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Teaching Place Value

Developing number sense is a priority for teaching mathematics.

Teaching place value is at the heart of teaching children mathematics. Number sense is the foundation which other mathematical thinking and processes are built on.

Kids know a lot about numbers when they enter school. However, their concepts are based mainly on a counting by ones approach.

To understand place value, children need to be taught the number sense behind groups of 10. It is possible to also show them that math is fun!

Recognition of equivalent numbers, regardless of the representation, is also critical in teaching children mathematics.

Children with poor number sense do not have a conceptual framework of how the value of numbers change with regard to their "place."

To begin teaching place value, we have to start with understanding groups of ten.

According to NCTM standards, "Making a transition from viewing 'ten' as simply the accumulation of 10 ones to seeing it both as 10 ones and as 1 ten is an important first step for students toward understanding the structure of the base-ten number system."

Base Ten Blocks & Teaching Place Value

Base Ten Blocks are the most useful tool for teaching place value, and no lesson ought to be without them. The units represent 1, the longs represent the regrouping of 10 units for one 10, the flats represent the regrouping of 10 longs for 1000, and the cubes represent the regrouping of 10 flats for 10000.

Base Ten Blocks are proportional, which means they are a concrete, physical representation of groups of 10.

Customer and Banker
When you start teaching place value using Base Ten blocks, begin with a simple lesson of exchanging units for longs. This is regrouping. Two students can work together, one as the banker and one as the customer. The customer rolls four dice, takes that number of units and counts them out in front of the banker, writing the total number of units on the recording sheet. Then the units are put into groups of 10 and the banker takes the units and gives the customer one long for each group. The number is recorded again on the sheet, but this time as longs and units.

Once students have mastered exchanging units for longs, introduce a flat. Begin with only flats and longs and use the recording sheet. Bring units back into the lesson at another time (you do not want to introduce two new concepts at once - just work with the idea of exchanging longs for flats, then introduce units to longs to flats).

Learning Box has a fantastic site for teaching place value concepts.

Guess the Mystery Number
Another way of teaching place value is to play math games like Guess the Mystery Number. All students will need a place value mat and Base 10 blocks. The objective is for students to understand that they must regroup their Base 10 blocks to figure out the mystery number.

For example, tell them to take 12 units and 4 longs. Working with a partner, they will need to physically regroup the blocks by exchanging 10 units for one long. They record the number in their math journals (52). You can differentiate teaching place value with this game by including flats and making it necessary to regroup in two places, such as 15 units, 9 longs and 2 flats (305).Note: This activity is best done after students have a solid grasp of groups of 10 within a base 10 number system.

Poker Chips and Hundreds Boards

There are other manipulatives that can be used to teach the concept of groupings in place value. Poker chips can easily be used: Whites equal ones, reds equal 10s, and blues equal 100. Have the children make a number that you say and place out the poker chips to represent that number. As you walk around the room, you will be able to ascertain immediately which students are experiencing conceptual difficulties with the concepts of regrouping and exchanging.

You could also use a 100s Number Board. Ask the children to observe the top row of numbers. Discuss how the digits 0-9 are different from other numbers (one digit as opposed to 2 or 3 for 100). Discuss how every number 10-99 has two digits: one in the 10s place and one in the 1s place. Next, have students cover numbers that have a 2 in the one's place. Do this for other numbers and discuss resulting patterns. You could then extend this to covering numbers with a 6 in the 10s place, or any other digit.

Differentiation in Teaching Place Vaue

Base Ten Riddles
Students write riddles that require the use of base-ten materials to solve. Examples are:

I have 3 hundreds, 5 tens and 4 ones. Who am I?
If you add 4 tens to me, I will be 63. Who am I>

Mayan Math
Your gifted students may enjoy learning about Mayan mathematics - they used a base number of 20. Dots and bars were used for counting, with a shell symbol meaning 0, a dot meaning 1 and a bar meaning 5. Whereas we would write the number 53 as 5*10 + 3, their large numbers were written as a power of 20 (2*20 + 13 = 53). Visit Mayan Math for more information.

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