45 Geometry Riddles

1. I have a flat top and bottom face. I have no vertices.

I am a cylinder!


2. I am a path of points continuing forever in both directions.

I am a line!


3. No matter how many sides I have, my sides are all the same length, and my angles are all the same measurement.

I am a regular polygon!

4.I am not a closed figure, so therefore…

I am NOT a polygon!

5. I am an angle with a measurement of less than 90 degrees.

I am an acute angle!

6. I am two figures of the same shape, but different size.

I am similar figures!

7. I divide a shape so that both sides look like mirror images.

I am a line of symmetry!

8. I am line segments that meet to form right angles.

I am perpendicular line segments!

9. I am a line segment that goes all the way across a circle, through its center.

I am a diameter!

10. I am a four-sided polygon.

I am a quadrilateral!

11. I am a five-sided polygon.

I am a pentagon!

12. I am a triangle with 3 sides of different lengths.

I am a scalene triangle!

13. I am a special kind of quadrilateral that has 2 pair of parallel sides.

I am a parallelogram!

14. I am the number of degrees in a triangle.

I am 180 degrees!

15. I am a triangle with 3 congruent sides.

I am an equilateral triangle!

16. I am a 3-D figure. All of my faces are quadrilaterals. My length is longer than my width and height.

I am a rectangular prism!

17. I am 2 angles that together create a 90 degree angle.

I am complementary angles.

18. I am a line segment from the circle to its center.

I am a radius!

19. I am a straight path of points that extend forever in one direction, and I have one endpoint.

I am a ray!

20. I am an angle with a measurement of 90 degrees.

I am a right angle!

21. I am the number of degrees in a quadrilateral.

I am 360 degrees!

22. I am the point where the 2 rays of an angle meet or the point where 2 edges of a cube meet.

I am a vertex!

23. I am the number you start at when measuring an angle with a protractor.

I am zero!

24. I am a quadrilateral with only 1 pair of parallel sides.

I am a trapezoid!

25. I am 2 shapes that are the same shape and size.

I am congruent figures!

26. I am the movement of a shape that consists of moving left, right, up, or down.

I am a slide or translation!

27. I am a transformation that is a pivot at one point.

I am a turn or rotation!

28. I am a path of points with 2 endpoints.

I am a line segment.

29. I am the distance around a circle.

I am the circumference!

30. I am lines that go in the same direction and therefore never meet.

I am parallel lines!

31. I am a quadrilateral with all 4 sides congruent. I do not have to have 90 degree angles, but I have 2 pair of parallel sides.

I am a rhombus!

32. I am a triangle with all angles measuring less than 90 degrees.

I am an acute triangle!

33. I am a triangle with all 3 sides different lengths.

I am a scalene triangle!

34. I am lines that cross each other.

I am intersecting lines!

35. I am a line segment connecting 2 points on a circle.

I am a chord!

36. I am a 3-D figure with 6 faces. All 6 faces are congruent, and the lengths of all my edges are congruent.

I am a cube!

37. I am 2 angles that combine to create a 180 degree angle.

I am supplementary angles!

38. I am an 8-sided polygon.

I am an octagon!

39. I am a triangle with 1 angle measuring more than 90 degrees.

I am an obtuse triangle!

40. I am a 3-D figure with 4 triangular faces that meet at one point.

I am a square pyramid!

41. I am also called a flip.

I am a reflection or mirror image.

42. I am a triangle with 1 angle measuring 90 degrees.

I am a right triangle!

43. I am a six-sided polygon.

I am a hexagon!

44. I am a curve between 2 points on a circle. (I am less than a semi-circle.)

I am an arc!

45.I am a 10-sided polygon.

I am a decagon!

Mental Math Strategies grade one to three

Here is a good link for mental math strategies for primary grades from Saskatoon Public School.

Click here.

Chess Problem of the Day

Sudoku for Children

One way to teach logic with children is to use Sudoku games. I have started with grade three students. If you are not familiar with this popular logic game, click here.

I would start with something simple, such as a 4 by 4 grid to teach the basic idea. Also I would be sure to start with easy problems or ones that have lots of clues. You can make your own puzzles with a 4 by 4 grid template and a puzzle generator of which there are numerous versions available online. Here is a link to my personal favourite entitled Sudoku for Kids.

Mathematical Curriculum Links

We promised an entry on mathematical curriculum links, especially at the primary level. Since we live in Ontario we will highlight these, although I suspect that the expectations, especially in primary grades, are similar to other North American jurisdictions.

1. If you want a summary of the expectations in mathematics, here is my personal favourite. It is called Ontario Curriculum Tracking Templates. Click on the link, and you will see all the expectations in mathematics in point form for grades K through 8.

2. Here is the link to the Ontario Ministry of Education, Elementary Mathematics Curriculum, in pdf format.

3. Here is the link to the Kindergarten Curriculum into which mathematics is incorportated. It is also in pdf format although there is a plain text version available.

4. The Ministry of Education has exemplars on line. They are examples of children's work at the four different levels in the different strands. Here are links for grade one, grade two and grade three. Other grades are also available on this site.

5. The ministry has published an early math strategy in 2003 to encourage problem solving based mathematics and to promote cooperation and sharing amongst mathematics teachers in the spirit of the Japanese Lesson Study method of curriculum development. Here is the link. In 2004 the ministry published a similar documument for the junior grades.

6. E workshops: The ministry of education has hosted documents and on-line videos to explain different aspects of the curriculum in elementary schools. These include numeracy.

7. Illuminations: This is the National Council of the Teachers of Mathematics site. It is an American site, but it has numerous links and ideas for elementary mathematics teachers.

8. The Hamilton-Wentworth District School Board has a very good numeracy site. Stop and visit here for they have numerous resources for both parents and teachers. In particular I am impressed with the plans that they have for teaching mathematics for grades one through eight. These plans suggest what to teach each term, the big ideas that you can address in so doing and the related curriculum links. They also suggest what resources to use, such as the relevant chapters from common textbooks which is a great help in planning. Here are the plan for grade one, grade two and grade three. If you are a junior or intermediate teacher you will also find your grades there.

9. The Upper Canada District School Board maintains a site called Aftermath with many useful links for literature, curriculum, online resources and etc, although I have the impression that it has not been updated for a little while as there are some dead links.

10. Proteacher: This is a special portal and search engine for teachers. There also links to blogs, discussion boards and even online chats if you need support and ideas. It is used by English language teachers around the world.

Chess for Children

“Life is a kind of Chess, with struggle, competition, good and ill events”

Benjamin Franklin

This is the fifth in a series of entries on games for children. It concerns one of the great games of the world, Chess. Click here for an introduction to the history, rules, strategy and tactics.

Chess is a game that we have successfully taught to older primary children. The rules are simple enough that children in grade three can master them in two to three periods of instruction.

All games have some mathematical value. There have been many studies in recent years about the numerous the cognitive benefits of learning Chess. If you do a web search, you will find numerous entries and citations in this regard, so we won't bother doing this for you. Chess is easy to learn but difficult to master. There are numerous books on the subject. If you look in the children's section of your local library or bookstore, you will find books on this game for children.

Chess is a game that has numerous applications for mathematical thinking. In Canada, there is an association that promotes the game entitled, Chess'n Math Association. They claim that it teaches : "problem-solving from start to finish. It forces you to look ahead and anticipate. Skills we all need to succeed in life." If you want to teach the game, it is worth visiting and looking around. Follow the many useful links.

There is an organization in New York City called Chess in the Schools. They claim numerous benefits for Chess. For example:

"In 1991 and 1996, Stuart M. Margulies, Ph.D., a noted educational psychologist, conducted two studies examining the effects of chess on children’s reading scores. The studies demonstrated that students who participated in the chess program showed improved scores on standardized tests. The gains were even greater among children with low or average initial scores. Children who were in the non-chess playing control group showed no gains."

Almost every country in the world has a Chess federation. Since we live in Canada, we will link to the Canadian version. It is available in French and English. It provides a free training manual for teachers in pdf format that can be downloaded. Click here for the link.

Chess is a subject of great fascination for mathematicians. Many have tried to write a program that can beat the best chess players in the world, in the same way that the Chinook program at the University of Calgary has mastered the game of Checkers. Perhaps the most successful attempt has been the Deep Blue program developed by IBM which had considerable success against the famous Chess Grand Master, Garry Kasparov.

As with Checkers, there are Chess problems which would serve as a good way to study the game if there were no other players available, and these multi step problems serve as an excellent source of enrichment for gifted students. Here is one site, with hints, called Bruno's Chess Problem of the Day. There are other sites for problems on the web, and one can buy books of these in virtually any bookstore.

Like many of the other games mentioned in this blog, inexpensive versions are available in many stores. If you are on a budget, check your local second-hand stores or dollar stores. In a pinch, you can make a set out of paper or other easily available materials. There are Chess clubs in most major cities, and it is easy to form one in your school.

As with most games, there are online versions such as Yahoo Games just to name one, and inexpensive software or freeware versions available to download or purchase. Check online or at your local computer store.