TIIE-End line Mathematics pilot

Providing multiple means of actions and expressions is a key principle of UDL which underlines the need to differentiate the ways in which learners can express what they know and understand.

The maths end-line assessment will incorporate this by evaluating students’ abilities in different formats.

Area 1: Place value:
Written: Students would be given a number and asked to write the number in expanded form, represent the number using the FLU model and identify the number of hundreds, tens and ones in it. They would also then be given a number in expanded format (200 + 40 + 6) and one represented in the FLU format (□ □ | | | ●●●●●●) and asked to write down the number.

Verbal interaction: Facilitator would ask the student what would be the composition of a given amount, say Rs. 238 if it only had to have Rs. 100, 10 notes and 1 Re. coins. They would also be

asked the reverse, if there were x Rs.100 notes, y Rs.10 notes and z 1 Re. coins, how much money would they have.

Rubrics to assess:


 * able to convert number to FLU structure
 * able to convert FLU to number
 * able to explain the place value in the given number/ combination of notes

Area 2: Number operations:
Writing + explanation: A numerical expression (addition/subtraction) will be presented to the student. Before they attempt to solve the problem, they will be asked to construct an example using any objects of their choice or explain how they would teach it to a younger child using some real life examples to represent the given numerical expression,. For eg., if the expression is 4 + 7, the child can say a person had 4 objects and another person gave them 7 more; Or that two people had 4 and 7 objects respectively and they put them all together in a box, etc. Alternatively, students can be asked to construct a ‘word problem’ using the given numbers. Only the child’s understanding of the meaning of the operation would be assessed in this stage.

Next, the student will be asked to solve the problem using any method of their choice (standard algorithm/FLU model). They will then be asked to explain the process of how they performed the operation and arrived at the answer.

Verbal interaction: In this case, the child would be presented a contextual number operation problem as part of a conversation and the child’s thought process and ability to explain/solve would be evaluated. For eg., the facilitator can say I had 23 rupees and wanted to buy a book which was 30 rupees. So my mom gave me another 10 rupees, how much do I have now? The student would not necessarily need to write down and solve the problem, but they could if they wish to.

Graphical representation: The problem in this case would be presented pictorially i.e., pictures of objects and the child would be asked to solve and explain how they did it. This format would be presented only if the child is unable to solve in the other two formats.

Process flow:

The number operation assessment included identification of single and double-digit numbers, and performing addition, subtraction and multiplication operations.

The assessment was conducted individually with each student where they were first asked to identify single and double-digit numbers, the signs of different operations and what they meant. Once they were able to do this, they were asked to perform the given operation. There was some level of choice given to students in choosing between problems of a certain category that they are comfortable/confident with and based on their attempt, they were asked to solve problems that were further difficult or easier.

1st double by single – written+ explanation will be assessed. If the child is able to do it, the assessment will be over through verbal conversation.

If the child is unable to solve/respond in the written + explanation, assessment will be done using drawing mode. First the student will be asked to try using the drawing of any object to try and solve. If they are unable to do it, the facilitator will draw the given expression in a drawing format and ask the student to try and solve.



Rubrics to assess :

Addition without carry-over

• able to do single digit addition in pictorial representation – using objects/ FLU

• able to do single digit addition in writing

• able to explain the numerical expression (single digit by single digit addition) using real life example

• able to do verbal interaction on single digit addition process

• able to do double-digit by single digit addition in pictorial representation – using objects, FLU

• able to do double-digit by single digit addition in writing

• able to explain the numerical expression (double-digit by single digit addition) using real life example

• able to explain double-digit by single digit addition process

• able to do verbal interaction on double-digit by single digit addition process

• able to do double-digit by double-digit addition in writing

• able to explain the numerical expression (double-digit by single digit addition) using real life example

• able to explain double-digit by double-digit addition process

• able to do verbal interaction on double-digit by double-digit addition process

Addition with carry-over

• able to do double-digit by single digit addition in pictorial representation – using objects/FLU

• able to do double-digit by single digit addition in writing

• able to explain the numerical expression (double-digit by single digit addition) using real life example

• able to explain double-digit by single digit addition process

• able to do verbal interaction on double-digit by single digit addition process

• able to do double-digit by double-digit addition in writing

• able to explain the numerical expression (double-digit by single digit addition) using real life example

• able to explain double-digit by double-digit addition process

• able to do verbal interaction on double-digit by double-digit addition process

Subtraction without regrouping

• able to do single digit subtraction in pictorial representation – using objects/ FLU

• able to do single digit subtraction in writing

• able to explain the numerical expression (single digit by single digit subtraction) using real life example

• able to explain single digit subtraction process

• able to do verbal interaction on single digit subtraction process

• able to do double-digit by single digit subtraction in pictorial representation – using objects, FLU

• able to do double-digit by single digit subtraction in writing

• able to explain the numerical expression (double-digit by single digit subtraction) using real life example

• able to explain double-digit by single digit subtraction process

• able to do verbal interaction on double-digit by single digit subtraction process

• able to do double-digit by double-digit subtraction in writing

• able to explain the numerical expression (double-digit by single digit subtraction) using real life example

• able to explain double-digit by double-digit subtraction process

• able to do verbal interaction on double-digit by double-digit subtraction process

Subtraction with regrouping

• able to do double-digit by single digit subtraction in pictorial representation – using objects/FLU

• able to do double-digit by single digit subtraction in writing

• able to explain the numerical expression (double-digit by single digit subtraction) using real life example

• able to explain double-digit by single digit subtraction process

• able to do verbal interaction on double-digit by single digit subtraction process

• able to do double-digit by double-digit subtraction in writing

• able to explain the numerical expression (double-digit by double-digit subtraction) using real life example

• able to explain double-digit by double-digit subtraction process

• able to do verbal interaction on double-digit by double-digit subtraction process

Understanding of multiplication

• able to represent the multiple factors in pictorial form (objects)

• able to explain the numerical expression using real life example

• able to explain the meaning of multiplication process