The ability to recognise two-digit and larger numbers indicates a stronger grasp of the concept of place value. Children at Level 2 and above receive regular practice with large numbers to reinforce their understanding of place value and learn how to solve operations using larger numbers.

PLACE VALUE

For these groups, instructors use an expansion chart to extend children’s place value knowledge to include hundreds, thousands, and ten thousands. They also use play money to reinforce place value, with 1, 10, 100 and 1000 denomination notes. Instructors show children how these denominations combine to form numbers and emphasise this idea by practicing addition and subtraction sums using play money. Similar to number charts, expansion charts are made by instructors and used daily in higher level classes, helping children to become familiar with higher-digit numbers. Play money is simple money modelled on familiar currency. The money is printed, cut, and given to instructors at training. The notes are used and reused. Money is usually familiar to children and they are able to understand sums involving giving or receiving money, for example.

In this video, the instructor introduces paper currency notes, explaining how the denominations combine to form a number, and  demonstrates the process of addition using paper notes.

MULTIPLICATION TABLES

For solving more advanced multiplication and division sums, Pratham recommends that children learn multiplication tables, at least up to 10. In TaRL classrooms, this is done in the form of multiplication chart activities, games, and competitions. To test multiplication, number cards written on recycled cardboard can be used. In one game, children flip over 2 randomly chosen cards and quickly say the product of the 2. Number cards might have a number of additional uses, helping children with mental mathematics.

Children are encouraged to practise multiplication tables by first using a multiplication chart, and then testing their knowledge through games or competitions. In the video above, the instructor uses number cards which he made, and children work together in small groups to practice multiplication tables. Instructors choose different methods to encourage children to memorise the multiplication tables.

BASIC OPERATIONS

Children practise basic operations at all levels. In order to develop a firm understanding of place value, and to organise sums, children use a number frame. When solving operations using larger numbers, children leave behind the words “bundles” and “sticks” and swiftly move to using “tens”, “units/ones,” and eventually “hundreds” and “thousands”.

Instructors focus first on addition and subtraction, in particular making sure that learners are well-equipped with place value understanding, particularly when ‘carrying over’ in subtraction
sums. Instructors teach the process of addition and subtraction using paper currency and a number frame. In the video below, the instructor uses play money to demonstrate the process of addition with larger numbers.

Similarly, instructors demonstrate the process of multiplication using a number frame, going step-by-step, as in the video below. Instructors move away from using tangible objects when teaching long division, to a more abstract tool – a division frame. Instructors demonstrate the process of each operation in a whole-group setting, and then give children time to work on sums together in their small groups.

Once children are able to solve addition, subtraction, multiplication and long division sums with larger numbers, instructors give them regular practice solving a large number of sums. Instructors give children individual attention where necessary, explaining the process, and making sure children understand.

PROBLEM SOLVING USING LARGER NUMBERS

Using number frames and following the process they learn in a whole-group setting, children practise solving more complex word problems in small groups. They read the problem, identify the information given, determine what the question is requesting, and which operation is needed to solve the problem. To solidify their skills, children are given word problems and sums to solve individually.

In the video above, the instructor demonstrates the process of reading and solving a word problem, and children learn how to solve multiplication problems using bigger numbers.

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