Many teachers begin teaching place value in new academic year, and for good reason. Without mastery of the value of digits in numbers, other areas of maths would not be accessible to many.
Zero
Children learn about zero as being a place holder and to show the absence of a value. As we explored here, this allows a familiar patterns when working with multiples of 10 too. The concept of 0 is therefore essential to unlock the curriculum.
Place value
Place value means that digits, singular or when combined, have value and that value differs depending on where the digits are placed in the number. Consider, 2, 20 and 200. Each number contains the digit 2, but the value of the 2 is different.
2 - Two ones (units)
20 - Two tens and zero ones (units)
200 - Two hundreds, zero tens and zero ones (units)
Using a place value chart, you can see how the zero creates places to change the value of each 2.
Decimals
The use of a decimal point differentiates between whole numbers and decimal (fractional) numbers. Decimals are often used in measurements, including money and therefore they are often required to be rounded. Rounding is context driven and dependent to what degree a number needs rounding. Essentially, rounding requires an understanding of which number a value if closest to. A solid understanding of the number system and place value is required to access problems. Using models which reveal the structure of the number system can be powerful.
Using a Gattegno board can allow children to strengthen and master this concept. The links to powers of 10 seems clear and logical.
Negative numbers
Negative numbers found their way into maths relatively recently (in comparison with other areas of the number system) due to a phenomenon familiar to many: debt. Taken at face value, using negative numbers for ideas like debt or temperature can be useful. Things can start to get a little sketchy when we try to apply operations to negative numbers.
Negative numbers - calculation.
When a positive number is added to a negative number, the answer seems logical:
-3 + 1 = -2
-3 - 1 = -4
This concept can take some time for children to master. Is 2 bigger than -5? but isn't 5 bigger than 2? Here, language and models collide to strengthen understanding. 2 is greater than -5 is a much more effective way of describing the relationship. Perhaps having a vertical number line will allow children to strengthen the concept?