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Your students will enjoy building Linear Llama, Graph Giraffe, and the Möbius Loop while learning about area and perimeter at the same time. Each carefully designed template is drawn over a centimeter square grid so that the area and perimeter can be calculated easily. The templates here are considered levels 3 and 4 because they include, not only squares but also fractions of squares and students will need to subtract some areas. The Möbius Loop is a very curious figure that has only one side and one edge. Study of this shape raises some interesting questions about area and perimeter that are sure to intrigue your students. This activity is geared to grades 4-8 but is adaptable to many grade levels as described below.

What you get:

Level 3: (Contains Squares, Fractions of Squares, & Cut-a-ways)

Graph Giraffe and Linear Llama (with grid)

Graph Giraffe and Linear Llama (no grid)

Area and Perimeter Summary Sheet

Level 1-4: (Contains only squares but may evoke deep questions about definitions)

Mobius Loop Template

Area and Perimeter Summary Sheet

Mobius loop ‘Discovery Notes’

Materials:

Scissors

Card stock paper-white preferably (Note: the templates work best if you print them directly onto thicker paper. However, you can print to regular paper and glue it onto thicker paper. You can also just make these using regular paper. These will not be quite as durable.

Optional: colored pencils, crayons, markers for coloring creations.

Rationale for the Complete Booklet:

Here’s an ingenious and ‘seriously → fun’ way to learn about area and perimeter, (and much more). This activity booklet will provide your students with a clever progression of beautifully designed paper geometric creations that will provide hours of student inquiry, and deep understanding of a number of important math concepts. And yes, you can use this activity book equally well in a kindergarten class or in a calculus class.

Here’s how this works, starting at Level 1 students cut out and fold figures into geometric creatures like ‘Flat Cat’ and ‘Square Hare’. At Level 1, the figures are divided into squares so students can find the area and perimeter by adding up the number of squares total, (area), and the number of square sides along the edge, (perimeter).

Note: If you’re a teacher K-2 you’re already thinking this is too hard – and for most kids this age you are right! However, I believe there is tremendous value in having students working with math concepts in their hands, so to speak, well before they work with them in their heads. (Personally I know the hours I spent building stuff as a young boy helped me earn my physics degree years later. Students in early elementary can recognize the shapes used and count them. They also might be inspired to create their own creations using geometric shapes.

Note: If you’re an advanced math teacher you’re thinking, this is too easy . But, please read on…

Right from the get-go, students will see that a ‘cat’ cannot be accurately represented using only squares just as our early ancestors did many, many years ago. However, you can get a decent estimate using just squares. More interesting shapes can be constructed using triangles, Level 4, but this does require some ‘hidden knowledge’ about triangles and the use of a ruler to find the perimeter. (Or you might apply the Pythagorean theorem depending on the age and level of your students.)

Next we move on to circles, Level 5, which of course requires a ‘secret’ formula and again the use of a ruler to measure the diameter, (again another important historical development – right? See where I’m going?)

Finally, students will be presented with shapes whose area and perimeter can only be calculated using advanced math – basically Calculus. It is NOT important that the elementary school teacher know how to calculate the area of these shapes using calculus! It is important, however, for teachers and students to understand the ‘end result’ of math in its continuum. (Calculus was one of the most exciting discoveries in math because it allows you to find the area and perimeter of nearly any shape. That allows us to build airplanes and send people to the moon! However, the basis of calculus is really exactly what students do to find the area of ‘Flat Cat’ – add up squares! But really, really small ones.)

So you see, this booklet provides a visual presentation of the math continuum that parallels, pretty closely, historical discoveries. Students, and teachers can see where the study of math might take them; also why more challenging classes in mathematics are needed.

What you get:

35 pages plus some (total in complete booklet)

Level 1 (Contains Whole or Half Squares)

Flat Cat and Square Hare (with grid)

Flat Cat and Square Hare (no grid)

Area and Perimeter Summary Sheets

Level 1/2 (Contains Squares; Optional: can be used for higher level discussions such as symmetry)

Several Student cover sheets

Photo of final creation, (to help with construction)

Ulam – The Dizzy Snake (Clockwise Spiral, with grid)

Malu – The Dizzy Snake (Counter Clockwise Spiral, with grid)

Ulam and Malu – The Dizzy Snake (Both Spirals, no grid)

Area and Perimeter Summary Sheet

Dizzy ‘Discovery Notes’ (for advanced students – Differentiated learning)

Discovery Journal (Template for teacher personalization)

Level 2: (Contains Squares & Fractions of Squares)

Archie the Dog (with grid)

Archie the Dog (no grid)

Area and Perimeter Summary Sheet

Archie ‘Discovery Notes’

Level 1-3 (Contains squares only but potential for experimentation – optional)

Whirly Bird Helicopter (with grid)

Whirly Bird Helicopter (no grid)

Whirly Bird ‘Discovery Notes’

Level 3: (Contains Squares, Fractions of Squares, & Cut-a-ways)

Graph Giraffe and Linear Llama (with grid)

Graph Giraffe and Linear Llama (no grid)

Area & Perimeter Summary Sheet

Level 1-4: (Contains only squares but may evoke deep questions about definitions)

Mobius Loop Template

Area and Perimeter Summary Sheet

Mobius loop ‘Discovery Notes’

Level 4: (Triangles)

Heron the Crocodile (with grid)

Heron the Crocodile (no grid)

Area and Perimeter Summary Sheet

Heron ‘Discovery Notes’

Level 5: (Circles)

Biblio-Birds [4 templates]

Area and Perimeter Summary Sheet

Slinky Snake (with design)

Slinky Snake (you design)

Area and Perimeter Summary Sheet

Level 6: (Parabolas)

3- Mini Boomerangs

(Turning Tern, Newton, & Leibniz)

Graphing workings

Area Calculations Summary Sheet

Launch Directions for Mini Boomerang

This unit activity meets or exceeds 21st Century and STEM learning expectations, and Common Core learning outcomes. (I think STEM, which stands for science, technology, engineering and math, should be changed to STEAM, where 'A' stands for Art. What do you think?)

What you get:

Level 3: (Contains Squares, Fractions of Squares, & Cut-a-ways)

Graph Giraffe and Linear Llama (with grid)

Graph Giraffe and Linear Llama (no grid)

Area and Perimeter Summary Sheet

Level 1-4: (Contains only squares but may evoke deep questions about definitions)

Mobius Loop Template

Area and Perimeter Summary Sheet

Mobius loop ‘Discovery Notes’

Materials:

Scissors

Card stock paper-white preferably (Note: the templates work best if you print them directly onto thicker paper. However, you can print to regular paper and glue it onto thicker paper. You can also just make these using regular paper. These will not be quite as durable.

Optional: colored pencils, crayons, markers for coloring creations.

Rationale for the Complete Booklet:

Here’s an ingenious and ‘seriously → fun’ way to learn about area and perimeter, (and much more). This activity booklet will provide your students with a clever progression of beautifully designed paper geometric creations that will provide hours of student inquiry, and deep understanding of a number of important math concepts. And yes, you can use this activity book equally well in a kindergarten class or in a calculus class.

Here’s how this works, starting at Level 1 students cut out and fold figures into geometric creatures like ‘Flat Cat’ and ‘Square Hare’. At Level 1, the figures are divided into squares so students can find the area and perimeter by adding up the number of squares total, (area), and the number of square sides along the edge, (perimeter).

Note: If you’re a teacher K-2 you’re already thinking this is too hard – and for most kids this age you are right! However, I believe there is tremendous value in having students working with math concepts in their hands, so to speak, well before they work with them in their heads. (Personally I know the hours I spent building stuff as a young boy helped me earn my physics degree years later. Students in early elementary can recognize the shapes used and count them. They also might be inspired to create their own creations using geometric shapes.

Note: If you’re an advanced math teacher you’re thinking, this is too easy . But, please read on…

Right from the get-go, students will see that a ‘cat’ cannot be accurately represented using only squares just as our early ancestors did many, many years ago. However, you can get a decent estimate using just squares. More interesting shapes can be constructed using triangles, Level 4, but this does require some ‘hidden knowledge’ about triangles and the use of a ruler to find the perimeter. (Or you might apply the Pythagorean theorem depending on the age and level of your students.)

Next we move on to circles, Level 5, which of course requires a ‘secret’ formula and again the use of a ruler to measure the diameter, (again another important historical development – right? See where I’m going?)

Finally, students will be presented with shapes whose area and perimeter can only be calculated using advanced math – basically Calculus. It is NOT important that the elementary school teacher know how to calculate the area of these shapes using calculus! It is important, however, for teachers and students to understand the ‘end result’ of math in its continuum. (Calculus was one of the most exciting discoveries in math because it allows you to find the area and perimeter of nearly any shape. That allows us to build airplanes and send people to the moon! However, the basis of calculus is really exactly what students do to find the area of ‘Flat Cat’ – add up squares! But really, really small ones.)

So you see, this booklet provides a visual presentation of the math continuum that parallels, pretty closely, historical discoveries. Students, and teachers can see where the study of math might take them; also why more challenging classes in mathematics are needed.

What you get:

35 pages plus some (total in complete booklet)

Level 1 (Contains Whole or Half Squares)

Flat Cat and Square Hare (with grid)

Flat Cat and Square Hare (no grid)

Area and Perimeter Summary Sheets

Level 1/2 (Contains Squares; Optional: can be used for higher level discussions such as symmetry)

Several Student cover sheets

Photo of final creation, (to help with construction)

Ulam – The Dizzy Snake (Clockwise Spiral, with grid)

Malu – The Dizzy Snake (Counter Clockwise Spiral, with grid)

Ulam and Malu – The Dizzy Snake (Both Spirals, no grid)

Area and Perimeter Summary Sheet

Dizzy ‘Discovery Notes’ (for advanced students – Differentiated learning)

Discovery Journal (Template for teacher personalization)

Level 2: (Contains Squares & Fractions of Squares)

Archie the Dog (with grid)

Archie the Dog (no grid)

Area and Perimeter Summary Sheet

Archie ‘Discovery Notes’

Level 1-3 (Contains squares only but potential for experimentation – optional)

Whirly Bird Helicopter (with grid)

Whirly Bird Helicopter (no grid)

Whirly Bird ‘Discovery Notes’

Level 3: (Contains Squares, Fractions of Squares, & Cut-a-ways)

Graph Giraffe and Linear Llama (with grid)

Graph Giraffe and Linear Llama (no grid)

Area & Perimeter Summary Sheet

Level 1-4: (Contains only squares but may evoke deep questions about definitions)

Mobius Loop Template

Area and Perimeter Summary Sheet

Mobius loop ‘Discovery Notes’

Level 4: (Triangles)

Heron the Crocodile (with grid)

Heron the Crocodile (no grid)

Area and Perimeter Summary Sheet

Heron ‘Discovery Notes’

Level 5: (Circles)

Biblio-Birds [4 templates]

Area and Perimeter Summary Sheet

Slinky Snake (with design)

Slinky Snake (you design)

Area and Perimeter Summary Sheet

Level 6: (Parabolas)

3- Mini Boomerangs

(Turning Tern, Newton, & Leibniz)

Graphing workings

Area Calculations Summary Sheet

Launch Directions for Mini Boomerang

This unit activity meets or exceeds 21st Century and STEM learning expectations, and Common Core learning outcomes. (I think STEM, which stands for science, technology, engineering and math, should be changed to STEAM, where 'A' stands for Art. What do you think?)

Total Pages

11 pages

Answer Key

N/A

Teaching Duration

N/A