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LESSON PLAN SUBJECT:
Mathematics
GRADE:
10
DATE:
September
WEEKS:
1 – 1 – 2 2
TOPIC OF LESSON : Sets GENERAL OBJECTIVES : At the end of the unit, the students should 1. analyze and solve problems which arise in familiar mathematical and nonmathematical situations.
SPECIFIC OBJECTIVES : At the end of the lesson, students should be able to: 1. identify regions in a Venn Diagram. 2. solve problems based on the intersection of three sets. CONTENT
Intersection The intersection of sets A and B is the set which contains all the elements that belong b elong to both A and B. Symbolically “A intersection B” is written A B . Union The union of sets X and Y is the set which contains all the elements that belong to X and Y. “X union Y” is written as X Y . Complement The complement of set A is the set of elements in the universal set which are not in set A. The complement of set A is written as A1. PROCEDURE
1. Review previous knowledge concepts – concepts – universal universal sets, subsets and the number of elements in a set. 2. Presents interactive charts to the students.
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3. Discuss concepts of union, intersection and complement 4. Leads students to identify the different regions in the Venn Dia gram.
Fig 1 Region 1 B
1
A
Region 2 A B
Region 3 1
A
B
Region 4 ( A B)1 or ( A B)1
Fig 2 Region 1 1 1 1 A ( B C ) or A B A C or A only
5. Observe question on the white/chalkboard. 6. Discuss steps taken in solving the question i. Draw a Venn diagram ii. Fill in the given information in the appropriate regions. iii. Use x for the unknown region. iv. Form an equation involving x to find for the unknown region. 7. Answer question on the chalk/whiteboard. 8. Discussion on students’ performance.
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ACTIVITIES
1. Given X = {2,4,6,8,10}, Y={2,3,5,7} and Z={1,2,5,6,10} and X Y Z U . Find the following: (i)
X Y
(ii)
X Y
(iii)
X Z
(iv)
X Z
(v)
Y Z
(vi)
Y Z
(vii)
n( X Y Z )
(viii)
X Y Z
(ix)
X Y Z
(x)
Y1
(xi)
Z1
(xii)
X1
2. In a class of 40 students 24 can play cricket, 20 can swim and 4 can do neither. Let x represent the number of students who can play cricket and who can swim. (i)
Draw a Venn diagram to illustrate the above data.
(ii)
Write algebraic expression for students who can play cricket on ly, swim only.
(iii)
Write an algebraic equation involving x for the above data.
(iv)
Hence solve the equation to find how many students can play cricket and swim.
Page 4 of 7 EVALUATION
________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________
Page 5 of 7
LESSON PLAN SUBJECT:
Mathematics
GRADE:
10
DATE:
September
WEEKS:
3-4
TOPIC OF LESSON : Sets GENERAL OBJECTIVES : At the end of the unit, the students should 2. analyze and solve problems which arise in familiar mathematical and non-familiar mathematical situations.
SPECIFIC OBJECTIVES : At the end of the lesson, students should be able to: 3. identify the shaded regions in a Venn diagrams. 4. draw Venn diagrams to illustrate given information. 5. use Venn diagrams to solve problems based on the intersection of sets. CONTENT Algebraic expression – an expression containing a variable and a constant. A only means the region that contain members that in A but not in B. It is the same as A B1
Equation – an equation involving x is a simple equation. All all the regions and equate with the universal set.
PROCEDURE
9. Review previous knowledge concepts – union, complement and intersection. 10. Observe question on the chalk/white board In a class of 125 students, 53 do Agriculture, 68 do Mathematics and 25 do neither subject. Let x represent the number who do both subjects (I). Draw a labelled Venn diagram to illustrate the above data. (II). Form a suitable equation involving x and solve it to find the number of students who did both subjects. (III). How many students did Agriculture only 11. Lead to (I). Draw a suitable Venn diagram (II). Form an equation How many students do Agriculture only? 53 – x How many students do Mathematics only? 68 – x Add all regions and equate with universal set.
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U
A
53-x
B
x
68-x
25
53-x + x + 68 – x + 25 = 125 12. Solve equation to find how many students did both subjects 144 – x = 125 x = 133 – 125 x = 19 13. Use the value of x in the expressions 53- x and 68-x to find how many students do Agriculture only and Mathematics only. 14. Solve problems on chalk/white board. Discuss students’ responses – common errors, incorrect labelling etc. ACTIVITIES
1. If R = {4,5,6,7} Q = {6,7,8,9} P = {1,2,3,4,5} Then (I). P Q R (II). ( P Q R )1 2. In a group of 21 students 17 liked Mathematics, 13 liked English while 3 did not like either Let x represent the number of students who liked both Maths and English (i) Draw a labelled Venn diagram from the above data. (ii) Write algebraic expressions for those students who liked Mathematics only; English only. (iii)Write an equation involving x for the above information. (iv)Hence find how many students liked both subjects. 3. U = {1,2,3,4 ……13,14,15} A = {Factors of 12} B= {Multiples of 3} (I). List the elements of sets A and B (II). Copy and complete the Venn diagram A
B 1
10
3
14
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(III). List the members of the set ( A B)1 . EVALUATION
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