# Monthly Archives: May 2019

## Maths by Month – June (updated 2019)

Category : Uncategorized

The summer holidays are in sight!

In this June overview for Operation Maths users, there are links to topic-specific posts and articles, as well as a whole host of extra suggestions, links etc. To ensure you don’t miss out on any future Maths by Month blog-posts, please subscribe to the blog via email, on the top right hand of this page.

Pssst! Book lists not finalised yet? Please consider Operation MathsNumber Facts, Bua na Cainte, Exploring Spelling, Let’s Talk Literacy, Explore with Me and My Learner ID. Click on the links for more information and to view sample pages from each program and/or contact your local Edco reps for samples.

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

• Junior Infants: will be reinforcing their understanding of the numbers 0-5 via the topic of money.
• Senior Infants: Further consolidation of amounts to up to ten via Counting and Numeration, Comparing and Ordering and Combining and Partitioning; the children will be exploring patterns to discover different arrays of the same number, patterns with colour and numbers and odd and even numbers. They are also learning to read time in one-hour intervals.
• First Class: Weight, Patterns, 3-D objects (in particular, connecting their understanding of 3-D objects to their understanding of 2-D shapes)
• Second Class:  More Place Value to 199, Area and revisiting half turns and quarter turns, as part of Lines and Angles
• Third to sixth classes: Operation Maths 3-6 is specifically structured so that the programme can be completed by the end of May, thus covering all of the topics in advance of the standardised testing.
So, you might now 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, there are a whole suite of suitable ideas on this blog post.

Teachers of Infants to Second Class: For helping out with the end of year reports, don’t forget to check out the Excel Record Spreadsheets to accompany all the assessments in the Assessment Booklets; if you have any suggestions for how to improve these, please leave them here.

Operation Maths users can also access a class specific, month-by-month list of relevant links and online resources via the Weblinks document, accessible on www.edcolearning.ie.

2. Click on the At School Book/Pupil’s Book for your class level.
3. Click on the Edco Resources icon (on book cover image on left-hand side)

Also accessible on  www.edcolearning.ie.  are the custom-made digital resources to support these topics. These will all be viewable when you click on the Edco Resources icon as directed above.

### Other suggestions for June:

• Outdoor Classroom Day was May 23 2019. This global event promotes the use of the outdoors to teach, explore and learn. If you missed this day, you might like to do an Outdoor Classroom Day in June instead. There are lots of resources with suggestions for all subject areas, including maths, https://outdoorclassroomday.com/. For more ideas for outdoor maths you could also check out:
• the Maths Around Us activity ideas in your Operation Maths book
• the Maths Around Us videos accessible at https://www.edcolearning.ie/
• this post, Maths fun in the sun
• Online problem-solving webinars: Following the success of their pilot webinar in December, NRICH are hosting two problem-solving webinars on the 11th June that are free and open to all; you just need to register. Starting at 10am, Irish time, they will introduce a problem and invite students to work on it and submit their questions and solutions if they want to. For all details: https://nrich.maths.org/webinar . And if you’re reluctant to get involved, not knowing what it entails, or whether it will be relevant for your class, you can watch and try out the recorded video from the previous pilot webinar here: https://nrich.maths.org/13821

We’re here to help!
If you have any questions on Operation Maths, Number Facts or anything related to primary maths over the course of the school year, please PM or contact Edco Primary Maths via Facebook and/or Twitter

## Digging Deeper into … Chance (3rd – 6th)

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

Chance is one of the most fascinating areas of primary mathematics, since it is concerned with the outcomes of random processes. Thus, the conceptual foundations for areas of mathematics such as probability and combinatorics, can be found in this strand unit.

### The big ideas about Chance:

• When considering random events and/or processes, we can use what we know (eg past experience and/or knowledge of the variables involved) to estimate/predict the likely outcome(s).
• If we identify all the possible outcomes in advance,  we can refine and/or express our prediction using mathematical language.
• However, no matter how accurate the mathematical prediction, the actual outcome(s) is not certain (except in the unlikely case where there is only one possible outcome); that is the element of chance!
• If we collate the results from repeated identical investigations of a specific random process, the actual outcomes (experimental probability) are more likely to reflect the original mathematical predictions (theoretical probability).

### Predicting Outcomes: Terminology

When beginning to discuss and predict the likelihood of various outcomes,  the initial focus should be on the language of chance, and the terminology that accompanies it.

It can be very useful for the children to identify the various terminology, to discuss their interpretation of it and to explore the contexts in which the terminology is used in everyday parlance.

And while some of the phrases are more objective (e.g. impossible, never, certain, sure, definite), much of the language can be more ambiguous and is open to personal interpretation (possible, might, there’s a chance, (highly) likely, (highly) unlikely, not sure, uncertain).

FACT: To avoid ambiguity, some organisations have agreed on a consensus that equates this terminology with a fractional expression or percentage; you can view one such consensus here.

It can be helpful to try to organise this language across a continuum for the children to interpret and establish their meanings in relation to the other phrases. Ask the children to identify terminology that is used when describing the likelihood of something occurring. Use questions/statements to elicit from the children the vocabulary for chance that they already have; this can be the language that they would use to answer the questions from the text above or could be from their responses to questions such as the following:

• What is the chance that it will rain today?
• What is the chance that it will be hot today?
• What is the chance that it will be dark tonight?
• What chance does my team have of winning the league?
• What chance does my county have of winning the All-Ireland Championship?

Ask the children to write this terminology on pieces/slips of paper. Sort the pieces of paper into groups and/or order them along a line (continuum), as shown in the images below, with words that have similar or identical meaning together.

This task is a perfect example of a low threshold, high ceiling task, in that all children can participate and there is no limit to the complexity of terminology that can be incorporated. If mathematical values such as percentages and/or fractions (eg 1 in 2 chance) are suggested, the children should be encouraged to incorporate these, as they see fit.

Indeed, in fifth and sixth class the children should be encouraged to use a continuum which is graded from 0-100% and/or 0-1, and to associate and align the vocabulary with mathematical values (eg impossible/never =0%, might or might not/even chance = 50%, definite/certain = 100% etc).

### Predicting Outcomes Mathematically

Irrespective of whether it is tossing a coin, rolling a dice, spinning a spinner, picking from a bag, choosing a card, etc., the children should always be encouraged to identify all the possible outcomes, to predict outcomes that are more or less likely, and to justify their predictions.

The children can also be encouraged to make more mathematical predictions based on their understanding of the variables involved e.g. if we repeated this investigation 30 times, how many times would you expect each colour would be picked? What about 60 times? 120 times? Express the fraction of the total number number of “picks”, that you would expect for each colour. Can you express any of these as a percentage?

When predicting the outcomes of random processes that involve a combination of variables, it can be very useful to use a type of pictorial structure, such as branching (NB these can also be referred to as tree diagrams), to illustrate the possible outcomes. For example, when predicting the outcomes of a double coin toss, children will often think that each of the three outcomes have an equal chance, when in fact there is double the chance (ie 2 in 4 or 1 in 2 chance) of getting a heads and tails combination, than either both heads or both tails (see diagram below).

However, it is worth noting that, unless the children come up with a similar structure to predict outcomes of combinations, it is preferable to hold back on showing such a structure until they have conducted an investigation, similar to above, where their predicted outcomes did not align to the actual outcomes.

### Conducting the investigations

Once all appropriate predictions have been recorded, we can move on to the most exciting part, the investigating! When conducting chance investigations, it is important that the children recognise that that they need to be conducted fairly and recorded clearly, similar to scientific investigations.

Encourage the children to consider what factors need to be kept the same each time, and how practices could affect the reliability of the results eg:

• When picking items (eg cubes from a bag, cards from a deck) does the chosen item need to be returned each time? Why/why not?
• How many times does an investigation needs to be repeated in order to get a reliable result?

To generate sufficient data, while not spending too much time on each investigation, ten can be a suitable number of turns per child. It can also be a good idea to organise the children into groups of three with rotating roles eg the first child has their turn, the second child records the outcome of each turn and the third child keeps count of how many turns the first child has had, and roles are rotated after ten turns.

### Recording and reflecting on results

As mentioned previously, the children should be encouraged to consider how best to record results. Tally charts and frequency tables can be very useful and link in well with the strand unit of Representing and Interpreting Data. Results of investigations can be displayed in various types of graphs and charts. Children in fifth and sixth classes could also be asked to calculate the average value for each outcome, when all the results of a class group are considered; for example, in the double coin toss, what was the average number of heads, tails and heads-tails combination per group.

Once the results have been collated, it is very important that the children be given time to reflect on the results and to compare them to their predictions. While we would expect an equal number of heads and tails in a single coin toss (ie theoretical probability), the actual results may not resemble these predictions (experimental probability). Such is the element of chance! And this can be a difficult concept for the children to accept, particularly the notion that, even though the mathematics behind their predictions was accurate, the actual outcomes are different.

To explore this further, using a spreadsheet, such as Google Sheets or Microsoft Excel, to collate the results of the entire class can be a great way demonstrate, that when we combine all the investigations, experimental probability (ie the results) is more likely to mirror theoretical probability (the predictions). This can often help reassure the children that the “maths” behind this does indeed work!

TIP: To make life easier for you, we have created a sample spreadsheet for the Double Coin Toss, please click on the link to view (and save/copy). For further information on the values of using spreadsheets to record results please check out this informative article on Probability Experiments with Shared Spreadsheets from NCTM.

• Dear Family, your Operation Maths Guide to Chance includes practical suggestions for supporting children, and links to a huge suite of digital resources, organised according to class level.
• The Operation Maths Digital Resources have specific resources designed to support this strand unit. Full details of these can be found in your TRB. Click here for the Quick Start Guide to the Digital Resources.
• Virtual Maths Manipulatives for Chance: Lots of tools that can be used in many different ways to explore this concept.
• PDST Data and Chance Handbook for Teachers
• Data and chance in the world around us: materials from the PDST workshop
• NRICH: selection of problems, articles and games for chance
• Playing dice, card, spinner games, or indeed any type of chance-based games, can be a great way to get students thinking about probability, while also providing practice with mental computation, estimation, subitising and experience of problem-solving via strategic thinking.
• Don’t forget to check out the games bank in your Operation Maths TRB and/or the last page of the Number Facts books for examples and ideas.
• Check out this Mathwire page for more games that focus on probability.
• For a fifth and sixth class who are exploring combinations, Mashup Math has two excellent videos (view both below) which demonstrate how tree diagrams and area models can be used to identify all possible combinations; both video use contexts to which the children could readily relate.

## Maths by Month – May (updated 2019)

Category : Uncategorized

Welcome to the May installment in this series of posts designed to explore the Operation Maths topics on a month-by-month basis, giving teachers greater insights into the concepts at hand, when they are most relevant.

While each monthly overview will specifically zone in on the Operation Maths topics for that particular month, the information and suggestions will be relevant to ALL primary teachers, whether they are Operation Maths users or not.

Pssst! Thinking about book lists? Please consider Operation MathsNumber Facts, Bua na Cainte, Exploring Spelling, Let’s Talk Literacy, Explore with Me and My Learner ID. Click on the links for more information and to view sample pages from each program and/or contact your local Edco reps for samples.

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

Teachers of Infants to Second Class: is you haven’t yet recorded your Operation Maths End of April Assessments, don’t forget to check out the Excel Record Spreadsheets to accompany all the assessments in the Assessment Booklets; if you have any suggestions for how to improve these, please leave them here.

Operation Maths users can also access a class specific, month-by-month list of relevant links and online resources via the Weblinks document, accessible on www.edcolearning.ie.

2. Click on the At School Book/Pupil’s Book for your class level.
3. Click on the Edco Resources icon (on book cover image on left-hand side)

Also accessible on  www.edcolearning.ie.  are the custom-made digital resources to support these topics. These will all be viewable when you click on the Edco Resources icon as directed above.

HINT: If you are new to Operation Maths this year or have changed class level, be sure to check out the Quick Start Guide to the Operation Maths books and the companion Quick Start Guide to the Operation Maths Digital Resources
Don’t forget that Operation Maths also has you covered for planning whether you’re teaching a single class or multi-class.

### Other suggestions for May:

• May the Fourth Be With You! International Star Wars Day (May the fourth) is almost here!
• Tech Week 2019 is from 11th-18th May next. Some suitable activities for this week could include:
• The Scratch lessons that accompany the Operation Maths scheme.
• These fantastic tasks to develop computational thinking from the Bebras Challenge.
• For more information on dedicated primary events and resources check out the Tech Week site.
• Outdoor Classroom Day is May 23 2019. This global event encourages us to use the outdoors to teach, explore and learn. There are lots of resources with suggestions for all subject areas, including maths, https://outdoorclassroomday.com/. For more ideas for outdoor maths you could also check out:
• the Maths Around Us activity ideas in your Operation Maths book
• the Maths Around Us videos accessible at https://www.edcolearning.ie/
• this post, Maths fun in the sun

We’re here to help!
If you have any questions on Operation Maths, Number Facts or anything related to primary maths over the course of the school year, please PM or contact Edco Primary Maths via Facebook and/or Twitter