enhance the conceptual of the value of digits

Place value notation boards

Place value notation boards may be used to enhance the child's conceptual understanding of the value of digits. In first class children are required to group and count in tens and units and express groups of counters as units or tens and units. Using the 'board' is a very effective way of engaging in this activity. Numeral cards may be used in conjunction with these boards.


Later, when the child is required to add tens and units, these boards are again very useful.

Example A: Addition (no regrouping), 35 + 21

Example B: Addition (involving regrouping), 24 + 48

Place value notation boards

When subtracting, the boards are used in a similar way. Only the greater, however, is represented by base ten materials on the board. Numeral cards represent the number of units and tens to be subtracted.

Example A: Subtraction (no renaming necessary), 58 - 23

Example B: Subtraction involving renaming, 64 - 38

Using place value notation boards for subtraction in this way will enable the child to recognise the relationship between addition and subtraction. The boards depicted on the previous page show only tens and units, but in third class the boards would include a column for hundreds, and in fourth class place value notation boards would have four columns, thousands, hundreds, tens and units. Simple games can be played by groups or pairs of children, using dice, base ten materials and notation boards, during which children attempt, for example to reach 'target numbers.' Such games could involve addition or subtraction.

Addition and subtraction transition boards

Transition boards are simple devices to aid childrens' conceptual understanding of
addition and substraction. Transition boards, foster the linking level of addition ansubtraction in base ten.

The general strategy for teaching is to lead the children through the concrete, linking and abstract levels as follows:

• they work only with the manipulatives on the transition board as the teacher orally states the problem while modelling on the overhead projector
• they write the numbers on the chalk board and use the manipulative pieces as they work with the materials on the transition board
• they represent the numbers with pictorial models of the manipulatives on a small paper model of the transition board
• they write the numbers in the spaces on a small paper model of the transition board
• they write the numbers on their paper.

Sequential use of addition board, 34 + 27

Sequential use of subtraction board, 37 - 18