# Dear Family, your Operation Maths guide to Place Value

## Dear Family, your Operation Maths guide to Place Value

Category : Uncategorized

Dear Family, given below is a brief guide to understanding the topic of place value as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about place value. The digital resources are organised according to approximate class level:

#### Understanding Place Value

Place value is about exploring the base-ten number system we use: how our numbers are made up of digits, each of which represent different values, depending on their position or place in the number. In the senior classes the children will explore place value in numbers with a decimal point, as well as numbers without a decimal point (whole numbers).

No matter how large a number is, you really only need to know how to read a three-digit number, to be able to read any size number. This is because the digits are always organised in groups of three, as you can see in the image below. However, we do also need to know the significance of the commas. For example, three (3) million, six hundred and twenty-three (623) thousand, nine hundred and fifteen (915) = 3,623,915: the comma closest to the units is read as thousand, the next comma is read as million, etc.

At its most basic level, central to understanding our place value system, is to recognise that 10 single items or units or ones, can be grouped together to make a ten; that 10 tens can be grouped together to make a hundred; that 10 hundreds can be grouped together to make a thousand etc. In school, the children have lots of different materials that they can group together, or exchange, such as cubes, bundles of sticks, counters on ten frames and place value discs. At home, the children could bundle cotton buds or cocktail sticks or trading cards into groups of tens and fasten them with an elastic, or group identical pieces of lego into sticks of ten, or count out beads or buttons or pieces of pasta into small containers or bags as groups of tens.

In school, the type of place value learning experiences that the children have, are very similar at every class level; the main difference is that each class level will have different number limits. In school, we expect that by the end of first class, most children will understand place value in numbers up to 99, in second class up to 199, in third class up to 999, in fourth class up to 9,999, in fifth class up to 99,999 and in sixth class there is no limit … millions, billions, trillions even!

That is not to say that you should limit your child to the number limit for his/her class level. In reality, children will encounter much larger numbers in the real world, than they will encounter in their maths book, so feel free to throw bigger numbers at them. But, bear in mind that, even if a child can read or say a complicated number, it doesn’t necessarily mean that they understand its place value.

#### Practical Suggestions for Supporting Children

• Ask your child to read out loud any numbers they meet around your home and in the wider environment, e.g. numbers on signposts, car registrations, the number of pieces in a jigsaw, page numbers on catalogues, the numbers on houses or hotel rooms, larger numbers on fact books e.g. Guinness Book of World Records, recorded times for races, etc.
• Correct language: When you are talking about numbers be careful to use the correct language e.g. for 91,856 say ‘ninety one thousand, eight hundred and fifty six’ not ‘nine-one-eight-five-six’ and for 23.95 say ‘twenty three point nine five’.
• Zero does not equal ‘oh’! It’s an unfortunate convention, but the way we talk about numbers every day can often be mathematically incorrect and/or misleading. For example, when calling out a mobile number, that starts with 08….. we will likely say ‘oh eight‘…… Yet 0 is a digit called zero, whereas O or ‘oh’ is a letter of the alphabet and not a number at all! So, when verbalising numbers with zero, try to get into the habit of saying ‘zero’ instead of ‘oh’.
• Numbers that end in ‘-teen’ or ‘-ty’ can be difficult for some children. In particular, some children can have difficulty hearing the difference between numbers ending in ‘-teen’ and ‘-ty’ when they are spoken out loud, e.g. ‘fifty’ (50) sounds very like ‘fifteen’ (15) when spoken, yet their values are very different. Try to say these type of numbers clearly, and encourage your child to say them clearly also, so that they appreciate the difference between these similar-sounding numbers.
• Rounding large or awkward numbers is something we do to make them easier to say or report. For example, if there was 91,856 people at a concert or a match, the media might report that there was just over ninety thousand or there was almost ninety two thousand people in attendance. When you encounter numbers in the media, encourage your child to round them; ask him/her what the number would be roughly/approximately. If you come across a number that has already been rounded, together you could guess/speculate as to what the exact number might have been.
• Make place value fun!
• Play counting games on car journeys, e.g. each child in the car picks a colour and counts every car of that colour that they see or meet on the road. The winner is the person who hits the highest number before the driver’s patience wears out!
• Race to the page! Challenge your child to try to find certain page numbers, in books with plenty of pages, as quickly as they can. Use a dictionary or other reference book, or even an Argos catalogue and call out a page number, for example ‘three hundred and ninety’ and see how quickly that page can be found. If you have more than one copy of a suitable big book or catalogue, two players can race against each other.
• Play some simple place value games using dice or playing cards
• Play any of the online interactive games below

#### Digital Resources for First and Second Classes

Khan Academy – Intro to Place Value: this video and the videos that follow, explore place value in 2-digit numbers and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other areas of Grade 1 maths.

Happy Numbers – Place Value Activities: A series of lessons and activities; do activities from Module 4 and/or 6.

Maths Visuals – Counting by one: Watch any of the videos and count out loud the numbers and images that are shown. Do you spot any patterns?

Maths Visuals – Counting above 100: Watch any of the videos and count out loud the numbers and images that are shown. Do you spot any patterns?

Maths Visuals – Place Value Concepts: Watch any of the videos and count out loud the numbers and images that are shown. Do you spot any patterns?

White Rose Place Value: a series of lessons on place value within 20. These lessons could be followed up with other place value lessons in year 1 or year 2

Place Value Grouping Video: Watch a video of how ones (units) can be grouped into tens, to make various numbers.

Candy Machine: Help make up the orders of candy sticks by using bundles of tens and ones

Dienes Penalty Shoot Out: Identify the number of counters and create numbers using Dienes blocks (aka Base Ten Blocks). Choose game mode to earn penalty chances, and then numbers up to 20, 50 or 100.

Place Value Basketball: Select the correct number to match the image. Work your way up through the various options/levels.

Lifeguards: Click and drag into the place value grid, the correct number of place value discs to make up the given number. Choose between 0-50 or 0-100 options. You can also play a similar game called Shark Numbers

Maths Goalie – Reading numbers:  Read the numbers in word form and then input the same number but in standard form. Choose reading numbers, and then number to 20 or 100.

Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then T O (Tens and Ones) in either column.

Rocket Rounding: A multiple choice game involving rounding numbers: start with rounding numbers up to 99 and with the easier option of having a number line and then try to play the other more difficult option, no number line.

Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct number on the number line, but then the game progresses in difficulty as the player must work out where a given number would be placed on the blank number line. Choose the whole number game.

I Know it! Place Value: Scroll down to place value to do any of the activities. For children at the beginning of first class try Place Value up to 20, Base Ten blocks up to 20 and Count to 100 instead. There are some more advanced activities in the second grade section.

Splash Learn – Place Value: An assortment of place value games organised according to US grade levels; start with the grade below your current class level i.e. for first class pupil’s start with Kindergarten games and for second class pupils start with first grade games.

Place Value: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)

#### Digital Resources for Third and Fourth Classes

Khan Academy – Place Value: in this video and the videos that follow, explore place value in 3-digit numbers and then answer the practice questions (says Grade 2, but is suitable for 3rd class). Fourth class student can access similar activities for 4-digit numbers and larger here. You can also register for a free Khan Academy account to record your progress and explore other topics.

Happy Numbers – Place Value Activities: A series of lessons and activities; for numbers up to 1,000 do Module 3. For rounding to the nearest ten and hundred do Module 2 here.

White Rose Place Value: a series of lessons on place value suitable for 3rd class. These lessons could be followed up with other place value lessons in year 3 or year 4

Place Value House: video lesson that explores hundreds, tens and ones (units), suitable for 3rd class.

Expanded Form: A video that introduces expanded form and explains how we can expand numbers to see the parts that make it, suitable for 3rd class.

Dienes Penalty Shoot Out: Identify the number of counters and create numbers using Dienes blocks (aka Base Ten Blocks). Choose game mode to earn penalty chances, and then numbers up to 1,000 or 5,000.

Place Value Basketball: Select the correct number to match the image. Work your way up through the various options/levels.

Lifeguards: Click and drag into the place value grid, the correct number of place value discs to make up the given number. Choose between 0-500 or 0-1,000 options. You can also play a similar game called Shark Numbers

Maths Goalie – Reading numbers:  Read the numbers in word form and then input the same number but in standard form. Choose reading numbers, and then number to 1,000 or 10,000.

Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then either H T O (for third class) or Th H T O (for fourth class) in either column.

Rocket Rounding: A multiple choice game involving rounding numbers to the nearest 10 or 100, up to 999 or 9,999. Start with the easier option of having a number line and then try to play the other more difficult option, no number line.

Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct number on the number line, but then the game progresses in difficulty as the player must work out where a given number would be placed on the blank number line. Choose the whole number game.

I Know It! – Place Value: Scroll down to place value to do any of the activities with suitable number limits. There are some more advanced activities in the third grade section.

Splash Learn – Place Value: An assortment of place value games organised according to US grade levels; start with the grade below your current class level i.e. for third class pupil’s start with second grade games and for fourth class pupils start with third grade games.

Place Value Games: An assortment of place value games using numbers of various sizes. Third class pupils should start with games up to 999 (three-digit numbers) and fourth class should start with games up to 9,999 (four-digit numbers)

That Quiz – Place Value: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. In place value, the lowest level is 3. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. There are lots of different types of activities: For Identification (it automatically starts on this) you must identify the value of certain digits; other options are conversions, rounding and sums.

Place Value: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)

#### Digital Resources for Fifth and Sixth Classes

Khan Academy – Place Value: in this video and the videos that follow, learn about place value in larger numbers and then answer the practice questions. You can also access similar activities for decimal numbers here. If you register for a free Khan Academy account, you can record your progress and explore other topics.

Happy Numbers – Place Value: A series of interactive lessons and activities on numbers up to one million. Do Module 1 Topic A, B and C

White Rose Place Value: a series of lessons on place value suitable for 5th class. These lessons could be followed up with other place value lessons in year 5 or year 6

How big is a billion? It is very difficult to visualise the size of a million, or a billion, of anything. This video demonstrates the length of a thousand, a million, and a billion coins if they were placed top to bottom.

Maths Goalie – Reading numbers:  Read the numbers in word form and then input the same number but in standard form. Choose reading numbers, and then numbers to 1,000,000 or 10,000,000.

Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then either whole numbers or decimal numbers, in either column.

Rocket Rounding: A multiple choice game involving rounding numbers, using whole numbers or decimal numbers. Start with the easier option of having a number line and then try to play the other more difficult option, no number line.

Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct number on the number line, but then the game progresses in difficulty as the player must work out where a given number would be placed on the blank number line. Choose the whole number or decimals game.

Who wants to be a Hundredaire? Game show-like quiz based on place value.

I Know It! – Place Value: Scroll down to place value to do any of the activities with suitable number limits. There are some more advanced activities in the fourth grade section.

Splash Learn – Place Value: An assortment of place value games organised according to US grade levels; start with the grade below your current class level i.e. for fifth class pupil’s start with fourth grade games and for sixth class pupils start with fifth grade games.

Place Value Games: An assortment of place value games using numbers of various sizes. Fifth class pupils should start with games up to 99,999 (five-digit numbers) and sixth class should start with games above this. There are similar games based on decimal numbers accessible here.

That Quiz – Place Value: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. In place value, the lowest level is 3. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. There are lots of different types of activities: For Identification (it automatically starts on this) you must identify the value of certain digits; other options are conversions, rounding and sums. Sixth class pupils looking for a challenge could try scientific notation.

Place Value: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)

## Digging Deeper into …. Place Value

Category : Uncategorized

For practical suggestions for families, and links to useful digital resources, to support children learning about the topic of place value, please check out the following post: Dear Family, your Operation Maths Guide to Place Value

### Place Value: A Fundamental Concept

When the new school year starts in September, for nearly every pupil from third to sixth class, the first mathematical topic they encounter is place value. This placement is logical; place value is the strand unit from which nearly all of the subsequent number, and measure, strand units build.

On the surface, place value may seem like it is one of the easiest topics to teach; the traditional activities simply involve counting dots on a notation board and/or beads on a place value abacus and, because of this, it is often viewed as an easy topic to kick-start the school year. And, it may appear to the teacher that the children have “got” it…..especially when they are getting all the correct answers in their books. However, it’s usually only later, when difficulties start to arise, often with operations or measures, that the teacher might start wondering “did they really get it?”

Place value is one of THE most important topics in primary mathematics, in that a child’s understanding of the fundamental concepts of place value will greatly impact on their understanding of almost all the other strand units, especially in operations, decimals and measures. Therefore, it is vital that teachers allow sufficient time for the children to explore this topic, moving from experiences with suitable concrete materials (e.g. base ten blocks) to pictorial activities (e.g. drawing base ten materials to represent a given number) and finally to abstract exercises, where the focus is primarily on numbers and/or digits.

That is why Operation Maths has a dedicated block of two weeks devoted to place value in third to sixth classes, and four weeks across the school year in first and second classes, so that there is sufficient time to explore the topic concretely and pictorially. This approach of moving from concrete to pictorial to abstract experiences is generally referred to as a CPA approach.

Indeed, spending sufficient time on meaningful activities now, may reduce potential hurdles later on. Furthermore, revisiting place value activities throughout the year, will allow the children to have ample opportunities to continuously revise and reinforce their understanding. One way to do this is to explore a Number of the Day on a regular basis; use the templates towards the back of the children’s Discovery Books or use the Number of the Day photocopiable in from the Teacher’s Resource Book (TRB). Indeed, a user of Operation Maths reported back to us “I found doing the ‘Number of the day activity’ as often as possible in September is crucial to the ‘Place Value’ chapter”.

### CPA

Concrete materials are key to the children developing a good conceptual understanding of place value. The children need lots of opportunities, in all classes to explore and manipulate a variety of base ten materials. Where suitable/available, these should be introduced in the following order:

• Groupable materials that the children can physically put together in collections of tens and physically take apart. These include lollipop/bundling sticks, straws (counting straws or ordinary drinking straws), unifix/multilink cubes, ten frames and counters etc.

Example of groupable materials: bundling sticks. Example of grouped materials: base ten blocks

• Grouped materials are those already pre-grouped as tens, hundreds, etc., e.g. base ten blocks (also known as Dienes blocks) and/or ten frame flash cards with a pre-set number of dots/counters. These can’t be physically taken apart or combined, instead exchanging/swapping is required.
• Lastly, non-proportional base ten materials.  These are materials that still operate on a base-ten system, but are not proportional to their value i.e. the piece that represents a ten is not ten times the size of the piece representing the unit. Examples include money and place value discs. Money in particular has the advantage that it can also be used to represent decimals i.e. 10c is one tenth and 1c is one hundredth of the unit (euro).

However, money is also limited in that it can only be used to represent numbers up to 999.99. This is where the Operation Maths place value discs become extremely useful. Inspired by similar discs used with Singapore Maths, these cut-outs are included in the free ancillary resources that accompany the scheme and can be used in conjunction with the place value mats on the inside back cover of the Discovery Books. With these discs, it is possible to concretely represent numbers up to 99,999, which had not been possible, using resources available in Ireland, prior to the publication of Operation Maths.

When exploring concrete or pictorial representations of numbers, most children will not have much difficulty interpreting the number once it is presented in the typical, canonical arrangement, i.e. 345 as 3H 4T 5U. However, many children may struggle
to interpret the number correctly if it is presented in a non-canonical arrangement, e.g. 345 as 3H 3T 15U or as 2H 14T 5U. Including activities based on these less common, non-canonical arrangements can encourage children to better understand the relationship between the places and can allow you to better assess the depth of the children’s conceptual understanding, while also preparing them for regrouping.

Operation Maths users can also use the excellent Place Value e-Manipulative, accessible on www.edcolearning.ie. This manipulative can be used to show blocks, straws, money or discs to represent a variety of numbers up to 99,999 and to two decimal places.

1. Log into your edcolearning account
2. Click on the Pupil Book icon for your class level.
3. Click on the Edco Resources icon (on book cover image on left-hand side)
4. Select e-Manipulatives from list of categories and then Place Value e-Manipulative.

Read also this post from Beyond Tradition Math showing children representing three-digit numbers in various ways. And watch this video from Origo One on using Numeral Expanders to show expanded form.

### Whole Numbers and Decimal Numbers

Since whole number place value and decimal place value are inherently linked, in Operation Maths for 5th and 6th classes, in the topic of place value the children will explore both whole number and decimal place value together in a very holistic way, thus reinforcing their connectedness, within this strand unit.

While place value understanding includes both whole and decimal numbers, it is important that the children appreciate the differences between them. For example, whole numbers and decimal numbers differ in the variety of correct ways in which they can be written. One ten in standard form is usually written as 10; however, one tenth can be written as 0.1, .1, 0.10, 0.100, etc. For decimals, many teachers often only use one form, usually 0.1, fearing that a variety of ways may confuse children. Conversely, using a variety of ways can actually help reinforce children’s understanding that all of the above forms show one tenth (i.e. a 1 in the tenth place immediately to the right of the decimal point), with most forms (excluding .1) having unnecessary zeros (i.e. in 0.3 the zero is unnecessary; without it the value is still 3 tenths). In other numbers, zero acts as a necessary placeholder between the digits in the neighbouring places; in 30 and .304 the zeros are necessary: without them the values would be 3 units and .34 respectively.

### Verbalising Numbers

For most of our number system, we read numbers in the order that we see the digits, e.g. 345 is three hundred and forty-five. However, the numbers from 11 to 19 are an exception, and as such can present extra difficulties for struggling children. Even for the child who begins to appreciate the meaning of ‘-teen’ as ‘and ten’, the numbers 11 and 12 are additional exceptions to this pattern. Some children may also have difficulties with the -ty numbers (e.g. 120, 130, 140) and in particular may confuse them with the similar -teen number, especially in its verbal form, e.g. fifty vs. fifteen. Even children in the middle and senior classes can struggle to distinguish between the -teen and -ty numbers and it is worth being aware of them as potential hurdles, during this topic.

The children should be given ample opportunities to say numbers out loud, with the emphasis being on the use of correct language to reinforce the concept, and the place value of each digit. One way to do this is to allow individual children to call out the numbers/answers when getting feedback or when correcting. Even when using the Operation Maths MWBs, ask a child each time to say what is written on the board. Encourage all adults supporting the children, including other teachers, assistants and parents, to use the correct word forms when reading out numerals. For the number 2,150, adults may say ‘twenty one fifty’, or ‘two one five oh’ instead of two thousand, one hundred and fifty. When verbalising zero make sure that zero is said instead of ‘oh’: O is a letter of the alphabet and not a digit (In your Operation Maths TRBs see also the Home–School Links section and the ‘Dear Family’ letters in the photocopiables section).

Regarding decimal numbers, the children can use both decimal language and/or fractional language, i.e. expressing 7.381 as seven point three eight one and also seven and three hundred and eighty one thousandths. Using fractional language to read decimals reinforces the value of the digit(s) in the decimal place(s). However, when using decimal language, it is incorrect to say ‘seven point three hundred and eighty one’, as this refers to hundreds and tens (–ty) which are both whole numbers.

### Number Sense and Visualisation Skills

What is bigger; 12.352 or 12.952? When ordering or comparing, children may use a procedure of comparing digits, which involves examining the digits and realising that both numbers have 1 ten, both have 2 units and the first has only 3 tenths, while the second has 9 tenths, so it is bigger. While this procedure may work successfully, it does not encourage the child to visualise the quantities involved. It would be better for the child to recognise that 12.952 is almost 13 and 12.352 is only a little more than 12 and is therefore smaller. Similarly, with younger classes, it is better for the child to recognise that 52 is just a little more than 50 whereas 58 is almost 60. Asking the children to place the numbers on an empty number line (see below) is an ideal way to promote the development of these visualisation skills. Empty number lines are also a great visual strategy to use when rounding; when rounding 12.352 to the nearest unit we can see that it is between 12.3 and 12.4 so it is closer to 12. The children can use the partial number lines in their Discovery Books as an introduction to this method and then be encouraged to solve the rounding activities in their Pupils’ Books by drawing their own number lines, either on their MWBs or in their copies.

When considering rounding, it it worth noting that it is preferable to use the phrase ‘round(s) to’ as opposed to ‘round(s) up’ and ‘round(s) down’ as these can confuse many children. For example, some people may say the number 69 rounds up to 70, which makes sense since the digit in the tens place has gone up from 6 to 7. However, if a child realises that 43 should be rounded down, they might change it to 30 instead of 40, since that looks more correct to them, i.e. the tens digit has gone down to 3.

For another idea on how to use number lines to aid rounding, please check out this short video from Origo One

Some traditional tasks and activities for place value regularly seen in maths books can give an incorrect picture of a child’s understanding of the concepts of place value. For example, tasks that involve no more than the children identifying the number of identical dots on a notation board, or the number of identical beads on a place value abacus (see opposite), are not good indicators of a child’s understanding of place value, as they are simply demonstrating their number knowledge of numbers to 9. Therefore, these types of tasks have not been included in the Operation Maths series.

### Bigger Numbers

It is vital the children realise that the digits in larger numbers are organised in groups of three with commas as the digit group separators. Insist that the children also use commas in this way, and reiterate that if you can read a three-digit number you can read any size number as long as there are commas present and that you understand the role of the different commas (i.e. one comma means thousands, two shows millions etc.). Interestingly, using commas as digit group separators is a convention largely in English-speaking countries , and other European countries tend to use stops/point or spaces. It is a good idea to highlight this to the older classes, as is done in Operation Maths 6.

It is also worth noting that the concept of the size of a thousand or the size of a million is in itself quite abstract for children. When tackling the large numbers, use all available opportunities to make them real and relevant to children. There is a Maths Around Us video available in the digital resources of Operation Maths 6 made for this purpose; just click on the hyperlink when accessing the digital book.

Also worth noting, is that Operation Maths explores numbers up to 5 digits (whole numbers) in 5th class and through millions in 6th class. However, in the curriculum there is no number limits in 5th and 6th class, therefore the children should not necessarily be limited to these numbers, particularly if they encounter bigger numbers in their environment, books, media, etc. The content in Operation Maths for these classes is deliberately presented in such a way as to encourage children to address numbers above millions where appropriate.

### Place Value in the Environment

As mentioned mentioned previously, it is very important that the children can relate their understanding of place value to numbers around them. To reinforce the relevance of place value, ask the children to collect examples of numbers from the environment. This could include photographs of numbers in the school grounds or locality e.g. car registration numbers, distances on road signs (for Operation Maths 3 users, check out the Maths Trail in the car park, on page 4 of the Discovery Book) . It could also include examples of numbers from print media e.g. newspapers, magazines. In the older classes, you could challenge the children to find an example of a very large number and/or one with the most places of decimals (Operation Maths 6 users, check out the Maths Trail on the internet, on page 6 of the Discovery Book).

What to do with the numbers that the children locate:

• Make a display for the classroom with the examples, in order of size, and giving information for the fact it relates to e.g. the distance to the nearest town etc
• For each example the children find, they must write out the number in word and expanded form (it will likely be in standard form)
• Round the number to the biggest place i.e. if the number is 312 round it to the hundreds, if it’s 0.012 round it to the hundredths etc.

### Further Reading and Resources

This was the first in a series of “Digging Deeper into …” posts, which will take a more in-depth look at the various topics in primary maths. To ensure you don’t miss out on any future posts, please subscribe to the blog via email, on the top right hand of this page.

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