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Place value progression


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Last updated 10 January 2013 11:06 by NZTecAdmin

The place value progression outlines groups of numbers and important place value concepts within the decimal number system that learners need to understand in order to solve problems. The earliest step is based around the unit 10. At the highest step, learners understand the value of the position of any digit in a number including decimal numbers.

Most adults will be able to:
Activities
1.
 

There is a gap at the first step of this progression because learners need to be able to count all objects before they can learn to count in tens.

 
2.
  • 10 as a counting unit, the tens in numbers to 100 and the place values of digits in whole numbers up to 100.

Learners know how many tens there are in numbers to 100 and can partition numbers up to 100 into tens and ones, for example:

  • 6 tens are 60
  • 34 = 30 + 4.

Introducing place value

Learners develop the understanding that our number system is based on the number 10.

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3.
  • the tens and hundreds in numbers to 1,000 and the place values of digits in whole numbers up to 1,000.

Learners know how many tens and hundreds there are in numbers up to 1,000 and can partition numbers up to 1,000 into hundreds, tens and ones, for example:

  • there are 64 tens in 645 (and 5 ones remaining)
  • 561 rounded to the nearest 10 is 560
  • 456 = 400 + 50 + 6.

Whole number place value

Learners extend their understanding of place value by adding and subtracting 1, 10, 100 and 1,000 from whole numbers.

Introducing place value

Learners develop the understanding that our number system is based on the number 10.

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4.
  • how many tens, hundreds and thousands
    there are in any whole number
  • that 10 tenths make one whole.

Learners know how many tens, hundreds and thousands there are in any
whole number and know that 10 tenths make one whole. For example:

  • there are 4,560 thousands in 4.56 million
  • there are 500 hundreds in 50,000
  • there are 20 tenths in 2.
 
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5.
  • how many tenths, hundredths and thousandths are in any number, including decimal numbers
  • how to convert percentages to decimals and vice versa
  • what happens when a whole number or decimal is multiplied or divided by a power of 10.

Learners can order and convert between tenths, hundredths and thousandths. For example, a learner knows that:

  • there are 3,420 tenths in 342
  • 137.5% is the same as 1.375
  • 6.49 rounded to the nearest tenth is 6.5
  • 4.5 x 100 = 450
  • 78.3 ÷ 100 = 0.783.

Connecting percentages decimals and fractions

Learners explore the connections between percentages, decimals and fractions.

Decimal number place value

Learners develop their understanding of the place value system to include the decimal numbers tenths, hundredths and thousandths.

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