Maths for June

Maths for June

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.

Operation Maths: A Unique Approach to Problem-Solving

In this post, we will look specifically at the Operation Maths approach to problem-solving in the senior end books (3rd to 6th classes). In a subsequent post, we will look at how this approach develops in the junior end books (infants to second classes).

Presenting children with an abundance of mathematical problems does not automatically transform them into competent and confident problem-solvers. Rather, the children must be explicitly taught a range of problem-solving
strategies and they must be facilitated in applying and practising the strategies repeatedly in a range of different contexts.
Operation Maths has an integral multilayered approach to problem-solving throughout the 3rd to 6th class books:

  • A variety of key problem-solving strategies is introduced, explored and applied to various real-life contexts in a developmental and spiral way through the classes (i.e. bar model drawing, empty number lines, T-charts , branching etc)
  • Regular Work It Out! sections throughout the chapters in the pupils books provide the children with opportunities to apply and hone their problem-solving skills.
  • Let’s Investigate! sections at the end of the Pupils’ Books where the focus is on open-ended problems
  • Thematic revision spreads with a strong problem-solving focus.
  • Extra problem-solving in Early Finisher photocopiables.

All of this happens as part of a larger problem-solving approach based on the acronym RUCSAC. This approach, which can be used as a whole school problem-solving approach, is also reinforced and explained for both children and parents on a convenient French flap/bookmark on the Discovery Book (see images from flaps below), which encourages the children to use RUCSAC as an aid when problem-solving.

Problem-solving skills

The ability to reason mathematically is fundamental to being able to solve mathematical problems. However, reasoning mathematically requires not just one, but a number of mathematical skills e.g. being able to
• Work through a problem in a systematic way
• Predict an answer
• Identify the relevant information and understand what type of answer is being sought
• Visualise the problem mentally or being able to represent the components of the problem in either a pictorial or abstract (using only numbers and symbols) way.
• Plan or decide what approach to take
• Work to get an answer
• Check that the answer is suitable and accurate.

What is fundamentally different about the Operation Maths approach to problem solving is that the children are being taught specific strategies to develop the aforementioned skills, in a spiral and progressive way, in order to equip the children with the necessary skills for them to become capable and confident problem-solvers.

Central to the Operation Math approach to problem solving is RUCSAC. This clear, sequential approach enables the children to work through problems in a systematic way, while simultaneously utilising the mathematical skills that are being developed with and throughout the chapters.

 

RUCSAC and the Specific Strategies taught in Operation Maths

RUCSAC is an acronym, where each letter represents one of the six distinct phases of this problem-solving approach (see below). However, this more than just a clever mnemonic, as each of these phases is supported by the development of specific strategies throughout the programme, which support this approach.  These specific strategies are as follows:

Read – Estimation strategies:

  • Reasonable answer: Would you predict a bigger or smaller answer? How many digits would you expect in the answer
  • Front-end estimation: Look at the digits at the front of the numbers
  • Rounding: Round each number to the place of the highest value digit e.g. tens, hundreds, thousands.
  • Rounding to fives: (only in OM6): Usually we round to the nearest tenth, unit, ten, etc. But if the number(s) involved are approximately in the middle, it is more efficient to round them to the nearest five tenths, 5, 50 etc. to get a more accurate estimate. (OM6, Pupils Book p 30)

Underline – Colour coding operational vocabulary:

  • Identifying specific phrases, colour coding them, and recording them on in the Discovery Book. This forces the child to engage with the language of problems and to decode them. However, this only suits word problems which contain obvious operational vocabulary or that which can be easily inferred.

Create – Creating visual representation to show the information in the problem, as part of a CPA approach:

  • Using concrete materials (e.g. counters, cubes, children etc.)
  • Using bar model drawings
  • Using empty number lines
  • Using T-charts (OM4 to OM6)
  • Making/completing a table, grid, list etc.
  • Creating number sentences (and/or equations with variables in OM6)

Select – Selecting a suitable and efficient approach:

  • Using a mental method, e.g. petitioning, sequencing, compensating etc.
  • Using a written method e.g. a formal algorithm, jottings, branching
  • Using guess and test

Answer – Answering the question:

  • The teaching panels demonstrate how to layout and position work clearly and sequentially
  • Children are encouraged to “show your thinking”

Check – Checking answer(s):

  • Comparing the answer to the estimate, e.g. does it look reasonable?
  • Using the inverse to check.

Furthermore, as part of this approach, specific visual strategies are introduced and repeatedly used where appropriate:

  • Empty Number lines
  • Bar Models
  • T-charts

 

Empty Number Line (ENL)

Simply, a horizontal line, initially with no numbers or markings that helps develop a child’s number sense, their ability to visualise numbers and to compute mentally.
Also known as a blank or open number line, empty number lines can be used to show elapsed time, operations, skip counting, fractions, decimals, measures, money (making change) and much more (see image below).

While, strictly speaking the number line should initially start empty (i.e. no numbers or markings), in Operation Maths, some of the required numbers and/or markings have been provided, to act as scaffolding for the child. Ultimately, it in envisaged, that as the child grows more confident of this structure, he/she should be able to construct an empty number line from scratch in order to help solve other problems. I is also hope that through using this structure the child would be able to develop this ability to visualise numbers in such a way and, in doing so, enhance their ability to compute mentally.


Bar Models

These are simply drawing(s) that resemble bars, (like that seen in bar graphs), that are used to illustrate number relationships. There are two main types, part-whole bar models and comparison bar models.


Part-whole model:
which can represent a whole amount that is subdivided into smaller parts. In Operation Maths these are used to represent:

  • Addition/subtraction: where a whole amount has been subdivided into two or three amounts/parts and either the value of one of the parts or the whole/total is required
  • Multiplication/division: where a whole amount has been subdivided into equal amounts/parts and either the value of one/some of the parts or the whole amount is required
  • Fractions, ratios, decimals and percentages: Where a whole amount has been subdivided into equal amounts/parts and either the value of one/some of the parts or the whole amount is unknown.

Comparison models:  which are used when comparing two or more quantities. In Operation Maths these can be used to represent:

  • Addition/subtraction and Multiplication/division: where two amounts are being compared and the value of one of the amounts or the difference between the amounts or the total value of the amounts is being sought.
  • Fractions, ratios, decimals and percentages: Where two or three amounts are being compared and the value of some of the amounts, the difference between the amounts or the total is unknown. This can also be a very effective way to calculate selling price and cost price when given percentage profit/loss

 

T-charts

A T-chart is simply a table, usually divided into two columns, giving it a T-shape. They can be used as a means to aid calculations and/or to identify patterns and connections within problems .

Other strategies

Other strategies used in Operation Maths which promote the visualising and decoding of problems include:
• Using number bonds and branching
• Making lists
• Using “guess and test” (also known as Trial & Error)
• Using the process of elimination (e.g. logic problems)


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