Math 8 Shape and Space Resource Kit Parent Guide

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1 Math 8 Shape and Space Resource Kit Parent Guide

2 Resources Included with this Resource Kit (To be Returned to HCOS): Parent Guide Student worksheets Jenga blocks (game) Set of mini geosolids (Right Start Math) ($17.75) math/geometry/mini-geosolids-set-of-32.html 3D Pentomino Puzzle $ sortby=ourpicks&sortby=bestmatchesdescend&&from=search Math 8 Outcomes Covered in this Resource Kit: Shape and Space (Measurement) draw and construct nets for 3-D objects determine the surface area of right rectangular prisms, right triangular prisms, and right cylinders to solve problems develop and apply formulas for determining the volume of right prisms and right cylinders Shape and Space (3-D Objects and 2-D shapes) draw and interpret top, front, and side views of 3-D objects composed of right rectangular prisms demonstrate an understanding of tessellation by explaining the properties of shapes that make tessellating possible, creating tessellations, and identifying tessellations in the environment General Outline: This kit is designed to use over five weeks, with four lessons per week. There are some enrichment activities that have not been included in those four lessons per week. Week 1: Nets for 3-D objects

3 Week 2: Draw and Interpret front, side and top views of 3-D objects composed of right rectangular prisms Week 3: Surface area of Right Rectangular Prisms, right triangular prisms and right cylinders Week 4: Formulas for volume of right prisms and cylinders Week 5: Tesselations

4 Week 1: Nets for 3-D objects Day 1: What is a net? Finding nets in common household items. What is a net? A net is a two-dimensional (planar) figure made up of geometric solid that can be folded easily. A net is a flat pattern of solid figures. It gives us with an easy way to analyze the different bases, edges, faces and even dimensions of any space figure. Two examples of nets: Net of a square prism Net of a cylinder Task: Use common household containers to deconstruct and find the shapes used to create the overall container. You will need a variety of containers and some scissors to do this. Try to cut containers in a way that will allow the original shapes to be reconstructed that means with all the flaps and sides attached in one piece. (some container suggestions: cereal box, pringles chip tube, toblerone chocolate bar box Try to find some smaller ones that you can trace onto paper in the next lesson) Reinforce: Which containers were easiest to cut apart? Why? Which containers were the most difficult to cut apart? Why? What do you notice about the different containers when they are laid flat (open)? (Hint, are they made up of irregular shapes, or shapes you recognize?) Reflect: Besides food packaging, where else would knowledge about 3D nets be useful? Day 2: Drawing nets: tracing household items When we create 3D nets, there are specific words we use to label our drawings.

5 You already know the basic shapes (rectangle, triangle, circle, hexagon ) These ones may be new: Face: a flat surface of a polyhedron. Vertex: a point where two straight lines meet to make an angle; in 3D solids, a point where three or more straight edges meet to make a corner Edge: the line interval where two faces of a solid meet.! Task: Use some of the smaller containers from day 1 to trace the nets on paper (suggestions include small toblerone box, jello box, small yogurt container ) On your drawing label the shapes (rectangle, circle, triangle), faces, edges and vertices Reinforce: Complete the 3-D shapes worksheet and the Evaluating 3-D shapes worksheet.

Day 4: Drawing Nets from 3-D Shapes When drawing a net, you need to look at all the individual faces of a 3-D shape. 1. Start by choosing and drawing one face (red) 2.

6 Day 3: Which Nets Create a Cube? Print two copies of the worksheet entitled Which Nets Can Create a Cube? Use the first copy to make your predictions, use the second copy to construct the cubes and answer the question at the bottom of the page. Day 4: Drawing Nets from 3-D Shapes When drawing a net, you need to look at all the individual faces of a 3-D shape. 1. Start by choosing and drawing one face (red) 2. Then draw the faces which are connected to the first face (blue) 3. Repeat the process until you have drawn all of the faces of the shape (yellow)!! Complete the worksheet entitled Drawing Nets for 3D Shapes. Bonus Activity: "This box (give student a box) contains a Christmas present for my mom. Because it's so special, I want to wrap it in special wrapping paper. The paper is so rare that it costs A HUNDRED DOLLAR PER SHEET! Luckily I only have to pay for the amount I use. "As I don't have much money, I need to find the smallest possible piece of paper that will wrap the present - no overlaps or pieces joined at corners. Can you find what shape that would be?" (Note, all measurements are in centimeters) Give out wrapping paper and boxes to the students and let them get on with it. They can cut only after they have decided what shape they are going to cut out. Check by wrapping the

7 present. After a while tell them that the piece of paper they have chosen is called the net of the shape, and yes, sometimes there is more than one possible way to do it. Extension: there is more than one way to wrap this cube; can you find them all? Week 2: Front, side and top views of 3-D objects Day 1: Jenga Use Jenga blocks to create composite 3-D structures. Begin with 3 blocks and stack them in a simple shape. Any blocks that you put on top of another block should be directly on top (not overlapping) of the block below. Draw front, side and top views. Use graph paper (There is a blackline master in the worksheet folder if you need one) to do your drawings and do them to scale (one square on the paper = on Jenga unit). Assume the Jenga blocks are 1 (tall) x 2 (wide) x 6 (long) units. Continue creating shapes with more Jenga blocks and drawing the three views until you are comfortable with the different viewpoints. Day 2: Three Dimensional shapes using right rectangular prisms and right triangular prisms, right cylinders Open the file entitled Creating 3D shapes. It contains numerous pages with many shapes to construct. You may print as few or as many as you wish. Cut out the images (you may want multiple copies of the shapes) and construct the three dimensional shapes, using tape or glue to secure the edges. Use the constructed 3-D objects to create compound shapes (Stack them like you did the Jenga blocks last lesson). (If constructing the shapes is to challenging, or to save time, use the set of geometric shapes supplied with this kit). Draw front, side and top views to scale using the graph paper.

8 Day 3: Use front, side and top drawings to create 3-D shapes Today you get to use the 3D Pentomino Puzzle resource to translate drawings of three-dimensional shapes into the real thing! Read through the Instruction booklet in the Worksheet folder. In it, you will find three levels of pictures that you can try to re-create with the shapes in the kit. Day 4: Tin Man assignment Today you have a challenge. It may take you more than one day and that is okay. Take your time, to a great job, and don t forget to take a photo (with explanation) for your teacher! Today you are going to use 3-D shapes from around your house to create a Tin Man, or robot. Look for things like cereal boxes, granola bar boxes, toilet paper tubes, paper towel tubes, etc. Once you have your collection together, brainstorm what your Tin Man will look like. NOTE do not begin attaching arms and legs to the body quite yet! Now that you have decided on your final structure, the real work begins! For each 3D shape, you will need to make careful measurements, draw a net, and calculate how much tin foil you will need to cover each shape. Cut out your tin foil, cover each piece, then construct your final product. Feel free to use buttons, eyes or other embellishments to really make your Tin Man shine!

9 Week 3: Surface area of right rectangular prisms, right triangular prisms and right cylinders Day 1: Review of area Area is defined as the extent of a 2-dimensional surface enclosed within a boundary. In everyday language, area is the entire area inside a complete shape (square, triangle, etc). So, to review, to find the area of: A RECTANGLE - Find the length (l) and the width (w) and multi- ply them together A = l x w b A TRIANGLE - Find the base (b) and the height (h). Multiply them together, then divide by 2 A = b x h 2 A PARALLELOGRAM - Find the base (b) and the height (h) and multiply the two numbers together.

10 A = b x h A CIRCLE - Find the radius of the circle, square the radius and multiply by pi (π = 3.14) A = πr 2 Complete the Area of Common Shapes Worksheet to review. Day 2: Surface area of rectangular prisms: Introduction: A rectangular prism has 2 ends and 4 sides. Opposite sides have the same area. The surface area is the sum of the areas of all six sides. How to find the surface area of Rectangular Prisms: Find the area of two opposite sides (Length x width) x 2 sides we multiply by two, because there are two identical sides Find the area of the other two opposite sides (Length x width) x 2 sides Find the area of ends (Length*Width)*2 ends Add the three areas together to find the surface area Example: Find the surface area of a rectangular prism that is 4cm long, 3 cm. wide and 12 cm. high. First step: side 1 = L x W x 2 = 4cm x 12cm x 2 = 96 cm 2

11 Second step: side 2 = L x W x 2 = 3cm x 12 cm x 2 = 72 cm 2 Third step: ends = L x W x 2 = 3cm x 4cm x 2 = 24 cm 2 Options for practice: Fourth Step: add them up 96 cm cm cm 2 = 192 cm 2 1. Jenga calculate the area of one long side, one short side. Assume the Jenga blocks are 1 (tall) x 2 (wide) x 6 (long) units. Create complex 3-D shapes with Jenga blocks and find surface area. 2. Use the mini geosolids set and calculate the surface area of the rectangular prisms. 3. Complete the Surface Area of Rectangular Prisms worksheet.

12 Day 3: Surface area of Triangular prisms Okay - first let s clarify what a right triangular prism is, exactly! A right triangular prims is a 3D shape that has three rectangular sides and two triangular ends. The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and 2 being triangular. Step 1: Find the area of the rectangular faces. Sometimes they are all the same and you can find one side and multiply by three, other times they are all different and you have to calculate the area of all three. Step 2: Find the area of the two triangular faces. These will be the same, so multiply your area for one triangle by 2 Step 3: Add all five sides together. For Example: Step 1: The area of a rectangle is L x W. For this prism, we have three different sides: - side A = 4cm x 11cm = 44 cm 2 - side B = 5cm x 11cm = 55cm 2 - side C = 3cm x 11cm = 33cm 2 then multiply by 2 = 12 cm 2 Step 3: Add them all up Step 2: The area of a triangle is (b x h)/2 - (3 cm x 4 cm)/2 = 6 cm 2 x 2 44 cm cm cm cm 2 = 144cm 2 Options for Practice: 1. Use the Mini Geosolids set and calculate the surface area of the right triangular prisms. (Note, there are other types of triangular prisms in the set choose wisely!) 2. Complete the Surface Area of Triangular Prisms worksheet Day 4: Surface Area of Cylinders

13 To find the surface area of a cylinder, we add the surface area of each end plus the surface area of the side. Remember, that the side of a cylinder is really one big rectangle! Step 1: Each end is a circle so the surface area of each end is π r 2, where r is the radius of the end circle. There are two ends so their combined surface area is 2 π r 2. Step 2: The surface area of the side (big rectangle) is the circumference of the end circle times the height of the cylinder or 2 π rh. (Remember, r = radius and h = height) Step 3: Add the two ends and the side together For example: Step 1: Area of the end circles 2 π x (2cm) 2 = cm 2 Step 2: Area of the side 2 π (2cm) x (4cm) = 50.24cm 2 Step 3: Add them up cm cm cm 2 = Options for Practice: 1. Use the mini geosolids cylinders and find the surface area of each. 2. Complete the Surface Area of Cylinders worksheet

14 Week 4: Formulas for volume of right prisms and cylinders Day 1: Volume of a Right Prism Volume is the amount of space inside a 3-dimensional object. To find the volume of a 3D object, we need to consider all three dimensions That means you have to find a measurement for the length, the width and the height of your rectangular prism! When calculating volume of a rectangular prism, you should always have three numbers to multiply together! For the rectangular prism to the left, our calculations would look like this: Notice Volume = Length x width x height = 4 cm x 3 cm x 12 cm = 144 cm 3 1. You are basically finding the area of one side, then multiplying by the length of the third dimension! 2.. The units are cubed! You multiplied three measurements, so the units in the answer must also reflect that. More practice can be found on the Volume of Right Prisms worksheet. Check out this website for a more detailed lesson on finding the volume of right rectangular prisms.

16 Day 2 Volume of a right Cylinder So, now that you know in order to find the volume of a prism, you find the area of one side, and multiply by the third side or dimension, we are going to apply the same principle to a cylinder. To find the volume of a cylinder, you find the area of the circle at one end, then multiply by the height of the cylinder. If you know the radius of the circle, the formula looks like this: volume = π r 2 x h Example: Volume = π r 2 x h = π (6.5 m) 2 x 8.0m = m 3 Sometimes you are given the diameter, rather than the radius. Remember, the radius is just half of the diameter! Example: The radius is ½ of 10 cm so 5 cm. Volume = π r 2 x h = π (5 cm) 2 x 15 cm = cm 3 You can do the Volume of a Right Cylinder worksheet for more practice.

17 Check out this website for a more detailed lesson on how to calculate volume of a right cylinder.

18 Day 3 Build a house or other simple structure. Your task is to take some sort of building materials and create a structure. You can use anything sugar cubes, graham crackers, lego to build your structure. When you are done building, see if you can calculate the volume of your creation! Days 4 and 5: - Putting it all together Now, let s work on a bigger project that will use all the skills we have learned so far. Option 1: Design a street scene from pre-made shapes, print the nets of the street shapes and build a town. For one of your buildings, calculate the surface area of the building and the volume of the building. Option 2: Create a floor plan of your dream house (keep it fairly simple, in terms of the basic shape.) Once your floor plan is complete, use the 3D shapes we have learned about to create a 3-D model of your house. (for example, if your bedroom is 4 meters by 3 meters, your cube representing that room would be those dimensions (scaled down, of course) plus the height of your ceiling. After your model is complete, you could go so far as to calculate the surface area, and volume of your home. Week 5: Tesselations Day 1: What is a tessellation Look around you can you find patterns in your environment? (some examples might be floor tiles, a beaded necklace, patio stones in your driveway). Tessellations are repeated patterns. However, not all repeated patterns are tessellations Tessellations are a very specific type of pattern. What are Tessellations? 1) tessellations are repeated patterns 2) tessellations do not have gaps or overlaps 3) tessellations can continue on a plane forever

20 Can you figure out which of the following diagrams are tessellations? A. B. C. D. E. F.

21 Answer: (A and F are not tessellations) Day 2: Identifying and Creating Tessellations There are only three regular polygons that can be used to form a regular tessellation, the triangle, square, and hexagon. Use the Creating Tesselations worksheet to create your own tessellations. Day 3: Art with Tessellations Do some research on M.C. Escher. You could do a brief biography, a showcase of his work, or another type of project on this famous tessellation artist. OR Do some research on tessellations in nature. Create a presentation that shares your findings.

Measurement 1 PYTHAGOREAN THEOREM. The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of

Measurement 1 PYTHAGOREAN THEOREM Remember the Pythagorean Theorem: The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two sides.