EMTH 350 - Inquiry Lesson

8/7/2019 EMTH 350 - Inquiry Lesson

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Polygon? Whats a Polygon?

Write a definition of a polygon according to the class activity:

Draw a 3 sided shape that has equal side length and equal angles.Draw a 4 sided shape with all the same side lengths and angles.Draw a 6 sided shape with equal side length and angles.

You have just drawn regular polygons!From this, can you make an educated guess about what an irregular

polygon is?

Go back to your classification sheet and label the irregular andregular polygons remembering that there are some shapes that arenot polygons at all.

Definitions:o Concave polygons have at least one interior angle that

measures greater than 180 such as number 9.


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o Convex polygons have interior angles less than 180such as number 1.

Go back to your classification sheet and label the convex andconcave polygons.

Explain the similarities and differences among the triangles.

Compare triangle X to triangle Y. Compare triangle X to triangle Z.What can you say about them?

Measure the sides and angles of the triangles if you have not

already done so. Can you add to your conclusion made from thesenew observations?

Side a Side b Side c Angle 1 Angle 2 Angle 3

Triangle X

Triangle Y

Triangle Z

Triangle X and Triangle Y are called congruent triangles.Triangle X and Triangle Z are called similar Triangles.

Choose two similar polygons from the shapes in the box set at your tables(not including the circle as it is not a polygon), and then fill in the chartbelow using as many columns as necessary. Pick one to be polygon A andthe other to be polygon B.

XY

Z

a a

a

bb b

c

cc

1 11 22

2

33

3


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8ft

Chart 1

Side 1Length

Side2Length

Side3Length

Side4Length

Side5Length

Side6Length

Side7Length

Side8Length

Polygon A

Polygon B

Scale:Polygon APolygon B

What can you say about polygon A compared to polygon B?

Because of this, we can say that the sides of these twopolygons are a proportion.

Construct your own irregular convex polygon using the geo-boards. Canyou make one that is similar to it? How can you make it bigger or smallerso that the sides are still in proportion? Draw it on the paper.

You are building the roof of a house. You know that the angle ofelevation of the roof is 30 degrees. You have already made andinstalled the centre support which is 8ft tall and 30 feet away fromthe corner of the roof. You realise that you need another supporthalf way between the centre support and the corner of the roof.What length do you need to cut the support?


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30 ft

30


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Where would you see other examples of similar convex polygons in

your community? How is knowing about this relevant to your life?


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Teacher Notes:

WA 10.7 Demonstrate an understanding of similarity of convex

polygons including regular and irregular polygons.

Day 1:

1. Give the students the polygon handouts (separate file).

2. We start by saying certain numbers are yes and no, then we ask them

a number and they have to decide if it is yes or no. This is having

them create their own definition of what a polygon is. There are two

separate handouts, one with plain shapes, and another with pictures.

3. Give students hand-outs (pages 1-5)

- This is a guided inquiry exploring the shapes and scale

4. When they are done they hand it in.

Assessment:

- The booklet, the last question is like an exit slip to see if they can connect

the math from the booklet to real life.

- During the inquiry there will be anecdotal assessment.

Adaptive Dimensions:

- Pair readers with non- readers

- Partner work, group work, or individual


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Day 2: Architecture and blueprint project

Explore

PWIM picture of our gym

1. Put up a picture of the school gym. The students would brainstorm all

of the words associated with the picture.

- The students should come up with things like shape, space and

lines which is where the lesson is heading.

2. Discussion: (Prompt questions) How would someone have built this?

How would they know how big to make everything? How would they

know how to space everything out? What are the dimensions?


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- If the students do not come up with blueprint, architect, or

something along those lines, ask if anyone knows what a

blueprint is.

3. Discussion about blueprints and scales, adding words to PWIM when

necessary.

4. Discuss ways we could make a blue print for the gym. What

information do we need?

5. Leading to going into the gym and measuring the lines

6. First have to know what lines are being measure, label them on the

board, give each student a picture of the gym so they can label the

lines, to fill out a chart of measurements (The importance has to be on

making the scale and theblueprint not on making the measurements

accurate, so we need to give them a clear and easy to fill out table for

that portion of the inquiry)

7. Give students table to fill out, go into the gym and measure the lines

- Adaptive Dimension: Have them measure the classroom if you

cant get into the gym

8. Discussion: How could you fit the gym on a piece of paper.

9. Give them graph paper

10. Tell them to make a blueprint of the gym on the graph paper. They

already have all the information they need because we went and found

it.

11. Give the students another copy of the table used to measure the gym.

Have them fill it out for their blueprint

Connect

12. Exit Slip/Journal entry: How were we able to make it fit on the paper.

How do we know that these two are in proportion

- Shows us if they understand scale.

- Shows they understood how to make the blueprint.

Practice:

Extension:

This would be going the other direction, so they would have to take a blue

print and find large-scale measurements.


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Math projects:

1) Have the student take a blue print and find the actual measurements.

Journal about why the scale has to be the way it is, and their process.

2) Have the students take or make a blue print and construct it. (wood

working, etc.) Journal about their process and how they created the

scale.

3) Have the students take a scale diagram of a sport (such as baseball)

and go out and create the playing field and position themselves to

play. Journal about the process.

4) Have the students create a sport and the playing field that goes along

with it. They have to construct the playing field and discuss how they

made the scale, why the scale is the way it is, and their entire process.

5) Make 3-Dimensional blueprints using Google Sketchup.

6) Students can come up with their own project, that must first be

discussed with the teacher, that pertains to blueprints and scales.

Assessment:

- Math Project

- Exit Slip / Journal

- Anecdotal (during discussion and completely through out)

Adaptive Dimension:

- In classroom instead of in gym

- Work in partners, group, or individual

- Have the students create their own math project

- Table given to students so its easier to organize their thoughts

- If students miss the class, or there isnt enough time, give them a filled out

table with all the measurements so they just have to make the blueprint


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Tentative Chart (Depends on what the gym looks like, lines you need

to label etc.)

Line Measurements

ABCDEFGH

EMTH 350 - Inquiry Lesson

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