  When children recognise single-digit numbers, but struggle to read two-digit numbers, they often need help understanding the concept of place value. (This is the idea that a digit’s size depends on its position in the number. In a base-ten number system, we have different positions for “units”; “tens”; “hundreds,” etc.) A primary focus for this group of children is to teach and reinforce an understanding of place value.

Instructors also continue to teach basic operations, giving children appropriately challenging word problems and sums to solve. Instructors continue to introduce tools to help children to organize their mathematical thinking, such as bundles and sticks, as well as a number frame with columns for tens and units. This helps children better understand place value, and to write numbers carefully when carrying out operations.

PLACE VALUE

Understanding that a digit’s value depends on its place in a number is a foundational skill. Without this skill, children are not able to read or understand larger numbers, or to carry out operations using larger numbers. In TaRL classrooms, instructors tie sticks in bundles of 10. In the video below, children are introduced to the bundle and stick method.

Through this activity, children begin to understand the importance of grouping numbers by ten,
and notice the pattern that the spoken numbers follow. When this is combined with representing the bundles and sticks in written form in a number frame, children learn that a ‘1’ in the bundles column means one bundle of ten sticks. In this way, they begin to understand place value. Instructors use easily available materials like sticks (the specific material used depends on context: for example, in parts of India, straws are cheap and easily available) to teach place value. String or rubber bands are used to tie groups of ten sticks into bundles. This helps children to understand the concepts of tens and units: by seeing 10 different sticks combined to form one bundle, they see that a ‘1’ in the ‘10s’ place represents a 10. Children are not intimidated by bundles and sticks, because they are familiar with these simple materials. In addition, they can find sticks on the ground and practise TaRL activities outside of the classroom.

BASIC OPERATIONS

Before instructors give children practice with basic operations, they introduce the concept of addition, subtraction, multiplication, and division, and make sure children understand why we use each operation. The video below illustrates how instructors introduce multiplication and division, using tangible objects that are familiar to the children.

Children begin to understand basic operations at a very early stage. Once they have learned how to count, they can begin to learn addition using small numbers. These concepts are often introduced using tangible objects. TaRL instructors give their classes regular practice with operations. According to Pratham’s
methodology, when practicing operations, children do not just copy the instructor’s process, but explain the process in their own words, reinforcing their understanding of the operation. This is especially important in the whole class setting when other children learn from their classmates’ demonstrations. During basic operations activities, instructors often divide the class up into small groups. To do this, they consider the child’s basic operations level and, where possible, assign children with similar levels to the same group. The instructor then gives appropriate sums to each group.

PROBLEM SOLVING

Instructors give the class word problems to solve either as a whole class, in small groups, or individually. Children apply their knowledge of basic operations to specific problems. The word problems involve everyday tasks, such as dividing chalk or adding up money, to spark children’s interest, and encourage them to extend their mathematical thinking beyond the classroom.

Children are prompted to identify information given in a problem, to understand what the question requires, and determine the mathematical operation needed to solve the problem. They next apply the process they have learned to solve the problem. This set of skills is fundamental to learning and applying mathematics.

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