# Monthly Archives: August 2017

## Digging Deeper into … Lines and angles

Category : Uncategorized

### Overview:

As can be seen from the overview table below, this topic is initially introduced to the children in 2nd class via “turns” and “square corners” and then develops with increasing complexity in 3rd- 6th classes.

 2nd 3rd 4th 5th 6th Lines vertical horizontal parallel perpendicular oblique Angles Full, half, quarter turns, square corner Right angle Greater/less than a right angle Acute angle Obtuse angle Straight angle Reflex angle Measuring and constructing in degrees Sum of angles in triangle  = 180° Sum of angles in quadrilateral  = 360°

As with every topic in Operation Maths, a CPA approach is also recommended for lines and angles:

• Concrete: allow sufficient time for the children to explore making turns, lines and angles with suitable concrete materials (e.g. the children themselves, lollipop sticks, straws, geo strips, construction materials, real-life examples from the school and home environment)
• Pictorial: activities where the focus is on drawing angles or lines on paper, MWBs etc
• Abstract: the final stage, where the focus is primarily on numbers,  digits  and or letters to represent variables eg given the measure of two angles in a triangle calculate the third angle.

### Lines:

Through exploration and activities, it is important that the children realise that:

• A line can be classified and identified according to its position and its relationship to another line.
• A single line can be horizontal, vertical or oblique but a single line cannot on its own be parallel or perpendicular; there must be two or more lines.
• Parallel lines do not all have to be the same length to be parallel.
• Parallel lines do not have to be horizontal or vertical, they can also be oblique.
• Perpendicular lines do not have to have a horizontal and vertical line, (again they can be oblique) but there must be at least one right angle where the two lines meet.

Lines can be drawn on the Operation Maths MWBs and then rotated to reinforce this point.
It is also worth noting that in maths, when we use the word “line”, it should be assumed that this is always straight; only if the word curved is given should it be assumed otherwise.

Watch: this video from Learnzillion about parallel, perpendicular and intersecting lines (suitable for 4th class up).

### Angles

“Two different types of experience of angles need to come together and to combine if children are to have a thorough understanding of the concept of angle…The first set of experiences is static. An angle is the shape of a corner. It may be sharp, or blunt, or right angled. Much more fruitful than the static conception of an angle is the dynamic conception of the measure of an angle. If a book is gradually opened, its pages make a growing angle with each other.”

### Williams and Shuard (1994)

In order for the children to recognise angles in terms of rotation, it is preferable initially, for the children to investigate the angles in their environment that are dynamic, (where the angle can be easily made bigger or smaller by increasing or decreasing the distance between the two lines) e.g. a door opening and closing, a scissors cutting paper, the angles made by the hands of a clock. The children can then proceed to examine static angles (where the angle is fixed) e.g. in 2-D shapes or 3D objects.

Operation Maths, Pupils’ Book 3: on the digital book, click on the icon on the bottom right to access a “Ready to go” activity.

In second class (and revised at the start of third class), the concept of rotation of an angle is taught through the terms quarter-turn, half-turn and full turn. Ideally, this should be introduced concretely by getting the children themselves to do half-turns and quarter-turns, and to turn in clockwise and anticlockwise directions:

• In the classroom, the children start facing the board/front of room and make half/full/quarter turns to left/right as directed by the teacher.
• Repeat, but this time with different starting points
• Repeat, but this time after the teacher gives the directions the children must say where they will be facing, before they do the actual turn. The children could also record their predictions quickly on their Operation Maths MWBs

The children will be also be asked to identify 90º angles as square corners (2nd class) or right angles (3rd class). This will also be reinforced as part of the 2D shapes chapter. The children can be asked how they might decide if a corner/vertex of a shape is a square corner/right angle. Prior to the introduction of the protractor, something as simple as a corner torn from a piece of paper would suffice as an instrument with which to measure these angles.

The children should be enabled to classify angles according to the criteria appropriate to their class level (see table above). In particular, the ability to identify angles as acute (or less than a right angle), obtuse (or greater than a right angle) or reflex will greatly help the children, to later, estimate the measure of the angle in degrees, and to accurately measure and construct angles when they encounter this in 5th  and 6th classes.

Operation Maths, Pupils’ Book 5

It is important to constantly reinforce the children’s understanding of what an angle actually is, i.e. an amount of turn and that this can be represented by two adjoining lines, one showing the starting position, the other showing the point after the turn. Return to concrete examples if necessary; the children stretch out two arms in front and, leaving one arm in original position, they move other arm a certain amount (90 º, 180º etc). This could also be repeated using geostrips, connected at one end using a brass clip, so as to be able to move one of the ‘arms’. Such concrete experiences also link well to measuring using a protractor; the original arm is  the ‘base’ line.

### Measuring and constructing angles (5th & 6th classes)

Operation Maths, Pupils’ Book 5

Using degrees to describe angles is introduced in 5th class, which develops to include measuring and constructing angles using degrees. This necessitates the use of a protractor for the first time, which in itself can lead to difficulties. The child may be unsure where exactly to place the protractor; this can come from a lack of understanding of what an angle actually is and where the angle actually is. Also, a child can be uncertain of which scale to use to measure the size of the angle eg for an acute angle measuring 45º, the child writes down 135º.

To reduce the likelihood of this arising you can ask some/all of the following questions:

• What important tips would you give to a person about using a protractor?
• How do you know which scale to use on the protractor?
• What type of angle is this? How do you know? (To save time, they can write A, O or Re for Acute, Obtuse or Reflex).
• Estimate the measure of the angle to the nearest 10º. Is your estimate/measurement sensible? Why?
• How can you use what you know about acute and obtuse angles to check your measurement?

You can also watch some of the tutorial videos for using a protractor on the internet, such as the one below, for example. These videos can be a very visual way of demonstrating this skill. This interactive tutorial is also very useful to demonstrate how to measure angles, while also offering the child a chance to practice them selves. See also the list at the end of the blogpost for many other interactive angle activities from the internet.

Angles is another area where it is important for the child to check the reasonableness of the answer. First, the child needs to identify whether the angle is acute or obtuse. Then, if measuring an acute angle, the measurement must be less than 90º. If it isn’t, then the correct scale wasn’t used.

### Lines and Angles all around us

It is a given that lines and angles are all around us, although children may often be oblivious to the examples! Again, appropriate to each class level, the children should be encouraged to identify different types of lines and angles in their classroom, school and home. Enrich your own classroom space with lines and angles by labeling the line types in the room and the measure of angles of the open door. Make it personal by relating this topic to the children themselves and to the geometry in their names. Incorporate lines and angles into your visual art lessons (see also image below). Operation Maths 4 and 5 users can show the Maths Around Us video to their class, accessible on www.edcolearning.ie. For more ideas, check out this Lines & Angles board on Pinterest.

Operation Maths, Pupils’ Book 4

### Online Interactive Resources

• Operation Maths users don’t forget to check out the extensive digital resources available for this topic on Edco Learning. These include Maths Around Us and Write, Hide, Show videos, Create Activities using the Clock and Fraction eManipulatives and full instructions for linked Scratch lessons.
• Math Games: Identify the parallel, perpendicular and intersecting lines
• Study Ladder: Identify parallel and perpendicular lines in shapes (you will need to register for a free teachers account, where you can also register your students if wished).
• That Quiz – Angles: A great interactive measuring test/practice. Ensure that only the “Measure” option on the left-hand side is ticked, and when you bring the mouse across the screen, it changes into a transparent protractor. Change the level on the drop-down menu also on the left-hand side to make the measurements required easier/more difficult. Another option is to use this quiz to calculate the value of a missing angle in a triangle; instead of ticking the “Measure” option, tick only “Triangle”. To find out more about the potential of That Quiz across all strands and subjects, please read on here.
• Measuring Angles: similar to the activity above, this offers more practice with an interactive protractor.
• This game from NRICH offers you an opportunity to improve your ability to estimate angles.
• Alien angles: Create a specified angle to destroy the aliens. Difficult but great for developing ability to estimate angles.
• Angle Kung Fu: Calculate the measure of the angle to beat your opponent
• Fruit Picker: Can you collect 6 apples in 6 shots?
• Guess the random angle: Use the onscreen protractor to measure the angle

For more interactive angles activities click here. For more general ideas, check out this Lines & Angles board on Pinterest.

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

## Digging Deeper into …. Place Value

Category : Uncategorized

### 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).

### 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.

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.

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).

Things 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.

### Place Value Online

To bring in the fun element, there are lots of simple games that the children can play to reinforce place value; check out some of these links for ideas:

• Place Value Activities: Including games, teaching ideas and loop cards (I have; who has) from Mathswire
• More Place Value Activities: again from Mathswire
• Place Value Games: using dice or cards, simple and adaptable to most classes
• Operation Maths users don’t forget to check out the place value games in the Games Bank of the TRB; relevant games are also conveniently listed in the Extra Exploration section of each daily plan in the TRB.

There are also quite a number of interactive games and activities for place value including:

• Place Value Games: Whole suite of online games, some of which also look at bigger numbers
• Rounding numbers: Interactive activities
• Operation Maths 3-6 users can also access a list of class specific online resources on the Weblinks document,  available as one of the downloadable documents that is part of the digital resources that accompany the digital Pupil’s book on edcolearning.ie

Programs that are useful teacher tools:

• Place value cards: This Interactive Teaching Program (ITP) allows you to explore place value up to 999
• Place Value Charts: Interactive activities involving making a given number, from thousands to thousandths

Other useful resources:

• Learnzillion have a whole suite of free resources and video tutorials, just sign up for a free teacher account to access them.
• That Quiz has a selection of place value quizzes, but as most start with 4-digit whole numbers it will only suit 4th class up. If you’re new to this excellent quiz site, find out more about it here.
• Number Talks: There is a whole set of number talks based on partitioning, or calculating by breaking up a number into its place value parts. To access a whole suite of free number talks resources, please click here. To find out more about Number Talks and Operation Maths, please read on here.
• Check out this Place Value Board on Pinterest
• Watch these related videos below from Origo One

This is 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.

## Operation Maths Quick-start Guide

Category : Uncategorized

Using Operation Maths for the first time? Here is a general quick-start guide for teaching the topics.

### Operation Maths for Junior Infants to Second Class:

1. Start with whole class warm-up and oral; see topic-specific suggestions in the Teacher Resource Book (TRB) or choose your own. Follow this with discussion questions (also in TRB).
2. Pair work, an activity based in the At School book.
3. Exploration of concrete materials via Maths Stations; again see topic-specific suggestions in the TRB.
4. Complete relevant activities in At School and At Home books. The introduction of the TRB includes a year plan that lists the relevant pages of each book per topic, along with other details such as strand and strand units. Bearing in mind that Operation Maths is based on a CPA approach, it is envisaged that the child would engage in all the concrete and pictorial activities for the topic before doing the pages in their books.

For more detailed information on managing the content with Junior Infants to Second Class please read on here.

For a quick-start guide to the digital resources, please read on here.

### Operation Maths for Third Class to Sixth Class:

• The Teacher’s Resource Book (TRB) for Operation Maths 3-6 is divided into daily sections, each dedicated to a specific learning outcome.
• Each topic has material for for either five or ten days, depending on whether it is a single/one week topic or double/two week topic. Double topics are indicated on the contents page of each book using an asterisk (*).

Teachers should start with the daily lesson suggestions in the Teacher’s Resource Book (TRB) as follows:

• Oral and mental starter
• Discuss and teach provides suggestions on how to achieve the learning outcome.
• Pupils’ book and/or discovery book: gives the details for the location of the specific questions that reinforce and consolidate the learning outcome(s) covered in the discuss and teach section.
• Digital Resources will briefly list any relevant digital activities that can be used from the comprehensive suite on edcolearning.ie . These are also referenced in the Pupils’ books as well and, if accessing the digital books, clicking on the hyperlinks in the Pupils Book will open the resource directly from the book (this is actually the easiest way to access the digital resources).
• Extra exploration: Suggested activity for early finishers.

Pupils’ Book & Discovery Book: Since Operation Maths is based on a CPA approach, the children’s experience of Operation Maths should not be a purely book-based one. That said, when navigating the children’s books, it will follow this general pattern:

• The topic (be it single or double), starts in the Discovery Book with the Starting Point activity (see example below), which revises familiar topics or sets the scene for new ones. There may often be no other book-based activities for Day 1.

• Subsequent “days” (excluding the last day of each topic ie day 5 or day 10) may focus on the Pupils book only, or move between the Pupils’ Book and the Discovery Book. On the days when both books are in use, icons are used to indicate when it would be most appropriate to move to the other book (see below)

The icon on the extreme bottom right indicates that the child should complete the companion activities on page 16 of the Discovery Book next. The icon to the left indicates that there is also a linked digital activity for this learning outcome.

When the child has completed the activities in the Discovery Book there is often a similar icon there, redirecting the child back to the Pupils’ Book.

• Consolidation is the focus of the last day of each topic i.e. day 5 or day 10. The children can complete the Learning Log activity in their Discovery Book either on this day or on the previous evening as a homework activity. They can also complete the topic assessment in
• their Pupil Assessment book.

For more detailed information on managing the content with Third to Sixth Class please read on here.

For a quick-start guide to the digital resources, please read on here.

If you are new to Operation Maths, we recommend that you:

• subscribe to the Operation Maths blog. This will ensure that you don’t miss out on any new post, as they will be emailed directly to you. To subscribe, just enter your email address in the box at the top right-hand side of this page.
• like/follow the Edco Primary Maths page on Facebook and/or Twitter to keep up-to-date on all the latest Operation Maths developments

## Operation Maths Jr Inf-2nd: Managing the content

Category : Uncategorized

As outlined in a previous post, Operation Maths 3 – 6 provides fulsome content for the senior classes. The complaints heard about other schemes – that there is simply not enough to do in the senior class books – is definitely not one heard about Operation Maths! At the junior end of Operation Maths – which is the focus of this post – the Teacher Resource Books (TRBs) are the jewels in the crown: the most comprehensive available and jam packed with the ‘how to’ of setting up maths’ stations, differentiation, oral maths, discussion topics, early finisher activities and a comprehensive stand alone problem solving section. And, since this programme is also based on a CPA approach, the TRBs are full of suggestions on how to promote those methodologies in a classroom.

Familiarity with any new programme takes time and time is a very precious commodity for all us teachers. Therefore, in this post I will give you some tips on how to successfully implement the programme in the junior classes – what in today’s game parlance our students might call ‘cheats’!

### 1. Start from the Teacher Resource Book

Start with the weekly lesson suggestions in the Teachers’ Resource Book (TRB). Typically these will be laid out as follows:

• A whole class warm-up and oral, designed to consolidate prior learning and lead logically into the lesson that follows. It is suggested that this lasts for 5-10 minutes  each day of the week, depending on content. While there are typically many suggestions here, it is not necessary to do all of them. If you find a starter that works particularly well, you could note this alongside the margin of your TRB, or in the notes section, to highlight it for future use.

The mini whiteboards are invaluable for this part of the lesson. Look out for children who lack the confidence or know how and are hesitant to write their answer or copy others. Encourage a growth mindset:
1. It’s okay to make mistakes, everyone does! We learn from them.
2. Often there is more than one correct approach; eg 17+19 can be modeled/thought of as move one to 19 to become 16 + 20, move 3 to 17 to become 20 +16, move one to 17 to become 18 + 18

• Discussion questions that stimulate talk and discussion in a relevant and meaningful way. Again, only do as many as suits your circumstance.
• Pair work, a book based activity to encourage co-operative learning. Modelling, especially when the concept of pair of group work is relatively new to a class, really sets the tone and promotes success. Choose a child to work with. Start the conversation:
• I went first the last time, would you like to go first today?
• Do you remember the first thing to do?
• I think we roll the dice twice and add the numbers, do you agree?
• Oh dear! Neither of us can remember what to do, will we quietly ask Tom?
• Will you watch me while I’m taking my turn just in case I go wrong? I’ll help you too!
• Stations: the organisation of these maths stations will depend on teaching style, the number of children, the ability level of the class and the assistance available from other staff members (SNAs, support teachers, etc.). And as with Pair Work it can take a little practice before the children approach stations successfully and productively – but it is well worth persevering! Station work promotes problem solving skills, group think and independence.The suggested stations can adapted in a number of ways:
• use with similar ability groups or mixed ability
• set up the activities at designated maths stations (tables or areas) which the class can rotate around eg 4 groups with 7 or 8 children per group; each group does two stations for 15 mins each for one class (30 mins total) and does the other two stations on the following day.
• Each group does a station for one class, with each group working at each station over the course of the week.
• Use the stations as a whole class activity e.g. on Monday all the class do the activities for station 1, on Tuesday do the activities for stations 2 etc. This does depend on there being enough of the required materials for the whole class to use them at the same time.
• Books: Bearing in mind that Operation Maths is based on a CPA approach, it is envisaged that the child would engage in all the concrete and pictorial activities for the topic before doing the pages in their At School and At Home books. Furthermore, sometimes it is envisaged that the concrete activities for the topic at hand will take place during one week, followed by the book activities in the subsequent week (this will be explained in a paragraph under the Activities heading in the weekly plan in the TRB). If you are teaching in a multi-class situation, it would be better to stagger/alternate these weeks among the classes eg Week 1, first class do the concrete activities while second class are mainly book based; week 2, second class do the concrete activities while first class are mainly book based.

### 2. You don’t have to do it all!

In the junior end TRBs,  the plans are laid out in fortnights which then break-down into weekly suggested activities. The important word here is “suggested”; you are not expected to do everything, so pick and choose the activities that are most suitable for you, your children, the physical limitations of your class and/or equipment, the availability of support personnel. For example there are Aistear-linked themes and activities in the infant TRBs, but if these don’t appeal to you, or are not practical in your specific situation, ignore them.

As explained earlier, there are regular suggestions for stations in the first and second TRBs and in places in the infant TRBs, but again if you don’t have available colleagues (eg L/S Resource teachers, SNAs etc) to help with the running of these stations, then they probably are not for you. However, you could take one or two of the station activities and instead do it with the whole class as the same time. The choice is up to you.

### 3. MWBs! MWBs! MWBs!

I can’t stress how fabulously adaptable are the free mini-whiteboards or how they can make getting through content so much easier. I was using them for many years before the inception of Operation Maths and found them to be an invaluable tool in the classroom. Some of the ways in which they can be used:

Give Doodle Time! The temptation to doodle is overwhelming so spare a couple of minutes for a quick doodle or two! Signal the end of doodle time with a fun rhyme such as “Rub, a dub, dub! Give your whiteboard a scrub!”

Display the ebook on your IWB for Write-Hide-Show: This works very well as the children are not looking down at their own books, only up at the board, so it’s easier for teacher to check that they are focused on the task. Highlight a specific calculation on the ebook eg 16 + 5 and ask the children to write the answer on their MWBs, hide it (place it face down on the desk, or hold it face in, to their chest) while the other pupils are afforded thinking time and finally on a specific signal (eg aon, dó, trí, taispeán dom) all the answers are revealed simultaneously. Thus, the teacher can quickly assess the accuracy of the answers and allow this feedback to inform whether the class are ready to move on, or need more reinforcement.

“Show your thinking” The children can use quick jottings to explain how they arrived at a certain answer. The MWBs are less structured and easier to use than maths copies and easier to change if you want to amend your ideas. Interesting responses or approaches could easily be brought up to the top of the class for further discussion and display. Again, encourage the growth mindset; mistakes and multiple correct answers are opportunities to learn more.

More maths done in less time. Rooting in bags, finding their book, pencil, rubber… this all leads to a delay in actually getting down to the maths at hand. Whereas, just writing on the MWBs is much quicker and gets more done. And don’t worry if the associated page in the pupils book is not completed; remember the teacher’s aim should be to enable the children to achieve a certain objective/learning outcome and however that is achieved still counts, book or otherwise.

Step-by-step to show algorithms: if you are teaching some of the standard algorithms (eg column method addition or subtraction in first and second class) the MWBs can be handy to allow the teacher and class to do it together, step-by-step, with the children holding up their MWBs at every suitable juncture to check what they have done to that point. This way, potential mistakes may be picked up quicker and addressed before they begin to occur repeatedly.

The plans are all done for you, the stations are all explained, the ideas are all there! This should significantly reduce the amount of time you were spending on maths preparation. However, it is still recommended to take the time at the beginning of each fortnight to go through the TRB and familiarise yourself with the content and the activities; this is time well spend that will translate into smooth running maths classes during the fortnight. But also be flexible, and don’t stick rigidly to everything.

One of the sections in the TRB where flexibility is advantageous is the photocopiables. There is a fantastic suite of resources here with great ideas, but don’t feel that if you don’t have 30 copies done in advance that you can’t use them. One example of this are the Yahtzee photocopiables in the TRB of Operation Maths 1. The children could simply write the target numbers ( eg 2-10, 2-20 or 0-5) on their whiteboards and cross them off when rolled. This also allows the game to be played repeatedly without needing other photocopies.

The one set of photocopies to have ready in advance are the Early Finishers and the Problem-Solving photocopiables. Initially, at the beginning of the school year, try to gauge how many copies you will need;you will probably not require 1 per child. As time goes on the number of copies of each can be adjusted, as necessary. These can then be kept near at hand to distribute to children in need of a more challenging or stimulating task.

### 5. Go digital!

The excellent suite of  digital resources available on Edco Learning can also aid efficient progress through content. The resources are very visual and help the child grasp a solid understanding of the concepts at hand quicker than might have occurred  otherwise. The resources can all be accessed directly via the hyperlinks in the digital books and it can be beneficial to have these tabs open in advance so as to save time during maths class. For more information on the extensive range of digital resources read on here

Teaching 3rd to 6th class? Read on to find out how to manage the content for those classes.