Topic: Tiling -- Using Prime and Composite Numbers
TEKS: (5.5) Patterns, relationships, and algebraic thinking. The student makes generalizations based on observed patterns and relationships. (C) identify prime and composite numbers using concrete models and patterns in factor pairs.
Performance Objective: The learner will learn what prime and composite numbers are and how to identify them by working in a group and demonstrating an understanding of one work problem with 100% accuracy using the manipulatives provided.
Strategies used in this lesson: Manipulatives, Problem solving, cooperative learning groups, layout worksheet
Materials needed: Overhead tiles, 4 baggies of cut tiles (each tile represents one square unit area), bathroom layout worksheets and transparency, Vocabulary Poster
Role-Play: apron, caulking gun, ruler, scraper, real tiles
Prior Knowledge needed for this lesson: counting, grouping, multiplication, area (l x w), factoring
Key vocabulary used in this lesson: prime number, composite number, multiply, group, sort, count, square unit area, caulking gun, ruler, tiles, scraper, glue, apron, cutter
Motivation/Focus: 1. Teacher has recently decided to re-tile her bathroom in her home. She has never done this before so she is asking the students to help her practice tiling.
2. Before they can begin practicing, they must become familiar with the vocabulary used in this profession. Go over vocabulary words.
3. We are going to use a layout of a bathroom worksheet and use tile manipulatives to practice tiling.
4. While we are practicing tiling we are going to learn about prime and composite numbers.
Procedures/Activities: Teacher will show many examples of prime and composite numbers through the process of tiling the bathroom layout on the overhead.
1. Take 4 tiles and ask students to arrange them into possible areas. There are only two configurations that are possible. Both cases show the area is 4 square units. 4 tiles arranged in a row (4 x 1 rectangle) and 2 tiles arranged in 2 rows (2 x 2 square) In this case we could say numbers 1, 2 and 4 are FACTORS of 4. (4 is divided by 1,2, 4)
2. Take 6 tiles and arrange into possible area. There are two cases. 6 tiles arranged in a row (6 x 1 rectangle) and 3 tiles arranged in 2 rows (3 x 2 rectangle) or 2 tiles arranged in 3 rows (2 x 3 rect) In this case we can say numbers 1,2,3, and 6 are FACTORS of 6.
3. Explain to students that when a number such as 4 and 6 has MORE than two factors, it is called a COMPOSITE NUMBER.
4. Now the teacher does the same examples with the numbers 3, showing 3 tiles in 1 row (3 x 1 rect) and 5, showing 5 tiles in 1 row (5 x 1 rect). Draw attention to the students that these numbers can only be divided by 1 and the number itself.
5. Explain to students when a number such as 3 and 5 has ONLY two factors, it is called a PRIME NUMBER.
Evaluation/Assessment: Have students get into 4 different groups. Each group will have a baggie of tile manipulatives and a layout of the bathroom. Each group will have a different number to determine the factors of and evaluate if it is a prime or composite number. Teacher will walk around and check each layout for accuracy.
Closure: Once each group's layout is checked the teacher will ask the following questions:
· How was it working in a group? Did everyone come up with the same conclusion? Were there different way to come up with an area for your number?
· Can you think of any other profession, other than tiling, that would require the knowledge of prime and composite numbers? Sorting? Multiplication?
Extend/Enrich: Have the student go a bit further with demonstrating prime and composite numbers.
· Is 1 a prime number or composite number? Why? (It is neither)
· Is 2 a prime number or composite number? Why? (It is prime)
· Use the tiles approach to find and list all the prime and composite numbers from 2 to 20.
Reteach: Use candy (M & M's) to find the area of certain numbers. Draw each possible answer on paper, possibly tracing what you put out with the candy. Write each factor beside the drawing and figure out if the number is prime or composite.