SAFAL

Structured Assessment for Analyzing Learning

Mathematics Assessment
Framework Handbook
 Table of Contents

Preface 5

Background and Overview of SAFAL 6

Purpose and Objectives of SAFAL 7

Principles for Development of SAFAL Assessment 8

Principles underlying Development of Mathematics 8

Framework under SAFAL
• Guiding principles and assumptions (content-related) 9
underlying mathematics framework
• Salient Features of SAFAL Mathematics Framework 10

Understanding the Structure of Mathematics 11

Assessment Framework
• Strands under Mathematics Framework - Grades 3, 5 and 12
8
• Grade 3 Mathematics Framework 13
• Grade 5 Mathematics Framework 18
• Grade 8 Mathematics Framework 26

Reporting and Interpretation of Results 35

Acknowledgements 37
Preface

The National Education Policy (2020) recognizes high quality Foundational Literacy
and Numeracy (FLN) as an urgent and necessary prerequisite to learning. The quality
of assessments in elementary grades can play a pivotal role in measuring progress
towards achieving this goal and also provide guidance to each stakeholder in the system
for improving learning levels. NEP 2020 recommends transforming the assessment
system to promote development of students and suggests a shift from testing rote
memorization to competency-based learning. To map progress throughout school years,
the NEP 2020 proposes an annual school examination for all students in Grades 3, 5, and
8. This assessment will focus on testing core concepts, application of knowledge and
higher order thinking skills.

Structured Assessment for Analyzing Learning (SAFAL) will ensure progress throughout
school years by providing diagnostic information about students’ learning to schools
and thus, support school education to move towards competency-based education.

A competency based SAFAL assessment framework has been designed for grades
3, 5 and 8 to achieve the same. The SAFAL Assessment Framework communicates
the purpose and characteristics of the assessments. It emphasises the validity of the
assessment by making explicit the aim of the assessment, and what it will cover in terms
of content, skills, knowledge, and context. It includes domains, strands competencies,
and defines learning outcomes or indicators at various levels. The framework is the key
guiding document for item development.

The objective of sharing the framework is to help the wider community understand
what the assessment is about and what the assessment results mean. The results of this
assessment will largely be used to provide development feedback to schools and not for
promotion of students to the next grade.

Team CBSE

SAFAL - Mathematics Assessment Framework Handbook 5

 BACKGROUND AND OVERVIEW OF

SAFAL
The effective use of data from learning and additional information for decision-
assessments is fundamental to education making. When embedded throughout
systems. teaching, assessment serves as both
Learning assessments provide data on a metric and a mechanism for quality,
the status of learning, which can be accountability, and equity in the classroom.
used to monitor the quality of education A strong learning assessment system can
systems and student learning outcomes. help students, their parents, teachers,
Assessments conducted at regular and school administrators track progress
intervals can reveal changes over time on learning, and intervene as and when
in response to interventions to improve needed.
student outcomes, providing feedback

6 SAFAL - Mathematics Assessment Framework Handbook

There are different kinds of learning and application of knowledge in real-life
assessments that are used for different situations, rather than rote memorization.’-
purposes and in different contexts: NEP 2020

1. System level assessments : assessments The National Education Policy 2020

that seek to evaluate the effectiveness proposes annual assessments in grades
of an education system 3, 5 and 8 to monitor progress on core
2. Classroom level assessments : competencies in all elementary schools.
assessments used to make changes to This assessment is intended to steer
curriculum or instruction away from rote memorisation and
test core concepts, higher order skills,
‘To track progress throughout the school and application. The data from these
years, and not just at the end of Grades assessments can be used to identify
10 and 12 - for the benefit of students, schools that are performing poorly on the
parents, teachers, principals, and the entire critical foundational competencies and
schooling system in planning improvements improve accountability to reach the FLN
to schools and teaching-learning processes - goals.
all students will take school examinations in
Grades 3, 5, and 8 which will be conducted In consonance with the NEP’s
by the appropriate authority. These recommendations, CBSE has launched
examinations would test achievement SAFAL (Structured Assessment For
of basic learning outcomes, through Analyzing Learning), a competency-based
assessment of core concepts and knowledge assessment for grades 3, 5, and 8.
from the national and local curricula,
along with relevant higher-order skills

PURPOSE AND OBJECTIVES OF SAFAL

SAFAL, as a diagnostic assessment, will measure the achievement levels of students
across grades 3, 5 and 8 and across the core competencies in curricular areas of
Language, Mathematics, and Environmental Studies/Science. It has been designed to
provide developmental feedback to schools and teachers to improve teaching-learning,
without additional examination pressure on students, in order to help students, parents,
and teachers to track learning progress throughout the school years and not just in
Grades 10 and 12. The purpose of SAFAL is to:

1. Nudge system towards competency based learning: SAFAL will establish a formal
protocol to collect valid and reliable data to chart students’ performance on
competencies at and below the grade-level and to monitor progress.
2. Measure school performance on key competencies: SAFAL will provide rich and
reliable data on a school's achievement across critical outcomes, aiding in measuring
system’s effectiveness through monitoring and reporting of students’ learning levels.
3. Identify areas of academic intervention: School managements and school systems
(eg. Kendriya Vidyalaya Sangathan, Navodaya Vidyalaya Samiti, State government
running CBSE schools, etc.) can use data from SAFAL for targeting academic support
and data-based management.

SAFAL - Mathematics Assessment Framework Handbook 7

 4. Provide remediation and support: SAFAL will provide teachers information on
students’ achievement levels, allow them to reflect on their instructional practices,
and identify how to support learning needs of students.

SAFAL will provide a reliable and comparable ‘absolute’ metric for parents, schools,
and state officials to assess school performance on core concepts. It is to be noted that
SAFAL will not decide to pass or fail at any stage. Rather it will be used for developmental
purposes as envisaged in NEP 2020.

PRINCIPLES FOR DEVELOPMENT OF SAFAL

ASSESSMENT
The SAFAL assessments will be developed developed at the outset of the assessment
to be valid and reliable for all the stated program. It acts as a communication
purposes and fair and accessible for all tool for the program, giving information
students who are assessed, and to assess to education agencies, school leaders,
content that is instructionally relevant. teachers, domain experts and the wider
In order to operationalise the above public. It provides information about the
principles, it will be ensured that the test purpose, content and structure of an
instruments and items comply with the assessment. It supports the work of those
design principles and best practices in involved in the design and implementation
educational assessments. Further, for an of the assessment. It gives technical
assessment to be robust and valid, it is guidance to test developers and supports
essential that the assessment framework is a program’s stability over time.

What does an assessment framework include?

An assessment framework is a description and discussion about what an assessment
intends to measure. It also helps them to understand what the assessment results mean.

The framework includes a definition of “domain” i.e. the area of learning that is being
measured. It explains which aspects of the domain are covered in the assessment.
The framework also outlines how the assessment is constructed, by highlighting the
proportion of items for each of the aspects of the learning domain that makes up the
assessment. Further, it describes the response or item formats that are used, the length
and the number of items in the assessment. The framework may also outline how results
of the assessment may be reported.

PRINCIPLES UNDERLYING DEVELOPMENT OF

MATHEMATICS FRAMEWORK UNDER SAFAL
The acquisition of mathematical become a required skill in everyday
knowledge in preschool, early primary, life (Steen, 2001). The importance of
and secondary settings has increasingly mathematical skills and knowledge has

8 SAFAL - Mathematics Assessment Framework Handbook

been recently highlighted by large-scale the usually practised computations and
studies investigating the predictive power constructions.
of mathematical skills on future academic
achievement and economic well-being Developing the ability of mathematization
(Hanushek & Woessman, 2008; Watts et includes developing abilities such as
al., 2014). problem solving, use of heuristics,
According to the National Curriculum estimation and approximation,
Framework (NCF) 2005, the main goal of optimization, use of patterns, visualisation,
Mathematics education in schools is the representation, reasoning and proof,
'mathematization' of a child's thinking. In making connections, performing
general, the term “mathematization” refers mathematical communication including
to the application of concepts, procedures developing aesthetic feeling. The goal
and methods developed in mathematics to behind cultivating such mathematical
the objects of other disciplines or at least faculties “is to develop the child’s
of other fields of knowledge. One is said to inner resources, to think and reason
have acquired the ability to mathematize mathematically, to pursue assumptions
when he/she is able to demonstrate orderly to their logical conclusion and to handle
and systematic ways of expression and abstraction. It includes a way of doing
behaviour with mathematical precision things, and the ability and the attitude to
in all his/her activities. Mathematics formulate and solve problems” (NCERT)
education from the earliest levels must aim
to achieve such goals besides mastering

Guiding principles and assumptions (con-

tent-related) underlying mathematics frame-
work

The proposed assessment framework remediation. This approach also helps

for Mathematics has been designed to avoid floor effects in assessments.
assess the students’ competencies in
mathematics across grades 3, 5 and 8. The choice of strands and competencies
The domain of mathematics has been proposed in the framework has been
represented in a broader sense to include guided by an extensive review of literature
foundational numeracy building up to core on foundational numeracy, and the critical
mathematical knowledge and skills. For knowledge/skills required in mathematics
the purpose of scaffolding, the framework across later years.
includes competencies that are two
grade-levels lower, in addition to grade- Further, the framework has been
level competencies. This has been done developed based on the Global Proficiency
to diagnose the key areas in mathematics Framework by UNESCO and other partner
that might require instructional focus or organisations. The Global Proficiency

SAFAL - Mathematics Assessment Framework Handbook 9

 Framework for Mathematics (also with a common reference or scale for
referred to as the GPF) defines the global reporting progress on indicator 4.1.1
minimum proficiency levels that learners of the SDGs in the form of a definition
are expected to demonstrate at the end of the minimum knowledge and skills
of each grade-level, from grades one to learners must demonstrate at key points
nine, providing a picture of the common along their learning trajectory. Finally, to
expectations countries have for learners’ ensure validity, a detailed mapping of the
performance. The larger purpose of the framework to the NCERT curriculum and
GPF is to provide countries and regional/ learning outcomes has been done.
international assessment organisations

SALIENT FEATURES OF SAFAL MATHEMATICS

FRAMEWORK
1. The curriculum of Grades 3, 5 and 8 is categorised under 5 domains - Algebra,
Geometry, Measurement, Number & Operations and Statistics & Probability.
2. The domains are divided into strands which are further divided into grade-level
competencies progressing from grade 3 to grade 8. Certain competencies scaffold
across the grades, build the foundational skills and develop proficiencies in related
strands.
• Grade 3 number sense starts with 3-digit numbers. In grade 5 this evolves to
large numbers and number patterns. In grade 8 it expands to rational numbers
and various interesting number properties like divisibility rules, squares and
cubes, roots, etc.
• Counting and comparison of numbers develop data interpretation and analysis
skills.
• Repeated addition and subtraction in grade 3 builds pre-competency for
multiplication.
• Number sense operations and problem sums related to day-to-day situations
build up foundational skill for pre-algebraic competencies.
• Identifying and comparing length and weight in grade 3 lays the foundation to the
competency of estimation in measurement and computation as well as patterns
and shapes, which further develops readiness to understand algebra.
• Identifying even/ odd, prime/composite numbers, and co-prime builds foundation
in grade 6 that helps develop competencies to perform mathematical operations
such as square root and cube root.
• In Geometry, the concept of triangles is taken into account before shifting to
the quadrilateral as competencies based on the properties of triangle builds
a basic understanding to deduce the properties of quadrilaterals and various
computations on its basis.
3. In algebraic understanding, the focus is not on complex methods of solving linear
equations and factorization but the learning outcomes are based on practical
applications of algebra (real-life situations that are solved through variables and
equations) to formulate skill level proficiencies.
4. Construction (basic geometry, triangles, and quadrilaterals) strand in the framework
is skipped as it is difficult to assess the proficiency of the learner in this area using

10 SAFAL - Mathematics Assessment Framework Handbook

. Multiple Choice Questions.
2. Concept of volume has been unfolding smoothly across the grades where an
understanding of capacity and volume is required. This is done by using unit cubes in
primary grades, and then deriving the formulas of the volume of three-dimensional
figures.
3. Basic properties of geometry have been taught using objects available in real life, for
example, the orientation of angles have been given through the arms of the clock.

UNDERSTANDING THE STRUCTURE OF

MATHEMATICS ASSESSMENT FRAMEWORK
This section describes how the domain of Mathematics is represented in the SAFAL
framework. It is a vital issue as the organisation and representation of the domain
determines the test design and, ultimately, the evidence about student proficiencies
that can be collected and reported.

The subject of Mathematics has been structured into four main elements:

I. Domains refer to the fundamental concept areas that are broken down into strands.
II. Strands represent the critical component skills within the domain.
III. Competencies are the specific sub-strands or key knowledge and/or skills proposed
under each strand.
IV. Proficiency level & Descriptors summarises what learners know and can do under
the four proficiency levels - Below Basic, Basic, Proficient and Advanced.

Table 1: Proficiency Levels

Proficiency Levels Description

The student is able to demonstrate skills and competency fit for 2 levels below the actual
Level 1 - Below Basic
grade of study. For eg. a grade 5 student is only able to solve grade 3 level questions

The student is able to demonstrate skills and competency fit for 1 level below the actual
Level 2 - Basic
grade of study. For eg. a grade 5 student is able to solve up to grade 4 level questions

The student is able to demonstrate skills and competency fit for the actual grade of
Level 3 - Proficient
study. For eg. a grade 5 student is able to solve up to grade 5 level questions

The student is able to demonstrate skills and competency fit for actual grade and
Level 4 - Advanced higher-order skills. For eg. a grade 5 student is able to solve a Higher Order grade 5 level
question

Organising the Mathematics subject in this format will help schools and
teachers build a more nuanced picture of learners across key competencies, and
track overall progress towards meeting or exceeding the grade-level proficiency
levels in numeracy.

SAFAL - Mathematics Assessment Framework Handbook 11

 STRANDS UNDER MATHEMATICS FRAMEWORK -
GRADES 3, 5 AND 8
Table 2: Strands under Mathematics Framework - Grade 3, 5 and 8

Domain Strand Grade 3 Grade 5 Grade 8

Patterns

ALGEBRA Relations And Functions

Expressions

Properties Of Shapes And Figures

GEOMETRY

Spatial Visualisations

Currency

Time
MEASUREMENT

Length, Weight, Capacity, Volume, Area And

Perimeter

Whole Numbers

Decimals

Fractions

NUMBER &
Exponents And Roots
OPERATIONS

Integers

Operations Across Number

Rational Numbers

Data Management
STATISTICS AND
PROBABILITY
Chance & Probability

12 SAFAL - Mathematics Assessment Framework Handbook

GRADE 3 MATHEMATICS FRAMEWORK
The grade 3 Mathematics framework has been designed in a matrix form,
covering the domains of Number and Operations, Algebra, Geometry,
Measurement and Statistics and Probability.

Each domain is divided into strands which is further subdivided into

competencies that dissect and break down the strand into isolated and
individual areas of evaluation. For the purpose of this assessment and to ensure
simplification for the end user we have limited the scope of the assessment to
only critical competencies mapped to each strand.
The topical areas covered under the grade 3 mathematics framework are
highlighted below:

1. Number and Operations

2. Algebra
3. Geometry
4. Measurement
5. Statistics and Probability

1. Number and Operations

The critical strand in this domain for the grade 3 mathematics framework is
Whole Numbers. The critical competencies assessed include:

1.1 Identify and count in whole numbers, and identify their relative
magnitude
1.2 Represent whole numbers in equivalent ways
1.3 Solve operations using whole numbers
1.4 Solve real world problems

2. Algebra

The critical strand that has been identified in this domain is Patterns. Key
competency that will be assessed:

2.1 Recognise, describe, extend and generate patterns

3. Geometry

This domain includes the critical strand Properties of Shapes and Figures. The
critical competency assessed is:

3.1 Recognise and describe shapes and figures

SAFAL - Mathematics Assessment Framework Handbook 13

 4. Measurement

This domain covers the following strands - Length, Weight, Capacity, Volume,
Area and Perimeter, Time and Currency. The critical competencies assessed
under these strands include the following:

4.1 Use non-standard and standard units to measure, compare, and order
4.2 Solve problems involving measurement
4.3 Tell time and solve problems involving time
4.4 Use different currency units

5. Statistics and Probability

This domain covers the strand Data Management. The critical competency
assessed is:

5.1 Retrieve and interpret data

Table 3: SAFAL Assessment Framework for Grade 3 Mathematics

L1- Below Basic L2-Basic L3-Proficient (Grade L4-Advanced

Domain Strand Competency (Grade 1) (Grade 2) 3) (Grade 3)

1. Count, read,
1. Count and write order
numbers from whole numbers 1. Count, read,
1. Count and 0-100 using up to 999 and write order
recognise objects 2. Skip count whole numbers
numbers from 2. Form the forwards up to 9999
0 to 9, 10 to greatest and using twos, 2. Form greatest
Identify and 20, 20 to 100 the smallest fives, tens, and and smallest 3
count in whole 2. Develops two digit hundreds till digit numbers
Number
Whole numbers, concept of numbers with 999 using the given
and
Numbers and identify zero and without 3. Form greatest digits
Operations
their relative 3. Counting in repetition of and smallest 3 3. Compare whole
magnitude order given digits digit numbers numbers up to
4. Compare upto 99 using the given 9999 for their
numbers from 3. Compare digits value based
1-99 numbers using 4. Compare on their place
the objects numbers using value
upto 99 the objects till
999

Use place value

Represent Use place value Use place value
to compose
Number & Whole whole numbers to compose and to compose and
Not applicable and decompose
Operations Numbers in equivalent decompose 3-digits decompose numbers
numbers upto
ways numbers upto 999 to 9999
2-digits i.e. 99

14 SAFAL - Mathematics Assessment Framework Handbook

 1. Add and
subtract 3
digit whole
1. Add and
numbers, sums
subtract two
not exceeding
digit numbers
999 (through
upto 99 with
horizontal 1. Add and
or without
and vertical subtract
regrouping
arrangement) whole
2. Add and
with or without numbers
subtract using
regrouping sums not
real objects
Solve 2. Frame exceeding
Adds and and pictures
Number and Whole operations problems for 9999
subtracts one digit using using
Operations Numbers using whole addition and 2. Apply the
numbers symbols ‘+’ and
numbers subtraction addition and
‘-’upto 99
facts for subtraction
3. Solve problem
numbers upto to real life
of reaching
999 situations
zero through
3. Estimate the for numbers
the subtraction
sum of, and upto 9999
pattern (such
difference
as 3 – 1 = 2,
between two
3 – 2 = 1, 3 – 3
given numbers
= 0)
by grouping for
numbers upto
999

1. Demonstrate 1. Multiply 2
fluency with and 3 digit
Preparation for
multiplication numbers
Solve multiplication and
facts up to 5 x upto 999
Number & Whole operations division by skip
Not applicable 5, and related 2. Solve real
Operations Numbers using whole counting forward
division facts life problems
numbers and backwards
2. Multiply 2 digit related to
upto 99
numbers upto numbers
99 upto 999

Apply the four

Solve problems
fundamental
related to the
Solve arithmetic
situations involving
real-world Solve real life operations in
Number & Whole repeated addition
problems Not applicable problems related to solving problems
Operations Numbers and situations
involving numbers upto 99 involving length,
involving equal
whole numbers mass, capacity
sharing for numbers
for numbers upto
upto 99
9999

Copy, recognize,
Copy, recognize, describe, or extend
Recognize, describe, or repeating patterns, Identify the
Identify the pattern
describe, extend repeating or identify missing pattern in
in multiplication
Algebra Patterns extend, and patterns, or elements multiplication and
and division (up to
generate identify missing of such patterns division (up to
multiple of 5 and 10)
patterns elements as well as patterns multiple of 9)
of such patterns in addition and
subtraction

Estimate and
1. Identify the
Identify and measure length/ 1. Estimate and
Length, Use non- relationship
compare longer, distances and measure length
Weight, standard and between the
shorter, taller, capacities of and distance
Capacity standard units relative size
Measurement thinner, thicker, containers using using non
, Volume, to measure, of adjacent
lighter and heavier uniform non- standard units
Area & compare, and units within
object between standard units like like handspan,
Perimeter order a standard
the two a rod/pencil, cup/ ropes
system of
spoon/bucket etc.

SAFAL - Mathematics Assessment Framework Handbook 15

 2. Estimate the
measure of
length and
distance using
standard units
. measurement
of m, cm and km
(eg. 5 kilograms
3. Estimate and
is heavier than 8
measure weight
grams)
Not applicable Not applicable through non
2. Relate
standard and
centimetre and
standard units
metre
4. Estimate
and measure
capacity
through non
standard units
5. Use of a ruler

1. Understand
the conceptual
definition of area
(i.e. the space
inside of a shape)
and distinguish it
Understand the from perimeter
Length,
conceptual definition 2. Explore the
Weight,
Solve problems of perimeter area of shapes
Capacity
Measurement involving Not applicable Not applicable (i.e. perimeter is (rectangle,
, Volume,
measurement composed of the square) and
Area &
lengths of all sides of perimeter
Perimeter
a figure) of simple
geometrical
shapes (triangle,
rectangle,
square) in terms
of given shape as
a unit

1. Estimate and
tile a given
region using a
tile of a given
1. Describe basic shape 1. Find out shapes
2D shapes 2. Acquire that can be used
with their understanding for tiling
observable about 2D 2. Acquire
characteristics shapes understanding
2. Identify basic 3. Identify about 2D and 3D
3D-shapes and make shapes around
1. Recognise
such as cuboid, 2D-shapes by 3. Identify the
the name of
Properties Recognize and cylinder, cone paper folding, centre, radius
solids/shapes
of Shapes describe and sphere by paper cutting and diameter of
Geometry in simple
and shapes and their names on the dot grid, the circle
language. Eg. a
Figures figures 3. Traces 2D using straight 4. Draw 3D shapes
ball rolls, a box
outlines of 3D lines etc as cube/ cuboids
slides etc
objects 4. Describe 2D using the given
4. Identify shapes by the nets
2D shapes number of 5. Draw top view,
(rectangle, sides, corners front view and
square, and diagonals side view of
triangle, circle) eg. the shape of simple objects
by their names the book cover
has 4 sides, 4
corners and
two diagonals

16 SAFAL - Mathematics Assessment Framework Handbook

 1. Read clock time in
hours and minutes
and express the
time in a.m. and
1. Identifies a
p.m. Tell time
particular day
using an analog
and date on a
clock to the
calendar
nearest half and
2. Understand the
quarter hour
relationships
Identify the days 2. Understand the
between
of the week and relationships
Tell Time Identify and different units
months of the year, between different
Solve mention of time, eg.
sequences the units of time, eg.
Measurement Time problems sequence and minutes, hours,
events occurring seconds, minutes,
involving duration of days, and weeks
according to their hours, days,
time events 3. Understand the
duration in terms of weeks, months,
sequence of
hours/days and years
events to make
3. Solve problems
a timeline
involving elapsed
4. Reads the time
time in half hour
correctly to the
increments
hour using a
within an hour,
clock/watch
eg. difference
between 3:00 and
3:30 or 3:15 and
3:45

1. Represent an
1. Adds and
amount up to
subtracts small
Rs. 100 using
amounts of
Use 3-4 notes and Find and estimate
money with
different Identify coins (of same/ the overall cost
or without
currency different coins different and unit cost using
Measurement Currency regrouping for
units and notes used denominations mathematical
numbers upto
to create in India of play money operations for numbers
999
amounts 2. Child counts upto 999
2. Makes rate
the money
charts and
amounting till
simple bills
99 in numbers

1. Represent
1. Record
the collected
data using
information in
tally marks,
tables and bar
Collects, represents
graphs and draws
records (using pictorially
inferences from
pictures/ and draws
these
numerals) and conclusions
2. Complete missing
interprets 2. Retrieve
information
simple information
in simple data
information from simple
displays using
Retrieve by looking at data displays
Draw inference data arranged
and visuals. Eg. in (eg. tally charts,
based on the into categories,
Statistics and Data Man- interpret a picture of pictographs)
data collected in with some
Probability agement data a garden the with more than
a chart or simple support provided
presented child looks four categories
pictograph (eg. labelled
in displays at different and/or a multi-
horizontal and/or
flowers unit scale
vertical axes)
and draws 3. Compare
3. Retrieve multiple
inference that between
pieces of
flowers of a categories of
information from
certain colour simple data
data displays to
are displays with
solve problems
more more than four
(eg. calculate a
categories and/
total represented
or a multi-unit
by multiple bars
scale
on a graph)

SAFAL - Mathematics Assessment Framework Handbook 17

 Sample item

Grade 3

Domain Measurement

Strand Time

Competency Tell Time Solve problems involving time

Proficiency level Proficient

Riya has circled the day of the school picnic on her calendar. What date is it on?

Stem

A) 26/12/2016
B) 26/10/2016
Options
C) 2016/26/10
D) 10/26/12

Riya has circled the 26th of December 2016.

December is the 12th month of the year.
Answer option A
So, we write this date as 26/12/2016 (day/month/year)
So, option A is correct.

GRADE 5 MATHEMATICS FRAMEWORK

The Mathematics framework has been designed in a matrix form with Grade
5’s primary focus being the domains of Geometry, Measurement and Algebra
and building further concepts in Number and Operations and Statistics &
Probability.

Each domain is divided into strands which is further subdivided into

competencies that dissect and break down the strand into isolated and
individual areas of evaluation. For the purpose of this assessment and to ensure
simplification for the end user we have limited the scope of the assessment to
only critical competencies mapped to each strand.

18 SAFAL - Mathematics Assessment Framework Handbook

The topical areas covered under the grade 5 mathematics framework are
highlighted below:

1. Algebra
2. Geometry
3. Measurement
4. Number & Operations
5. Statistics & Probability

1. Algebra
The critical strands in this domain for the grade 5 mathematics framework
are Patterns and Relations & Functions. We identified the following critical
competencies pertaining to Algebra:

1.5 Recognize, describe, extend, and generate patterns

1.6 Estimate sum/difference/product and quotient of given numbers

2. Geometry

The critical strands that have been identified in this domain are Properties of
Shapes and Figures and Spatial Visualisations. Key competencies that will be
assessed include:

2.1 Recognize and describe shapes and figures

2.2 Compose and decompose shapes and figures

3. Measurement

This domain includes the following critical strands- Time, Currency, Length,
Weight, Capacity, Volume, Area & Perimeter under the grade 5 mathematics
framework. The critical competencies assessed under these strands include the
following:

3.1 Use non-standard and standard units to measure, compare, and order
3.2 Solve problems involving measurement
3.3 Tell time / solve problems involving time
3.4 Use different currency units to create amounts

4. Number & Operations

This domain covers the following strands - Whole Numbers, Fractions and
Decimals. Key critical competencies assessed under these strands include the
following-

4.1 Identify and count in whole numbers, and identify their relative magnitude

SAFAL - Mathematics Assessment Framework Handbook 19

 4.2 Represent whole numbers in equivalent ways
4.3 Solve operations using whole numbers
4.4 Solve real-world problems involving whole numbers
4.5 Identify and represent fractions using objects, pictures, and symbols, and
identify relative magnitude
4.6 Solve operations using fractions
4.7 Solve real-world problems involving fractions
4.8 Identify and represent decimals using objects, pictures, and symbols, and
identify relative magnitude
4.9 Represent fractions and decimals in equivalent ways (including fractions
and percentages)
4.10 Solve operations using decimals
4.11 Solve real-world problems involving decimals

5. Statistics & Probability

Critical strand under this domain is Data Management which assesses the
following critical competency:

5.1 Retrieve and interpret data presented in displays

Table 4: SAFAL Assessment Framework for Grade 5 Mathematics

L3-Proficient L4-Advanced
Domain Strand Competency L1- Below Basic L2-Basic
(Grade 5) (Grade 5)
(Grade 3) (Grade 4)
1. Identify 5 digit
number in
context with
• Size
1. Count, read, and • estimation of
write order whole 1. Count, read, numbers
1. Count, read, and
numbers up to and write order • identifying
write numbers
999 whole numbers smaller and
bigger than 9999
2. Skip count up to 9999 greater
being used in her/
forwards using 2. Form greatest number
Identify and his surroundings
twos, fives, tens, and smallest 3 (recapitulation
count in whole 2. Performs four
Number and hundreds till digit- numbers and extension)
Whole numbers, basic arithmetic
and 999 using the given 2. Use of symbols
Numbers and identify operations on
Operations 3. Form greatest and digits =, <, > and use
their relative numbers bigger
smallest 3 digit- 3. Compare whole of brackets
magnitude than 9999 by
numbers using the numbers up to 3. Word
understanding
given digits. 9999 for their problems
of place value of
4. Compare numbers value based on number
numbers
using the objects on their place operations
till 999 value involving large
numbers up to
a maximum of
5 digits in the
answer after
all operations.

Use place value Use place value Use place value

Number Represent whole Use place value
Whole to compose and to compose and concepts of
and numbers in concepts for numbers
Numbers decompose 3-digits decompose numbers numbers upto 6
Operations equivalent ways upto 5 digits
numbers upto 999 to 9999; digits and more

20 SAFAL - Mathematics Assessment Framework Handbook

 1. Add and subtract
3-digit whole
numbers, sums
not exceeding
999 (through 1. Add and
horizontal subtract whole
and vertical numbers sums
arrangement) not exceeding
with or without 9999
regrouping 2. multiply 2 and
1. Add, subtract,
2. Estimate the sum 3 digit numbers
multiply, divide Solves problems
of, and difference (Grade 4
whole numbers involving 5 digit
Solve between two NCERT LO)
Number upto 5 digits numbers by applying
Whole operations given numbers 3. Apply the four
and 2. Identify and appropriate operations
Numbers using whole by grouping for operations
Operations compute the (addition, subtraction,
numbers numbers upto 999 to real life
meaning of multiplication and
3. Identify the situations for
factors and division)
pattern in numbers upto
multiples
multiplication 9999
and division (up 4. Identify the
to multiple of 5 pattern in
and 10) multiplication
4. Demonstrate and division (up
fluency with to multiple of 9)
multiplication
facts up to 5 x
5, and related
division facts

Solve word problems Solve word problems

Solve real life involving addition, involving addition,
Solve real life problems
problems related subtraction, subtraction,
Solve real- related to numbers
Number to numbers upto multiplication and multiplication and
Whole world problems upto 99 including
and 999 including division for numbers division for numbers
Numbers involving problems involving
Operations problems involving upto 9999 including upto 99999 including
whole numbers measurement and
measurement and problems involving problems involving
currency units
currency units measurement and measurement and
currency units currency units

1. Multiples and
factors, divisibility
rule of 2, 3, 4, 5, 6,
8, 9, 10, 11
2. Represent
contextual
1. Represent the
1. Compare and situations through
fractions as
Identify and order given fractions
half, one-fourth
represent fractions 3. Represent
and three-
fractions 2. Identify and fractions on
fourths by
Number using objects, Divide quantities by form equivalent number line
using numbers/
and Fractions pictures, and equal grouping and fractions of a 4. Identify different
numerals
Operations symbols, repeated subtraction given fraction types of fractions
2. Show the
and identify 3. finds the number - proper, improper,
equivalence of
relative corresponding mixed, like and
unit fraction
magnitude to part of a unlike fractions
with other unit
collection 5. Identify and
fractions
find equivalent
fraction(s) of a
given fraction
6. Compare like and
unlike fractions

SAFAL - Mathematics Assessment Framework Handbook 21

 1. Add and
1. Add and subtract
subtract
fractions and
fractions and
mixed numbers
mixed numbers
Number Solve 2. Multiply and divide
Add and subtract of 2. Multiply and
and Fractions operations Not applicable fractions by whole
fractions divide fractions
Operations using fractions numbers, fractions,
by whole
and mixed
numbers,
numbers
fractions, and
mixed numbers
Solve real-world
Uses fractions in
problems involving
different situations
addition or
which involve money,
Solve real- subtraction or
Number length,
world problems multiplication,
and Fractions Not applicable Not applicable temperature etc. eg.
involving or division of
Operations 7½ metres of cloth,
fractions fractions (proper and
distance between two
improper), whole
places is
numbers, and mixed
112.5 km etc.
numbers
Identify and
represent
fractions
Represent and
Number using objects, Represent and
identify tenth and
and Decimals pictures, and Not applicable Not applicable compare decimals upto
hundredth of a
Operations symbols, thousandths
decimal number
and identify
relative
magnitude
Represent
fractions and Convert fraction into
Number decimals in decimal not directly Express fractions as
and Decimals equivalent Not applicable Not applicable there but pictorial decimals and vice versa
Operations ways (including mapping to decimals upto hundredth
fractions and and fractions
percentages)

Number Solve Add and subtract

and Decimals operations Not applicable Not applicable Not applicable decimals in contextual
Operations using decimals problems

1. .Solves problems
on daily life
situations
involving addition
and subtraction of
decimals
Solve real- 2. Uses decimals in
Number
world problems different situations
and Decimals Not applicable Not applicable Not applicable
involving which involve
Operations
decimals money, length,
temperature etc.,
eg. 7½ metres of
cloth, distance
between two
places is 12.5 km
etc.
1. Identifies and
extends the
patterns using Recognises and
Identifies and
Recognize, numbers and appreciates (through
Identifies the rule in explores patterns
describe, letters. patterns) the broad
a growing number in special numbers ,
Algebra Patterns extend, and 2. Solves magic classification of
sequence and extends for example, square
generate squares and numbers as
them numbers/hexagon
patterns magic triangles. even, odd, prime, co-
numbers etc
3. Identifies and prime, etc.
extends various
number patterns

22 SAFAL - Mathematics Assessment Framework Handbook

 Estimate sum,
difference, product
and quotient of
Estimate sum/ numbers and verifies Estimating the
Estimate sum/
difference/ Estimate sum/ the same using measure of angles
Relations and difference
Algebra product and difference/product of different strategies using
Functions of given two
quotient of given two numbers like using standard 45°, 90°, and 180° as
numbers
given numbers algorithms or reference angles
breaking a number
and then using
operation

1. Estimate
and
measure
length and
distance
using non
1. Estimates the
standard 1. Estimates the
length of an
units like volume of a
object/distance
handspan, solid body in
between two
ropes known units.
locations, weight
2. Estimate the 2. Make
of various
measure of conversions
objects, volume
length and between
of liquid, etc.,
distance adjacent units
and verifies
using of length and
them by actual
Use non- standard weight within
Length, measurement
standard and units of a standard
Weight, 2. Identify the
standard units m,cm and system of
Measurement Capacity , relationship Not applicable
to measure, km. measurement
Volume, Area between the
compare, and 3. Estimate (e.g., meters to
& Perimeter relative size
order and centimeters).
of adjacent
measure 3. Relate different
units within a
weight commonly
standard system
through non used larger and
of measurement
standard smaller units
(eg. 5 kilograms
and of length, and
is heavier than 8
standard converts larger
grams).
units units to smaller
3. Relate
4. Estimate units and vice
centimetre. and
and versa
metre
measure
capacity
through non
standard
units Use of
a ruler

1. Explore the area 1. Calculate the

and perimeter 1. Solve problems, perimeter of the
of simple including real- square rectangle
geometrical world problems, and circle in
shapes (triangle, involving contextual
rectangle, the area of problems
square) in terms a rectangle 2. Deduce the
of given shape as using concrete formula of
Length,
Solve a unit or pictorial perimeter of
Weight,
problems 2. Solve problems, representations square, rectangle
Measurement Capacity , Not applicable
involving including re- of units (e.g. and circle using
Volume, Area
measurement al-world prob- grid squares or pattern and
& Perimeter
lems, involving tiles); formula
the perimeter 2. solve problems, 3. Calculate the
of a rectangle including real- area of shapes
using concrete world problems, using squared
or pictorial involving the paper
representations perimeter of a 4. Calculate the
of units (e.g., grid polygon area of square
squares) using the formula

SAFAL - Mathematics Assessment Framework Handbook 23

 1. Read clock time
in hour and
minutes and
expresses the
time in a.m. and
p.m.
2. Tell time using
1. Identifies a an analog clock
particular day to the nearest
1. 1. Calculate
and date on a half and quarter
time intervals/
calendar. hour.
duration of
2. Understand the 3. Understand the
familiar daily
relationships relationships
life events by
between between
using forward
different units different
or backward
Tell Time / of time, e.g., units of time,
counting/
Solve minutes, hours, e.g. seconds,
Measurement Time addition and Not applicable
problems days, and weeks. minutes, hours,
subtraction
involving time 3. Understand the days, weeks,
2. Apply the four
sequence of months,and
fundamental
events to make years.
arithmetic
a timeline. 4. Solve problems
operations
4. Reads the time involving elapsed
in solving
correctly to the time in half hour
problems
hour using a increments
involving time.
clock/watch within an hour
(e.g., difference
between 3:00
and 3:30 or 3:15
and 3:45).
5. Relate 24 hr
clock with
respect to 12 hr
clock.

1. Combine
commonly
used currency
denominations
to make a
specified
Find and estimate
amount in a Find and estimate the
Use different the overall cost Uses fractions and
variety of ways overall cost and unit
currency units and unit cost using decimal in different
Measurement Currency 2. Solves cost using mathemat-
to create mathematical situations which
simple 2 digit ical operations for
amounts operations for involve money
addition and numbers upto 999
numbers upto 999
subtraction real
life problems
involving money
3. Read and
interpret rate
charts and bills

1. identify various
1. Describe 2D
1. Recognize and (3-D) objects like
shapes by the 1. Acquire
name three-di- sphere, cube,
number of sides, understanding
mensional cuboid, cylinder,
corners and about 2D and 3D
figures by their cone from the
diagonals shapes around
Properties Recognize and more complex surroundings
2. Identifiy 2. Draw cube/
of Shapes describe attributes (e.g., with he help of
Geometry and makes cuboids using the
and shapes and faces, edges, examples from
2D-shapes by given nets.
Figures figures vertices); surroundings.
paper folding , 3. Draw top view,
2. identify a line 2. Describe and
paper cutting front view and
of symmetry in provide examples
on the dot grid, side view of
two-dimension- of edges, vertices
using straight simple objects
al shapes and faces of 3-D
lines etc
objects

24 SAFAL - Mathematics Assessment Framework Handbook

 4. Recognize and name 3. Describe the
two-dimensional defining attrib-
shapes by from a utes of complex
written or spoken two dimensional
description of their shapes;
simple attributes 4. Identify and com-
Not applicable 5. dentify the centre, pare attributes of Not applicable
radius and diameter familiar three-di-
of the circle mensional
figures, including
terminology such
as front, top, and
side views

1. Identify
different
triangles
1. Recognize types (based on
of angles by their sides and
magnitude (e.g., angles)
right, straight, 2. Identify
Recognize
acute, obtuse); different
Properties of and
2. Classify angles types of lines
Geometry Shapes and describe Not applicable Not applicable
into right angle, and angles
Figures shapes and
acute angle, 3. Identify
figures
obtuse angle and different
represents the types of
same by drawing polygon
and tracing based on the
number of
their sides
(n=3 to n=8)

Compose a larger
Compose Compose and decompose
two-dimensional
and a larger two-dimensional
Spatial shape from a small
Geometry decompose shape from a small Not applicable Not applicable
Visualisation number of shapes in
shapes and number of shapes in more
more than one way
figures than one way (if possible);
(if possible).

1. Record 1. Collects and records

1. Collect data
data using data in a tabular
related to
tally marks, form
various daily
represents 2. Reads and
life situations,
pictorially interprets the
in the form of
and draws data recorded in a
table,
conclusions tabular form. 1. Collect data
2. Presents the
2. Retrieve 3. Draws a strip chart related to
data in form of
information to represent a given various daily life
a pictograph
from simple information situations
and bar graph
data displays 4. Reads and 2. Represent the
Retrieve and interprets
(e.g., tally interprets a strip data it in tabular
and them
charts, chart. form, and create
Statistics and Data interpret 3. In Pictograph
pictographs) 5. Draws a chapati bar graphs,
Probability Management data adds scaling
with more chart to represent chapatti chart.
presented and deals
than four the information 3. Interpret the
in displays with its
categories given in a tabular information
interpretation
and/or a multi- form given in charts
&
unit scale; 6. Retrieve multiple and draw
construction.
3. Compare pieces of inferences
4. Interpret the
between information from
information
categories data displays to
given in a
of simple solve problems (e.g.,
pictograph
data displays calculate a total
and bar graph
with more represented by
and draw
than four multiple bars on a
inferences..
categories graph).

SAFAL - Mathematics Assessment Framework Handbook 25

 Sample item

Grade 5

Domain Number and Operations

Strand Fractions

Competency Identify and represent fractions using objects, pictures, and symbols,and identify relative magnitude

Proficiency level Basic

Soumya bought a roti as shown in the picture. If she shares half roti with her sister, how many slices will she get for
herself?

Stem

A. 1
B. 2
Options
C. 3
D. 6

Total number of slices of Roti = 6

Soumya shares half with her sister.
Answer option C Half of 6 = 3
So, Soumya gets 3 slices.
Option C is correct

GRADE 8 MATHEMATICS FRAMEWORK

The Mathematics framework has been designed in a matrix form with Grade
8 primarily focusing on the domains of Number & Operations and Statistics &
Probability with and building knowledge on domains of Measurement, Algebra
and Geometry.

Each domain is divided into strands which is further subdivided into

competencies that dissect and break down the strand into isolated and
individual areas of evaluation. For the purpose of this assessment and to ensure
simplification for the end user we have limited the scope of the assessment to
only critical competencies mapped to each strand.

26 SAFAL - Mathematics Assessment Framework Handbook

The topical areas covered under the grade 8 mathematics framework are highlighted
below:

1. Measurement
2. Algebra
3. Geometry
4. Number & Operations
5. Statistics & Probability

1. Measurement

Critical strand under this domain is Length, Weight, Capacity, Volume, Area & Perimeter
which assesses the competency:

1.1 Solve problems involving measurement

2. Algebra

Expressions and Relations and Functions form the critical strand for this domain under
the grade 8 Mathematics framework. We identified critical competencies pertaining to
Algebra:

2.1 Evaluate, model, and compute with expressions

2.2 Solve problems involving variation (ratio, proportion, and percentage)
2.3 Solve equations

3. Geometry

The critical strand for this domain is Properties of Shapes & Figures and Spatial
Visualisations. Key competencies covered are:

3.1 Recognize and describe shapes and figures

3.2 Compose and decompose shapes and figures

4. Number & Operations

In Grade 8, number sense expands to rational numbers and various interesting number
properties like divisibility rules, squares and cubes, roots, etc. This domain covers the
following strands in the grade 8 Mathematics framework - Whole Numbers, Fractions,
Decimals, Integers, Exponents and Roots, Operations Across Numbers and Rational
Numbers. Key critical competencies assessed under these strands include the following:

4.1 Solve operations using whole numbers

4.2 Identify and represent fractions using objects, pictures, and symbols, and
identify the relative magnitude
4.3 Solve operations using fractions
4.4 Solve real-world problems involving fractions
4.5 Represent decimals in equivalent ways (including fractions and percentages)

SAFAL - Mathematics Assessment Framework Handbook 27

 4.6 Solve operations using decimals
4.7 Solve real-world problems involving decimals
4.8 Identify and represent integers using objects, pictures, or symbols, and identify
the relative magnitude
4.9 Solve operations using integers
4.10 Solve real-world problems involving integers
4.11 Identify and represent quantities using exponents and roots, and identify the
relative magnitude
4.12 Identify and represent numbers using scientific notation and exponents,
compare and order numbers expressed in scientific notation, Solve operations
involving exponents and roots
4.13 Solve operations involving integers, fractions, decimals, percentages, and
exponents
4.14 Compare, order and solve problems involving rational numbers

5. Statistics & Probability

Critical strands under this domain are Data Management and Chance & Probability
which assess the following critical competencies:

5.1 Retrieve and interpret data presented in displays

5.2 Calculate and interpret central tendency
5.3 Describe the likelihood of events in different ways

Table 5: SAFAL Assessment Framework for Grade 8 Mathematics

L3-Proficient L4-Advanced
Domain Strand Competency L1- Below Basic L2-Basic
(Grade 8) (Grade 8)
(Grade 6) (Grade 7)
1. Solves problems
involving 5
digit numbers
by applying
appropriate
operations
(addition, Add, subtract,
Number Solve operations
Whole subtraction, multiply, divide Prove divisibility rules
and using whole Not applicable
Numbers multiplication and whole numbers 6 of 2, 3,4, 5, 6, 9 and 11
Operations numbers
division). digits and more
2. Find multiples and
factors of a given
number
3. Apply divisibility
rule of 2, 3, 4, 5, 6,
8, 9, 10, 11

1. identify different
types of fractions
Identify and
- proper, improper,
represent Compare and order
mixed, like and unlike
Number fractions using positive and negative
fractions
and Fractions objects, pictures, fractions (proper and Not applicable Not applicable
2. Identify and find
Operations and symbols, and improper) and mixed
equivalent fraction(s)
identify relative numbers
of a given proper,
magnitude
improper, mixed, like
and unlike fraction

28 SAFAL - Mathematics Assessment Framework Handbook

 3. Compare like and
unlike fractions
4. Represent
contextual
situations Not applicable Not applicable Not applicable
through fractions
represent
fractions on
number line

Add and subtract Multiply and divide

Number proper, improper, proper, improper,
Solve operations
and Fractions mixed, like and unlike mixed, like and unlike Not applicable Not applicable
using fractions
Operations fractions in contextual fractions in contextual
situations situations

1. Solve real-
world problems
involving the
1. Express addition and
percentages as subtraction
fractions or mixed of proper
numbers (and vice and improper
versa) fractions and
2. Solve real- mixed numbers
Solve real-
Number world problems with unrelated
world problems
and Fractions involving addition denominators Not applicable Not applicable
involving
Operations and subtraction 2. Solve real-
fractions
of improper world problems
fractions and involving the
mixed numbers multiplication
with different and division
but related of fractions
denominators (including proper
and improper
fractions and
mixed numbers)
1. Round decimal
numbers to
1. Round decimal any place value
numbers to beyond the
the nearest hundredths place
hundredths place 2. Identify and
2. Identify express fractions
Represent and express with any Identify and express
decimals in fractions with denominator percentages less than
Number
equivalent denominators of using decimal 1% and greater than
and Decimals Not applicable
ways (including 100 and everyday notation and vice 100% as fractions or
Operations
fractions and fractions, using versa mixed numbers and
percentages) decimal notation, 3. Identify vice versa
and represent and express
fractions with percentages as
denominators fractions with
of 100 as denominators of
percentages 10 or 100 or as
decimals and vice
versa

1. Add and subtract

any positive and
negative decimal Multiply and divide two
Number Add and subtract
Solve operations numbers. decimal numbers and
and Decimals decimal numbers up to Not applicable
using decimals 2. Multiply and divide a whole number
Operations the hundredths place.
divide a decimal by a decimal
number by a
whole number

SAFAL - Mathematics Assessment Framework Handbook 29

 1. Solve real-
world problems
involving
addition and
subtraction of
Solve real world Solve real-world Solve real-world
decimals beyond
Number problems problems involving problems involving
the tenths place Not
and Decimals involving the addition and the multiplication or
2. Solve real- applicable
Operations decimals subtraction of decimals division of two decimal
world problems
to the tenths place numbers
involving the
multiplication
or division of
a decimal by a
whole number
1. Identify and
represent
Identify and
integers using
represent
objects, pictures,
Number integers using
or symbols, and Compare and order Not
and Integers objects, pictures, Not applicable
identify relative integers applicable
Operations or symbols, and
magnitude
identify relative
2. Represent
magnitude
integers on
number line.
1. Identify, apply
and verify
properties 1. Identify, apply and
of arithmetic verify properties
operations on of arithmetic
Number Add and subtract integers/ rational operations on
Solve operations Not
and Integers inetegers using number numbers rational number
using integers applicable
Operations line 2. Perform 2. Identify common
calculations factors and
involving two or common multiples
more operations of two numbers
with positive
integers
Solve real-world
problems involving
combinations
of any two or
more of the four
operations, including
problems involving
measurement and
Solve real-world
currency units and:
problems involving
Number Solve real- • addition and
the multiplication or Not
and Integers world problems Not applicable subtraction of
division of two integers, applicable
Operations involving integers any integers
including at least one
• multiplication
negative integer
of any positive
integers
• division of any
positive integers
by a positive
two-digit number
with or without a
remainder

Identify and
1. Find squares and
represent 1. Find the area of
Perform long square roots of
quantities using squares of given
Number division and prime numbers
Exponents exponents length(s) by using Not
and factorization on 2. Solve contextual
and Roots and roots, the formula applicable
Operations given numbers to find problems by
and identify (multiply a
factors of a number finding squares
the relative number by itself)
and square roots
magnitude

30 SAFAL - Mathematics Assessment Framework Handbook

 3. Find cubes and
2. Multiply cube roots of
a number numbers
thrice with/ Not applicable 4. Solves Not applicable
without formal problems
algorithm with integral
exponents.
1. Express
Identify and
numbers in 1. Simplify and
represent
exponential represent
numbers using
form exponential
scientific
2. Apply laws numbers
notation and
1. Identify 5 digit of positive having negative
exponents,
number in exponents powers
Compare and
Number and Exponents context with 3. Express large 2. Apply laws
order numbers Not applicable
Operations and Roots place value. numbers in of negative
expressed
2. Multiply and standard exponents
in scientific
divide numbers exponential 3. Multiply and
notation, Solve
form divide positive
operations
4. Multiply and negative
involving
and divide exponential
exponents and
exponential numbers
roots
numbers

Solve operations Perform calculations

involving involving two or
Operations integers, Perform prime more operations of
Number and
across fractions, Not applicable factorization on given integers, decimals, Not applicable
Operations
Numbers decimals, numbers and fractions,
percentages, and respecting the order
exponents of operations

1. Write, compare
and represent
rational 1. Represent
numbers rational
Compare, 2. Write rational numbers on
order and numbers number line
Number and Rational
solve problems Not applicable between 2. Find rational Not applicable
Operations Numbers
involving given rational numbers
rational numbers numbers between given
3. Identify and two rational
write equivalent numbers
rational
numbers

1. Calculate the
1. Calculate area
perimeter of
of a circle; area
the square
of sectors and
rectangle 1. Calculate and
1. Use perimeter segments of a
and circle in solve problems
to solve circle.
contextual related to
problems and 2. Solve Problems
problems the area and
deduce the area based on areas
2. Deduce the perimeter/
in contextual and perimeter/
Length, formula of circumference
problems circumference
Weight, perimeter of rectangle,
Solve problems 2. Calculate the of the above
Capacity of square, square,
Measurement involving area of triangle, said plane
, Volume, rectangle using parallelogram,
measurement parallelogram figures.
Area & pattern and circle, semi-
and circle using 3. Calculate
Perimeter Formula circle
formula the area of
3. Calculate the 2. Calculate
3. Calculate the triangle and
area of shapes the area of
circumference parallelogram
using squared trapezium and
of circle using and use their
paper. rhombus using
formula relationship
4. Claculate the formula
to solve
area of Square
contextual
using the
problems
formula .

SAFAL - Mathematics Assessment Framework Handbook 31

 1. Deduce the
formula and
solve contextual
problems of
volume of
1. Calculate the
combinations of
volume of cube,
1. Differentiate any two of the
cuboid, cylinder
between following: cuboid,
using formula
volume and cube, cone, sphere
Calculate volume for in contextual
capacity. and right circular
solving contextual problems
2. Calculate cylinder.
problems by arranging 2. Calculate the
volume/ 2. Deduce the
unit cubes in cubes surface area of
capacity by formula and
and cuboids cube, cuboid,
arranging unit solve contextual
cylinder using
cubes in cubes problems of
formula in
and cuboids surface area of
contextual
combinations of
problems
any two of the
following: cuboid,
cube, cone, sphere
and right circular
cylinder.
1. Verify the
1. Identify and properties of
differentiate parallelograms
between line, line and establishes
segment and ray the relationship
2. Identify and between
differentiate them through
between reasoning.
different pairs 2. Differentiate 1. Apply triangle
1. Identify
of angles- different types properties (angle
different types
complementary, of polygons- sum property,
of lines and
supplimentary, regular, exterior angle
angles
adjacent and irregular and property) to
2. Identify
linear pair finds concave, convex solve geometrical
different types
value of the one and sum of their problems
of polygon
when the other is angles 2. Apply the concept
based on the
given.. 3. Identify square, of congruency of
number of
3. Identify and rectangle, kite, triangles through
their sides (n=3
differentiate parallelogram, SSS,SAS,ASA
to n=8)
between rhombus and RHS criteria
3. Classification
different types through their in solving
of triangles
of angles made properties geometrical
Properties Recognize based on their
by parallel and (sides, angles problems
of Shapes and describe sides and
Geometry intersecting lines and diagonals) 3. Solve geometrical
and shapes and angles
and verifies the 4. Solve problems
Figures figures 4. Identify
properties geometrical by applying
different
4. Identify problems properties of
types of
congruent plane related to angles made by
quadrilaterals-
figures, angles quadrilaterals transversal on
square,
and line segments through their parallel lines/non-
rectangle,
5. Identify median properties parallel lines
trapezium,
and altitude of a (sides, angles 4. Solve geometrical
parallelogram,
triangle and diagonals) problems by
rhombus
6. Solve problems 5. Identify and applying the
through
based on the recognise properties of
their basic
properties various parallelogram,
properties
of triangles- polyhedrons rectangle,
(sides and
exterior angle based on their rhombus and
angles)"
property, angle properties square
sum property, (convex-regular
sum of 2 sides polyhedron;
is greater than faces,
the third side edges,vertices
property and of the solid)
pythagoras 6. Verify Euler's
theorem Formula of given
Polyhedrons

32 SAFAL - Mathematics Assessment Framework Handbook

 Identify alternate
Identify the net of
views of the same Identify a cross-
Identify front, top, a familiar three-
compound or irregular section of a familiar
and side views of dimensional figure
three-dimensional three-dimensional
a familiar three- (i.e. prism, cylinder,
shape, such as its figure (i.e. prism,
Compose dimensional figure cone, or pyramid) (e.g.,
front, top cylinder, cone,
and (i.e., prism, cylinder, fold or
Spatial Vis- and side view, a or pyramid) (e.g.,
Geometry decompose cone, or pyramid) unfold mentally to
ualisation rotated view, or a view identify that the
shapes and (e.g., identify that answer the question,
of a hidden side (e.g., cross
figures the top view of an "What figure does this
label images (i), (ii), and section of a cylinder
upright cylinder is a make when folded?";
(iii) as the front, top that is not parallel
circle). "What figure does this
and side view of the to the base is an
make when
three-dimensional ellipse).
unfolded?").
shape)
1. Multiply
algebraic
1. Use of variable expressions e.g
to write the expands (2x-5)
rule of a (3x2+7).
pattern 2. Apply four
Identify different
2. Use of variable standard 1. Find value
terms,factors and
in writing identities to and zeroes of
coefficients of an
mathematical simplify algebraic polynomials
algebraic expression
formulas expressions based on
2. Identify and
3. Write 3. Find value of an the value of
differentiate between
expressions expression based variable(s)
Evaluate, different types of
using a variable on the given 2. Divide given
model, and expressions based on
and arithmetic value of the 2 polynomials
Algebra Expressions compute their number of terms
operation(s) variable and apply/
with (monomial, binomial
uses variable 4. Write rules and verify
expressions etc)
with different formulas in the remainder
3. Add and subtract
operations to form of algebraic theorem
algebraic expressions
generalise a expressions 3. Find factors of
4. represents daily life
given situation. 5. solve puzzles polynomials by
situations in the form
For example, and daily life applying factor
of a simple equation
Perimeter of a problems using theorem
and solves it
rectangle with variables.
sides x units 6. use various
and 3 units is algebric
2(x+3) units. identities in
solving problems
of daily life

1. Finding percent
1. Convert ratio,
change on given
fractions, decimal
transaction
numbers to
2. Computing
percentage vice
discount and
versa
discount
2. Determine and
percentage on
deduce cost
given transaction
price, selling
3. Determine cost
price, profit,
Solve 1. Compare price, selling
loss, profit
problems quantities in price, profit,
percentage, loss
involving the form of loss, profit
Relations percentage of the
variation ratio percentage, loss
Algebra and Func- quantities Not applicable
(ratio, 2. Find the value/ percentage and
tions 3. Determine simple
proportion, number of tax of the given
interest on given
and units using transactions
transaction
percentage) unitary method 4. Determine
4. Compare
compund
quantities in
interest on given
the form of
transaction
ratio(s) and find
5. Solve contextual
equivalent ratio.
problems
5. Solve contextual
related to ratio
problems using
using direct
unitary method
and inverse
proportion(s)

SAFAL - Mathematics Assessment Framework Handbook 33

 1. Write linear
1. Solve real equations in two
life problems variables in it's
through linear general form
equations in one 2. Solve real
variable having life problems
Solve real life
variable on through linear
Relations problems through
Solve one side of the equations in one
Algebra and Func- Not applicable linear equations in
equations equation. variable having
tions one variable using
2. Solve real variable on both
transpose method.
life problems sides of the
through linear equation.
equations 3. Express real
reducible to the life situations in
linear form. linear equations
in two variables

1. Identify and
interpret bar Identify and interpret
1. Identify and
Retrieve graph and double histogram, piechart of
interpret
information from bar graph of a a given data
frequency
data displays that given data some support is
polygon
Retrieve and arrange data into 2. Interprets provided (e.g.,
2. Calculate the
interpret categories and data using bar construct a line graph
Statistics and Data Man- empirical (or
data sub-categories with graph such as when given labeled
Probability agement experimental)
presented in a single- or multi- consumption horizontal and/or
probability P(E)
displays unit scale (e.g., How of electricity is vertical axes, or match
of an event E
many girls liked more in winters a table to the
by repeated
green in this bar than summer, correct pie chart given
conducting of
chart?). runs scored by a a range of pie chart
experiment
team in first 10 options).
overs etc.

Calculate the
Solve problems,
Calculate measures of
including real-world
and Identify and interpret central tendency
Statistics and Data Man- problems, involving
interpret Not applicable frequency distribution (mean,median, mode)
Probability agement calculation of the
central table of a given data for ungrouped data
mean, median, or
tendency using respective
mode of a set of data.
formulas

1. Identify
happen,can
happen and
Compare the impossible
1. Find the
likelihood of two situations
probability of
or more events recognises
inferences of an
happening, using variability in real
experiment
descriptive words life situation such
2. Find the
(e.g., Given a as, variations
expected
picture of a spinner in the height
number of
with 5 equal of students in
occurrences
Describe the colored sections— her classand
of a specific
likelihood red, blue, yellow, uncertainty
Statistics and Chance and independent
of events green, and purple— inhappening Not applicable
Probability Probability outcome when
in different the question is: "If of events like
a probability
ways the spinner is spun throwing a coin.
experiment
two times, what is 2. Calculate the
is repeated
the chance that it probability of
many times
will land on blue a simple event
(e.g., calculate
both times?" The happening, with
the expected
possible answers the answer
number of heads
are a) impossible, expressed as a
with 50 flips of a
b) unlikely, c) likely, fraction, decimal,
fair coin)
and d) certain). or percentage,
and place
probability values
or events on a

34 SAFAL - Mathematics Assessment Framework Handbook

 continuum from 0
(impossible) to 1
(certain), with 0.5
meaning equal chance
Not applicable of occurring or not Not applicable Not applicable
occurring. (e.g., What
is the probability
of rolling a 6 on a
standard number die?).

Sample item

Grade 8

Domain Number and Operations

Strand Decimals

Competency Solve operations using decimals

Learning
Add and subtract decimal numbers up to the hundredths place
outcome

Proficiency level Below Basic

39.92 + 10.1 = ?
Stem

A. 40.93
B. 49.93
Options
C. 50.02
D. 50.92

Answer option C Adds the numbers as per their place value

REPORTING AND INTERPRETATION OF RESULTS

Reporting for SAFAL will focus on school level achievement of learning/
proficiency levels across grade-level competencies demonstrated in the
assessment. Proficiency bands provide a convenient way to describe the profile
of a school’s achievement. A national minimum standard (benchmark) would be
established for each grade.

SAFAL results will be reported using scaled scores. A scaled score is a

conversion of a student's raw score on a test to a common scale that allows for a
numerical comparison between students. Scaled scores are particularly useful

SAFAL - Mathematics Assessment Framework Handbook 35

 for comparing test scores over time, such as measuring year-to-year growth
of individual students or groups of students in a content area. The reports will
provide diagnostic information to enable schools to plan for remediation for
students, and professional development for teachers.

School Performance on SAFAL: Grade 5 EVS Percentage of Students across Proficiency

Levels

Below Basic Basic Proficient Advanced

Understand need for food and

procurement of food

Understand importance of
spices and reasons for food
spoilage Describe methods of
food preservations

Describe the process of eating

and digestion

Knowing about the different

type of houses and their
construction

Understanding about the

need and types of houses in
different places and climates
20%
Applying the knowledge on
the construction of houses its
cleanliness and disposal of
waste

0% 25% 50% 75% 100%

A sample reporting format is presented above highlighting the proficiency level

of grade 5 students across different competencies.

SAFAL data can be used by school systems, school managements, and parents to
improve learning outcomes by reporting school performance on predetermined
competencies and proficiency levels. Student data will not be publicly disclosed
and the data won’t be used to pass/fail students. Additionally, the school reports
would provide insights and suggestions for targeted academic support and
management. This would provide headmasters and teachers with actionable
steps that would drive change from bottom-up right from the classroom level.

36 SAFAL - Mathematics Assessment Framework Handbook

Acknowledgements
We would like to express our deepest appreciation to all those who provided their
guidance, support, advice and expertise in developing the framework and creating the
handbooks.

We give special gratitude to the members of the Central Board of Secondary Education,
whose contribution in coordination, stimulating suggestions and encouragement,
helped the building of the framework. We are deeply grateful to the Principals and
teachers of CBSE affiliated schools who have contributed to developing the framework.

Furthermore, we would also like to acknowledge with much appreciation the crucial
role of the members of Sage Perspectives, LLC, Central Square Foundation, Azim Premji
University and other organisations who have invested their effort towards developing
the framework. Lastly, a special thanks to those who reviewed the framework and
designed the handbook.

SAFAL - Mathematics Assessment Framework Handbook 37