Factors Of The Form (x+a) (x+b)

Learning Outcomes

1. Student will learn to factorise the expression
2. Student will understand concept of factorization.
3. Student will develop understanding about the reality and apply them in real life.
4. Student will develop the abilities of reasoning and observation.
5. Student will learn the process to factorise the expression by splitting the middle term.

Description Of Activity

How to play

1. All the student of class VIII having strength of 40 will be participating activity for which they will accompany the teacher on the Basketball ground.
2. First of all, students will be instructed to stand in a proper way  at the around  bank of the ground.
3. Some of the students will be standing parallel to the length and some other students stand parallel to its breadth. Rest will remains at the bank of ground.
4. Assumed that the students who were allowed to stand at length and breadth are x in numbers.
5. Now, the students will be explaining the factor of total strength which is 40. It is expected that student will be explaining as (8,5) , (10,4) , (20,2) etc.
6. Now students will be given a polynomial x2+ 13x + 40
7. They will be asked to explain  split the middle term in two terms such that the product of terms becomes equal to product of extreme terms.
8. They might be assuming as 8 and 5 .
9. Now they will be rearranged to stand 8 on the length and 5 of them on the  breadth.
10. Hence the total strength standing along the length will be (x+8) and the strength standing on the breadth will be (x+5).
11. Teacher will ask question to the students regarding area of the rectangular play field (Basketball).
12. They will answer as length breadth. i.e. (x+8) (x+5)
13. Teacher will summarise through this activity Factor of x2 + 13x + 40 = (x+8) (x+5)
14. Students can also verify it multiplying (x+8) (x+5)

 

Variations

1. The same activity can be do it for negative middle term  (x2 - 14x + 40)
2. All the class VIII student having strength 40 are on the Basketball ground.
3. Students are instructed to stand on the boundary of the ground i.e. on its sides.
4. Assumed that the students who were allowed to stand at length and breadth are each x in numbers.
5. The student will be given a polynomial x2 -14x + 40
6. Student will be asked to explain how to split the middle term in two terms so that the product of these two terms becomes equal to product of extreme term.
7. They might be assuming -10 and -4
8. Now 10 student from each length side and 4 students from each breadth side will left out.
9. Hence the remaining strength standing on the length will be (x-10) and the Strength standing on the breadth side will be (x-4).
10. Teacher will ask area of play field (Basketball)
11. Student will answered length × breadth i.e. (x-10) (x-4)
12. Now teacher will summarise through this activity factor of  x2 -14x + 40 = (x-10) (x-4)
13. Students can also verify it multiplying (x-10) (x-4)

Coaching Tips

1. Teacher should integrate mathematical knowledge in daily life even during playing in the field. It means learning anything does not limit us to be present in the class room situation only.
2. The teacher should encourage the students to factorize the other polynomials, correlating them within the number of students in the class.

Equipment/Material Required

Measuring Tape, Limestone for making the line.