# Teaching place value to young children

• Published on February 8, 2019

Teaching place value is a vital part of mathematics programs in lower primary classrooms. It is essential that children develop a firm understanding of place value right from the start to avoid later confusion and maths anxiety.

Sadly, many children and adults confess to having an aversion to mathematics. My belief is that the aversion is often learned from ineffective teaching methods. For this reason, there is a strong focus on number in readilearn resources with lessons and activities that provide opportunities to develop understanding in fun and meaningful ways.

### It starts with understanding number

Before we begin to teach place value, we must ensure that children have a strong sense of number. Understanding number is more than simply being able to rote count or recognise numerals. While even very young children may learn to memorise and recite the sequence of numbers from one to ten, they don’t always understand what the words mean.

Rushing children through to abstract processes before they have developed a strong foundation creates confusion. It sets them up for frustration, fear, failure, and a dislike of maths.

This can be avoided by encouraging an “I can do it. I get this. Maths is fun” attitude.

To develop an understanding of number, children require many and varied experiences using concrete materials in many different situations.

##### One-to-one correspondence

First, they need to count with one-to-one correspondence. This means they need to understand that each number recited in sequence refers to one object, and that the last number spoken tells us how many objects there are. This understanding takes time to develop. Children need to count many different things in many different situations. Pointing to each object, taking a step or clapping hands as a number word is spoken helps to consolidate this understanding.

##### What is a number?

Then children need to understand what a number is; for example, they need to understand the ‘four-ness’ of things. They need to know that there can be four of many different things, and that not all fours look the same; e.g. four houses, four elephants, four fish, four plates, four buttons, four children, or a collection made up of four different things (not all items in a group of four need be the same). You will notice that each group of four in the illustration looks very different from the others.

##### Conservation of number

Children also need to understand conservation of number: four items are always four items, no matter how they are arranged; whether in a circle, in a square, close together, far apart, or in a line.

##### Subitising

The ability to subitise, to recognise how many objects there are in a small group without counting, is also important. Subitising avoids having to always count each item and helps with understanding addition; for example, “I can see there are four here and I can count on these: four, five, six, seven.”

### readilearn resources for teaching number understanding

Below is a selection of readilearn resources that support your teaching of number concepts.

#### Understanding of numbers up to ten

I Spy a counting game helps children to learn to count to ten by rote, count by ones, count with one to one correspondence, and recognise numbers, numerals and words.

One Lonely Ladybird is a rhyming, animated story involving counting up to ten.

Busy Bees and Insects – Subitising 1 – 6 is suitable for display on the whiteboard and shows groups of up to six insects in a random arrangement.

Busy Bees and Insects Subitisation Cards are suitable for printing and using with the whole class or small groups.

Exploring Number Combinations, a lesson ready to teach on the interactive whiteboard, helps to develop understanding of number, subitisation, recall of basic number facts up to ten, and problem-solving skills.

#### Understanding of numbers greater than ten

Busy Bee number lines and dice provides opportunities for consolidation of understanding of numbers up to twenty.

Busy Bees 100 chart  This interactive chart can be displayed on the interactive whiteboard and used for developing understanding of numbers up to 100.

Collect 100 flowers for Busy Bee — a counting game also provides practice in counting and understanding numbers up to 100.

Busy Bees celebrate 100 days of school provides suggestions for developing the concept of one hundred.

### Beginning place value

#### Understanding grouping

In our decimal system we organise items in groups of ten. It is beneficial for children to develop an understanding of grouping before they are expected to understand place value.

Playing games using smaller numbers is effective in introducing the idea of grouping. That way, when the base ten is introduced, children already understand the concept and it is only a small step to understand grouping in tens and place value.

#### The Train Game

A game I use to introduce this concept is The Train Game.

The game can be played with the whole class or small group.  Everyone is involved all the time. There is no waiting for another player to have a turn.

The game can be played daily over successive days until children fully understand the concept. Rushing won’t achieve a better result in the long term. It is more important to establish a solid foundation on which to build further understanding.

In the game, children use interlocking blocks to make groups of a “special” number; e.g. four. A large number of interlocking blocks are placed in the centre where all children can reach them.

Each day, the special number is introduced with a scenario; for example, “Today we are going to make trains. Each train must have four carriages.”

On a signal by the teacher (e.g. tapping a tambour, clapping hands), the children take one block and put it in front of them. With each block they take, children say how many they have; for example, zero trains and one carriage. The blocks are only put together when the special number is reached. As soon as they have the number (e.g. four) they must put them together to make a train. Then they would have one train and zero carriages.

The game finishes when the maximum number is reached.  (With base ten, nine is the maximum that can be kept in each place e.g. nine ones, nine tens, nine hundreds. If there are ten, they are moved to the next place. In this game there is no next place. If the special number is four, the game stops when they have three trains and three carriages. There is no need to explain why this is; simply finish the game there.)

More detailed instructions and other scenario suggestions for playing the game can be found in the resource Beginning place value – the train game.

When the children have developed the concept of putting blocks together, introduce the idea of bundling using popsticks and rubber bands.

The popsticks could represent; for example:

• balloons tied into bunches,
• fingers on hands,
• bananas in bunches, or
• flowers in vases.

The children may have suggestions for other scenarios.

#### Keep the learning going

##### Break up the trains

When the children have the idea of building or bundling into groups, introduce them to taking away.

After they have built their six trains and six carriages (e.g. for special number seven) explain that all the carriages need to be returned to the factory (centre) for servicing. They need to be returned one at a time.

This time when you clap your hands, they are to return one carriage to the centre.

When they have only trains and no individual carriages, ask for suggestions of what they could do to put one carriage back. Through questioning, help the children to realise that:

• they can’t take just one block off a train because a train must have seven carriages
• they will have to take the train apart (break it up and then put one back.

Continue until there are no trains or carriages. Each time, ask the children to tell you how many trains and carriages they have; e.g., five trains and six carriages.

By practising building and breaking up, they are learning the process of adding and subtracting across the tens, as well as the concept of place value.

##### Introducing tens

When the children are playing the game competently, introduce the “special” number ten, playing the game as before.

Play the game with ten for a few days using different scenarios.

Then begin using the terms “tens and ones”.

Give the children a tens and ones board.

(Make your own or print copies of the free readilearn Tens and ones board.)

Explain to the children that the loose ones must go on the ones’ side, and as soon as they are put together to make a tower (or train) of ten, they must go on the tens’ side. At every addition (or subtraction) ensure children say how many they have; e.g. five tens and six ones.

Introduce use of cards numbered 0 – 9 (also available as a free printable readilearn resource). Each child requires two sets of cards from 0 –9.

As they add (or subtract) each block and tell how many they have, they turn over the cards to show the number; for example, two tens and nine ones. (There’s no need to say the number names; e.g. twenty-nine at this stage. Use the number names when children notice for themselves.)

When the children have developed a good understanding of bundling and breaking up, they should have a good understanding of place value with 2-digit numbers. There are other readilearn resources that will help them consolidate that understanding.

They will be able to play games such as Race to 99 in maths groups. In this game, children roll a dice to find out how many blocks to collect. They form groups of ten and compete to be the first to collect 99 blocks.

The interactive resource Let’s read 2-digit numbers can be used on the interactive whiteboard with the whole class or for small group discussion and practice. Children observe the number of tens and ones and choose the correct 2-digit number from those shown.

Another interactive resource Let’s write 2-digit numbers can be used independently or to follow up Let’s read 2-digit numbers. Children write the number of tens and ones they see. They then check to see if they are correct and discuss how they knew or where they made a mistake.

In the Trick or Treat game for Halloween, children collect treats as they travel around a board. To extend the learning from the game, they could be asked to arrange their treats in groups of ten.

Turtle Tens and Ones can also be used in lessons and activities for developing understanding of place value.

This week I have uploaded new Flower domino cards to provide another activity for developing understanding of number. The dominoes can be used with the whole class, in small groups or by individuals. Dominoes are versatile and can be used in a variety of ways to develop understanding of number in maths groups. These are great when used in conjunction with the interactive resource Fun with Flowers or as part of a spring or minibeast unit.

##### Resources beyond worksheets – lessons for teachers made by teachers.

In college, I took a class called Math for Liberal Arts Students. Anyone who signed up for the class was admitting to math anxiety. Our instructor explained, as you do, that we likely missed a foundational step along the line. He brought math to life for us and explained foundations in a new way. I even was able to pinpoint what I had missed. I like your train game. These are great tools for teaching those foundations.

Norah Colvin says:

I love the sound of your maths classes, Charli. Having an instructor who brings maths to life would be amazing. How wonderful that you were able to pinpoint where you had misunderstandings and then correct them. I think if just take time to establish strong foundations in the beginning, it will all follow easily later on. When we rush too quickly into the abstract, children’s understanding become undone all too quickly.

A brilliant post, Norah. I have shared. I wish I knew more places to share this is so important and you advice is so good.

Norah Colvin says:

Thanks so much, Robbie. I’m pleased you see the value in the post and appreciate that you shared it. 🙂

Games and chores at home can go a long way towards building number sense and place value understanding. It is sadly amazing to me how math anxiety is created and excused at home and even in schools.

Norah Colvin says:

I agree. It doesn’t take a lot of effort to work maths into everyday activities. After all, we are using some aspect of it in most activities, including those as simple as setting the table and deciding the order in which we put on our clothes. It is sad that so many have an aversion to maths and it is often accepted as ‘normal’ as so many have a distaste for it.

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