Overview of Improvements
Subject: Mathematics (1 - 8)
Grade 1 - 5
After having a detailed analysis of SNC in terms of:
Horizontal Progression & Alignment (Across Grades)
Vertical Progression & Alignment (Within a Grade)
Topics overload in certain strands/competencies
Teaching and learning approaches
The following addendums were created to ensure breadth, balance and continuity and progression in the syllabus.
Numbers and Operations:
Class 4 and 5 contained a maximum number of concepts which could have easily been justified in other levels as task demand for these concepts was not very high, therefore they have been spread evenly across the levels (1 - 5) to ensure breadth and depth to learning as well as concepts being reinforced over a period of time. the following is a gist of addendums introduced in classes 1-5:
The concept of multiplication and division existed in class 2, but at a very basic level. It was a skill not included in class 1. This concept has now been introduced in Grade 1 and extended in grade 2 as well. However the suggested approach is not that of formal multiplication, but using groups and arrays. As the underlying approach suggested for teaching and learning mathematics curriculum is that of CPA, therefore teaching it using groups and arrays through concrete objects and pictorial representations would not be very challenging for students as well as teachers. In addition, the learning activities would also focus on supporting teachers in providing strategies for teaching these concepts effectively.
An essential aspect is skip counting, which was not introduced in either class 1 or 2, therefore the concept of counting in 2s, 3s, 4s, 5s, 10s were introduced in both levels to help students make connections with times tables as well as multiplication.
Rounding, another essential skill that was not introduced in lower classes, that has also been added to lower classes.
Fractions, which are an everyday concept for a child that was not introduced in class 1. as the child already knows how to take halves of quantities, objects, therefore the concept of fraction through halves is introduced in class 1. Furthermore the concept of fractions has been redefined in all levels ensuring that breadth and balance is provided in learning about this concept across the levels.
The use of roman numbers was introduced at a very basic level and not followed in higher classes, it has been ensured that ample opportunities for learning about roman numbers was spread evenly over the levels.
An essential aspect of numbers, even and odd was non-existent in lower classes, it is also introduced in lower classes as it connects very well to skip counting and through introducing pairs of objects and progressing to numbers.
The concept of decimals is spread evenly over level 3 -5 so that a breadth of experience, reinforcement and ample practice leading to a deeper understanding is provided across levels.
Estimation, an essential skill for everyday mathematics, is also introduced from class 2 onwards.
SNC only encouraged basic operations of addition, subtraction, etc to be utilised while adding or subtracting numbers. Numbers have a value attached to it in real life, it could be a number of quantities, measures, time etc. Therefore it has been ensured that the basic four operations are not restricted to an abstract notion of numbers, but of quantities, measures, and time as well.
The concept of money (including international currency notes/coins) have been introduced at an awareness level in classes 1 and 2.
Measurements:
The concept of measuring, comparing and ordering measures in terms of length, mass/weight and capacity was not spread evenly across the levels. All these concepts have been redefined in levels starting from class 1 onwards.
Class 1 only contained defining length through mathematical language. Non-standard units of measurement for all the aspects, namely length, mass, capacity have been introduced in class 1. The reason being that as per 21st century skill, it does not seem logical that if a child can define measurement of length, then similar aspects of measurement namely mass (weight) and capacity could also be managed through the same approach.
The concept of time is also redefined in class 1 and 2 and spread evenly across levels. Analogue and digital clocks both have been added (and not just analogue)
The concept of intervals of time has also been introduced in early classes.
Similarly basic four operations (addition, subtraction, multiplication and division) have been included in lower classes, as a child comparing two or more lengths (or mass/capacity) would also be involved in addition and other operations in relation to it.
Measuring area and perimeter is also an aspect of measurement, therefore it has been moved from Geometry to the measurement strand.
Geometry:
The concept of geometry was split into strands/sub-topics which mathematically overlapped. Therefore Geometry has been introduced as a distinct strand in itself, including all aspects of two/three dimensional. practical geometry as well as symmetry (line/reflective).
A child is interacting with 3-dimensional objects and things on a daily basis, however teaching and learning of 3-D objects was not included in class 1. It has now been added in class 1, as anything that a child interacts with on a daily basis is a 3-D object. Exploring 3-D objects have been evenly distributed over lower levels (including prism and pyramid, which were missing earlier)
The concept of polygons was introduced in class 3, as they had not been included.
the concept of parallel and perpendicular lines was also introduced in class 2, as a child holding a 3-D object would easily locate parallel and perpendicular faces (leading/making connections to parallel and perpendicular lines)
An essential aspect of position, direction, movement and turns has been added, which was missing previously. This would connect very well to angles, coding, and other technology information in further classes.
The construction of angles has been moved to class 4, as children not only have the motor skills, but the prerequisite knowledge to know and be able to construct angles.
calculation of complementary and supplementary angles has also been included in class 5 to ensure progression in knowledge and skills. In addition, calculation of unknown angles in a triangle is also included for continuity and progression.
Statistics and Probability:
First and foremost, this has been renamed from Data handling to Statistics and Probability.
The concept of probability has been introduced from class 1 onwards as it was non-existent in the previous document.
The entire concept of reading and interpreting data (from various sources such as pictographs, bar/block graphs, tally charts, tables etc) was missing in class 1 and 2. These have been added in these classes and progressed to more complex concepts of data management in further classes.
Algebra:
This strand was included in numbers and operations. It is now introduced as a distinct strand in itself.
The concepts of patterns (including objects) were not introduced in classes 1 and 2. These have been added and progressing to numbers, shrinking/growing/easier to difficult patterns.
The concept of polynomials (i.e. linear equations including balancing equations, missing numbers in equations etc) has also been introduced from earlier classes such as class 3. The reason being that a child can easily make connections with number facts to find the answer of the unknown.
Abstract Approach:
The CPA (Concrete-Pictorial-Abstract) approach was mentioned as an aim of the Mathematics curriculum, however the suggested SLOs mostly focused on teaching concepts as abstract. Thus keeping in mind the CPA Approach the SLOs have been reworded to encourage including concrete objects and pictorial representations while teaching and learning a variety of concepts.
Furthermore an essential aspect of CPA approach is making connections between different mathematical concepts and not being taught as an isolated concept. For instance addition could be of lengths, weights, mass, time, money etc however the concept of addition was only introduced through numbers. Thus these connections between topics have also been incorporated in the way the SLOs have been coined.
Progression Grid:
The progression grid throughout mentioned the specific SLOs which led to the main concept. For instance, read numbers up to 9 in numerals and in words, write numbers up to 9 in numerals and in word; read numbers up to 99; write numbers up to 99 etc. Therefore the progression grids have been modified to include the broader concept that the child has to achieve by the end of the academic year. The specific skills of these broader targets are provided in the curriculum template document.
Grade 6 to 8
Cartesian plane is introduced in class 6 along with the plotting of points before moving on to plotting of graphs of linear equations in two variables in the next classes
Added drawing and interpretation of simple distance time and Speed-time graphs (Travel Graphs) in real life contexts in Class 7 - added as Advanced/Additional concept in CT
Added concentric and eccentric circles in Class 7 as Advanced/Additional concept in CT
Named polygons and angles mathematically (e.g. using different notations such as ∠ABC or ∠A etc.) - This is an essential skill that preludes depper concepts of Angles
Added the concept of calculating the three quartiles and Interquartile range for ungrouped data - added as Advanced/Additional concept in CT
The concept of rounding off to the specified number of decimal places and significant figures has been added (with the age-appropriate progression) in class 5 to 8 - This is an essential skill at this level
Recognition of gradient and intercept from linear equations in two variables has been included in class 7, followed by interpretation of the gradient of the straight line from graphs in class 8
Variance, Standard deviation, effect of spreads and outliers has been included in class 9 instead of class 8.
Laws of indices along with standard form has been included in class 9 rather than class 8.
Demonstration of union and intersection through Venn diagram has been moved to class 9 in order to make it age appropriate.
Recognition of gradient and intercept from linear equations in two variables has been included in Class 7 followed by Interpretation of the gradient/ slope of the straight line from graphs in Class 8 by making it age-appropriate
Eliminating repetitive SLOs 4.
Division of Algebraic Expressions to be included in class 8 instead of class 7
Linear inequalities along with representation of the solution of linear inequalities on the number line to be included in class 8.
Some contents from ‘Practical Geometry of Class X, consisting ‘Congruence of Triangles, ‘Construction of circles and Polygons is moved to Class VIII. Rest of the topic is kept in Class X. This will enable students to master the use of mathematical instruments and basic ideas will be developed in Class VIII which will be further strengthened in Class IX and Class X.
Additional/Advanced Content:
Grade 1:
Read and write temperature.
Use appropriate mathematical vocabulary to compare temperature (such as hot, hottest, warm, warmer, cool, cooler, coolest, twice as, half as etc)
Read and write time to half past hour using:
analogue clock and
digital clock.
Draw the hands on a clock face to show half past time.
Describe the properties of 3-D shapes including the number of sides, corners and edges.
Construct simple pictographs, blocks graphs, bar graphs and tally charts (including real-world problems).
Grade 2:
Use of appropriate standard unit to measure temperature (C )
Express standard units of length in m and cm (154 cm is same as 1 m 54 cm)
Express standard units of mass in kg and g (1542 kg is same as 1 g 542 g)
Express standard units of length in litres and ml (2367 l is same as 2 l 367 ml)
Express standard units of length in m and cm (154 cm is same as 1 m 54 cm)
Express standard units of mass in kg and g (1542 kg is same as 1 g 542 g)
express standard units of length in litres and ml (2367 l is same as 2 l 367 ml)
Recognize and identify 2-D shapes (Rectangle, square, circle, triangle, semi-circle and quarter-circle) with respect to their characteristics (i.e. vertices, sides and line of symmetry in a vertical line)
Recognize and identify 3-D Shapes in different orientations (cube, cuboid, cone, cylinder, sphere, prism and pyramid).
Recognise and identify quarter turns as a right angle (and vice versa), half and three quarters turns (clockwise and anti-clockwise) as two and three right angles respectively.
Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.
Grade 3:
Read, write, compare and order numbers with one decimal place.
Round decimals with one decimal place to the nearest whole number.
Recognise and identify parallel and non-parallel lines
Read bar graphs
Read column graphs
Grade 4:
Describe positions on a grid using coordinates
Describe movements using instructions such as moving up and down or left and right
Draw polygons with coordinates of a point
Grade 5:
Use mental strategies of multiplying numbers with multiples of 10, 100 and 1000.
Calculate the HCF of three numbers (up to 2-digit) using various methods. For e.g.
Prime factorization
Division Method
Calculate the LCM of three numbers (up to 2-digit) using various methods. For e.g.
Prime factorization
Division Method
Write simple algebraic sentences
Convert measures of length between km, m, cm and mm. (e.g. 2 km = 200,000 cm)
Express measures of length in expanded form.(e.g. 1400 m = 1 km + 400 m)
Convert measures of mass between mg, g, kg and tonne. (e.g. 2 kg = 2,000,000 mg)
Express measures of mass in expanded form. (e.g. 1650 g = 1 kg + 650 g)
Express measures of capacity in expanded form. (e.g. 4320 mℓ = 4 ℓ + 320 mℓ)
Convert measures of time between hours, minutes and seconds. (e.g. 2 hours = 7200 seconds)
Express measures of time in expanded form. (205 minutes = 3 hours + 25 minutes)