Elaboration on this Achievement Objective

This means students will use a mental number line that includes the relative size of integers and decimals to three places and the whole numbers they know from previous levels. They should be able to locate the position of integers and decimals to three places on a given number line with adherence to scale, particularly where tenths and hundredths divisions are given, for example

Knowing decimal place value involves more than knowing the significance of the position of digits in a whole number, for example in 24.671 the 7 means seven hundredths. Strategies for computation require a nested view of place value and understanding the scaling effect as digits move to the right and left in place value. This means that nested in the ones are tenths, hundredths and thousandths in the same way that nested in the hundreds are tens, ones, tenths, etc., for example 3.509 has 35.09 tenths, 350.9 hundredths, 3509 thousandths, etc... Understanding of nested place value is best demonstrated by calculations where place value units must be constructed by combining or decomposing other place value units, for example 4.2 – 2.68 = as the difference between 420 hundredths and 268 hundredths. Students should know the multiplicative relationship between place values, for example one hundredth equals ten divided by one thousand, and the effect of multiplying and dividing a given decimal by ten, one hundred, or one thousand, for example 30.4 divided by one hundred equals 0.304. Students should know the effect of adding and subtracting integers and be able to represent these operations on a number line, for example +3 - -2 = and +3 + +2 = have the same answer, +5.