Month: August 2018

Digging Deeper into … Counting and Numeration

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Category : Uncategorized

For practical suggestions for families, and links to useful digital resources, to support children learning about the topic of counting and numeration, please check out the following post: Dear Family, your Operation Maths Guide to Counting and Numeration.

Counting and numeration are listed as strand units in the strand of number for Junior Infants, Senior Infants, First and Second Class in the Primary Maths Curriculum (1999) and counting and numeration at each of these classes require similar skills, although the range of numbers will differ. However, while counting and numeration is specified as strand units only in infants to second, the understanding required is just as relevant and as important in the higher classes e.g. counting with larger numbers, counting fractions, decimals, percentages, etc.

Learning to count: rote versus rational counting

You are probably all familiar with the scenario: a parent declares that their pre-school age child can count because they can rattle off numbers to ten! As we all know, counting involves much more that just listing off numbers (rote counting). Watch this one minute video, which synopsises the difference between rote and rational counting.

While rote counting is relevant when learning to count, to count with understanding (i.e. rational counting) depends on the child developing an appreciation of rational counting, via the five counting principles, (briefly outlined in the video above); each of these counting principles are explained further in these follow-on videos from Origo Education:

HINT: For more information on the Counting Principles, including suggestions on what to look out for and what to ask/do, check out this blog post.

Apart from rattling off numbers, a child’s main interest in counting is to identify the quantity of objects in a set. “How many cars do you have? I have six cars”. Cardinality is using counting to find out “how many”.  And, since most of the sets that children will encounter, and will want to count, will be randomly arranged, then teaching the order-irrelevance principle will probably be most relevant to the children themselves. Therefore, the children must develop some strategies to ensure that they count every object, once only:

  • Count and tag: as each item is counted it is touched (this works quite well if the set to be counted is already in a line, or a rectangular array, but doesn’t work as well with scattered sets .
  • Count and push/put: as each item is counted it is pushed to the side or put into a pot, tray etc.
  • Count and mark: put a mark beside each item as it is counted; this works well for pictorial representations that cannot be physically moved.
  • Count and group: in the case of large collections (for example in first and second classes), rearrange the objects into “friendly” groups (eg two, tens or fives) that the children can easily skip-count. Using the Operation Maths frames and structures to help to reorganise the objects can be of particular benefit.

This ability to demonstrate one-to-one counting should not be taken for granted; while it seems quite a simple concept, many children can struggle. Therefore, when the focus is on the cardinality of counting (establishing how many), all counting activities should be counting something; lining toys up and counting how many by tagging each one, etc.

When observing children as they count, check:

  • Do they “tag” each object as they count (eg pushing them aside)?
  • Can they count regular arrays or rows?
  • Can they count random groups in some sort of systematic way so that they don’t miss or double up on objects?
  • Can they count the same set several times, starting with a different object each time?
  • Can they show how rearranging the objects does not change the quantity?

HINT: use relevant number rhymes and stories to reinforce counting and number word sequence. Many of the short-term plans (STPs) in the Operation Maths TRBs list various possibilities; see the Literacy suggestions in section on Integration

Counting without Counting!

When can you count without counting? When you subitise! Subitising is the ability to recognise a quantity at a glance, without counting. When you throw a five on a die, usually it is not necessary to count the individuals dots; we recognise that there are five dots from their shape. So, while it is very important that we spend significant time practising one-to one counting initially, this is not the most efficient approach, and we do want the children to progress to a point where they do not need to count each item/object individually.

Ways to promote subitising:

  • Play lots of dice and domino games; the Operation Maths TRBs have game suggestions and station activities in every STP plan, many of which are based around dice etc.
  • Use the Operation Maths frames: the visual layout of various numbers in the frames (see image below) encourages the children to internalise a picture of how the numbers look and to recognise this in other situations.
  • Play dot flash: briefly show the children dot cards in various arrangements and ask them to tell you what they saw. There are photocopiable dot cards at the back of the Operation Maths TRBs for this purpose.
  • Use other structures that have a definite layout eg rekenreks (or maths rack) can also be used. This visual structure features quite strongly in the Number Talks presentations for junior infants, senior infants and first class, all available at the link above.
  • Arrangements of Base Ten blocks, bundled sticks and/or place value discs can also be used.
  • Use online games (eg Number Flash from Fuel the Brain) and/or suitable apps (such as this free one)

HINT: For more suggested subitising activities read this blog post Counting With Your Eyes

Numeration

Numeration involves the children being able to match a numeral and its matching number word to each other and to various different arrangements of objects (both identical and non-identical) of that amount eg 3 = three = 🏀⚾⚽ = 🚗🚗🚗.

As the children move into first and second classes, numeration will move beyond the numbers to ten, through the teen numbers and all the way up to 199. Numeration in these classes involves much more than just matching a quantity to the numeral and to the number word:

  • The children need to appreciate the visual pattern of numbers in sequence: 20, 21, 22, 23, 24, 25, 26…
  • The children need to recognise the patterns in the number word sequence when spoken: “twenty one, twenty two, twenty three, twenty four…”
  • From this understanding the children should be able to count forwards and backwards from various starting points. They should also be able to identify the number before or after a given number.

Visual structures, such as the Operation Maths 100 Square e-Manipulative (see below), can be very useful, as:

  • they provide the numbers in order
  • the patterns can be easily identified
  • individual squares and/or large sections can be hidden and then revealed for the children to test their ability to identify preceding and subsequent numbers in a sequence.

HINT: Particular attention should be given to the multiples of ten ie the “ty” numbers and a deliberate distinction should be made between the “ty” numbers and the “teen” numbers, especially when being verbalised i.e. there is little difference verbally between eighteen and eighty, but there is a significant difference between these numbers in value . Like the “teen” numbers, “ty” numbers are also widely acknowledged as common hurdles for children and so time spent now will be time well spent for the future. 

Further Reading and Resources:

This is part of the series “Digging Deeper into …” which takes 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.

Digging Deeper into … Early Mathematical Activities

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Category : Uncategorized

For practical suggestions for families, and links to useful digital resources, to support children learning about the topic of Early Mathematical Activities, please check out the following post: Dear Family, your Operation Maths Guide to Early Mathematical Activities. 

Early Mathematical Activities (EMA) is a strand in the Primary Mathematics Curriculum (1999) for children in junior infants only, although the activities might also be suitable for children in senior infants as revision, as well as being suitable for many children in their final preschool year.

It includes the strand units of:

  • Classifying
  • Matching
  • Comparing
  • Ordering

While comparing and ordering appears as a strand unit also in the strand of Number, for EMA the emphasis should not be on using number or counting to describe relationships, rather on the attributes themselves. However, once the children have been introduced to the numbers,  the early mathematical activities can be repeated, but now to include using the opportunities presented to incorporate numbers or counting to describe relationships.

Sets

EMA is fundamentally all about sets; a set is any collection that has been grouped together in some meaningful way. Sets are all around us, and much of a young child’s exploration of the world involves the child seeing things in terms of sets e.g. my toys, the set of toys that belong to me as opposed to all other toys. Sets are also fundamental to developing an understanding of number and operations: numbers are used to describe the quantity in a set;  a quantity will be removed from a set to model subtraction etc.

Matching

Although classifying is listed before matching in the Primary Mathematics Curriculum (1999), matching is actually less complex, as typically we understand matching as completing a pair, whereas classifying is typically interpreted as organising a collection into two or more subsets. For this reason, in Operation Maths for junior infants, the children first match pairs of identical objects (reinforcing one-to-one correspondence), using the language same for those that match and different for those that don’t match.

  • Start with a limited amount of objects e.g. eight, where each has a match that is the same (ie fully alike). This can be demonstrated using real objects and/or on the class IWB, using a representation of real objects, using the Operation Maths Sorting e-Manipulative (see image above).
  • Working with a small group of children, isolate one of the objects and ask a child to “find the match/find the one that is the same” i.e. identify the other that is fully alike, and most importantly, to verbalise why it is the same and therefore the correct match. In this way, you are asking them to justify their choice using the language of the attributes.
  • The children can also be asked to orally justify why certain objects are not the same/are different.
  • Initially, you can use objects where each pair is completely unlike the other pairs e.g. four different shapes, in four different colours. Then, progress towards collections where, while there are like objects, there is only one match that is fully alike/exactly the same (see example above).
  • To make this task more complex:
    • introduce more attributes (e.g. size) and a larger range of attributes (e.g. more shapes and colours).
    • increase the size of the collection
    • remove/conceal an object and ask the children to identify the object which now has no match and to use this to be able to describe the object that has been removed/concealed.
    • See also the Clothesline activity in the Junior Infants TRB (p 16). The materials could be expanded to include gloves as well as socks. Initially try to ensure that there is two of everything (in order to make complete pairs). When the children locate the matching items, they should explain why they are the same, before hanging them up using clothes pegs (clothes peg activities have the added advantage of developing pincer grip and fine motor skills necessary for correct pencil grip). A development of this activity if the teacher deems it suitable: include odd socks/gloves and observe how children react. Use questioning to elicit their own “rules” for dealing with these and how they might describe them. If appropriate, use the opportunity to discuss and introduce language such as even, odd etc., if the children do not suggest this terminology themselves.
    • For further experience using one-to-one correspondence, the children should also have opportunities to match pairs of related objects,  i.e. objects that are not the same, but that purposely go together,  e.g. putting out knives and forks, buttoning coats, putting lids on boxes/tubs. Again, many of these activities, using objects from the children’s daily lives, will also be useful for developing and strengthening fine motor skills.

HINT: Commercial products such as attribute bears, shapes and people are very useful for all EMA and may appear to even be the most suitable material because the attributes, and therefore the “rules” that govern a set can be deciphered clearly. However, they can also be limited, in that there is little negotiation required. Thus more arbitrary materials, such as items from nature (stones, rocks, leaves etc), children’s own clothing items (socks, shoes, gloves) and assorted toys (threading beads, toy cars, soft toys etc) and indeed any objects in the classroom for which there is at least one other that is fully alike, can provide greater opportunities for mathematical discussion and thinking, as the children have to come up with their own ways to group them. In particular, see the Aistear play suggestions in the Operation Maths TRB for Junior Infants.

Classifying

Classifying (or sorting) is different from matching as classifying involves reorganising a collection into two or more subsets. When presented with a large set of objects e.g. toys, children will often isolate a certain group of objects e.g. take out all the toy cars. In this way they have made a set of cars and (by default) a set that is not cars. This is referred to as a binary sort, where two subsets have been created: one which has the chosen attribute and one which does not. In mathematical terms this “opposite” set is the complement of the chosen set.

  • The children should have lots of opportunities to explore various collections of objects from which they will likely create their own sets. Through questioning, elicit from the children an explanation (ie rule) for their set.
  • The teacher can also isolate objects to create sets and then ask the children to identify the rule of the set: “What’s my rule?” (see image above). This is more complex than matching since, while the objects are all the same shape, they are not all the same size or colour. The children can also be encouraged to play the “What’s my rule?” game in groups.
  • Initially, the isolated objects should only have one attribute in common, e.g. in the image above, there is the set of all the shapes that are square and all the shapes that are not squares.
  • Ultimately, it is hoped that the children appreciate that while the collection above has been classified according to  a certain attribute (i.e. whether it is a square or not a square), that the same collection can be sorted in various other ways  e.g. triangles/not triangles; pink/not pink; big/not big. And then for these children, they can be asked to identify the rule of a set that have two attributes in common e.g. a set of yellow squares (which then also creates by default a set of shapes that are not yellow squares).
  • The children will likely begin themselves to sort objects into multiple sets. Instead of two sets of yellow shapes and non-yellow shapes (i.e. a binary sort) they will produce a set of yellow shapes, red shapes, blue shapes etc. The production of multiple sets will naturally lead on to comparing and ordering these sets (see next section).

HINT: The children themselves can also be used for classifying; use rope or yarn circles on the ground, and ask a small group of children up to stand at the top of the class. Point to each of the sets saying “This is for the children wearing glasses and this is for the children not wearing glasses”; “This is for the children with curley hair and this is for the children who don’t have curly hair”; “This is for the children with brown eyes and this is for the children who don’t have brown eyes” etc. 

Comparing and Ordering

Comparing is instinctive in humans, and children are no exception to this: “He got more than me! I have a smaller piece!”

Comparing is also intrinsically connected with matching and classifying: when a child explains that two shapes are different/not the same because one is yellow and one is red, they are already comparing according to colour. When a child classifies a set into big toys and small toys, they are already comparing the items in the sets according to size. Therefore, to compare is to measure or quantify in some way how two items or two sets are similar or different.

As well as colour and size, the children can also compare objects according to length, width, height, weight or thickness.

  • Use collections of pencils, crayons, ribbons, strings etc., to compare length. Note how the children do this; do they use a common baseline/starting point, and if not, highlight the need for the same.
  • Sort attribute shapes into sets that are thick and thin
  • Use the opportunities to introduce vocabulary that will reinforced later in the year as part of measures e.g. long/short, longer/shorter, heavy/light etc.
  • Compare sets without counting: when sorting, look for opportunities where the resulting sets are obviously different in quantity and ask the children to identify which has more and which has less. Some children may even demonstrate their ability to verify their comparison by counting; this is an added bonus, but not required from all the class at this stage.

Ordering is a development of comparing, in that the children are now comparing three or more objects and ordering them according to length, height etc. The children can compare and then order sets also; “there are more yellow shapes than red shapes, there are more blue shapes than yellow shapes, (then in desceneding order) so it’s blue shapes, then yellow shapes, then red shapes”. An important conceptual development is where the child realises that if A is more/bigger than B and B is more/bigger than C, then A has to be more/bigger than C, and thus A must be the largest and C must be the smallest.

HINT: In your materials for EMA include (real or play) coins and notes, with the  emphasis being on their attributes of material, colour, shape, size and design. Provide the children with opportunities to suggest ways to classify the coins themselves. Using money in this way is an excellent way to prepare them for the strand units of money, later in the year.  NB: While the emphasis should be on the attributes of the coins/notes, as opposed to their value and/or the numbers visible on them,  if children recognise their value and use as an attribute for matching, classifying, comparing and ordering the coins/notes, then this should be acknowledged as a valid response to the activity.

Further Reading and Resources:

This is part of the series “Digging Deeper into …” which takes 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.

Start as you mean to go on!

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Category : About Operation Maths

Tús maith leath na hoibre!

So it is with every maths lesson. It is recommended that each maths lesson should start with an oral and mental starter, which:

  • reinforces some previous learning; not only does this serve to consolidate understanding but, if the content is more familiar to the child, this builds confidence and encourages participation.
  • should be active so as to further encourage the participation of all children eg using activities that incorporate mini-white boards (MWBs) requires more children to be involved
  • should only last for about 5-15 minutes; it should not take over the main part of the lesson

Below are some suggestions for oral and mental starters, both for those who are Operation Maths users and for those who are not.

Operation Maths starters:

In the Teachers Resource Books there are recommended oral and mental starters, designed to consolidate prior learning and lead logically into the lesson that follows. It is suggested that this phase of the lesson lasts for 5-15 minutes.

  • In the junior end TRBs for infants to 2nd class, within the weekly breakdown of suggested activities to teach the topic, there are suggestions for whole class warm-ups  and oral activities (starters).
  • In the senior end TRBs for 3rd to 6th class, within the day-by-day breakdown for each lesson there is an oral and mental starter listed (see image below); this is then explained in more detail within the starters bank, a section of the TRB that follows the topic chapters. To view a sample, click on the link to download the Operation Maths 5 Starters Bank

HINT: While there are typically many suggestions given in the Operation Maths TRBs, 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. And, if you are working with more than one class (ie multi-class), use the starter suggestions from the class level that suits the ability of the majority of the room. 

Other Starters:

There are many other types of starter activities that can be used interchangeably with the starters in the Operation Maths TRBs so as to add further variety to lessons.

    • Number Talks (infants to sixth) is an excellent maths methodology,which promotes the development of number sense and mental calculation skills. The rationale behind Number Talks aligns itself very closely with the underlying principle of Operation Maths, i.e.  teaching children to understand maths, not just do maths. To find out more about number talks and to access a whole suite of ready-made resources for all class levels just click on the link above. To find out more about the overlaps between Number Talks and Operation Maths please read on here.
    • Same but different Math (infants to sixth) is a collection of fantastic images, arranged, in a very teacher-friendly way, according to topic. The teacher can pick out images relevant to the current topic, and suitable for the ability of the children and then ask them to come up with ways in which they are the same and also different. The children could use their MWBs in landscape layout, with a line drawn down the middle, on which to record points. Similar to this is Same or Different images
    • Splat! (first to sixth) from Steve Wyborney, is an engaging activity that helps build students number sense, while having math conversations. The difficulty increases from number bonds of ten through to multi variable equations. There is even a Fraction Splat! series. He also shares lots of free resources to aid implementation. Furthermore, a teacher could develop Splat! into a game/activity played in pairs or small groups, using concrete materials, where a child hides a number or quantity of objects/counters under Splats! (cut out pieces of card or fabric) for others in the groups to identify.
    • The Estimation Clipboard, (first to sixth) again from Steve Wyborney, encourages the children to look closely each time at set of four images, and to use what they have learnt from the initial images to refine their estimate for the latter images. Another number sense building activity on his site is Primary Tiles.
    • WODB (which one doesn’t belong), is based on four images/symbols/quantities, to which the children must give a reason for why one of them doesn’t belong. However, the content of the images has been deliberately chosen so that it could be argued that each one of the images doesn’t belong to the group! In this way, it encourages the children to think outside the box and appreciate that there is often more than one correct answer.
  • Thinking of a Number  (first to sixth class) is a simple but effective game to play with the whole class on the IWB as a starter. This is one possible way to use it:
      • Choose a number range that suits your class and click on three clouds to reveal their clues.
      • Ask the children (in pairs perhaps) to record all of the possible answers  on MWBs which are then revealed when called upon.
      • The children should look around the room to see if there are any possible answers given with which they do not agree (eg an even number written when one of the clues is that it’s an odd number) and to explain why they don’t agree.
      • Click on a fourth cloud to reveal the fourth clue; the children should X out all of the previous answers that can now be discarded and could be asked to explain why this is so.
      • Reveal the fifth clue; this should conclusively point at one actual answer. Again the children could be asked to explain why this is so.
      • On occasion, the actual answer may have already been identified by the fourth clue. In this case, ask the children to suggest what the fifth clue might be.
    • While Thinking of a Number is limited to whole numbers up to 100, once the children get the hang of the game they could be prompted to come up with five similar clues for a shape, measurement, fraction, decimal number etc. For more ideas on how to use this please check out this post here.
  • Bar Models are one of the three visual strategies for problem solving that are used and developed throughout the Operation Maths books for the senior end. While the children and the teacher are still less familiar with bar models, a great way to make your collective introduction to bar models much easier, is to use the Thinking Blocks site (which are based on bar models; suits second to sixth class) as an oral and mental starter. The teacher can display the Thinking Blocks site on the class IWB and to get the children to respond by drawing the bar models and/or giving answers on their MWBs.
  • Solve Me Mobiles are a fantastic suite of progressive puzzles that work as a lead-in to solving simple equations and variables in algebra. That said, these could be used from third class up (and perhaps even with  pupils in second class). Again, this tool will work well displayed on a class board and in conjunction with the pupil’s own MWBs. It also has the added advantage that the children can log-in  and use this site on a device at school or at home, so that their progress can be recorded and continued each time, rather than having to start from the beginning. Indeed, it would work well if the teacher sets up a generic account so that, even when using this with the whole class, they can pick up from where they left off.
  • That Quiz is an excellent assessment tool; it can also be used to generate a random selection of quick questions to which the children respond on their MWBs.
  • Operation Maths also includes useful Follow-on weblinks. Each follow-on weblink is author-approved and is linked to a specific topic and for a specific class level. As many of these are games, they could be used as a whole class starter (as well as for for consolidation and assessment) when displayed on the class IWB. The weblinks can also be printed for the children to take home and have fun practicing maths with their parents or guardians.

And if you exhaust all the ideas above there are some more suggestions on this list of Daily Routines and on this list of Useful Websites

Operation Maths Digital Resources – Quick Start Guide

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Category : About Operation Maths

If you are a new, or relatively new, Operation Maths user, you should definitely check out this quick start guide to the extensive digital resources which accompany the scheme. And, even if you think that you are relatively familiar with the resources, it might still be worth a read, as you are likely to pick up some new tips to help you get the most out of the resources.

Edco Learning

All of the Operation Maths digital resources are accessed via Edco Learning. All new users will have to first register on the Edco Learning site and follow the instructions to verify the account. If you are not familiar with the Edco Learning site, watch the tutorial below.

After login, you are presented with a virtual book shelf of all your available books. If the Operation Maths books for your class(es) are not visible on the virtual bookshelf, click on the Contact Us link at the top of the Edco Learning home page.

HINT: If you find this virtual bookshelf is too “busy” or is taking a while to load, reduce the number of books you can see when it opens by using the drop-down filters at the top of the screen. Your selection will be remembered for the next time you login. You can amend these choices at any time. 

Operation Maths Digital Resources

As there are some small, subtle differences in the way that the resources are organised for the junior end classes and for the senior end classes, they are dealt with separately below.

Digital Resources for Infants to Second Class:

To get an overview of the digital resources available for each week/fortnight start with the Short Term Plan (STP) for that period, in the Teachers Resource Book (TRB); here the various digital activities are briefly listed (see highlighted below). The TRBs to accompany each class level of the Operation Maths schemes are available both in hard copy (free to all adopting schools) and in digital form (accessible via your bookshelf on Edco Learning).

HINT: To find out more about accessing both the Long Term Plans (LTPs) and Short Term Plans (STPs) for Operation Maths, in both hard copy and digital forms, check out this post: Planning for Operation Maths

This overview lists the digital resources available for that fortnight/week, and in each case specifies:

  • the type of digital activity that it is e.g. Create activity, Write-Hide Show video etc (to find out more information about the different types of digital activities read on here)
  • the page of the At School book to which the activity is relevant
  • a brief description of the activity

To get a more detailed description of the specific digital resources for each week, navigate towards the end of the relevant week, again in the TRB. Here, under the subheading Digital resources, each activity relevant to that week will be given again, accompanied by a detailed description of the activity, suggestions for how to use it in class and extension suggestions (see example below).

To open each specific resource, the simplest way is via the digital version of the At School book. In this digital book, navigate to the page to which the activity is relevant (e.g. in both of the two previous images they list the first create activity as being relevant to page 17 of the At School book). On the specified page, there will be a icon visible (see circled in the example below), which acts as an embedded hyperlink i.e. when you click on the icon, it will automatically open the relevant digital resource, in another tab. For instructions/suggestions on how to use this resource refer back to the detailed description in the TRB (as previously shown in the image above).

 

HINT: While there are other ways to access all of the resources and digital activities (eg via the Edco Resources pop-out tab to the right-hand-side of the screen), the way described above can often be the easiest way to open each embedded resource, as the icons are located in exactly the relevant place in the digital books and so saves the teacher time that might have been spent deciding which resource was the most appropriate.

 

Digital Resources for Third to Sixth Class:

One way to get an overview of the digital resources available for each topic is to start with the Short Term Plan (STP) for that topic, in the Teachers Resource Book (TRB); here, the various digital activities are briefly listed (see image below). The TRBs to accompany each class level of the Operation Maths schemes are available both in hard copy (free to all adopting schools) and in digital form (accessible via your bookshelf on Edco Learning).

HINT: To find out more about accessing both the Long Term Plans (LTPs) and Short Term Plans (STPs) for Operation Maths, in both hard copy and digital forms, check out this post: Planning for Operation Maths

This overview lists the digital resources available for that topic, and in each case specifies:

  • the type of digital activity that it is e.g. Create activity, Write-Hide Show video etc (to find out more information about the different types of digital activities read on here)
  • the page of the Pupil’s Book to which the activity is relevant
  • a brief description of the activity

An alternative place to view an overview of the digital resources available for each topic is on the footer of the first page of each chapter in the Pupil’s book (see opposite), as this also provides the same synopsis of the digital resources that are available to use for that chapter.

To get a more detailed description of the specific digital resources for each topic, navigate to the last section of each chapter in the TRB. Here, under the subheading Digital resources (see circled below), each activity relevant to that topic will be given again, accompanied by a detailed description of the activity, suggestions for how to use it in class and extension suggestions.

 

To open each specific digital resource, the simplest way is via the digital version of the Pupils Book. In this digital book, navigate to the page to which the activity is relevant. On the specified page, there will be a icon visible (see circled in the example opposite), which acts as an embedded hyperlink i.e. when you click on the icon, it will automatically open the relevant digital resource, in another tab. For instructions/suggestions on how to use this resource refer back to the detailed description in the TRB (as previously shown in the image above).

 

HINT: While there are other ways to access all of the resources and digital activities (eg via the Edco Resources pop-out tab to the right-hand-side of the screen), the way described above can often be the easiest way to open each embedded resource, as the icons are located in exactly the relevant place in the digital books and so saves the teacher time that might have been spent deciding which resource was the most appropriate.

 

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 – Digital Resources Overview

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Category : About Operation Maths

New or relatively new to Operation Maths? Want to know more about the various types of digital resources that are available? Read on!

Operation Maths provides an extensive range of digital resources with endless possibilities. These digital resources include:

  • Create activities (each of these is based on one of seven e-Manipulatives)
  • Ready to go activities (also based on the e-Manipulatives, but more structured than Create activities)
  • Write-hide-show videos
  • Maths Around us videos
  • Scratch activities
  • Follow-on weblinks

Create activities

Create activities are based on one of seven e-Manipulatives and can be used as very powerful online, interactive, teacher tools. The create activities are so called because the teacher can open a specific e-Manipulative and choose how to use it to best suit them, their class and the concept at hand. Therefore, teachers can use the e-Manipulatives in any way that they see fit.

Furthermore, there are numerous suggestions for create activities in the Teachers Resources Book (TRB) which show how the e-Manipulatives can be re-used in numerous ways to achieve a countless number of specific learning outcomes. The detailed suggestions for how to use the create activities, can be found under the subheading Digital resources, located towards the end of the listed activities for each relevant week/topic, in the TRB.

HINT: There are not separate, individual create activities per each hyperlink in the digital Pupils or At School book; clicking on a create activity icon will bring you to the starting point of one of the e-Manipulatives. However, within each of the topics in the TRB, there will be separate and specific suggestions given each time.

The full range of Operation Maths e-Manipulatives cover key maths areas:

  • Sorting & Shop e-Manipulative
  • Place Value e-Manipulative
  • 100 Square e-Manipulative
  • Bar Modelling e-Manipulative
  • Counting Stick e-Manipulative
  • Fractions e-Manipulative
  • Clock e-Manipulative

To explore the seven e-Manipulatives in more detail, please read on here.

 

Ready to go activities

Ready to go activities are specific activities, based again on the seven e-Manipulatives, but these are all pre-set and have suggested questions inbuilt on the left-hand side of the screen, that the teacher can click to reveal and hide. This means that the teacher doesn’t have to waste valuable time looking in a separate book for the accompanying questions. These questions can be directed to specific children and/or can be answered on the children on their Operation Maths MWBs, thereby encouraging whole-class participation.

While both are based on the e-Manipulatives, there is a distinct difference between ready to go and create activities. The former are more structured than their create counterparts and, as each ready to go activity is tailored to a specific learning outcome, they will have a specific title e.g. Ready to go 3.5, Ready to go 4.6 etc

HINT: The ready to go activities can also provide the teacher with examples of how each e-Manipulative may be used. Thus, the teacher can use a previous ready to go activity to inspire a create activity or come up with a completely different activity of their own. 

 

Write-Hide-Show videos

These are videos, of the e-Manipulatives in use, that focuses on the teaching method of ‘Write – Hide – Show’ i.e. teacher plays the video and the children respond by answering on their Operation Maths mini white-boards (MWBs), thus ensuring the maximum participation of the children.

These videos provide quick, easy-to-use scenarios and set-ups that engage children and pose meaningful maths questions. They also showcase the flexibility of the e-Manipulatives and provide inspiration for teachers’ own expansions. Take a look at this sample video below:

 

Maths Around Us videos

The series of Maths Around Us videos is full of real-world examples of maths in the environment and provides numerous opportunities for discussion and engagement. Take a look at this sample video below:

 

 

HINT: An advantage of both types of Operation Maths videos is that they have been designed so that the teacher need only press play, since the questions and wait times are all built in, allowing the children to look, listen and respond on their MWBs. This means that, they not only encourage active participation, but they also allow the teacher the opportunity to informally assess the pupils via observation of their responses.

Scratch programming activities (3rd to 6th class)

Not only have these activities been written especially for Operation Maths but Operations Maths is the only maths scheme available currently in Ireland with integrated programming (coding) activities. Each activity is integrated with the Pupils’ Books, comes with step-by-step instructions for teachers and pupils and highlights the connection between maths and coding in an easy-to-follow, visual manner.
The scratch programming activities can again be downloaded via the icons in the pupils books. Teachers or children can access the Scratch software for free online (click here).

Follow-on weblinks

Encourage your pupils to practice maths ideas at home with the useful Follow-on weblinks based on recommended games. Each Follow-on weblink is author-approved and is linked to a specific topic, for a specific class level, in the Pupils’ Book. The weblinks can be printed for children to take home and have fun practicing maths with their parents or guardians. Teachers can also use the weblinks in class as a lesson starter, for consolidation and assessment or, indeed, at any time.

These follow-on weblinks can be downloaded as word documents from Edco Learning:

  • Open the Edco Resources pop-out tab to the right-hand-side of the screen
  • From the menus select your book (eg “Operation Maths 3rd class Pupils Book”) and “Follow-on Weblinks”

And finally….

  • All the digital resources are all completely integrated with the print and eBooks; when viewing the Pupils eBook, the teacher need only click on the specific digital icon on the page to open the resource up in a new window/tab.
  • Nearly all of the digital resources can be used in conjunction with the free mini white-boards, ensuring the maximum participation of the children.
  • As there are numerous ways to use each of the e-Manipulatives, they offer unlimited opportunities for assessment for learning and whole-class participation
  • They have been specially designed to help children to focus on the maths
  • They are user-friendly and approachable with bright, clear colours and layout

Teachers can access all the Operation Maths digital resources through Edco’s dynamic online digital hub, www.edcolearning.ie.

 

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

Planning for Operation Maths

Tags :

Category : About Operation Maths

If you’re an Operation Maths user, then planning is ‘easy, peasy’, since all the plans are already done!

Long Term Plans (Yearly Schemes):

 There is a hard copy of the each Long Term Plans (LTP) in the front of the Teachers Resource Book (TRB) for each class level, that can be photocopied.
 Open the digital ebook version of the TRB (via Edco Learning) to view the Long Term Plans (Yearly Schemes) and click on the hyperlink in the top corner; this will automatically download a word version of the same plan, allowing you to edit/amend/copy as required.

Short Term Plans (Fortnightly/weekly schemes):

 As before, there is a hard copy at the beginning of each topic in the Teachers Resource Book (TRB) for each class level, that can be photocopied and then annotated, ticked etc.


 Furthermore, to access an editable version of these plans, you need only open the digital ebook version of the TRB to view these same plans and click on the hyperlink in the top corner; this will automatically download a word version of the same plan, allowing you to edit/amend/copy as required.
 In addition, for each of the classes from 3rd to 6th there is a single document compilation of all the short term plans (see image below):
– Login to your Edco Learning account;
– Click on Edco Resources tab on right hand side of screen to open
– From the menus select your TRB (eg “Operation Maths 3rd class TRB”) and “Editable Lesson Plans” and then click on “Short Term Plans Overview” (image 4 below).
You can also use this resources tab to access the word version of the Long Term Plan

 

Multi-Class Plans

For Operation Maths 3-6, as well as including a Long Term Plan (Yearly Scheme) for each class level, there is also a second combined LTP in each TRB; in Operation Maths TRB 3 and 4, there is a combined plan for third and fourth class, and likewise in each Operation Maths TRB 5 and 6 (see image below)

 There is a hard copy in the front of the Teachers Resource Book (TRB) for each class level, that can be photocopied.
 To access a word doc of each plan, open the digital ebook version of the TRB to view the Long Term Plans (Yearly Schemes) and click on the hyperlink in the top left hand corner; this word version allows you to edit/amend/copy as required.

While there are no combined multi-class plans in the Operation Maths TRBs for infants to second class, in response to requests for the same, we now have completed the following:
 A LTP for a combined junior & senior infants class
 A LTP for a combined first & second class
 A LTP for a combined second & third class

And just added:

 A LTP for a combined fourth & fifth class

These plans can be downloaded via the links above or they can be downloaded direct from Edco Learning:

– Login to your Edco Learning account;
– Click on Edco Resources tab on right hand side of screen to open
– From the menus select your TRB (eg “Operation Maths 1st class TRB”) and then “Word Document”.

 

 

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 e-Manipulatives

Tags :

Category : About Operation Maths

The fully flexible, easy-to-use, online Operation Maths e-Manipulatives (interactive teacher tools and virtual manipulatives) are designed for teacher-led learning and to encourage whole-class participation. This impressive range of e-Manipulatives is optimised for use on an Interactive Whiteboard or a whiteboard with a projector so that teachers get the best results every time. They also facilitate a CPA approach to maths instruction.

The full range of e-Manipulatives cover key maths areas:

  • Sorting & Shop e-Manipulative
  • Place Value e-Manipulative
  • 100 Square e-Manipulative
  • Bar Modelling e-Manipulative
  • Counting Stick e-Manipulative
  • Fractions e-Manipulative
  • Clock e-Manipulative

Let’s explore each of these in more detail.

 

 The Sorting & Shop e-Manipulative allows the teacher to easily drag and drop shapes, animals, fruit, classroom objects, shop items, upper and lowercase letters, and numbers onto a workspace. It can be used blank or with various backgrounds, including frames, sets,  2×2, 5×5 grids etc . Of all the backgrounds, the shop background is particularly useful as it allows the teacher to create a shop scene with price tags, coins and sale tags, which can be used to explore a wide range of mathematical scenarios such as using small amounts of money in infants right up to scenarios involving percentage increase and decrease in the senior classes.

The Place Value e-Manipulative provides a wide range of place value tables which the teacher can use to demonstrate re-grouping. Each place value table contains either base-ten blocks, counters to represent the place value discs that accompany the 3rd-5th books, straws or money, and decimal values are included in a selection of the tables. Two tables may be shown on screen at the same time to facilitate comparisons between numbers. There is also the facility to display up to 5-digit whole numbers, which, in my experience, had not been possible previously as all other interactive manipulatives only extend to 4-digit numbers at most.

The 100 Square e-Manipulative is another extremely versatile tool. It can be used in numbers only, counters only or counters and numbers. You can very easily hide and reveal individual cells, whole sections of the grid or the entire grid.  I have gotten a huge amount of use of out it recently, with first and second classes, using it in numbers only mode, hiding all the numbers and just revealing one number. I then ask the children what number comes after/before this, what numbers is missing above/below etc. This is particularly good to assess the children’s ability to identify numbers around the decuples/decades (ie 30, 40, 50 etc) which are widely recognised as hurdles for many children.

This tool can also be used to model the 100 dots grid (on the inside back cover of Operation Maths 3 and 4) as a means to explore the commutative and distributive properties and the connections between various groups of facts.

The Bar Modelling e-Manipulative allows the teacher to create the bar models used in the text books quickly and easily. Bars can be dragged, dropped and resized and the teacher can change their colour. The teacher can also type and draw freehand on the workspace, making this a very useful resource for demonstrating the strategy of bar modelling

The Counting Stick e-Manipulative replicates the physical counting stick that a teacher might use in the classroom. The teacher can set the starting value and the steps value, and reveal or hide numbers along the counting stick. Decimal and negative numbers may also be shown on the Counting Stick e-Manipulative and two counting sticks can be shown at the same time, in order to compare various numbers.

The teacher can use the Fractions e-Manipulative to present fraction bars (linear models), fraction circles and pizzas (both area models). The teacher can change the fraction that is shown on screen, randomise fractions and hide or show the fraction value, decimal value and percentage value. Two fractions may be shown on screen at the same time.

Analogue and digital clocks are provided with the Clock e-Manipulative. The teacher can choose to show one analogue clock, one digital clock, two analogue clocks, two digital clocks or an analogue and a digital clock at the same time.

 

All of the e-Manipulatives can be used as Ready to go or Create activities

Ready to go activities are already set up within each e-Manipulative with pre-programmed questions that appear on screen, meaning that the teacher doesn’t have to waste time looking in a book for the accompanying questions. The questions can also be answered on the children on their MWBs, thereby encouraging whole-class participation.

Create activities are so called because the teacher can open the e-Manipulatives and choose how to use it to best suit them, their class and the concept at hand. There are suggestions for Create activities printed in the TRB which show how the tools can be re-used in infinite ways to achieve a countless number of specific learning outcomes. And the Ready to go activities themselves will also provide the teachers with examples of how each e-Manipulative may be used.

Write – Hide – Show videos

These are videos of the e-Manipulatives in use that focuses on the teaching method of ‘Write – Hide – Show’. These videos provide quick, easy-to-use scenarios and set-ups that engage children and pose meaningful maths questions. They also showcase the flexibility of the e-Manipulatives and provide inspiration for teachers’ own expansions. Take a look at this sample video below:

 

Teachers can access all of the Operation Maths e-Manipulatives and other digital resources through Edco’s dynamic online digital hub, www.edcolearning.ie.

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