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A clear understanding of place value builds the foundations of decimal system familiarity. However, many children have trouble learning how to shift a multiple of ten from one column to the next. Discovering that the "ten" part of "eleventy-one" actually shifts to represent one unit in the hundreds column represents a big leap in the child's mathematical understanding.

How to help them make that leap?

To begin, the child needs to learn that each separate digit in a number actually represents a multiple. Manipulatives are particularly effective in helping to teach this lesson. Set out one hundred and ten popsicle sticks. Have the child bundle together ten groups of ten popsicle sticks with elastic bands, emphasising that each bundle of ten popsicle sticks represents ten loose popsicle sticks. You may need to let the child bundle and unbundle the ten popsicle sticks several times before the association is solid. Leave one group of ten popsicle sticks loose.

Once the child understands that a bound group of ten popsicle sticks represents the same thing as ten loose popsicle sticks, it is time to start working with columns.

You can draw the next example on the blackboard for the class as a whole. Have the children each copy your columns onto their own pieces of paper.

Draw two columns: with the right-hand column representing the ones and the left-hand column representing the tens. Write "Ones" over the ones column, and "Tens" over the tens column. Now write a two-digit number in the columns. Emphasise to the child that only one digit can go into each column: the furthest right digit always goes in the furthest right column, and the digit next to it goes in the column next to it. A column can NEVER contain more than one digit.

Explain that the column furthest to the right is the ones column: this digit represents the number of SINGLE popsicle sticks. Then explain that the column on the left is the tens column: this digit represents the number of bundles of TEN popsicle sticks. Bundles only ever go over the tens column, loose popsicle sticks only ever go over the ones column. Have the child count out the number of popsicle sticks and popsicle stick bundles the number represents, and place them above each column. For example, the number 35 would have three popsicle stick bundles above the tens column, and five popsicle sticks above the ones column. Repeat this part of the lesson until the child is always counting out the correct number of bundles above the tens column and

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