1. Geometry Mini - Unit By: Ms. Lauren Zecca

2. Objectives of this unit… Upon completion of this unit students will be able to … • Find the perimeter of a shape • Find the area of any given shape • Find the surface area of any given shape • Find the volume of any given shape

3. Standards that will be addressed… • 5.G.1 Calculate the perimeter of regular and irregular polygons • 6.G.2 Determine the area of triangles and quadrilaterals (squares,rectangles, rhombi, and trapezoids) and develop formulas • 6.G.4 Determine the volume of rectangular prisms by counting cubes and develop the formula • 7.G.4 Determine the surface area of prisms and cylinders, using a calculator and a variety of methods Lesson 1: Perimeter Lesson 2: Area Lesson 3: Surface Area & Volume

4. Lesson 1: Finding the Perimeter… • Connection – The first part of this unit will have to be reviewing polygons and their characteristics. You will also want to go over key vocabulary such as lines, edges, points, etc. • Objective – To have students understand the concept of perimeter and to develop strategies on how they can find the perimeter.

5. Perimeter (cont.) • The perimeter of a polygon is the distance around the outside of the polygon. A polygon is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units. To help us make this distinction, look at our picture of a rectangular backyard. The perimeter of this yard is the distance around the outside of the yard, indicated by the red arrow; It is measured in linear units such as feet or meters. To find the perimeter of a polygon, take the sum of the length of each side.The polygons may be much smaller than a fenced-in yard. Thus, we use smaller units such as centimeters and inches.

6. Activities that go with this lesson … • Give your students a model of finding the perimeter of any regular polygon. Using a grid draw random shapes and have them find the perimeter. • Give the students measurements of sides of polygons and have them calculate the perimeter. • Give the students the perimeter of a shape and have them determine a missing side of the shape • You may also want to have students develop the circumference formula by asking for ways you could measure the perimeter of a circle (need this extension activity to do the webquest) • Have them respond to the following blog… http://zeccaperimeter.blogspot.com/ • Homework can be found on the wiki

7. Resources… • http://www.shodor.org/interactivate/activities/PerimeterExplorer/ - interactive web application • http://www.teachers.ash.org.au/jeather/maths/dictionary.html - math dictionary for children • http://ibm.mentorplace.epals.org/MeasureUP.htm - activity dealing with chocolate bars! Back to Menu

8. Lesson Two: Finding the Area… • Connection - Review everything you have learned about perimeter before beginning the area lesson. • Objective – To have students understand the concept of area and to develop formulas for finding the area

9. Area… • Definition of Area A = sum of unit squares     Area is a count of how many unit squares fit inside a figure. To fully understand this classic definition of area, we need to picture the unit square. A unit square is a square that is one unit long by one unit wide. • Area of Rectangles A = lw    A rectangle is an equiangular quadrilateral. Opposite sides are congruent and parallel. All internal angles are right angles. Let's look at a rectangle that is 4 mm by 6 mm. If we count the number of 1 mm by 1 mm squares that are inside the rectangle we can easily see there are 24 of these squares. After performing the same task with a rectangle that has different dimensions, we can see a pattern. The total number of squares that rest within a rectangle can be found by multiplying the length of a rectangle by its width. So, 4mm x 6mm = 24 mm2, hence the formula A = lw. Counting square units fits nicely with the concept of counting squares and it also coincides with a property of algebra. In algebra, we already know (x)(x) = x2. The same is true for mm times mm, or any unit times the same unit.

10. Area (cont.) • Similar to the rectangle, finding the area of a parallelogram requires two known distances. We need to know its height and the length of the side that is perpendicular to the height, called the base of the parallelogram.  If we start with a typical parallelogram, we can make a few alterations to it in order to calculate its area. If we cut it along its height, we can remove a portion that is a right triangle. If we move this right triangle to the opposite side of the figure, it will fit perfectly and create a rectangle. • A triangle can be defined by the length of its base and its height. The height is always perpendicular to the base, exactly like the base and height of a parallelogram. We can find the area of a triangle by performing three tasks. We know the area of a parallelogram to be A = bh. In our newly formed diagram, we can use those same distances to arrive at the exact same area for the two-triangle area. However, if we want to know the area of one of those triangles instead of the whole parallelogram, we have to divide the area into two equal portions since the triangles are congruent to each other. Therefore, the area of a triangle is A = ½bh.

11. Resources Back to Menu • http://www.mathguide.com/cgi-bin/quizmasters/AreaTour.cgi - interactive quiz on area • Video -

12. Lesson Three : Finding the Surface Area and Volume • Connection – Review what the students know about area and vocabulary words dealing with three dimensional shapes • Objectives – Students will be introduced to the notion of surface area and volume. They also will have learned the terminology used with surface area and volume and have experimented with the surface area and volume of different prisms.

13. Surface Area and Volume … • surface area - A measure of the number of square units needed to cover the outside of a figure • Have you ever wrapped a birthday gift? If so, then you've covered the surface area of a polyhedron with wrapping paper. • volume- A measure of the number of cubic units needed to fill the space inside an object • Have you ever poured yourself a glass of milk? If so, then you've filled the volume of a glass with liquid.

14. Modeling how to find surface area and volume… • http://www.learner.org/interactives/geometry/area_surface.html - this is a website that shows how to unfold a prism to see where surface area comes from • Have students ‘unroll’ a cylinder in the same way to determine surface area of a cylinder • http://www.learner.org/interactives/geometry/area_volume.html - this is a website that shows how to fill a rectangular prism with cubes to represent volume • Using the formula you have developed for volume how does that apply to cylinders

15. Resources… • http://www.teachervision.fen.com/tv/printables/0130533688_ALFL0514-3.pdf - formulas • http://www.enasco.com/product/TB17690T - product you can buy • http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html - game to play about perimeter and area

16. RETURN TO THE WIKI