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.

How to Multiply Using Lines and Dots

One of the great things about mathematics is that sometimes, you find mathematical concepts in places that you don’t expect them to be. There are also concepts or representations that seem not connected to mathematics, but you will realize that it is indeed mathematics.

In the video below, observe how to multiply using lines and their intersections.

Don’t just watch  the video for the sake of entertainment. I encourage you to think about it.

Why does the method work?

Can you think of other concepts that is similar to the intersection of lines?

Is there a similar representation or idea that is also connected to this representation?

In the next post, we will try to answer the questions above, so keep posted.

The Geometric Representation of Greatest Common Factor

A factor is an integer that divides another integer. The number 6 is a factor of 12 since 6 divides 12. It is easy to see that 1, 2, 3, 4, and 12 are also factors of 12. Looking at the numbers in the tables below, we can see that some numbers have only 2 factors, 1 and itself. These numbers are called prime numbers.

Two or more numbers can have common factors. For example, let us consider the factors of 12 and 18.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18  Continue reading

Notable Posts in Elementary School Mathematics

Mathematics and Multimedia has grown extensively since I first created in 2009, and honestly, I have stopped updated the pages or have created categories. There are many interesting posts that have been buried in this blog. Therefore, I will slowly post these categories in the days to come.

As part of this long term goal, I am now creating a list of topics under one category and create them as posts. This way, it will be easier for you to navigate them later. This is the first among these category posts.

In this post, I am going to share to you my notable posts in Elementary School Mathematics.

Area Derivation Series

I hope you enjoy these posts.

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