## SNC-Mathematics-Overview

The basic aims of mathematics curriculum from grade I-V are as follow:

• Instill Mathematical skills for everyday use.
• Strengthen basic mathematical skills to set the foundation for higher level mathematics.
• Develop the ability to think in a logical manner to analyze diverse situations.
• Develop a sense of appreciation and enjoy learning mathematics.
• Develop a long lasting understanding of the concepts through Concrete, Pictorial and Abstract (CPA) approach by Jerome Bruner.
• Engage in investigations and enquiries to develop skills in mathematical reasoning, processing information, making connections to real life situations and making judgments.

Benchmarks

The Standards for Mathematics are further sub-divided into the following Benchmarks for Grade Level-I-V:

 Standards Benchmarks  Grade-(I-III) Benchmarks Grade-(IV-V) express and match fractions in figures and compare fractions with same denominators using symbols <, > or = identify and write equivalent fractions for a given fraction add and subtract two fractions with same denominators apply unitary method for solving real life situations identify and recognize decimal numbers convert decimal numbers into fractions and vice versa add and subtract numbers up to 3 decimal places multiply and divide decimal numbers with whole numbers round off decimal numbers up to specified number of decimal places solve real life situations involving decimal numbers (up to 3- decimal places) convert percentage to fraction and to decimal and vice versa ALGEBRA   analyze number patterns; known facts, properties and relationships to analyze mathematical situations, examine real life situations by identifying mathematically valid arguments and drawing conclusion to enhance mathematical thinking develop the concept of equality using addition and subtraction of numbers identify and complete geometrical patterns on square grid according to attributes like shape, size and orientation. develop the concept of equality using addition, subtraction, multiplication and division of numbers. identify and describe repeating pattern using relationship between consecutive terms and generate number patterns

 Standards Benchmarks  Grade-(I-III) Benchmarks Grade-(IV-V) GEOMETRY AND MEASUREMENT identify measurable attributes of objects, construct angles and two-dimensional figures; analyze characteristics and properties of geometric shapes and develop arguments about their geometric relationships examine real life situations by identifying, mathematically valid arguments and drawing conclusion to enhance mathematical thinking use language to compare heights/ lengths, masses and capacity of different objects read, recognize and use units of length (kilometer, meter and centimeter), mass (kilogram and gram) and capacity (liter and milliliter) and time (minute and second). add and subtract in units of length, mass, capacity and time for solving real life situations use solar and Islamic calendar to find a particular dates/ day. recognize and identify two- and three-dimensional figures determine perimeter of square, rectangle and triangle identify and differentiate straight line and curved line. identify and draw points, lines, line segments, and rays. identify and describe symmetrical shapes convert standard units of length, mass, capacity and time solve the real-life situations involving addition and subtraction of units of distance/ length, mass, capacity and time distinguish parallel and non-parallel lines. identify, classify and construct different types of angles describe and classify 2-D figures and 3-D geometrical objects determine perimeter and area of square and rectangle describe and complete symmetric figures with respect to given line of symmetry and point of rotation.

 Standards Benchmarks  Grade-(I-III) Benchmarks Grade-(IV-V) DATA HANDLING   collect, organize, analyze, display and interpret data/ information examine real life situations by identifying mathematically valid arguments and drawing conclusion to enhance mathematical thinking read, interpret and represent data using Carroll diagram, picture graph and tally charts read and interpret bar graphs, line graphs and pie charts represent real life situations using pie chart find an average of given quantities in the data draw and read simple bar graphs both in horizontal and vertical form solve real life situations using simple bar graphs

Progression Grid

 Compare and Order Numbers Grade I Grade II Grade III Grade IV Grade V arrange numbers in ascending and descending order up to 9 identify which number (up to 9) comes before/after a given number, between two given numbers compare and order the numbers 0-10. compare one- and two-digit numbers order numbers from 0 to 99 in ascending and descending order identify which number (up to 99) comes before/after a given number. between two given numbers identify and write missing numbers in a sequence from 1 to 100 compare two or more groups of objects in terms of numbers match objects having one to one correspondence identify the number of objects in two groups to show ‘more than’ or ‘less than’ compare 2 - digit numbers   with 3 - digit numbers (hundreds, tens and ones) compare 3 - digit numbers   with 3 - digit numbers (hundreds, tens and ones) count backward ten steps down from any given number arrange numbers up to 999, written in mixed form and in ascending or descending order count and write in 10s (e.g.10,20, 30,...) count and write in 100s (e.g.100,200, 300,...) identify the smallest/large st number in a given set of numbers compare two numbers up  to 3 - digit numbers using symbols  “<”, “>”, or “=” write the given set   of numbers in ascending and descending order (up to 3 - digit numbers) compare and order numbers up to 6 - digit

 Place Value of Numbers Grade I Grade II Grade III Grade IV Grade V recognise the place values of a 2 - digit number (tens and ones) Identify the place value of the speci?c digit in 2 - digit numbers decompose a number  up  to 99 to  identify the value of a number in ten’s and one’s place recognise that 1,000 is one more than 999 and the first 4 - digit number recognise the place value of a 3 - digit numbers identify the place value of a specific digit in a 3 - digit numbers identify the place values up to 5 - digit numbers represent a given number on number line up to 2 - digit numbers identify the value of a number on number line up to 2 - digit numbers identify place values up to 6 - digit numbers

 Subtraction of Numbers Grade I Grade II Grade III Grade IV Grade V compare numbers  from 1- 20 and find ‘how many one is less than the other? recognise subtraction  as a  difference and take away, (use  the symbol ‘-’) subtract 1 - digit numbers  from 1 - digit numbers (which results in positive) subtract 1 - digit numbers from 2 - digit numbers subtract tens from 2 - digit numbers subtract 2 - digit numbers  from 2 - digit numbers (which results in positive) recognise the use of symbols to   represent an unknown such as 9-?=7 subtract numbers (up to 20) using mental calculations construct subtraction sentences from given pictures or number stories subtract 1 - digit numbers from 2 - digit numbers with borrowing subtract 2 - digit numbers from 2 - digit numbers with borrowing subtract numbers up to 50  using mental calculations solve real life number stories of subtraction with borrowing subtract 1 - digit numbers from 3 - digit numbers without borrowing subtract 2 - digit numbers from 3 - digit number without borrowing subtract 3 - digit numbers from 3 - digit numbers without borrowing solve real life number stories of subtraction without borrowing subtract 1 - digit numbers from 3 - digit numbers with borrowing subtract 2 - digit numbers from 3 - digit numbers with borrowing subtract up to 4 - digit numbers with and without borrowing subtract numbers up to 100 using mental calculations solve real life number stories involving subtraction subtract up to 5 - digit numbers with and without borrowing solve real life situations involving subtraction of up to 5 - digit numbers subtract up to 6 - digit numbers solve real life situations involving subtraction of up to 6 - digit numbers

 Subtraction of Numbers Grade I Grade II Grade III Grade IV Grade V subtract 3 - digit numbers from 3 - digit numbers with borrowing solve real life number stories of subtraction up to 3 - digit numbers with borrowing analyze simple real-life situations identifying correct operation of addition and subtraction with carrying/borro wing in mixed form.

 Multiplication  of  Numbers Grade I Grade II Grade III Grade IV Grade V recognise multiplication as repeated addition (for example 2+2+2=6 is equivalent to 3 times 2 which is 3 x 2 = 6) and use multiplication symbol “×” complete number sequences in steps of 2,3,4,5 and 10 (for example in ?eps of 2 the sequence is expressed as 2,4, 6…) develop multiplication tables for 6, 7, 8, and 9 multiply 2 - digit numbers by 1 - digit numbers multiply a number by 0 and 1 apply mental mathematical strategies to multiply 1 - digit numbers to 1 - digit numbers solve real life situations involving multiplication of 2 - digit numbers by 1 - digit numbers multiply  up  to 4 - digit numbers by up to 2 - digit numbers solve real life situations involving multiplication of up to 4 - digit numbers by up to 2 - digit numbers multiply up to 5 - digit numbers by 10, 100, and 1000 multiply up to 5 - digit number, by a number up to 3 - digit solve real life situations involving multiplication of up to 5 - digit numbers, by a up to 3 - digit numbers

 Multiplication  of  Numbers Grade I Grade II Grade III Grade IV Grade V develop multiplication tables of 2,3,4, 5 and 10 till the multiplication of 10x10 multiply numbers within multiplication table write number sentence for multiplication from the pictures such as 2×[] ?=6 solve number stories on multiplication up to 1-digit

 Division of Numbers Grade I Grade II Grade III Grade IV Grade V recognize and use division symbol “÷” recognize division as successive subtraction divide numbers within the multiplication tables with remainder zero solve number stories involving division up to 1 - digit numbers solve real life situations (using Pakistani currency as well) involving addition, subtraction, multiplication, and division. give reasons for choosing the correct operation divide 2 - digit numbers by a 1 - digit numbers (with zero  remainder) apply mental mathematical strategies to divide 1 - digit number by a 1 - digit number solve real life situations involving division of 2 - digit numbers by a 1 - digit numbers divide numbers up to 4 - digit by numbers up to 2 - digit solve real life situations involving division of numbers up to 4 - digit by numbers up to 2 - digit solve real life situations using appropriate operations of addition, subtraction, multiplication and division of numbers up  to 2 - digit identify divisibility rules for 2, 3, 5, and 10 use divisibility tests for 2, 3, 5 and 10 on numbers up to 5 - digit divide up to 5 - digit numbers by 10,100 and 1,000 divide, up to 5 - digit numbers by up to 2 - digit numbers solve real life situations involving division of numbers, up to 5 - digit by a number  up  to 2 - digit find HCF of two or three numbers, up to 2 - digits, using prime factorization method and division method

 Division of Numbers Grade I Grade II Grade III Grade IV Grade V identify and differentiate 2 - digit prime and composite numbers find factors of a number up to 50 list the first ten multiples  of  a 1 -  digit number differentiate between factors and multiples factorize a number by using prime factors determine common factors of two or more 2 - digit numbers determine common multiples of two or more 2 - digit numbers find LCM of two or three numbers, up to 2 - digit, using prime factorization method and division method solve real life situations involving HCF and LCM

 Fractions Grade I Grade II Grade III Grade IV Grade V recognize fraction  as equal parts of a whole identify half, one-third and quarter   with the help of objects and figures (without writing 1/2, 1/3, 1/4) represent half (1/2), one third (1/3) and quarter (1/4) in numerical form shade  the equal parts of a given figure to match a given fraction recognize and name unit fractions up to 1/10 recognize fractions like two thirds (2/3), three fourth (3/4), four fifth (4/5), and so on up to nine tenths (9/10). express the fractions in figures and vice versa match the fractions with related figures recognize proper and improper fractions differentiate between proper and improper fractions identify equivalent fractions from the given figures write three equivalent fractions for a given figure write three equivalent fractions for a given fraction compare fractions with same denominators using symbols “<”, “>” or “= “ add two fractions with same denominators represent addition of fractions through figures subtract fractions with same denominators represent subtraction of fractions through figures recognize like and unlike fractions compare two unlike fractions by converting them to equivalent fractions with the same denominator simplify fractions to the lowest form. identify unit, proper, improper fractions and mixed numbers convert improper fractions to mixed numbers and vice versa arrange fractions in ascending and descending order add fractions with like denominators subtract fractions with like denominators multiply fractions by whole numbers multiply two or more fractions (proper, improper, and mixed numbers) divide a fraction by a whole number analyze real life situations involving fractions by identifying appropriate operations add and subtract two or more fractions with different denominators multiply a fraction by a 1 - digit numbers and demonstrate with the help of diagrams multiple two or more fractions involving proper, improper fractions and mixed numbers solve real life situations involving multiplication of fractions divide a fraction by a whole number divide a fraction by another fraction involving proper, improper fractions, and mixed numbers solve real life situations involving division of fractions recognize percentage as a special kind of fraction. convert percentage to fraction and to decimal number vice versa only for numbers without decimal part i.e. 35 %, 75% etc. solve real life situations involving percentage

 Decimal Numbers Grade I Grade II Grade III Grade IV Grade V recognize a decimal number as an alternate way of writing a fraction express decimal number as a fraction whose denominator is 10 or 100 or 1000 identify and recognize the place value of a digit   in decimals numbers  up  to 3  decimal places convert a given fraction to a decimal number when denominator of the fraction is 10, 100 or 1000 convert a given fraction to a decimal number when denominator of the fraction is not 10, 100 or 1000 but can be converted  to 10, 100 or 1000 convert decimals numbers (up to three decimal places) to fraction. add and subtract 3 - digit numbers (up to 2 decimal places). multiply a 2 - digit numbers (up to 1 decimal place) by 10, 100, and 1000. compare numbers up to 3 - digit with two decimal places arrange numbers up  to 3 - digit numbers with two decimal places in ascending and descending order add and subtract 4 - digit numbers up  to 3 - decimals places multiply a 3 - digit numbers up to two decimal places by 10, 100, and 1000 multiply a 3 - digtnumbers up to two decimal places by a whole number up to 2 - digit multiply a 3 - digit number up to two decimal places by a 3 - digit numbers up to two decimal places divide a 3 - digit numbers up to two decimal places by 10, 100, and 1000 divide a 3 - digit numbers up to two decimal places by a whole number up to 2 - digit divide a 3 - digit numbers up to two decimal places by a 2 - digit number up to one decimal place

 Decimal Numbers Grade I Grade II Grade III Grade IV Grade V multiply a 2 - digit numbers with one decimal place by a 1 - digit number divide a 2 - digit numbers with one decimal place by a 1 - digit number solve real life situations involving 2 - digit numbers with one decimal place using appropriate operation convert fractions to decimals numbers using division. solve real life situations involving division of 3-digit numbers up to two decimal places

 Estimation Grade I Grade II Grade III Grade IV Grade V round off a whole number to the nearest 10 and 100 round off a whole number to the nearest 10, 100 and 1000 round off decimal numbers (with one or two decimal places) to the nearest whole number round off a 4 - digit numbers up to three decimal places to the nearest tenth or hundredth estimate sum or difference of the numbers up to 4 - digit

## GEOMETRY AND MEASUREMENTS

 Measurement of Mass Grade I Grade II Grade III Grade IV Grade V compare the masses of two or more objects using  the terms: Heavy, heavier, heaviest. Light, lighter, lightest. compare the mass of different objects recognise the units of mass, (kilogram and gram) use standard metric units of mass (kilogram, gram) and their abbreviations to measure and record mass of verity of objects use standard metric units of mass (kilogram and gram) including abbreviations add  measures of mass in same units without carrying solve real life situations involving same units of mass for addition without carrying use standard metric units to measure the mass of different objects convert larger to smaller metric units (2-digit numbers with one decimal place) kilograms into grams, grams into milligrams

 Measurement of Mass Grade I Grade II Grade III Grade IV Grade V use addition and subtraction within 100 to solve real life situations involving mass in same units subtract measures of mass in same units without borrowing solve real life situations involving same units of mass for subtraction without borrowing add and subtract measures of mass in same units solve real life situations involving conversion, addition and subtraction of units of mass

 Measurement of Capacity Grade I Grade II Grade III Grade IV Grade V compare capacity of different objects using non-standard units (jug, glass, cup, etc.) recognise and use the standard metric units of capacity, (liter and milliliters) use addition and subtraction within 100 to solve real life situations involving capacity in same units use standard metric units of capacity (liter and milliliter) including abbreviations add measures of capacity in same units without carrying solve real life situations involving same units of capacity for addition without carrying subtract measures of capacity in same units with and without borrowing solve real life situations involving same units of capacity for subtraction without borrowing use standard metric units to measure the capacity of different containers convert larger to smaller metric units (2-digit numbers with one decimal place) liters in to milliliters add and subtract measures of capacity in same units solve real life situations involving conversion, addition and subtraction of units of capacity

 Perimeter and Area Grade I Grade II Grade III Grade IV Grade V calculate perimeter of square, rectangle, and triangle find perimeter of a simple figure on square grid recognise that perimeter is measured in units of length find area of a simple figure on square grid recognise that area  of  a square is measured in m2 and cm2 differentiate between perimeter and area of a square and rectangular region differentiate between perimeter and area of a region identify the units for measurement of perimeter and area find and apply formulas for perimeter and area of a square and rectangular region solve real life situations involving perimeter and area of square and rectangular region

 Geometry Grade I Grade II Grade III Grade IV Grade V recognise and identify shapes of similar objects in daily life identify the following basic shapes rectangle square circle triangle match similar basic shapes in daily life distinguish basic shapes by considering their attributes (sides) classify 2-D shapes according to the number of sides and corners identify whether an object is placed inside or outside above or below over or under far or near before or after of a given picture identify the figures like square, rectangle, triangle, circle, semi-circle, and quarter-circle identify vertices and sides of a triangle, rectangle and square differentiate between a straight line and a curve identify straight lines  and curves from the given drawings recognise point, line, ray and line segment classify figures according to number of sides as quadrilaterals (rectangles, squares) and triangles identify circle, its center, radius and diameter recognise and identify horizontal and vertical, parallel and non-parallel lines recognize an angle formed by intersection of rays and measure it in degrees recognize right angle identify center, radius, diameter and circumference of a circle identify different types of angle (acute, right, obtuse) recognise straight and reflex angle describe adjacent, complementary, and supplementary angles identify and describe triangles with respect to their sides (equilateral, isosceles, and scalene triangles) identify and describe triangles with respect to their angles (acute angled, obtuse angled, and right angles triangle) recognise the kinds of quadrilateral (square, rectangle, parallelogram, rhombus, trapezium, and kite)

 3-D SHAPES Grade I Grade II Grade III Grade IV Grade V recognise and name 3-D objects (cubes, cuboids, cylinder, cone, sphere, pyramids) describe and differentiate 3-D objects (cubes, cuboids, pyramids) with respect to the number of edges and faces compare and sort 3-D objects (cubes, cuboids, pyramids, cylinder, cone, sphere) describe and make 3-D shapes (cubes, cuboids, cylinder, cone, sphere, pyramids) and their nets.

 Practical Geometry Grade I Grade II Grade III Grade IV Grade V use ruler to draw a straight line of given length (exclude fractional length) draw and measure lines to the nearest centimeters and millimeters measure and draw an angle and recognise the symbol (  ) to represent it recognise and draw acute and obtuse angles with reference to a right angle use protractor and ruler to construct a right angle a straight angle reflex angles of different measures use protractor and ruler to construct a triangle when two angles and their included side is given. two sides and included angle is given. use protractor and ruler to construct a square and rectangle when lengths of sides are given.

 Symmetry Grade I Grade II Grade III Grade IV Grade V identify reflective symmetry in simple two- dimensional (2-D) shapes identify and draw lines of symmetry recognise lines of symmetry in two-dimension al (2-D) shapes complete a symmetric figure with respect to a given line of symmetry on square grid/dot pattern recognise different types of symmetry (reflective and rotational). identify lines of symmetry for given shapes find point of rotation and order of rotational symmetry of given shapes

ALGEBRA

 Patterns Grade I Grade II Grade III Grade IV Grade V identify the next shape in the patterns with 2 or 3 elements extend a given pattern of 2 or 3 elements make/ complete geometrical patterns on square grid according to one or two of the following attributes shape size orientation recognise a given increasing and decreasing pattern by stating a pattern rule. describe the pattern   found in a given table or chart complete the given increasing & decreasing number sequence identify and apply a pattern rule to determine missing elements for a given pattern identify the pattern rule  of a given increasing and decreasing pattern and extend the pattern for the next three terms describe the pattern   found in a given table or chart

DATA HANDLING