Expanding: Place Value 1 (Multiplying and Dividing by 10 (With Objects))
Vocabulary
number
thousands, hundreds, tens, ones, units
one-digit, two-digit three-digits four-digit
first digit, second digit, third digit fourth digit
place, place value
Hints and Tips
All about Place Value Labelled Place Value Grid
Place value is one of the fundamental concepts your child has to learn as it is the basis of our number system.
In order to be a competent mathematician and be able to manipulate numbers, your child must have a solid understanding of this concept.
In order to understand our number system, your child must be taught that the same digit can mean different things, for example, the symbol 5 can mean 5 ones, or 5 tens or 5 million depending on the position (place) it takes in the number.
The idea that one ten is the same as ten ones needs to be introduced carefully, as does the idea that the two in twenty represents two tens or twenty ones.
You must be careful to make sure this concept is really understood by your child as this is the foundation for many other areas of maths.
Moving slowly through this topic and allowing plenty of time for your child to understand the underlying concepts will reap rewards throughout the rest of his/her maths learning.
It is easy to move on too quickly; for instance, your child may be able to recognise, say and write 36, but this doesn't mean they understand the value of the digits in the number.
We cannot emphasise enough the amount of time and effort needed in this area of maths. It may seem tedious to you but please do not rush it as this is a concept at the very foundation of your child's future maths learning.
In this activity we use coloured cards to re-enforce the concept that large numbers come in groups of 3, that is, units (or ones), tens of units or ones (tens) and hundreds of units or ones (hundreds). This continues as thousands, tens of thousands and hundreds of thousands. The next group is millions, tens of millions and hundreds of millions. This pattern continues through billions, trillions and so on.
Essential Prior Knowledge
Know that the Place Value grid has a never ending number of columns.
Know that each column represents a different value.
Know that each column is ten times bigger than the one on its right and ten times smaller than the one on its left.
Activity
For this activity you will need a large Place Value grid and coloured card for headings.
3 green and 3 orange and 2 blue. These are only suggestions for colours, you can use any you like but whatever colours have been used previously, continue with those so there will be no confusion.
With your child, make a Place Value grid of, H, T, U, 1/10th, 1/100th
Activity 1
When we multiply by 10, all the digits move one place to the left. When working with whole numbers, this can leave a space in the ones column. It is important to remind your child that there is a digit to fill that column.
Ask him/her if he/she remembers zero as a place holder Placeholders and have a discussion about what happens if the column is left empty.
Using money to support the activity, place £1 in the ones column. Ask your child what happens when it is multiplied by 10. Look at a £10 note. Talk about how it has a value of 10 ones so it would be placed in the tens column. So £1 multiplied by 10 equals £10.
Repeat the discussion using 10p and £1. Look at the way multiplying by 10 moves the answer one place to the left as the answer becomes 10 times bigger.
Continue this activity until most of the columns have money in them. (The thousands columns will be hard to fill!)
As in the video, Multiplying and Dividing by 10 and 100 reinforce the idea that each column, when multiplied by 10, becomes 10 times bigger so 10 of those (£1s) makes 1 of them (£10)
Repeat this activity in reverse, dividing by 10.
Activity 2
To reinforce this concept and to check understanding, repeat the above activity using drinking straws, for example. In this case, use 1 straw as the ones and bundles of 10 straws for 10s and bundles of 100 straws for 100s, etc. In this case, for tenths, ask your child what he/she will need to do, his/her answer will show you if the concept has been fully understood. Your child should cut a straw into 10 pieces and for hundredths cut one of those pieces into 10. (This will prove a challenge!)
Of course, if you think of other resources, please feel free to use them!