# Spiderwebs

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### Where’s the Math? Geometry in Nature: Spider Webs:

Where’s the Math? Geometry in Nature: Spider Webs Sarah R Teacher Candidate Faculty of Education Queen’s University Kingston, ON

### Information for Educators:

Information for Educators This power point presentation is intended as a teacher facilitated resource for students in grade four. The following is a list of curriculum expectations addressed by this presentation: Grade 4: Geometry and Spatial Sense Overall Expectations: identify quadrilaterals and three-dimensional figures and classify the by their geometric properties, and compare various angles to benchmarks Identify and describe the location of an object, using a grid map, and reflect two dimensional shapes Specific Expectations: Geometric Properties: draw lines of symmetry of two dimensional shapes, through investigation using a variety of tools and strategies identify benchmark angles using a reference tool and compare other angles to these benchmarks relate the names of the benchmark angles to their measures in degrees Location and Movement: identify and describe the general location of an object using a grid system identify, perform, and describe reflections using a variety of tools create and analyse symmetrical designs by reflecting a shape, or shapes, using a variety of tools, and identify congruent shapes in the designs

### Spiders as Mathematicians:

Spiders as Mathematicians Do you know another word for a spider? Spiders are arachnids and so the word for someone who is afraid of spiders is arachniphobia…but you’re not scared…are you? If you were a spider, you would spend a ton of money on shoes because you would have eight legs! Wow! Do you know how many pairs of shoes you would need? But I guess that you would only have to buy shoes once, because most spider live only one year, except Tarantualas which can live to be 25! There are two main groups of spiders, wandering spiders that have to fight for survival and food and web builders. What do you think makes these two types so different?

### Web Builders:

Web Builders Web building spiders have very small eyes and poor eyesight. Do you think that might be a problem in the animal world? Web builders have to make up for their lack of sight with other senses and abilities. Their sense of touch is very good and they use it to find prey (by vibration). So why are theses spiders called web builders? Well because they have to spin webs to catch their prey? Do you know what the material is that they make their webs from? It’s called silk and it’s an amazingly strong material that is being studied by biologists, physicists, and of course mathematicians! What kind of uses do you think their could be for such a strong material? Have you ever really looked at a spider’s web? Have you ever seen the amazing different designs of different webs? What sorts of shapes do you see in a web? How do you think these shapes affect catching of prey?

### Geometry in the World Around Us:

Geometry in the World Around Us You may have noticed that there are different kinds of webs, depending on which spiders created them. Four of the most common types of spider webs are triangle, cob, sheet, and Orb (pictured here).

### Orb Web Construction:

Orb Web Construction We will be studying the Orb web. Now let’s take a peek and see how this type of web is constructed. Click on the link below and then switch programs to open webpage (Must have Quick Link) http://www.cs.ubc.ca/nest/imager/contributions/gslee/Project/orbLow.mpg

### Orb Web Formation:

Orb Web Formation Spiders are great web spinners and guess what? They are never taught to do this – it’s instinct! Let’s learn how a spider spins an Orb web step by step: 1. The bridge line First the spider makes a bridge with its silk between two posts. It then reinforces the bridge with more strong silk! Note to Educators: You can follow the direction of the spider with the audio loop and with a pointer

### Orb Web Formation:

Orb Web Formation 2. The anchor line Next the spider drops down and makes an anchor which will radiate from the centre of its web.

### Orb Web Formation:

Orb Web Formation 3. The silk framework The spider then continues to add more rays to the web (A ray is a line that shoots straight out from a point – can you see the point?)

### Orb Web Formation:

Orb Web Formation 4. Additional Rays The spider then adds more rays to strengthen the structure of the web. What sort of angles can you see in this web?

### Orb Web Formation:

Orb Web Formation 5. A dry spiral The spider then starts at the point in the centre and begins to make a large dry spiral that travels outwards along the radial lines.

### Orb Web Formation:

Orb Web Formation 6. The sticky spiral The spider then re-traces its steps and lays down a sticky spiral to catch its prey. It then waits in the centre for its dinner. (Don’t worry…spiders secrete a special oil to prevent them from getting stuck to their own webs).

### Creating an Giant Orb Web :

Creating an Giant Orb Web Are you ready to make our own Orb web? Maybe we’ll even catch some prey! Yummy! Vocabulary you should review first Angle -The amount of turn measured in degrees Vertex- Where the 2 arms of an angle join together Ray- A straight line extending from a point Protractor – A tool used to measure angles Degree – A unit of measurement more measuring angles Acute angle – An angle which is less than 90° Obtuse angle – An angle which is larger than 90° Line of Symmetry – A line that divides a shape into half Right angle – An angle which is 90° Parallel Lines – Lines that will go on forever and never touch Quadrilateral – A closed four sided shape Parallelogram – A quadrilateral with 4 parallel opposite sides Rectangle – A parallelogram with 4 square corners Rhombus – A parallelogram with 4 equal sides Square – A parallelogram with 4 equal sides and 4 square corners Trapezoid – A quadrilateral with 1 set of parallel lines

### Getting into a Sticky Situation:

Getting into a Sticky Situation Materials You Will Need: White Wool or yarn White boards and markers (one each) Large cardstock laminate letters What You Need to Do: Everyone needs to be in a big circle or rectangle (depending on the shape of the web you want to make) Have your teacher hold the ball of yarn and begin to pass it clockwise until everyone has a hold of the yarn Next you need to start making some rays – so holding onto the yarn – begin by calling/signing a person’s name who is across from you in the rectangle and when they acknowledge you - toss them the ball of yarn Continue this process until everyone has had a chance to toss the yarn Carefully place the web on the carpet – making sure that there is a clear centre point/vertex from where all the angles meet Now your teacher can place the laminate letters on the point (A), and all the other ending point of the rays (or every other if there are a lot) Now with your whiteboards you are going to have a spider web quiz – are you ready?

### Examples for Spider Web Whiteboard Quiz:

Examples for Spider Web Whiteboard Quiz Find two perpendicular lines (Ex. AB and AD) Find an angle that is acute (Ex. <BCA) Find an angle that is a right angle Find an angle that is obtuse Is there a line of symmetry in the web? Etc. Note to Educator: Observe students’ whiteboard answers to gain assessment information

### Cold Spaghetti Spider Webs:

Cold Spaghetti Spider Webs Now that we have seen how to make a web, are you ready to get your hands messy? Let’s try to make some Orb shaped webs from cold spaghetti… eew!

### Cold Spaghetti Spider Webs:

Cold Spaghetti Spider Webs Materials you will need: • Paper (8.5 x 11 - one each) Glue Uncooked spaghetti (20-25 pieces per student) A pencil A protractor A ruler Paper to record your observations Coloured pencils (See Art Activity Extensions for more things to do with the spaghetti web) What you need to do: Place your piece of paper horizontally on your desk Place a point in the centre of the paper and label it A Glue 8 pieces of spaghetti onto the paper (they must radiate from A to the edge of the paper) Label these points as well (B,C,D,E,F,G,H,I and so on) Record all of the angles that you have created and measure them Glue rings around point A (make sure that you make the rings two pieces of spaghetti thick…remember why? To make a dry silk and sticky spiral!!)

### Note to Educators: Modifications and Extensions:

Note to Educators: Modifications and Extensions Modifications: Some students may measure the line segments and add/subtract number of spaghetti strings Extensions: Students may identify different triangles, parallelograms, trapezoids, rhombuses, rectangles etc. and colour them in different colours on the paper They may also identify which lines are parallel and perpendicular

### Bonus Question:

Bonus Question Describe in words, pictures and numbers the relationship between how many rays your spider web has and the size of the angles with point A as their vertex.

### Note to Educators:

Note to Educators Assessment for this task: Observe students while creating webs and collect webs and data. Compare students’ measurements to your own. Monitor their understanding of the relationship between angle ( fraction) size and number with bonus question.

### Try Some of These Fun Spider Web Art Activities! :

Try Some of These Fun Spider Web Art Activities! Spaghetti Webs: Now that you’ve made cold spaghetti webs once – it will be easy to make this cool art activity Take cold spaghetti and place pieces accordingly to make a web Make sure due this on top of wax paper – that way when your webs dry, you can easily peel them off Tie some fishing line around the top of the web and hand Makes a great Halloween decoration! Sparkle Webs: On a piece of graph paper, draw a simple Orb web (make sure to use a ruler!) Place a piece of wax paper over the graph paper and trace your web with glue and glitter or glitter glue markers When your design is dry, carefully peel it off and display as a decoration

### Try Some of These Fun Spider Web Science Activities!:

Try Some of These Fun Spider Web Science Activities! Catching a Web: (make sure to ask permission) Go on a web hunt to find a real spider web (try to find an old, unused web) Lightly spray the web with white spray paint (if appropriate) or baby powder to make it easier to see Spray a piece of black construction paper with hair spray Carefully place the construction paper over the web, wait a moment and viola – you have you own web to study! Making a web Go on a spider hunt with your class and humanely catch a spider Take a large baking pan and place two knitting needles inside lengthwise and hold in place with plasticine Place the spider inside and cover the pan with plastic wrap Poke holes in the wrap and watch as the spider spins its web -Make sure to release the spider back where it was found when you are finished

### Check Out Some of These Great Books, Poems, and Tongue Twisters!:

Check Out Some of These Great Books, Poems, and Tongue Twisters! The Very Busy Spider by: Eric Carle Spiders Spin Webs by: Yvonne Winer Spider and the Sky God: An Akan Legend by: M.Newton Chocolate The Itsy Bitsy Spider Authour Unknown Wise spiders will weave webs wonderfully well! Six silly spiders spin silken socks! (Try that one six times fast!)

### References:

References Children’s Theatre. Charlotte’s Web: Web Angles. http://www.thechildrenstheatre.com Gauggel, J. Web of Lines. Information Institute of Syracuse. http://www.eduref.org/cgibin/printlessons.cgi/Virtual/Lessons/Mathematics/Geometry/GEO0200.html Mathematics and Science Centre (Virginia) http://www.spiderroom.info Petti, W. Math Cats. http://www.mathcats.com/grownupcats/ideabankfallmath.html Winkler, P. Spider Math. http://hs.houstonisd.org/debakeyhs/Lessons/SpiderMath.htm Zschokke, S. Web Construction. http://www.conservation.unibas.ch/team/zschokke/webconstruction.html