Author Archives: Operation Maths

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

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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

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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.

Maths for June

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Category : About Operation Maths

Hooray! June is nearly here! You can almost smell the summer holidays!

If you’re a user of Operation Maths 3-6 you are quite likely to be finished, or nearly finished your books, as the programme is designed to be completed by the end of May, so as to have it all covered in advance of the standardised testing.

So now, you might find yourself looking for inspiration to fill the maths lessons from now until the end of month. Whether you’re an Operation Maths user or not, look no further than the following ideas.

For Operation Maths users:

If you hadn’t had a chance to dip into these specific features of the Operation Maths programme so far this year then why not try these out now?

  • Let’s Investigate! These sections are the last one or two pages at the end of the Pupils’ Books ( for third to sixth classes) where the focus is on open-ended problems. Some of these are “big” enough to fill a whole lesson, others might become additions to a lesson or be combined to become a lesson. The children could also select which particular investigation(s) they’d like to explore, either as a whole class or with individual groups selecting different investigations, with results to be communicated/presented back to whole class when complete.
  • Early Finishers Photocopiables: These can be found in your Teachers Resource Book (TRB) and can also be  a great way to help deepen the children’s understanding of a topic covered earlier in the year. For 3rd to 6th classes, problem solving is also an integral part of these activities. In the TRBs for Junior Infants to 2nd classes, there are both Early Finishers photocopiables and dedicated problem-solving activities.
  • Maths Around Us: If your class has access to recording devices, why not challenge them to make their own Maths Around Us video based on maths content they covered this year. Watch some of the Operation Maths Maths Around Us videos on www.edcolearning.ie for inspiration.

As mentioned in a previous post, don’t feel under pressure to complete all of the above activities, only just what appeals most to you or is most suited to your class.

For everybody!

  • Change their attitude to maths generally: Most people have this belief that there is such a thing as a maths brain, a belief which Jo Boaler, among others, strongly challenges. In conjunction with her youcubed team at Stanford University, in 2015 they put together resources, videos etc for a Week of Inspirational Maths. Since then their catalogue of resources has grown and includes videos, resources and tasks. There is enough here to keep a class going for an entire month!
  • Take time to problem-solve: often, during the school year, time is at a premium, yet Dan Finkel argues in this TEDx Talk that “allowing children time to struggle” is one of the Five Principles of Extraordinary Math Teaching. So after watching this video, why not present the images he uses to a 5th or 6th class and give them time to “notice and wonder”. The children could use sentence/questions stems like “I notice that…” and ” I wonder why/how/what ….” to get them thinking and discussing. Read on here for more sources of deep and rich problems.
  • Try out a new methodology with your class: It can be a good idea to try out something new in June when there’s less pressure to succeed and you’re familiar with your class, rather than trying out something new in September when you’re trying to get to grips with new class, new books, perhaps new room etc!  One initiative I would wholeheartedly recommend is Number Talks. You could do a number talk with your class aimed at their current level or challenge them to do a number talks session aimed at the class they’ll be in next September.
  • Do a maths project: In the Maths Curriculum Teacher Guidelines (DES, 1999) maths projects are listed as one of the examples of maths problems that we are encouraged to incorporate into our teaching. It can be difficult to include maths projects earlier in the year when the pressure is on to cover the content, making June an ideal time to explore them. For 10 “awesome” ideas, check out this post from the Mashup Math blog. One of the suggested projects, Plan your Dream Vacation, has so much opportunities for real-life maths, costs, budgeting, estimating costs of luggage, time needed to get to the airport, distance from destination to airport etc. And, if a foreign holiday, is not relevant, with a small twist, and access to some online hardware catalogues it could easily become Plan your Dream Bedroom; again lots of real-life maths, costs, budgeting, measuring, dimensions, proportions etc. Or even plan a virtual Road Trip! Research where to start, where to go, how to travel there, what attractions to visit, the costs involved, and how long it would take.
  • Financial Maths: In a similar vein to that of the previous suggestion, the NCETM Primary and Early Years Magazine also has suggestions for projects, the first one again focusing on financial education. Here they have links to a fantastic suite of primary resources for My Money Week (UK), that are also very applicable to children to children in Ireland. To access the resources, you need to set up a free account, which requires email details etc and entering any UK postcode. Once registered and logged in, scroll down to the bottom of the primary resources and click on Start journey; this will start off a series of excellent videos on Max’s Day Out, in which Max is deciding how best he might spend the money that he got for his birthday. The videos are designed in such a way that each one presents two possible options; the viewer selects an option, which automatically brings them to the follow-up video for their choice. There are many other resources also available here that focus on managing money.
  • Revise wise! Ask your class to put together revision materials for their chosen topic from the past school year. They can show their creative side, using a variety of approaches, including digital media, to complete the task. The types of materials produced could include posters, presentations, video tutorials, raps, songs, poems, models, fact sheets and or revision work-sheets. These child-produced materials could be collected and shared with the next cohort of classes.
  • Picture This: Similar to the revision project above, and to the Maths Around Us videos, the children could be allocated maths terminology that they had encountered during the past year, and be tasked to produce images or video that illustrate the terminology. The children could be encouraged to use real world examples, especially from around their homes and local environment.
  • Online Surveys: The children could be asked to survey the other children in their class, by setting up online surveys (eg using Google Forms, Mentimeter etc) and then to collate and present their conclusions and findings, using spreadsheets, graphics (pie chart, and bar graph) and/or slideshows (eg Google Sheets, Google Slides, etc).
  • Calculator Activities: For any sixth class students transitioning to secondary, it can be a good idea to brush-up on calculator skills; secondary teachers may expect them to be relatively comfortable with this piece of technology. That’s said, calculator activities shouldn’t be just about getting through more calculations in a shorter time; the children should be enabled to use the calculator to explore number patterns, more complicated numbers, real life situations, and to gather evidence to support reasoning, such as in this consecutive numbers concept cartoon.
  • Take it outdoors: Another type of maths problem listed in the Teacher Guidelines is maths trails. If the rain stays away for long enough why not get outside and do some maths trails? Or if you teach a more senior class, why not get them to design a maths trail for a junior class based on the school grounds or nearby environment. For more trail ideas read on here.
  • Maths is Magic! There is a lot of mathematics behind magic. You could give the children magic tricks to investigate. Check out this article, again from the NCETM Primary and Early Years Magazine for sites to explore.
  • Break the code: Explore the maths behind codes and code-breaking. You could ask the children to make up their own codes and crack a friend’s. Click here for links to suitable sites.
  • Have a maths game-themed day: Another one of Dan Finkel’s Five Principles of Extraordinary Math Teaching is play. Most games and puzzles are mathematical in nature. Get the children to bring in a favourite game from home, to play in class, that requires mathematical thinking. Alternatively, get them to research a suitable one on the internet.

Digging Deeper into … Number Sentences, Equations and Variables (3rd – 6th)

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For practical suggestions for families, and helpful links to digital resources, to support children learning about this topic, please check out the following post: Dear Family, your Operation Maths Guide to Number Sentences and Equations

In the Primary Mathematics Curriculum (1999), this topic appears as three separate strand units, all within the strand of Algebra:

  • Number Sentences (3rd & 4th class)
  • Equations (5th & 6th class)
  • Variables (6th class)

However, since these concepts are intrinsically connected, in Operation Maths they are taught in a cohesive and progressive way through third to sixth class.

  • Number sentences are mathematical sentences written using numerals (e.g. 1, 5, 67, 809, 1.45, 1/2  etc.) and mathematical symbols (e.g. +, -, x, ÷, <, >, =).
    • They include both equations (see below) and inequalities (64 < 82, 23 > -16), although the term inequalities is not specifically used.
    • The unknown or missing value in a number sentence (i.e. a variable) can be represented by a frame (box), by a shape, or by a letter, although it should be noted that the Primary Mathematics Curriculum (1999) specifies a preference for a frame (box), up to the introduction of variables in 6th class
  • An Equation is a special type of number sentence, containing an equals sign, to show that two expressions are equal (e.g. 5 = 3 + 2, 5 + 6 = 20 – 9, etc.)
  • A variable is a value in an expression that can  change or vary. However, when there is only one variable in an equation then the value of that variable can be calculated e.g. a + 6 = 9, 20 = 4b.

Thus, while these strand units are only being formally introduced from third class on, the children have actually been exposed to number sentences, equations and variables (i.e. the frame) since the infant classes.

 

Equations

(aka Number sentences with an equals sign)

Understanding equations necessitate the appreciation of the correct meaning of the equals symbol. Many children incorrectly translate the equals symbol (=) as meaning ‘and the answer is…’. This incorrectly reinforces that both its purpose and position is to precede the answer in any calculation, a misconception also reinforced by calculators, where you press the = button to get the answer. Such misunderstanding is
evident when you see responses like these:
5 + 6 = [11] + 3 , i.e. ‘5 + 6 is 11’
5 + 6 = [14] + 3 , i.e. ‘5 + 6 + 3 is 14’
Adults may also unwittingly compound this, by using ‘makes’ or ‘gives’ as a synonym for equals.

It is vital that the children recognise that the equals symbol indicates that both sides of the equation (which will be referred to simply as a number sentence until fifth class, when the term “equation” is introduced), are equal to one another/are the same value/are balanced. In this way an actual balance (pan or bucket) and cubes can be extremely valuable to model (and solve) equations e.g. in the images below, the first balance shows that 5 equals a group of 3 and a group of 2, and the second balance shows that 12 equals 3 groups of 4.

From Operation Maths 4

From Operation Maths 5

Furthermore, teachers should reinforce the correct meaning for the symbol = by only translating it as ‘equals’, ‘is equal to’ and/or ‘is the same as’.

 

Inequalities

(aka Number sentences with greater than/less than sign)

Despite the fact that the children have been using the greater than and less than symbols since 2nd Class, many still have difficulties reading them and interpreting their meaning. Using a balance and concrete materials, in a similar way as when teaching equations, can greatly help children to gain deeper understanding of the symbols and their meanings.

From Operation Maths 4

Through exploration they can identify what is the maximum number of cubes they can put on a side that is less than the other side, before it makes the balance tip in the other direction, thereby invalidating the number sentence; or the minimum number of cubes they can put on a side that is greater than the opposite side, so as to keep the number sentence true.

 

Using estimation strategies

Often, when having to indicate if a given number sentence is true or false, it is not always necessary for the children to calculate both sides of the number sentence exactly. There is (usually) only one true or correct option, meaning that every other answer is incorrect or false. Encourage the children to use their estimation and number sense skills to quickly recognise when a statement is obviously false, e.g. a big difference in the size of numbers on one side versus the other.

While some might view this as a type of ‘cheat’ strategy, in truth, it is more about identifying the most efficient approach, while also reinforcing the value of estimation in general and, particularly, as a way to make calculations easier.

 

Translating number sentences into word problems and vice-versa

As mentioned earlier, this is in fact a skill that the children would have been exposed to, and been using, since the infant classes. Furthermore, as this topic is deliberately positioned towards the end of the yearly plans in Operation Maths 3-6, the children will have already been using this skill very regularly in the number, data and measures chapters, prior to this point of the school year.

The curriculum specifies that the children should be enabled to translate number sentences into word problems, both of which can be viewed as abstract representations. Worth noting, is that the curriculum doesn’t emphasise the importance of the translating the number sentences and word problems into concrete and/or pictorial representations. Whereas, in Operation Maths, (in keeping with its overarching CPA approach) , there is significant emphasis placed also on utilising various concrete materials and visual strategies to represent the word problems and number sentences.

From Operation Maths 5

The development of visual strategies for problem-solving,  is a central focus of the work throughout the Number chapters. Thus, this topic allows the teacher to revise the visual strategies covered so far and assess how well the children understand them and can apply them.

The interconnectedness of real-life scenarios and mathematical sentences/equations should also be emphasised. At primary level, there should always be some relatable context for any number sentence.
For many children, when looking at a number sentence, it can be difficult to appreciate how a collection of digits and symbols could relate to a real-life scenario with which they can identify. That is essentially what a word problem is; it provides a real-life context within which to frame the numbers and operators involved. Emphasise to the children throughout this topic how the number sentences could be given a real-life story (i.e. word problem), and encourage them to come up with possible stories either verbally or written down.

And, depending on the context given to a particular story, the visual representation may also be different, even though the number sentence/equation may stay the same. For example for the number sentence 7 – 4 = ? the word problem (context) could be either of the following:

  • Ali had 7 cookies. He ate 4 cookies. How many cookies does he have left?
  • Áine has 7 cookies. Abdul has 4 cookies. How many more cookies has Áine than Abdul?

Image created using Bar Modelling eManipulative, accessible on edcolearning.ie

And while the number sentences are the same, both the contexts and the pictorial representations (e.g. bar models, as shown above) are different, as they represent different types of subtraction. In the case of the first word problem, this is describing subtraction as deduction, and a part-whole bar model is more suitable. In the case of the second word problem, this is describing subtraction as difference, and a comparison bar model is more suitable.

 

Identifying operation phrases

When the children are translating word problems into number sentences, it is very important that they can understand the context being described and are able to identify that phrases that indicate the operation(s) required.

Regularly interspersed throughout the operations chapters in the Discovery books for Operation Maths 3-6,  there are activities which enable the children to identify and colour-code the specific vocabulary that an indicate the required operation (see example below). This topic provides an ideal opportunity to review this skill and assess/re-teach the children accordingly.

From Operation Maths 4, Discovery Book

In particular, many of the Talk Time activities, require the children to suggest ways to verbalise the various equations, e.g:

  • The difference between 46 and 18 is equal to the product of 4 and 7; true or false?
  • 18 subtracted from 46 equals 4 times 7; true or false?

Where possible the children should suggest alternative phrases for the same equation thus reinforcing the use of correct mathematical language.

 

Input and Outputs

In Operation Maths 4 & 5, activities based on inputs and outputs are included as a means to consolidate the children’s understanding of number sentences and their ability to write number sentences (see below).  Input-output activities can provide great scope for problem solving, as well as preparing the children for calculations involving variables in sixth class.

From Operation Maths 4

 

Variables

Variables are formally introduced in sixth class, although the children have encountered variables (as a symbol or shape to represent a missing value) since they first encountered the frame (answer box).

When calculating with variables, both part-whole bar models and comparison bar models can be very useful to represent the relationship between the known and unknown values.

From Operation Maths 6

Further Reading and Resources

Digging Deeper into … Capacity (all classes)

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For practical suggestions for families, and helpful links to digital resources, to support children learning about the topic of capacity, please check out the following post: Dear Family, your Operation Maths Guide to Capacity

Strictly speaking, capacity is the amount (or measure) of a substance (which can be solid, liquid or gas) that something can hold (i.e. a container). That said, in primary mathematics we tend to use capacity as a measure of liquids only (ie not solids or gases), both to avoid confusion and since the children would most commonly see examples of liquids measured using the standard units of capacity (ie litres and millilitres).

Initial exploration – CPA approach

Like the topics of Length and Weight, and in keeping with the over-arching CPA approach of Operation Maths, children’s initial experiences of capacity at every class level should focus on hands-on activities, using appropriate concrete materials.

In the younger classes, this should occur through exploration, discussion, and use of appropriate vocabulary eg full, nearly full, empty, holds more, holds less, holds as much as/the same as etc. The children should also be enabled to sort, compare and order containers according to capacity.

From Operation Maths 1

 

Irrespective of the class level, introductory exploration in this topic could follow the following progression or similar:

  • The children examine pairs of empty containers and make comparisons, so as to identify, from sight, which holds more/less. Use questioning to encourage them to assess all available information:
    • Which container is wider/narrower?
    • Which container is taller/shorter?
  • Elicit from the children how they might verify their estimates. Introduce a non-standard measure (e.g. egg-cup, yogurt container, plastic cap from an aerosol, tea/table spoons, plastic syringe, flask etc) and demonstrate how to measure the capacity of a container using a non-standard measure eg (using egg-cup as standard measure):
    • Fill an egg-cup with water. Pour this into the target container to be measured. Repeat until container is full and then record the number of egg-cups required.
    • OR fill the container with water. From this, pour out an egg-cup full, which is then poured out into a third container (eg basin, plastic box). Repeat until the target container is empty and then record the number of egg-cups that were filled from it.
    • OR fill the target container with water. Pour this into a larger container and record the level of the water by marking the level on the side. Pour out the water out into a third container (eg basin, plastic box) to be used as a water store/reservoir. Repeat with other containers to be measured and use the marking on the side of the measuring container to identify which container held the most/least etc. Please note though, that while this method can be used to identify which container holds the most/least, it will not provide a measure of the capacity as a quantity of  non-standard units (unless of course the measuring container has existing markings for litres and/or millilitres)

 

 

From Operation Maths 1

 

HINT: In order to be avoid unnecessary water wastage and/or a very wet classroom (!), it can be a good idea to conduct the capacity activities outside and over a number of plastic basins/boxes. These can be used to catch spills and to hold the water which can be re-used repeatedly to measure the capacity of the various containers. 20 ml or 50 ml plastic syringes can also be very useful; they are easy for smaller hands to use draw up water and squirt it into a container. And instead of counting ml, ask the children just to record the capacity of the container as the number (count) of syringes that it can hold.

Move on to pairs of containers whose difference in capacity may not be obvious because of the shape and dimension of the containers. Thus, it is important to use a selection of containers that vary in height and width.

This can then progress to incorporate a direct comparison of the capacity of three or more containers. It is important at this stage that the children realise that if A holds more than B and B holds more than C, then, without further direct comparisons, we know that A holds more than C, that A holds the most of all three and C holds the least. This is a very important concept for the children to grasp.

HINT: Use brainstorming to elicit the names of various liquids and container types with which the children are familiar. Use the list to make up an odd one out game, as outlined below

From Operation Maths 2 TRB (similar activity also in Operation Maths 1 TRB)

  • In a similar way, the children can estimate and record the capacity of containers of objects using standard units (i.e. litres and millilitres; the latter is introduced in third class). Initially, when using the standard unit of a litre (starting from first class) the children will be recording the capacity of containers as being able to hold more than/less than/the same as a litre.

HINT: In 2nd class & 3rd class the children will be using 1/2 litre and 1/4 litre (as opposed to millilitres). This will necessitate using bottles etc that are marked in 1/4 litre intervals. Challenge the children in these classes up to come up with ways to measure and mark these intervals, without having to use millilitres or some type of commercial graduated measure (eg a jug). This task could be given as an alternative homework activity.

When finding the capacity of a container, it is important also to highlight to the children that it is not necessary to fill it to the brim. Show them an example of an unopened litre bottle of water – the height of the water in the
bottle is not to the brim, yet the label shows it contains 1 litre. Thus, the children will develop an understanding that the actual capacity of containers are typically greater than the indicated capacity of the liquid it contains.

Problem Solving: How many are needed to fill? It takes 4 of container A to fill container B. It takes 2 of container B to fill container C. How many of container A are needed to fill C? This can be a very difficult concept to grasp for many children. Some suggestions include using multiples of the real containers to show the relationships between each and drawing pictorial representations using bar models, one of the three key visual strategies for problem-solving used throughout Operation Maths, (shown below). 

Using more accurate measures

As the children progress in their understanding of the concept of capacity they will begin to appreciate the need for more accurate means to record it; both using smaller standard units (ie millilites) and using measures/containers which are already calibrated/graduated with markings. It is an advantage to have a wide selection of different types of measuring instruments available (including plastic jugs, syringes, measuring spoons, graduated cylinders etc) so that the children appreciate that different measuring instruments are more suitable for certain tasks. When measuring, advise the children also to read the level of liquid at eye level to obtain a more accurate reading.

HINT: Some jugs etc can be purchased relatively cheaply from value shops. Alternatively, ask the children to bring in measuring jugs, containers etc., from home to use in class while working on this topic.

As always, the children should be encouraged to estimate before measuring.  And, rather than estimating the capacity of A, B, C and D before measuring A, B, C and D, it would be better if the children estimated the capacity of A and then measured the capacity of A, estimated the capacity of B and then measured the capacity of B and so on. Thus, they can reflect on the reasonableness of their original estimate each time and use this to refine their next estimate so that it might be more accurate. This helps them internalise a sense of capacity, and to use this sense to produce more accurate estimates.

When the children have experienced using a variety of instruments for measuring capacity, they should then be afforded the opportunity to choose which instrument (and which standard unit) is most appropriate to measure the capacity of various containers. In this way, the children start developing the notion that while many approaches can be taken, some are more efficient than others, and the most efficient approach will also depend on the target object being measured. This is the same as the Operation Maths approach to operations throughout the classes; there can be many approaches and some are more efficient than others, depending on the numbers/operations involved.  The aim is for the children to become accurate, efficient and flexible thinkers.

Renaming units of capacity

From fourth class on, the children will be expected to rename units of capacity, appropriate to their class level. While changing 1,250 ml to 1 l 250ml or 1.25 l, will typically be done correctly, converting figures which require zero as a placeholder (eg 1 l 50 ml, 2.6 l ) can be more problematic, and can reveal an underlying gap in understanding, that is not revealed by the more obvious measures. In these cases, the children should be encouraged to return to the concrete experiences as a way of checking the reasonableness of their answers, eg:

  • “1 l 5o ml…well 1 l  is 1,000 ml and then there’s 50 ml more so it’s 1,000 plus 50, which is 1,050 ml.
  • “2.6 l equals 2,600 ml because 1 l is 1,000 ml, so  2 l is 2,000 ml and .6 is slightly more than .5, which is half of a l or 500 ml, which means .6 must be 600 ml”

T-charts, another one of the three key visual strategies for problem-solving used throughout Operation Maths, can be very useful when renaming units of capacity, as can be seen below. These can be partially started on a class board and the children then asked to complete the T-chart with their own choice of capacities as is relevant to the tasks required of them. The children could construct these also to use as a reference, as they progress through this topic.

 

 

Capacity & Volume

Volume is introduced officially for the first time in 6th class. It is preferable to introduce the children to volume via cubed units (eg blocks) as opposed to via cubed centimetres (see below).

From Operation Maths 6

 

HINT: Did you know that the smallest base-ten blocks (ie those often used as units or thousandths),  are 1 cm cubed? This means that these could be used to build shapes from which the volume of the shapes can be measured and they can be used to measure the approximate volume of an open cuboid eg lunch box, pencil box, etc.

The children may find it challenging to appreciate the relationship between capacity and volume, especially since they may think capacity is exclusive to liquids while volume relates to solids. Providing the children with opportunities to measure the the capacity of a variety of different sized cuboids (eg lunch box) and then measuring its volume using 1 cm cubes, will likely lead the children to discover the connection between the two concepts and that 1cm cubed equals 1 ml.

From Operation Maths 6



Further Reading and Resources:

Digging Deeper into …. Weight (all classes)

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For practical suggestions for families, and helpful links to digital resources, to support children learning about the topic of weight, please check out the following post: Dear Family, your Operation Maths Guide to Weight

NB: While strictly speaking, the term “mass” is more correct to use than the term “weight” (since mass is measured in kilograms and grams), in Operation Maths, we defer to using the term “weight” as that is the term used in the Primary Maths Curriculum (1999), as well as being the term most frequently used by the general population. To find out more about the difference between mass and weight, click here.

 

Initial exploration – CPA approach

Like the topic of Length, and in keeping with the over-arching CPA approach of Operation Maths, children’s initial experiences of Weight at every class level should focus on hands-on activities, using appropriate concrete materials.

In the infant classes, this should occur through exploration, discussion, and use of appropriate vocabulary eg heavy/light, heavier than/lighter than, weighs more/less etc. The children should also be enabled to sort, compare and order objects according to weight.

Irrespective of the class level, introductory exploration in this topic could follow the following progression or similar:

  • The children examine pairs of objects and make comparisons, e.g. lunchbox and schoolbag, chair and book, crayon and pencil case. Encourage the children to ‘weigh’ these objects in their hands; using outstretched hands, either to the side or in front of the body, as this can help the children get a better sense of which object is heavier/lighter.
  • Elicit from the children how they might verify their hand-weighing. Introduce a balance and demonstrate how to use it. If sufficient balances are available allow one per group of four to six children. If there are not enough commercial balances, a simple alternative is to use a clothes hanger, from which two identical (ask the children why these need to be identical) baskets, trays or bags are hung (see video below).

  • Move on to pairs of objects whose difference in weight may not be obvious, e.g. crayon and marker. Let individual children test pairs of objects on the balance.
  • Examine pairs of objects where one is larger but lighter, (e.g. a big piece of paper and a stone, a ball of cotton wool and a pebble, a feather and a marble) and pairs of objects where the objects may have a similar size but different weights (eg a ping pong ball and a golf ball). These experiences enable the children to understand that weight is not related to size.
  • This can then progress to incorporate a direct comparison of the weight of three or more objects, to now also include the labels heaviest/lightest. It is important at this stage that the children realise that if A is heavier than B and B is heavier than C, then, without further direct comparisons, we know that A is heavier than C, that A is the heaviest of all three and C is the lightest. This is a very important concept for the children to grasp.
  • In a similar way, the children can estimate and record the weight of objects using non-standard units (e.g. cubes, marbles etc) and standard units of weight (e.g. a bag of sugar as a kilogram weight). Initially, when using standard units (e.g. kilogram) they will be recording the weight of objects as being heavier than/lighter than/the same weight as a kilogram.

HINT: 1/2kg and 1/4 kg weights for comparison can be made using that weight of rice, sand etc in ziploc bags. Challenge the children in 2nd class up to come up with ways to make these, and other, weights using only the balance (ie without using a scales). Making these weights could become an alternative homework task.

 

Using scales: estimating & measuring

From Operation Maths 5, Pupils’ Book

As the children progress in their understanding of the concept of weight they will begin to appreciate the need for more accurate means to record weight, i.e. using a weighing scales. It is an advantage to have a wide selection of different types of scales available (including kitchen and bathroom, digital and dial) so that the children appreciate that not all scales are the same, and that their measuring skills have to be flexible enough to be able to adapt to the different types.

HINT: Some scales (eg luggage scales, etc) can often be purchased relatively cheaply from value shops. Alternatively, ask the children to bring in a scales from home to use in class while working on this topic.

As always, the children should be encouraged to estimate before measuring.  This can be done by hand-weighing and can incorporate the comparison of the weight of the unknown object with that of a known weight eg holding a lunch box and a bag of sugar in outstretched hands and estimating the weight of the lunchbox in kg and g based on how much heavier/lighter it feels in comparison to the 1kg weight.

Rather than estimating the weight of A, B, C and D before weighing A, B, C and D, it would be better if the children estimated the weight of A and then measured the weight of A, estimated the weight of B and then measured the weight of B and so on. Thus, they can reflect on the reasonableness of their original estimate each time and use this to refine their next estimate so that it might be more accurate. This helps them internalise a sense of weight, and to use this sense to produce more accurate estimates.

When measuring weight using scales with dials, advise the children to first examine the markings to identify the major makings and to calculate the measure of the minor makings/intervals. When appropriate to the type of scales, encourage the children to read the scales at eye level to obtain a more accurate reading. For demonstrations purposes, a large interactive scales such as the one here, could be used

When the children have experienced using a variety of scales they should then be afforded the opportunity to choose which instrument (and which standard unit) is most appropriate to measure the weight of various items. In this way, they start developing the notion that while many approaches can be taken, some are more efficient than others, and the most efficient approach will also depend on the target object being measured. This is the same as the Operation Maths approach to operations throughout the classes; there can be many approaches and some are more efficient than others, depending on the numbers/operations involved.  The aim is for the children to become accurate, efficient and flexible thinkers.

Renaming units of weight

From fourth class on, the children will be expected to rename units of weight, appropriate to their class level. While changing 1,250 g to 1kg 250g or 1.25 kg, will typically be done correctly, converting figures which require zero as a placeholder (eg 1 kg 50 g, 2.6 kg ) can be more problematic, and can reveal an underlying gap in understanding, that is not revealed by the more obvious measures. In these cases, the children should be encouraged to return to the concrete experiences as a way of checking the reasonableness of their answers, eg:

  • “1kg 50g…well 1 kg  is 1,000g and then there’s 50g more so it’s 1,000 plus 50, which is 1,050g.
  • “2.6kg equals 2,600g because 1kg is 1,000g, so  2kg is 2,000 g and .6 is slightly more than .5, which is half of a kg or 500g, which means .6 must be 600g”

T-charts, one of the three key visual strategies for problem-solving used throughout Operation Maths, can be very useful when renaming units of weight, as can be seen below. These can be partially started on a class board and the children then  asked to complete the T-chart with their own choice of weights as is relevant to the tasks required of them. The children could construct these also to use as a reference, as they progress through this topic.

Further Reading and Resources:

Digging Deeper into … Symmetry (2nd to 4th)

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

Symmetry is officially a strand unit for second to fourth classes, although it also features as a content objective in 2-D shapes for fifth and sixth class where the children “classify 2-D shapes according to their lines of symmetry”.

While there are different types of symmetry, the curriculum specifies line symmetry, also known as mirror symmetry, reflective or reflection symmetry.

In Operation Maths, this chapter is placed after 2-D shapes, so that the children can identify symmetry in the shapes that they have previously encountered, and, in third  and fourth class, it is placed after Lines and Angles so that they can use their knowledge of different line types when describing the lines of symmetry.

Concrete exploration

To complete or create symmetrical patterns, requires the children being able to visualise the mirror image of the given arrangement/image. But children cannot visualise what they have not experienced. Thus to experience symmetry the children must:

  • be made aware of examples of symmetry all around them, and locate examples themselves e.g. flowers, leaves, objects at home and at school, numbers and letters of the alphabet.
  • be afforded ample opportunities to use real mirrors to explore symmetry. The type of child-safe mirrors that are often used in science investigations (eg in the strand unit of light) are ideal for this purpose.

Using mirrors allows the children the opportunity to observe symmetry and to check the accuracy of their completed patterns.  When using mirrors:

  • Try to have enough mirrors for one between two (the child-safe mirrors can often be cut into smaller sizes, 10cm x 7cm approx is big enough), or if supply is limited the mirror exploration could be incorporated as a station in a station/team teaching maths lesson.
  • Initially, allow the children free exploration and then, when suitable, guide it towards a purpose using questioning:
    • What letters or numbers look the same in the mirror? What shapes or images in the environment look the same in the mirror?
    • Can you put the mirror along the middle of any shapes and numbers so that they look complete? Does this work with any shapes or images from the environment? Don’t specify “middle” as being horizontal or vertical, and then see if the children realise that, on some figures, there is more than one than one way that the mirror can be placed.
  • At this point you could use this as the introduction to a separate and distinct What do you notice? What do you wonder? activity, and use the children’s wonder questions to guide the course of the rest of the lesson.
  • Explain that, on the symmetrical figures, the position of the mirror, is referred to as the line of symmetry. Then ask the children to use the mirrors to identify/draw the line of symmetry on the figures or mark the line of symmetry first (more challenging) and then check using the mirror.
  • Using the mirrors the children can create and check symmetrical patterns using cubes, counters, objects etc. One child can create a pattern that their partner has to complete symmetrically. Since children often incorrectly replicate the pattern (eg as done in the first image below) rather than reverse it, the mirror can show them their error (as used in second image below). Encourage the children to realise that whatever is closest to the mirror/line of symmetry on one side will also be closest to the mirror on the other side.

  • The children could then progress to creating symmetrical arrangements of more than one row. The Operation Maths twenty frames (free with Operation Maths 1 and 2) can be very useful for this (see below). Again the children should be encouraged to recognise that the colour and type of object/figure that is closest to the line of symmetry on one side should also be closest to the line of symmetry on the other side.

When the children have had sufficient experience with actual mirrors they should progress to completing activities without them, although they could always be returned to again if needs arose.

Further Reading and Resources

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