**Focusing on children having a deep understanding of concepts in Mathematics when they are young, will set them up to be successful problem solvers and critical thinkers in the future.**

Welcome to my second blog in the series “Teaching Mathematics to young children” In this blog, we look at the importance of “place value” in contributing to a child’s number sense. This blog outlines the growth points (see my previous blog for a definition of growth points) that children go through to achieve an understanding of place value.

Place value is the understanding of “where” a digit is in a number and knowing the value of it. For example, in the number 6 023, the place value of 2 is “tens” and in the number 2.43, the place value of 3 is “hundredths”. A solid understanding of place value allows the child to read, write, order and interpret numbers confidently.

Below is a list of the growth points of “place value” that children should move through and parent tips of how to support their child at home to achieve a given growth point.

**Growth Point 1: Reading, writing, ordering and interpreting single digit numbers.**

For this growth point to be achieved children need to be able to read all 1 digit numbers (1 – 9), be able to write them (number reversals are fine eg The numeral 2 is written backwards), can order the numbers from smallest to largest and largest to smallest and can show the relevant objects to match the numeral eg 6 cars for the number 6. This growth point is usually achieved between 4 – 6 years old.

*Parent Tips to get your child to achieve this growth point*

- Play the game “memory” with some numeral cards (numbers) and dot cards (dots on a card to match a numeral).
- Make towers with blocks (1-9 blocks) and get the child to write the corresponding number on a post it note to stick in front it.
- Ask your child to collect a specific amount of objects that they roll on a dice. (eg if they roll a 4, they have to get 4 balls)
- The main focus is getting the child to recognise the name of the number, what the numeral looks like and to show how the number is represented (show amount with objects). This is called the number triad. All three aspects must be taught together so the child learns the relationship between all of them.
- The adult and child can walk around the house with post it notes and count things they see. (objects between 1-9). After they count it, help the child to write the number on the paper and stick it up next to object/s. Eg write the number 4 next to the light switch that has 4 buttons.
- Mix up all the numeral cards (1-9) and ask the child to put them from smallest to largest. You can include dots on the card so they can see it is increasing. Also expose your child to the terms; lowest to highest and ascending order. Then mix it up again and ask them to order the cards from largest to smallest. (or highest to lowest or descending order). Ask lots of questions about how they knew how to do it. If they can explain, it shows a deep understanding and knowledge of the concept.

**Growth Point 2: Reading, writing, ordering and interpreting two digit numbers.**

For this growth point to be achieved children need to be able to read all 2 digit numbers (10 – 99), be able to write them, can order the numbers from smallest to largest and largest to smallest and can show the relevant objects to match the numeral eg 37 cars (shown by 3 rows of 10 cars and 7 cars by themselves) for the number 37. This growth point is usually achieved between 6 – 8 years old.

*Parent Tips to get your child to achieve this growth point*

- The child must gain the understanding of tens being their own value of 1. Many children still consider the tens as large collections of ones. (For example 30 needs to be seen as 3 tens and not 30 ones) Parents can help this concept by making bundles (tens). Use paddle pop sticks and get the child to make bundles of 10 and wrap an elastic band around them. You could count these bundles by tens with the child. Explain to your child that this is a ten as there are 10 in it.
- Play a bundling game. The child rolls a dice and collects that amount of paddle pop sticks from the middle. They roll again. Once they have got ten paddle pop sticks they use an elastic band to make a bundle. They keep rolling and making bundles until they get to 99. Once they get there, when they roll the dice you could go backwards. They will have to separate a bundle when they need to take away ones but they have no more ones left. Constantly ask your child what number they have made and write the number on a paper. (ask before each roll) You want them to make the connection that for two digit numbers, the first numeral represents how many bundles (tens) and the second numeral represents how many ones.
- Play ordering number games. Give your child a variety of two digit numbers (about 10 of them) to peg up on a piece of string in ascending order. (make sure you use all the different terms for ordering as mentioned above). Then mix them up and get them to peg them up in descending order.
- A lot of children when they start to write two digit numbers write the numerals in the wrong order. (eg fourteen is written as 41) This error shows that a child does not have the understanding of the place value for writing numbers. They make the same error when they read numbers.
- The ‘teen numbers’ are particularly difficult for children as they are said differently to how they are written. (children hear the eight first in 18 and write it with an 8 then a 1) We need to do lots of work on teen numbers with our children. Play lots of games where the focus is reading and recording teen numbers. (eg get the child to start with a teen number, roll a dice and you decide whether they have to add or subtract (try to get them to stay within teen numbers), the child needs to make the number, write the new number and say it. The child rolls again and you can choose again whether they add that amount or take it away. – Remember to use bundles as we want them to know that the first numeral represents tens.

**Growth Point 3: Reading, writing, ordering and interpreting three digit numbers.**

For this growth point to be achieved children need to be able to read all 3 digit numbers (100 – 999), be able to write them, can order the numbers from smallest to largest and largest to smallest and can show the relevant objects to match the numeral eg 136 to be shown as 1 hundred, 3 tens and 6 ones. This growth point is usually achieved between 8 - 10 years old.

*Parent Tips to get your child to achieve this growth point*

- To continue on from the two digit numbers, hundreds need to be seen as having a value of 1 and not a very large collection of objects.
- Many children who begin writing 3 digit numbers always write them as they hear them (eg 326 is written as 30026) To help this concept, you could continue to play the bundling game and show them that 100 is 10 bundles together. You can call this a mega bundle. Start the game at a high two digit number. Focus the child’s attention on having a zero for the tens when the number has just gone over 100 or 200.
- Play a game focusing on the role of zero in a three digit number. Give the child 3 numeral cards, one being a zero and get them to chose an order. Once the child has chosen an order get them to make that number with equipment. Then ask the child to change the order of the numerals and get them to make the new numeral. Ask the child if changing the order of numerals in a number makes a difference?
- Play a 3 digit recording game. Tell the child a number and get them to type it into a calculator. Press the clear button. Then tell them another 3 digit number. Make sure you include numbers with a zero. (harder numbers are 316, 204 etc)
- Play an ordering game. Give the child a variety of 3 digit numbers and he/she puts them in ascending order or descending order.

**Growth Point 4: Reading, writing, ordering and interpreting four digit numbers.**

For this growth point to be achieved children need to be able to read all 4 digit numbers (1000 – 9999), be able to write them, can order the numbers from smallest to largest and largest to smallest and can show the relevant objects to match the numeral. Eg 4561 to be shown as 4 thousands, 5 hundreds, 6 tens and 1 one. This growth point is usually achieved between 9 - 12 years old.

*Parent Tips to get your child to achieve this growth point*

- To continue on from the three digit numbers, thousands need to be seen as having a value of 1 and not a very large collection of objects.
- Ask your child to write down a variety of 4 digit numbers that you say to them. Ensure you say lots of numbers with a zero in them. (eg 2016, 4510, 5003)
- Ask your child to read lots of environmental print that has 4 digit numbers. (prices of furniture etc)
- Get your child to make up an imaginative shopping trolley filled with items from a catalogue. (find a catalogue with many items that all cost a four figure amount) After your child has chosen many items ask them to order them from the most expensive to least expensive or the other way around.

**Growth Point 5: Extending and applying place value knowledge.**

For this growth point to be achieved children need to be able use their knowledge and understanding of place value to solve challenging mathematical problems. This growth point is usually achieved between 10 - 13 years old.

*Parent Tips to get your child to achieve this growth point*

- Expose your child to lots of word problems that involve place value. (eg What number is 6 hundreds more and 3 tens less than 8722?)
- Get your child to roll the dice 4 times. Each time they roll it represents a numeral in a different place value. (Eg Roll One= 3, Roll Two = 4, Roll Three= 3 and Roll Four= 6. The number would be 3436) Ask the child lots of place value questions about this numeral. Eg What is 10 more, 10 less, 100 more, 100 less, 1000 more, 1000 less, 20 more etc)
- Begin to expose them to decimals. Show them lots of prices in supermarkets and explain that anything before the decimal point is a whole and anything after is part of a whole. Introduce terms such as “tenths”, “Hundredths”, “Thousandths”. Explain to them that the addition of the ‘th’ at the end of the word means it is smaller than 1. (This concept is further developed in other growth points)

Place value is a very important element in understanding ‘number’. It is often assumed that a child has a good understanding of it, but when specific questions about place value are asked, many gaps in their understanding are discovered.

I hope you have enjoyed reading the second blog in my series “Teaching Mathematics to young children” as much as I have enjoyed writing it. The final blog in this series will be focusing on the development of a child’s understanding in addition and subtraction.

Until next time …

Kelly Pisani