Mathematical Tasks: Number of Solutions and Answers

Different types of mathematical tasks let us tests the various skills of students. Close ended tasks let us test students basic knowledge of facts and procedures, while open-ended tasks lets us elicit various solutions answers. In the book Mathematical Thinking, Isoda and Katagiri classified mathematical tasks into three types:

Type 1: one solution, one answer

Type 2: many solutions, one answer

Type 3: many solutions, many answers

Examples of such problems are shown below. The first task is a Type 1 task, or a task with one solution and one answer. Students who have already learned how to calculate the area of rectangles can just use the formula to calculate the area of the rectangle.  Continue reading

CK-12 Lessons and Videos for Elementary School Math

If you are familiar with the CK-12 Foundation, then you are probably familiar with the free resources that they are offering in science, mathematics, and other subjects. Most of these resources are in Grade 6-12, but recently, they have starting adding materials in lower grades (see Elementary School Mathematics).   Included in the resources are videos that tackles mathematical concepts. For example, the video on Using Cubes and Creating Place Value Diagrams  introduces the concept of place value using cubes that are grouped into hundreds, tens, and ones. After the video, the students can answer questions in the assessment section. One sample question about the lesson above is shown below.

ck-12

via CK-12 Foundation

 

CK-12 Foundation offers K-12 resources for FREE in Mathematics, Science, English, History, Astronomy, Engineering, and SAT Preparation.

Top 100 Tools for Learning for 2014

Every year, Jane Hart provides a list of the top 100 software used by professionals around the world. The result last year came from 1038 respondents from 61 countries around the world.  Twitter, Google Drive and Youtube still retained their positions as Top 1, 2, and 3 in the list. Powerpoint is on the fourth and Google Search is on the fifth. The free blogging platform WordPress (used by Math and Multimedia) is on the sixth. To know more about the list, explore the slide share below.

The Top 100 Tools for Learning 2014

Some of the FREE software/website on the list that you might want to explore are the following:

  • Haiku Deck (67) – a presentation, quiz and report software
  • IFTTT (67)- If this then that is an if then software which let’s you set conditions that will trigger actions.
  • Kahoot (81) – a game based classroom response system
  • Edpuzzle (90)- a presentation and quiz tool that let’s you crop, annotate, embed quizzes on videos from popular sources such as Youtube.

Enjoy learning!

New Lesson Study Book Now Available

To all my readers from the Philippines, our new book on Lesson Study is now off the press. The book is titled Lesson Study: Planning Together, Learning Together.  It is a documentation of the actual experiences of teachers and students in mathematics and science classes as well as learning that arise while doing Lesson Study. It was published by the the University of the Philippines National Institute for Science and Mathematics Education Development (UP NISMED).

Lesson Study

The book is 258 pages and costs Php300.00. You can buy it at the UP NISMED Bookstore in the University of the Philippines, Diliman.

By the way, I am also glad to tell that I am one of the writers of this book. 🙂

Here are the contact details:

Tel: +632 927-4276, 928-1563
Fax: 928-3545
Email: nismed@upd.edu.ph

5 Misconceptions About Rational Numbers

Before, I discuss the misconceptions, let us recall the definition of rational numbers. A rational number is a number that can represented by the fraction \frac{a}{b} where a and b are integers and b not equal to 0. From this definition and other previously learned concepts, let us examine the following misconceptions about rational numbers.

Misconception 1 : Zero is not a rational number.

Truth: YES, it is. Zero, and negative and positive integers are all rational numbers. For example, 0 = \frac{0}{1}, -5 = \frac{-5}{1}, and 100 = \frac{100}{1} are all fractions whose numerators and denominators are integers and denominator 1 (which is clearly not equal to 0). Continue reading

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