Virginia - Mathematics Standards of Learning (2009): 3.10b, 3.9d,

Transcription

1 1 U n t er r ich t splan Calculating Area of Right Triangles Altersgruppe: Grade 4, Grade 3 Virginia - Mathematics Standards of Learning (2009): 3.10b, 3.9d, 5.8a Virginia - Mathematics Standards of Learning (2016): 3.8.b, 4.7 Fairfax County Public Schools Program of Studies: 3.10.b.1, 3.9.d.1, 3.9.d.2, 5.8.a.5 Online-Ressourcen: Shape s o n t he Gri d Opening Teacher present s Students pract ice Math Pract ice Closing M at h Obj ect ives E xpe ri e nc e aligning right triangles with a grid to detere their area P rac t i c e finding area of rectangles Learn to calculate area of a right triangle De vel l o p facility with comparing traits of different polygons

2 2 Ope ni ng 5 Display the following: Ask: What is the area of this rectangle? How do you know? This rectangle has area 20 square units. We can count the unit squares inside the rectangle. There are 20 unit squares within the rectangle. Display the following: Say: It may be harder to detere the area of the right triangle because some of the unit squares within it are incomplete. However, if we compare this triangle to the rectangle we just looked at, we will be able to detere its area.

3 3 Display the following: Ask: How does the triangle compare to the rectangle? The triangle is half of the rectangle. If we draw a line segment from the top left corner of the rectangle to the bottom right corner, we would form the triangle. Say: We detered that the area of the rectangle is 20 square units. What is the area of the triangle? How do you know? The area of the triangle is 10 square units. The triangle is half the size of the rectangle. Half of the rectangle s area, 20, is 10 square units. T e ac he r prese nt s M at h game : Shape s o n t he Gri d - Area: R i ght T ri angl e s 12 Present Matific s episode Shape s o n t he Gri d - Area: R i ght T ri angl e s to the class, using the projector. The goal of the episode is to find the area of right triangles by using a grid under the polygon.

4 4 Say: Please read the question. Students can respond based on the episode. Ask: How can we detere its area? We can rotate the shape and move it to align it with the grid behind it. Then we can count the small squares of the grid to find its area. Move the polygon so that it is aligned with the grid. Ask: What is the area of this polygon? Click on the to enter the students answer. If the answer is correct, the episode will proceed to the next question.

5 5 If the answer is incorrect, the question will wiggle. The episode will present a total of six questions. Two of them will ask for the area of a square or rectangle. The other four questions will ask for the area of a right triangle. St ude nt s prac t i c e M at h game : Shape s o n t he Gri d - Area: R i ght T ri angl e s 12 Have the students play Shape s o n t he Gri d - Area: R i ght T rii angl e s on their personal devices. Circulate, answering questions as necessary. M at h P rac t i c e : Area o f R i ght T ri angl e s Wo rkshe e t 15 Before class begins, prepare cutouts of squares and right triangles in two different sizes each. (One large square, 3 large triangles, 6 small squares, and 14 small triangles per student will be more than sufficient.) The edge of the larger square should be twice the edge of the smaller square. The leg of the smaller triangle should equal the edge of the smaller square. The leg of the larger triangle should equal the edge of the larger square. For example: Distribute rulers and copies of the four polygons.

6 6 Ask the students to measure the edges of the squares and triangles and calculate their areas. When the students are done working, display a banner: Say: Now we re going to use the polygons to make a banner. Make available glue, paper, and more cutouts of the polygons. Display the following instructions: 1. Using any of the cutouts you wish, make a banner by gluing the cutouts onto a white piece of paper in the same shape as the displayed banner. 2. Add up the areas of the individual polygons in order to calculate the area of the entire banner. When the students are done working, review the areas of each polygon. Collect the banners, to display later. A possible banner:

7 7 The area of the entire banner is 14 times the size of the smaller triangle. If time allows, lead a discussion relating the areas of the smaller polygons to the larger polygons. Students may be surprised to learn that even though the edges of the larger polygons are twice the edges of the smaller ones, the areas are 4 times the size.

8 8 Cl o si ng 3 Distribute a small piece of graph paper to each student. Display the following triangle and instructions: Collect papers, to review later. A possible response: 3. This triangle has a base of 6 units and a height of 4 units. To find the area of a triangle, we multiply times the base times the height. When we multiply by 6 by 4, we get 12.

9 9