Posted in Math blogs

Math Problems for K-12 with solution

Math Problems for K-12 is my new site that contains problems with solutions, explanations and common errors students commit in solving the problem.  Sample students answers are shown with the corresponding marks. The posts are written for students but teachers, I’m sure, will also find them helpful. You can say this is the student version of Math for Teaching blog. The problems are categorized according to math area and year level. Here is a sample problem for middle school algebra. Click the image to go to the site.

And here’s another for high school mathematics. This post links equation solving and graphing functions, a key concept in algebra.

If you are a teacher and wishes to contribute a problem you have done with your class, feel free to share it here together with students’ solutions. It would be great if you can also show how you marked it together with comments. It is through assessment and marking that we communicate to students what we value. Email me at mathforteaching@gmail.com so I can invite you as author. Thank you.

Posted in Elementary School Math, Number Sense

Bob is learning calculation

Bob is an elementary school student. He is learning to calculate. He just learned about addition and multiplication but there are some things that he doesn’t understand. For example, how come 1+3 = 3 + 1? How can it be the same thought Bob? Every morning I have 1 piece of bread for breakfast while Dad has 3 pieces. If I have 3 pieces while Dad has 1 piece, I will be too full and Dad will be hungry?

When they added three numbers, Bob did not understand (1+2) + 1 = 1 + (2+1). Usually I like to drink 1 cup of coffee with 2 spoons of milk then afterwards have a piece of bread. I would not feel well if I first drink a cup of coffee then afterwards drink 2 spoons of milk while having 1 piece of bread. How come they are the same, thought Bob.

The most confusing part was after the lesson on fraction. Bob learned that 1/2 = 2/4. So when he got back home he tried to share 6 apples with his sister Linda. He divided the 6 apples into two groups – 2 apples in one group and 4 apples in another group.

apples, dividing apples

From the set of two apples he gave 1 to Linda. That’s 1/2. From the set of four apples, he took 2, that’s 2/4. It is equal he said. But Linda did not agree with him because she got 1 apple less that he. Bob thought, how can this be? Why would 1/2 = 2/4 not work for apples!

The next day, the teacher asked Bob to add 1/2 and 2/4? Bob wrote 1/2 + 2/4 = 3/6 because taking 1 apple from 2 apples then 2 apples from 4 apples, he must have taken a total of 3 apples from 6 apples!

This story is adapted from A Framework of Mathematical Knowledge for Teaching by J. Li, X. Fan, and Y Zhui at the EARCOME5 2010 conference.

Point for reflection:

What has Bob missed about the meaning of addition of natural numbers? the meaning of fraction?

You may want to read the following posts about math knowledge for teaching:

Posted in Algebra, Math blogs

Math Teachers at Play at Math Mama

Math Teacher at Play (MTAP) #51 is now live in Math Mama Writes …. Really great collection of 51 posts from teachers, lecturers, professors, bloggers, … in the following categories: Arithmetic, Patterns and Logic, Visual Math, Algebra-Geometry-Trigonometry, Puzzles and Games, Notations and Logic, and Breaking News, and may favorite, Teaching Mathematics.  I even got two posts in the carnival. Thanks Sue.

The next MTAP carnival will be hosted in Let’s Play Math. Submit your post first week of July using the MTAP submission form.

Posted in Algebra, Math Lessons

Ten problem solving and geometric construction tasks

I’ve written a number of posts the last couple of months which I published in other sites. They are problem solving tasks mostly in geometry using GeoGebra and a few on function, trigonometry and calculus. May I share 10 of them here. The first six are teaching resources which I posted in AgIMat, a site about science and math teaching resources. The last four problems are in Math Problems for K-12 to help students in their revision.  Both sites are new ones. I hope you subscribe and promote them in your social networks. Thank you.

  1. Problem solving on congruent segments
  2. Square and triangle problem
  3. Triangle Congruence by ASA
  4. Angle bisector – two definitions
  5. Constructing the perpendicular bisector
  6. Exponential function and its inverse
  7. How to sketch the graph of the derivative of a function
  8. Ratio and probability problem
  9. Trigonometric equations and their graphs
  10. Proving trigonometric identities #1