6th Class Maths:
- Knowing our numbers
- Whole numbers
- Playing with numbers
- Basic geometrical ideas
- Understanding elementary shapes
- Data handling
- Ratio and proportion
- Practical geometry
Knowing our numbers
This is an introduction to the number system. Students get to understand and appreciate the meaning of the words thousand, lakhs, millions etc, and are expected to know how to write big denominations of numbers and count them in this chapter in 6th class maths. They learn the Indian system of counting and the International system of counting. For example,
1 thousand = 10 hundreds
1 lakh = 100 thousands
Seventy three lakh seventy five thousand three hundred seven = 73,75,307
Twenty three lakh thirty thousand ten = 23,30,010
78,921,092 = Seventy eight million nine hundred twenty one thousand ninety two.
This introduces students to natural, whole, non-decimal numbers. It introduces the concepts of predecessors and successors in the number system. For example:
Three natural numbers after 10999 = 11000, 11000 +1=11001, 11001+1 =11002 etc.
Predecessor of 102 = 102 – 1=101
Successor of 102 =102 + 1=103
The number 204 lies to left or right of 210? Ans: since 204 is less than 210, it lies to the left.
Playing with numbers
This is an introduction for students to the concept of factors of numbers, multiples of numbers etc. For example
1 * 24=2 * 12=4 * 6=3 * 8 =2 * 2 * 3 * 2. Thus, 1,2,3,4,6,8,12 and 24 are factors of 24.
49=1 * 49=7 * 7 thus 1,7,49 are factors of 49.
60 = 1 * 60 = 2 * 30= 2 * 2 * 15 =4 * 15 =4 * 3 * 5 =2 * 2 * 3 * 5. Thus, 1,2,3,4,5,15,30,60 are all integers.
Basic geometrical ideas
This introduces students to the concepts of point, line, rays, segments etc.
For example, How many lines can pass through two points? Ans – Only one.
How many lines can pass through one point? Ans – Infinite.
Understanding elementary shapes
This is an introduction to basic shapes like circle, triangles, rectangles, squares etc.
This chapter is about conceptualizing the number line and the positions of the numbers on the same. It enables students to have a vision about which number lies where which is more or which is less etc. This is an important chapter in 6th class maths. For example, a list of temperatures of cities on a particular day:
Siachen – 10 degrees below zero
Bhopal – 30 degree above zero
Shimla – 2 degree below zero
Delhi – 20 degree above zero
Srinagar – 5 degree below zero
Students are expected to write these in integer forms This is solved as :
Siachen = – 10o
Srinagar = -5o
Shimla = -2o
Delhi = 20o
This chapter introduces the concepts of fractions as parts of a whole. For example,
what fraction of a day is 6 hours? Ans = total hours of a day is 24 hours. Therefore 6/24=1/4th of a day.
What fraction of an hour is 25 minutes? Ans = I hour = 60 minutes. Thus, 25/60= 5/12. Thus, 25 minutes is 5/12th fraction of an hour.
This is an introduction to the concept of point and decimals, and their relationship to fractions. For example:
Express 1/10 as a decimal. Ans: 0.1
Express 0.007 as a fraction. Ans: 7/100
Express 85 mm in centimeter. Ans = 85 mm = 85/10 =8.5 cm
This shows students how to arrange numbers or items in a list according to a specified order using tally marks. It is a prerequisite to study statistics.
Teaches concepts of perimeter and areas of simple geometric figures. For example, find the perimeter of a triangle of sides 10 cm, 20 cm and 15 cm. Ans: Perimeter = 10+20+15 = 45 cm.
Ratio and proportion
Building on the previous concepts of fractions, this chapter prepares the student to see ratios and proportions as relationships of parts with respect to the whole. For example,
in a class there are 10 boys and 15 girls. What is the ratio of boys to girls, and proportion of boys to total number of students?
Ans: Ratio = 10/15 = 2/3 or 2:3. Thus for 2 boys there are 3 girls in the class. Total number of students = 10+15 =25. Thus proportion of boys = 10/25 = 2/5. Thus 2 students out of 5 students are boys which is the proportion of boys of the class.
This introduces students to the concepts of algebra; finding out the value of an unknown quantity using what information is known, or assessing the relationship between unknown variables using known variables. For example,
A large box of apples is emptied into 2 mall boxes, and then 5 apples are left. How many apples were in the large box? Ans: If in each box there were x apples, then in two boxes, number of apples = 2*x. Now, the number of apples left outside = 5. Therefore, total apples that originally were in the larger box = 2*x + 5
This chapter builds on the conception and understanding of geometrical figures and shapes to introduce the concept of symmetry to students. Students are given incomplete figures and are expected to make them symmetric, or identify how given figures are symmetric or not, etc.
This chapter is an introduction to how to draw basic geometric shapes using the geometric equipment. Students are given specified instructions and are expected to follow the same to draw the figures. For example: – draw two circles of radii 2.5 cm and 4 cm which have a common centre. Students are expected to measure these radii on their scales and use their compasses to draw these circles to complete the exercise.