Page 1 of 7
LESSON PLAN SUBJECT:
Mathematics
GRADE:
10
DATE:
September
WEEKS:
1–2
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 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 – universal sets, subsets and the number of elements in a set. 2. Presents interactive charts to the students.
Page 2 of 7
3. Discuss concepts of union, intersection and complement 4. Leads students to identify the different regions in the Venn Diagram. Fig 1 Region 1
Region 2
B1 ∩ A
A∩ B
Region 3 A1 ∩ B
Region 4 ( A ∩ B )1 or( A ∪ B )1
Fig 2 Region 1 or A only A ∩ ( B ∪ C ) or A ∩ B ∪ A ∩ C 1
1
1
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.
Page 3 of 7
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
1. 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 only, swim only.
(iii)
Write an algebraic equation involving x for the above data.
(iv)
Page 4 of 7 Hence solve the equation to find how many students can play cricket and swim.
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 1. 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: 1. identify the shaded regions in a Venn diagrams. 2. draw Venn diagrams to illustrate given information. 3. 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 1. Review previous knowledge concepts – union, complement and intersection. 2. 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 1. 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
Page 6 of 7 Add all regions and equate with universal set.
U
A 53-x
B x
68-x
25 53-x + x + 68 – x + 25 = 125 1. Solve equation to find how many students did both subjects 144 – x = 125 x = 133 –125 x = 19 2. Use the value of x in the expressions 53- x and 68-x to find how many students do Agriculture only and Mathematics only. 3. 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
)1
(II.( P ∩Q ∩ R
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 A (II.Copy and complete the Venn diagram
1
10
B
3
14
Page 7 of 7
(III.List the members of the set
. ( A ∪ B)
1
EVALUATION _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ ___________________
