project #2 - wordpressstorageaccount.blob.core.windows.net€¦ · pass out the regular and...

1215 K Street, Ste. 1200 | Sacramento, CA 95814 916-340-3340 | mychf.org/bita

PROJECT #2: HEXAGON SERVING TRAY

BUILDING INDUSTRY TECHNOLOGY ACADEMY: YEAR TWO CURRICULUM

© BITA: A program promoted by California Homebuilding Foundation

YEAR TWO PROJECT #2 HEXAGON SERVING TRAY Table of Contents

Lesson 1: Regular/Irregular Polygons and Interior/Exterior Angles of a Polygon (2 Class Periods)

Lesson 2: Building a Hexagon Serving Tray (10 Class Periods)

Project #2: Hexagon Serving Tray


Lesson #1: Regular/Irregular Polygons & Interior/Exterior Angles of a Polygon (2 Days)

Objectives

Students will be able to…

Identify regular/irregular polygons.

Identify interior and exterior angles of a polygon.

Construct a regular hexagon shape.

Common Core Standards

LS 11-12.6 RSIT 11-12.2 RLST 11-12.2 Writing 9-10.5 Problem Solving/Critical Thinking 5.4 Health and Safety 6.2, 6.3, 6.6, 6.12 Responsibility and Leadership 7.4, 9.3 Residential and Commercial Construction Pathway D2.1, D3.1, D3.7 CCSS.MATH.PRACTICE.MP6 CCSS.MATH.PRACTICE.MP2 CCSS.MATH.PRACTICE.MP1

Materials

Regular and Irregular Polygons Handout Constructing a hexagon inside a circle worksheet Interior Angles of a Polygon Worksheet Exterior Angles of a Polygon Worksheet

Lesson Sequence

Pass out the Regular and Irregular Polygons Handout. Review as a class. Have students highlight important information and fill in the chart at the end. Answer any questions. (25 minutes)

Pass out the Constructing A Hexagon Inside A Circle Worksheet. Go through this activity together as a class. Model for students. Answer any questions. (25 minutes)

http://www.corestandards.org/Math/Practice/MP6/





Pass out the Interior Angles of a Polygon Worksheet. Review together as a class. Answer any questions as needed. (25 minutes)

Pass out the Exterior Angles of a Polygon Worksheet. Review together as a class. Answer any questions as needed. (25 minutes)

Assessment

Check for student understanding through questioning. Be sure to call on random students and clarify any mis understandings as needed. Collect worksheets to grade based on student following whole class discussion.

Accommodations/Modifications

One on One Support Check for Understanding Provide Additional Visuals as Needed



Regular and Irregular Polygons Handout

What is a polygon?

A polygon is a simple closed figure formed by three or more segments. A triangle is a polygon and a quadrilateral are a polygon too. Here are three pictures of polygons.

Polygon You can see that all three of these figures are simple closed figures that are created by three or more-line segments.

Different Types of Polygons

Not a Polygon These figures are not polygons. A polygon does not have a curve in it. The first two figures have curves in them. The third figure is not a closed figure. The last figure has sides that overlap. A polygon does not have sides that overlap.

Distinguish Between Regular and Irregular Polygons

Now that you have been introduced to the different types of polygons, it is time to learn about classifying polygons. All polygons can be classified as regular or irregular polygons. You have to understand the difference between a regular or irregular polygon to classify each shape. Let’s learn how we can tell the difference between them.

Regular Decagon Regular Octagon Regular Dodecagon

Regular Hexagon Square Equilateral Triangle Regular Pentagon



Regular Polygon A regular polygon is a polygon where all the side lengths are equal, and all of the angle measures are equal. In other words, the polygon is an equilateral polygon where all the side lengths are congruent, and an equiangular polygon where all the angles are congruent.

Example: This triangle is a regular triangle. All three side lengths are congruent, and all three angles are congruent.

Here is an example of an irregular polygon.

By counting the sides, you can see that this is a five-sided figure. It is a pentagon. However, the sides are not congruent. Therefore, it is an irregular pentagon. Irregular polygons have side lengths that are not congruent.

Relate Sides of Polygons to the Number of Diagonals from a Vertex

We can divide polygons into triangles using diagonals. This becomes very helpful when we try to figure out the sum of the interior angles of a polygon other than a triangle or a quadrilateral.

Remember that the sum of the interior angles of a triangle is 180o. The sum of the interior angles of a quadrilateral is

360o. Why is this important? You can divide a quadrilateral into two triangles using diagonals. Each triangle is 180o, so the sum of the interior angles of a quadrilateral is 360o.

Example: Here is one diagonal in the quadrilateral. We can only draw one because otherwise the lines would cross. A diagonal is a line segment in a polygon that joins two nonconsecutive vertices. A consecutive vertex is one that is next to another one, so a nonconsecutive vertex is a vertex that is not next to another one.

How do we use this with other polygons?

We can divide up other polygons using diagonals and figure out the sum of the interior angles.

Here is a hexagon that has been divided into triangles by the diagonals. You can see here that there are four triangles formed. If sum of the interior angles of each triangle is equal to 180o, and we have four triangles, then the sum of the interior angles of a hexagon is: 4 (180) =720o

Explore the relationship of the number of sides of a regular polygon and the Central Angles.



(Because the polygon is regular, all central angles are equal. It does not matter which side you choose. All central angles would add up to 360° (a full circle), so the measure of the central angle is 360 divided by the number of sides.)

Name # of Sides

Measure of a Central Angle Sum of the Measure of the Central Angles

Equilateral Triangle

Square

Regular Pentagon

Regular Hexagon

Regular Octagon

Regular Decagon

Regular Dodecagon


Regular Hexagon Square


Regular Pentagon



Constructing a Hexagon Inside a Circle Worksheet

A Hexagon is ANY shape composed of 6 intersecting lines. A regular hexagon is a 6-sided shape where ALL lines are the same length and ALL angles are equal in size.

A Regular Hexagon is identified by a combination of the number of sides to the shape, the length of the sides AND the size of its angles. A Regular Hexagon has Six Sides equal in length ... and Six Angles equal in size (all are 120 degrees).

After doing this Your work should look like this We start with the given circle, center O.

Mark a point anywhere on the circle. This will be the first vertex of the hexagon.

Set the compasses on this point and set the width of the compasses to the center of the circle. The compasses are now set to the radius of the circle

Make an arc across the circle. This will be the next vertex of the hexagon. (It turns out that the side length of a hexagon is equal to its circumradius - the distance from the center to a vertex).

Move the compasses on to the next vertex and draw another arc. This is the third vertex of the hexagon.

Continue in this way until you have all six vertices.

Draw a line between each successive pairs of vertices, for a total of six lines.

http://www.mathopenref.com/vertex.html



1. Construct the largest regular hexagon that will fit in the circle below.

2. Find the center of the circle below and construct a hexagon inscribed in the circle.



Interior Angles of a Polygon Worksheet

Explore the relationship of the number of sides of a regular polygon and the Interior Angles.

Name # of Sides

Measure of an Interior Angle

Sum of the Measure of the Interior Angles


Square

Regular Pentagon

Regular Hexagon

Regular Octagon

Regular Decagon

Regular Dodecagon

Write an assumption about Interior Angles of a Regular Polygon. Think about breaking apart the polygon into triangles as shown below.

___________________________________________________________________________________

___________________________________________________________________________________


Regular Square


Regular Pentagon



Interior Angles of a Polygon Worksheet – Answer Key

Name # of Sides

Measure of an Interior Angle

Sum of the Measure of the Interior Angles

Equilateral Triangle 3 60° 180°

Square 4 90° 360°

Regular Pentagon 5 108° 540°

Regular Hexagon 6 120° 720°

Regular Octagon 8 135° 1080°

Regular Decagon 10 144° 1440°

Regular Dodecagon 12 150° 1800°



Exterior Angles of a Polygon Worksheet

Explore the relationship of the number of sides of a regular polygon and the Exterior Angles.

Name # of Sides

Measure of an Exterior Angle

Sum of the Measure of the Exterior Angles


Square

Regular Pentagon

Regular Hexagon

Regular Octagon

Regular Decagon

Regular Dodecagon

Write an assumption about Exterior Angles of a Regular Polygon. Think about breaking apart the polygon into triangles as shown below.

___________________________________________________________________________________

__________________________________________________________________________________


Regular Hexagon Square


Regular Pentagon



Exterior Angles of a Polygon Worksheet – Answer Key

Name # of Sides Measure of an Exterior Angle Sum of the Measure of the Exterior

Angles

Equilateral Triangle 3 120° 360°

Square 4 90° 360°

Regular Pentagon 5 72° 360°

Regular Hexagon 6 60° 360°

Regular Octagon 8 45° 360°

Regular Decagon 10 36° 360°

Regular Dodecagon 12 30° 360°



Lesson #2: Building a Hexagon Serving Tray (10 Days)

Objectives

Students will be able to…

Apply math skills to building a hexagon serving tray.

Produce a hexagon serving tray product.

Common Core Standards

LS 11-12.6 RSIT 11-12.2 RLST 11-12.2 Writing 9-10.5 Problem Solving/Critical Thinking 5.4 Health and Safety 6.2, 6.3, 6.6, 6.12 Responsibility and Leadership 7.4, 9.3 Residential and Commercial Construction Pathway D2.1, D3.1, D3.7 CCSS.MATH.PRACTICE.MP6 CCSS.MATH.PRACTICE.MP2 CCSS.MATH.PRACTICE.MP1

Materials

Hexagon Serving Tray Order of Materials Materials List on The Order of Materials Handout Bill of Materials Self-Evaluation

Lesson Sequence

Pass out and review the Hexagon Serving Tray Order of Materials. Answer any questions.

Have students fill out their Bill of Materials. After they have been checked, allow students to begin working on their projects. Monitor progress along the way.

At the end of the project have students set out their finished products and walk around the room to look at one another’s final project. Have students fill out their Self-Evaluation for project.






Assessment

Informal assessment through questioning and student observations throughout the project time frame. Use rubric to grade student’s product.

Accommodations/Modifications One on One Support Check for Understanding Peer Support as Needed Extra Time If Needed



Hexagon Serving Tray Order of Materials

The serving tray is made up of over 50 small trapezoids of different species of wood, which are all laminated into hexagons, and then glued together into a big single piece. This video will show you the process of making the hexagons. You will be using them to make the bottom for a serving tray, so some measurements have been changed. Making a Serving tray run time 6:01 (the individual is making a cutting board, but we will be using the board as the bottom of our serving tray. https://www.youtube.com/watch?v=iPeSxhdP6Dw Materials: 3 different grained hardwood, 2 or 3 strips off each board - dimensions are: length

13.4in x 1 1/2in width x 1 in. high. 1″ x 3″ of the same wood to create a mitered frame around the tray bottom. 3/8 x 3/8 x 3′ Square Dowel to make cleats 60 grit sandpaper stapled onto a piece of plywood grit 80, grit 120, and 240 grit Brush to apply glue – Titebond 3, Gorilla wood glue, or similar water-resistant glue Elastic bands Damp rag Polyurethane

Order of Construction: Step 1: Rip 2 or 3 strips off each board. Step 2: Measuring and Cutting Angles The small topside of the trapezoid needs to be the same length as the slanted sides. Mark out a few pieces with a bevel guide, and then set the angle of the blade to a little over 30 degrees. The actual angle is 60 degrees measuring from the table to the left side of the saw blade when using a table saw. The angle of the blade could best be measured with a bevel box. You attach it on the blade, and it measures the angle of the saw blade digitally very accurate.

https://www.youtube.com/watch?v=iPeSxhdP6Dw



Step 3: Sanding Sand off the tear out from the saw blade with some 60-

grit sandpaper stapled to a board. Step 4: Gluing Part 1 Lay out all the pieces before starting and glue all the

pieces in steps. Take two pieces of the same kind of wood and glue

them with the longest sides butted up against each other.

To clamp them, use thick rubber bands and wipe off excessive glue with a damp cloth. Glue all the pieces and wait for the glue to dry.

Step 5: Gluing Part 2 Next step of gluing is to put the hexagons into groups of

four. Again, use rubber bands, to clamp together. Wipe off excessive glue with a damp cloth. Try to keep

all the pieces level and flat as they are drying. If there are slight gaps showing up between the pieces,

which come from slight imperfections when cutting the pieces, fill the gaps with little wedges of wood glued in or sawdust mixed with wood glue.

Step 6: Gluing Part 3 Take the groups of 4 hexagon pieces and arrange the

blocks as tightly as possible in a rectangular fashion. Glue and clamp.

Step 7: Cutting Square Drawing lines with a straight edge, square off your

board to your size. Follow your lines and cut with a band saw. Use a belt sander to smooth the edges.

Step 8: Flattening Block plane the top to make the uneven pieces as level

as possible before sanding. Sand first with grit 80, then grit 120, and finish with 240

grit To flatten the bottom, use the thickness planner. Make

sure the top is level as possible before doing this. You may use a portable belt sander, which will take

much longer.



Step 9: Framing 3/8 x 3/8 Cleats or square dowels – 2 - (1½” less than

width of 1x3 sides) 3/8 x 3/8 Cleats – 2 - (1¼” less than length of 1×3 sides) 1x3 sidepieces to frame the hexagonal bottom

How to Cut a Board to Length w/ Angles - A Beginner Tutorial https://www.youtube.com/watch?v=yMPF40sExcM Using a miter saw and the cut list above cut the 1×3

pieces and square dowels to size. Miter one of the edges of the 1×3″ at a 45-degree angle and then hold it up to the bottom piece of wood and mark where the edge is.

Then use that mark on the miter saw to measure where to start the 45-degree angle cut out.

Sand the sidepieces. Step 10: Dry Fit the Sides Attach the first set of cleats. Position the cleats on the 1×3

pieces flush with their bottom edges and ends. Apply a bead of wood glue to the cleat, reposition it, and then nail it in place using a pneumatic nail gun and ¾-inch finish nails.

Then glue the corners together and use some masking tape or clamps to hold them together, you may also nail them.

Step 11: Finishing Once the glue has dried use polyurethane on the tray. Or any other finish to bring out

the differences in the woods.

https://www.youtube.com/watch?v=yMPF40sExcM



Hexagon Serving Tray Self-Evaluation

1. What I had learned from this project …

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

2. Parts of the project I am most proud of …

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

3. Safety practices I have been observing…

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

4. What I have learned that I should be doing, from this point on, to ensure any other projects have an excellent outcome.

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________



Bill of Materials

Part # Description Material Dimensions Footage Quantity Unit Total Cost

Type (calculate footage) (bd/ft, lin/ft,

sq/ft) Of Parts Cost

= $-

= -

= -

= -

= -

= -

= -

= -

= -

To calculate board feet with all measurements in inches:

T x W x L

Total

144

Cost: $-

project #2 - wordpressstorageaccount.blob.core.windows.net€¦ · pass out the regular and...

Documents