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Introducing place value


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Last updated 26 October 2012 15:30 by NZTecAdmin
Introducing place value (PDF, 44 KB)

Place Value progression, 2nd and 3rd step

The purpose of this activity

In this activity, the learners develop the understanding that our number system is based on the number 10. The place of a digit in a number indicates the size of that digit and the places increase by a factor of 10 as you move to the left and decrease by a factor of 10 as you move to the right.

The teaching points

  • There is a system to our numbers that the learners need to understand. This system developed over time, and there are other number systems. A few interesting facts are as follows:
    • The first number system developed in Mesopotamia (now Iraq) approximately 4,800 years ago, based on 60. Our system of measuring time comes directly from that number system.
    • Not all number systems are place value systems. In the Roman number system, a number is often the first letter of the word it represents – some learners may be familiar with Roman numerals.
    • Base ten systems developed independently in China and India.
    • Our current system travelled from India through Arabia to Europe, arriving in Europe in the thirteenth century.
  • The system we use is based on 10 and developed because we have 10 fingers. It requires the use of the digit 0 as a place holder. Once ten objects have been counted, a place holder is used to indicate the number of groups of ten (10). Once ten groups of 10 have been counted, a second place holder is used to indicate the number of groups of 10 tens (hundreds) (100), and so on.
  • The value of the places increases to the left by a factor of 10 and decreases to the right by a factor of 10.
  • The pattern of ones, tens, hundreds repeats for thousands and millions, and recognising this pattern helps with reading large numbers.

    Image of pattern of ones, tens and hundreds.

  • One billion is used to describe both one thousand million (1,000,000,000, 1 x 109 , United States of America) and one million million (1,000,000,000,000, 1 x 1012, United Kingdom). Increasingly, the meaning of one billion as one thousand million is used in English-speaking countries.

Resources

  • Calculators.

The guided teaching and learning sequence

1. Write 44 on the board and ask the learners whether both fours mean the same thing. Listen for the response that one 4 means 4 ones and the other 4 means 4 tens. Ask whether the learners agree that the place of the 4 indicates its value and reinforce that, in 44, the bold 4 indicates 4 ones and the 4 on its left indicates 4 tens.

2. Write 444 on the board and ask the learners what the new four represents?

3. Draw a three-column place-value chart on the board and ask the learners what the relationship is between the value of the three places: ones, tens, hundreds. Listen for and reinforce the response that each place increases by a factor of 10 as you move to the left.

Image of three-column place-value chat.

4. Ask the learners why our number system is based around 10. If necessary, prompt the response that it is because we have 10 fingers. Model counting 12 objects on your fingers. Record the 1 group of 10 in the tens column before reusing your fingers to count the remaining 2. Record the 2 in the ones column.

Image of three-column place-value chat.

Ask what you would write in the place-value chart if you had only 10 objects. Discuss the use of 0 as a place holder.

5. Ask what happens when you have counted 9 groups of 10 and you add another group of 10. Listen for the response that you have 100, record this in the place-value chart and reinforce that 100 is the same as 10 groups of 10.

Image of three-column place-value chat.

If necessary, the learners can count toothpicks into groups of 10 to develop a better understanding of this idea. Keep the groups in place with rubber bands.

6. At this point, you may wish to discuss the fact that not all number systems are based around 10 and perhaps talk about other number systems used around the world. The learners could do some research themselves into different number systems and their history. This is an opportunity for the learners to recognise that there is a cultural aspect to number and for you to value the different cultural backgrounds of your learners.

7. Draw the place-value chart below on the board.

Image of place-value chart.

Ask the learners what value the place to the left of the ‘hundreds’ has. Listen for the response ‘thousands’ and ask the learners to confirm that this place is greater than the ‘hundreds’ place by a factor of 10 (10 x 100 = 1,000).

Repeat the questions:

“What value does the place on the left have?”
“Is it greater by a factor of 10?”

for each section, until the chart is complete.

Image of place-value chart.

8. Ask the learners to look for and describe any pattern.

9. Redraw the chart.

Image of three-column place-value chat.

10. Put numbers in the chart and ask:

Read this number aloud.

“What is the value of the 8?”
“What is the value of the 3?”
“What is the value of the 6?”

Image of three-column place-value chat.

Follow-up activity

Have the learners work in pairs with a calculator.

One of the pair keys a three-digit number into the calculator and asks the other to read it.

The first learner then asks the second learner to change a digit to another specified digit.

For example: A learner keys in 469 and says, “Read the number to me”.

Then that same learner says, “Change the 4 into a 3”. (It is necessary to subtract 100 on the calculator to change the 4 into a 3.)

And then they say, “Change the 6 to 7”. (It is necessary to add 10 on the calculator to change the 6 into a 7.)

Note: If the learners are operating above step 3 on the Place Value progression, they could work with larger numbers, for example, 25,482.

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