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Students manipulate tiles to discover prime and composite numbers in the clever lesson

Subject:

Math  

Grades:

6, 7  

 

Title – Prime and Composite Numbers
By – Jawa Mariappan
Primary Subject – Math
Grade Level – 6-7
Title: Prime and Composite Numbers 6

Learning Objective:
Learn what prime and composite numbers are and how to identify them.

Materials Needed:
Have several square cards (or tiles). At least 20 cards would be useful. You can even use “Post-It” notes. Each card (tile) is assumed to have one square unit area for simplicity. If you can’t make these cards, you can draw them on the board and complete the lesson.

Teacher Instructions:
Take 4 cards and ask the students to arrange them into possible areas. Students will easily figure out that only the following two configurations are possible. In both cases, area is 4 square units.

In the first case, 4 tiles arranged in 1 row form the area. It is a 4 x 1 rectangle.

In the second case, 2 tiles arranged in 2 rows form the area. It is a 2 x 2 square.

Both figures represent the same area. This means number 4 can be written as 4 x 1 or 2 x 2.
Tell the students, in such cases, we can say numbers 1, 2 and 4 are factors of 4. Draw students’ attention to the fact that number 4 can be divided by 1, 2 and 4.

Ask the students to do another example with 6 tiles.

In the first case, 6 tiles arranged in 1 row form the area. It is a 6 x 1 rectangle.

In the second case, 3 tiles arranged in 2 rows form the area (2 tiles arranged in 3 rows will be the same). It is a 3 x 2 rectangle (or 2 x 3 rectangle).

All figures represent the same area. This means number 6 can be written as 6 x 1, 3 x 2 or 2 x 3. So, 1, 2 and 3 are factors of 6. Draw students’ attention to the fact that number 6 can be divided by 1, 2 and 3.

If necessary do more example with numbers such as 8 and 10 till all the students understand this concept.

Now tell them, when a number such as 4, 6, and 8 has more than two factors, it is called a composite number.

Now ask the students to do the same exercise with 3 tiles.

In this case, there is only one option and that is 3 tiles arranged in 1 row. There are no other configurations available. So number 3 can only be written as 3 x 1. This means there are only two factors for 3, and they are 1 and 3. Draw the students’ attention to the fact 3 can be divided only by 1 and 3 (itself).

Ask the students to do another example with number 5.

Here again, 5 x 1 is the only option. This means there are only two factors for 5, and they are 1 and 5. Draw the students’ attention to the fact 3 can be divided only by 1 and 3 (itself).

If necessary do more example with numbers such as 7 and 11 till all the students understand this concept.

Now tell them, when a number such as 3, 5 and 7 has only two factors (1 and itself), it is called a prime number.

*Teachers* Important Non-Intuitive Observations

1 is neither a prime nor a composite. Most students think 1 is a prime number.
2 is NOT a composite number. It is a prime number. Ask students, why?

Don’t confuse odd numbers and even numbers. Many students tend to believe odd numbers are prime. Give them some examples such as an odd number 9, which is a composite.

Ask students to use the tiles approach to find and list all the prime and composite numbers from 2 to 20
(Answer: The prime numbers between 2 and 19 are: 2, 3, 5, 7, 11, 13, 17 and 19)

 

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