Unit Lesson Plan: Measuring Length and Area: Area of shapes

Unit Lesson Plan: Measuring Length and Area: Area of shapes

Day 1: Area of Square, Rectangles, and Parallelograms Day 2: Area of Triangles Trapezoids, Rhombuses, and Kites Day 3: Quiz over Area of those shapes. Day 4: Area and Perimeter of Irregular Shaped Figures Day 5: Area of Similar Figures Day 6: Quiz over Area of Similar Figures and Irregular Shaped Figures Day 7: Area of Circles and Sectors Day 8: Area of Regular Polygons Day 9: Geometric Probability Day 10: Review for test Day 11: Test over Area of All Shapes and Geometric Probability

Area of a Square Lesson Grade: 10th/11th

Content: Mathematics- Geometry

Materials: pencil, paper, textbook, whiteboard, markers, Tiling floor worksheet

Standards:

Standard- Solve real-life and mathematical problems involving area. Solve real-world and mathematical problems involving area of two- dimensional quadrilaterals; square, rectangle, parallelogram and triangles.

Objectives:

1. TLW demonstrate their knowledge of area and perimeter. 2. TLW relate the area of parallelograms to rectangles and triangles to parallelograms

and derive a formula 3. TLW determine area of shapes put together. Triangles and parallelogram

Learning Activities:

1) Review the area of a square and a rectangle make sure everyone has a good understanding of both of those. Give a examples. a) Find the area of a square whose perimeter is 30. i) Since p = 4s and s=7 . Then Area = s2 = (7 ) = 56

b) Find the side and perimeter of a square whose area is 20

i) Area = s2 = 20; Then s =

. Then perimeter = 4s = 8

c) Find the area of a rectangle if the base has length 15 and perimeter 50.

i) P=50 b=15. Since P=2b+2h; 50=2(15)+2h so h=10

d) Find the area of a rectangle of the altitude has length 10 and the diagonal has length 26.

i) D=26 h=10. In

, so 262=b2 + 102 so b=24 Area = 240

2) Introduce the area of a parallelogram. Give them an example of how the area of a

parallelogram is similar to the area of a rectangle. A=h*b

3) Example problems Give them four points, tell them

to find the area and perimeter. A(-2,-1) B(-2,1) C(2,3) D(2,1)

4) Review properties of triangles

5) Demonstrate the area of a triangle is one half

of the area of a parallelogram.

6) Example problems: find area and perimeter height 8 base 21

Hypotenuse 15 leg 12; height 5 hyp 13

7) Draw figure 3 on the board and see if students can find the area

8) Distribute the Finding Area ? Tiling the floor worksheet.

9) Give the students a quick exit slip 5-10 min before the end of class

To check for understanding

11

10

16

Assessment:

1. Students will be assessed informally thought the lecture. 2. Students will be assessed with the worksheet, exit slip, and with homework problems

Reflection:

I think this lesson might run a little short. Some students might already know some of this content. I feel like it is a review.

Trapezoid Lesson

Grade: 9th/10th

Content: Mathematics- Geometry

Materials: pencil, graph paper, straight edge, scissors tape,

Standards:

Standard- Solve real-life and mathematical problems involving area. Solve real-world and mathematical problems involving area of two- dimensional quadrilaterals; Trapezoids, Kites and Rhombuses.

Objectives:

1. TLW relate the area of trapezoids to parallelograms. Also the area of kites/rhombuses to rectangles.

2. TLW derive a formula for trapezoids, kites, and rhombuses from those relationships 3. TLW determine area of trapezoids, kites, and rhombuses from those formulas

Learning Activities:

Direct instruction 1. Introduce the key terms of the section Height of a trapezoid- the perpendicular distance between the basses Diagonal- segment that connects two nonconsecutive vertices Basses of a trapezoid- the parallel sides of the trapezoid

Guided instruction Trapezoids 1. Fold the graph paper in half. 2. Then draw a trapezoid the graph paper. 3. Label the height with h and the bases with b1 and b2 within the trapezoid. 4. Now cut out the trapezoid. You should get two congruent trapezoids. 5. Label the second trapezoid with h height and bases b1 and b2. 6. Now have the students tape the trapezoids together to create a parallelogram. 7. Now ask them this question: how does the area of one trapezoid compare to the area of the parallelogram formed from two trapezoids? Write expressions in terms of b1, b2, and h for the base height and area of the parallelogram. Then write a formula for the area of the trapezoid Kites and Rhombuses 1) Next pull another out a piece of graph paper of a kite. 2) Then draw a kite and the perpendicular diagonals 3) Label the diagonal that is a line of symmetry d1. Then label the other diagonal d2. 4) Now cut the kite out. Then cut along d1 to form two congruent triangles. 5) Then cut one triangle along part of d2 to form two right triangles 6) Turn over the right triangles. Place each one with its hypotenuse along a side of the larger triangle to form a rectangle. The tape the pieces together.

7) Now ask the students; how do the base and the height of the rectangle compare to d1 and d2? Write an expression for the area of the rectangle in terms of d1 and d2. Then use that expression to write a formula for the area of a kite.

8) If they haven't figured out the formula yet give it to them.

a) Trapezoid

b) Kite/Rhombus

9) Then have them work on example problems. To turn in at the end of class. a) Find the area of a trapezoid if the bases have length 7.3 and 2.7, and the altitude4 has length 3.8

i) Here = 7.3; = 2.7; h = 3.8; then

= 19

b) Find the area of an isosceles trapezoid ABCD if the bases have length 22 and 10; the legs

have length 10.

i) Here = 22; = 10; AB = 10; In rectangle EBCF, EF = 10 and AE = .5(22-10) = 6

In

, h2 = 102 ? 62 = 64 so h = 8. Then

c) Find area of a rhombus if one diagonal has length 30 and side 17.

i) 172 = 2 + 152 then

; d= 16; Area =

d) Find length of a diagonal of a rhombus if the other diagonal has length 8 abd the area equals 52.

i) D = 8 A= 52;

and 52 = d8 and d= 13

10) Assign homework.

Assessment:

Objectives 1. Through guided instruction cutting the shapes and seeing the relationships 2. Finding the formula from guided instruction 3. At the end of class having the problems due.

Reflection:

I really like this lesson because it isn't just another boring lecture. It is a nice change up to get the kids involved with hands on activities.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download