova Scotian Art. Outcome: Students will investigate the diversity of cultural groups. 

Grade Two 

Mathematics: Patterns and Relations (PR):Students can build patterns with objects they have found in nature.  They can also identify the patterns they see in tessellations and nature. Ask them to draw patterns they see in nature and art.

PR01 Students will be expected to demonstrate an understanding of repeating patterns (three to five elements) by describing, extending, comparing, and creating, patterns using manipulatives, diagrams, sounds,and actions.

Grade Three

Mathematics: Numbers (N): Students will begin to understand patterns in multiplication in activity 2, Spirolaterals. 

N11 Students will be expected to demonstrate an understanding of multiplication to 5× 5 by; representing and explaining multiplication using equal grouping and arrays, creating and solving problems in context that involves multiplication, modelling multiplication using concrete and visual representations, and recording the process symbolically, relating multiplication to repeated addition, relating multiplication to division. 

Patterns and Relations (PR):  Students can learn patterns through tessellations and nature.

PR01 Students will be expected to demonstrate an understanding of increasing patterns by describing, extending, comparing, and creating numerical (numbers to 1000) patterns and non-numerical patterns using manipulatives, diagrams, sounds, and actions. 

Science: Have discussion while on the nature walk. Outcome: Learners will investigate plants in the environment.

Social Studies: Explore the resources in the background information section relating to Mi’kmaq and African Nova Scotian Art.  Outcome: Students will investigate various groups including Acadians, African Nova Scotians, Gaels, and Mi’kmaq through their expression of culture. 

Grade Four 

Mathematics: Number (N): Students will practice their multiplication skills when creating their spirolateral.

N05 Students will be expected to describe and apply mental mathematics strategies, to recall basic multiplication facts to 9 × 9, and to determine related division facts.

Patterns and Relations (PR): Students will identify patterns in their multiplication tables when creating their spirolateral.

PR01 Students will be expected to identify and describe patterns found in tables and charts, including a multiplication chart. 

Grade Seven 

Mathematics: Students will make connections to geometry they visualize in nature on the outdoor walk.

Unit 9 Geometry – SCO G01: Students will be expected to perform geometric constructions including    perpendicular line segments, parallel line segments, perpendicular bisectors, angle bisectors (Performance Indicator G01.01: Students will be able to describe examples of parallel line segments, perpendicular line segments, perpendicular bisectors, and angle bisectors in the environment.)

Science: Students will take a walk in nature and inquire how to sort things found in ecosystems leading into a discussion about abiotic and biotic factors.

From the Pilot Inquiry-Based Grade 7 Curriculum; Learners will analyse the interconnectiveness of living things and the environment, in relation to the concept of netukulimk (Indicator: Analyse the interconnectedness of biotic and abiotic components in nature, inclusive of a Mi’kmaw perspective).

Grade Eight

Mathematics: Students will observe and sketch 3-D objects they observe on a nature walk.

Unit 8 Geometry – G01.06: Sketch and label the top, front, and side views of a 3-D object in the environment, with or without the use of technology.

Students will observe polygons in nature and describe any transformations they see on their nature walk.

Unit 8 Geometry – SCO G02: Students will be expected to demonstrate an understanding of the congruence of polygons under a transformation. 

Science: On a nature walk, students will observe, inquire, and discuss key concepts such as the greenhouse effect, climate change, and human impact on the environment 
From the Pilot Inquiry-Based Grade 8 Curriculum; Learners will evaluate the impact of human activity on climate change.

Resources 

http://collections.musee-mccord.qc.ca/scripts/printtour.php?tourID=VQ_P1_3_EN&Lang=2

https://www.contemporary-african-art.com/african-art-history.html

https://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html

 

With support from: