1. Making and Testing Generalizations about Polygons
Aligns with Envisions 4th Grade Curriculum

2. Today’s Learning Goals
Target:
Make and test generalizations about polygons.
Success Criteria:
When shown a set of polygons:
-Make a generalization
-Test that generalization
-Explain why the generalization did or did not work.

3. Generalization
A generalization is a statement about all the members of a group or set.
Some generalizations may work, but some may not.
What generalizations can you make about the students in this class?

4. Make a generalization about this group:
Animals, Pets, Mammals

5. Make a generalization about this group:
Plants, Trees

6. Make a generalization about this group:
Food, Fruit

7. Make a generalization about this group:
People, Jobs, Careers

8. Make a generalization about this group:
People, Celebrities, Singers

9. Problem of the Day All right triangles have 2 acute angles.
All right triangles have 2 equal sides.
Work with a partner to test each generalization about right triangles. Then tell if each generalization works. Record your work on a sheet of paper.

10. Practice Problems

11. Look at each group of three letters below
Look at each group of three letters below. Give a generalization for each group of letters that does not apply to the other group of three letters.
EFT COS

12. Is the generalization that every four sided polygon has at least one right angle correct? If not, draw a picture to show why not.

13. Select 3 items and make two correct generalizations about them.
EXAMPLE:
Desk
Chair
Stool
Generalizations: All have 4 legs,
All are in our classroom

14. Look at each group of numbers below
Look at each group of numbers below. Compare the size of the factors to each product. What generalization can you make about factors and products for whole numbers?
6 x 8 = 48
46 x 5 = 230
1 x 243 = 243

15. Write the factors for 8, 16 and 20
Write the factors for 8, 16 and 20. What generalization can you make about ALL multiples of 4?

16. What generalization can you make about each of the polygons at the right?
All sides of each polygon are the same length.
All polygons have 5 sides.
All polygons have 4 angles.
All polygons have 3 angles.

17. The factors for 3 and 6 are shown in the table below
The factors for 3 and 6 are shown in the table below. Jan concluded that if you double a number, then you double the number of factors. Is Jan correct? Why or why not?
Number 3 6
Factors
1, 3
1, 2, 3, 6

18. How many sides does an octagon have
How many sides does an octagon have? How many vertices does an octagon have?

19. Look at the pattern below. Draw the shape that would come next.

20. Susan said that all squares are rectangles and therefore all rectangles are squares. Is Susan correct? Why or why not?

21. How many acute angles can an isosceles triangle have?

22. What generalization can be made about all of these triangles?

23. Michael lives on the 22nd floor of a 25 story building
Michael lives on the 22nd floor of a 25 story building. If each floor is 12 feet in height, how many feet above ground level is Michael’s apartment?