How to Integrate Math & Art in the Classroom

Color and shapes bring math to life.

Integrating math and art in the classroom allows kids to use stimulating colors and shapes to enhance their mathematical understanding. There are surprising associations between the two subjects. Kids can apply math theory to real things like pictures and objects, bringing life to math and new perspectives on art. Visualization and creativity can be used t convey mathematical concepts in several different ways, increasing kids' motivation and adding enjoyment to learning math.

Things You'll Need

• Pencil
• Ruler
• Protractor
• Scissors
• Squared paper
• Colored paper

Instructions

Pythagorean Spirals

1. Draw a right angled isosceles triangle with two sides of 4 cm each.

2. Draw a second triangle touching the first one. Start with a line of 4 cm perpendicular to the hypotenuse of the first triangle and join this line to the other end of the hypotenuse.

3. Keep repeating step 2 to create new triangles from previous ones. You should see a spiral start to appear.

4. Ask questions about the shape. What does the shape resemble? What are the lengths of the sides of each triangle? Is there a pattern emerging? What is the area of each triangle? What is the total area of the shell and what would the area be with n number of triangles?

Tessellations

1. Draw and cut out eight identical equilateral triangles from colored paper. Put them together so that there are no gaps or overlaps. This is called a tessellation.

2. Discuss how it is possible that there are no gaps or overlaps. Each interior angle in a triangle is 60 degrees. 60 multiplied by 6 is 360 degrees; therefore the triangles tessellate. The sum of the interior angles that meet at a point where there is no empty space must be 360 degrees. In other words, at the point in the middle where six triangles meet, the total of all angles must be 360 degrees.

3. Cut out squares and arrange them with the flat edges touching. Discuss whether they tessellate and why. 90 multiplied by 4 is 360 degrees.

4. Arrange hexagons into a tessellation. Discuss this. 120 multiplied by 3 is 360 degrees.

5. Try other shapes like pentagons and hexagons. These do not tessellate, explore why.

6. Try a combination of two different shapes and investigate whether they tessellate and the reasons why.

Digit-Sum Spirals

1. Write multiples of 3 in a column. Stop at the number 45. Add together the digits of each of these numbers and write them in a new column. For example, the digit-sum of 27 is 9. A pattern of numbers should appear in the second column; 3,6,9,3,6,9 etc.

2. Draw a horizontal line 3 squares long. Start near the center-top of your squared paper to ensure plenty of room. From the end of this line, using the numbers obtained in step 1, draw a line downwards 6 squares long. From this, draw a line 9 squares long to the left. From this, draw a line 3 squares long upwards. Draw the next line to the left and so on, repeating the pattern with the digit-sums until you reach the starting point.

3. Discuss how the sequence of numbers created this shape.

4. Repeat steps 1 to 3 with multiples of other numbers such a 2,6 and 7. Discuss which digit-sum spirals look similar and why.

Tips & Warnings

• Enhance patterns by using colored pencils.

References

• Math to Art: Using Art to Teach Math
• Coolmath4kids.com: What Are Tessellations?