# Monthly Archives: October 2017

## Digging Deeper into … Time (all classes)

Category : Uncategorized

Time is an integral element of our daily lives and therefore an essential, “need-to-know” topic in primary maths, particularly for those children with special educational needs or learning difficulties. However, it is also a very difficult mathematical concept, and one with which many children struggle, for a number of reasons:

•  Time is abstract; it cannot be touched, or manipulated, or seen (although we can see its effects when we look in the mirror!).
• The standard units of time do not reflect the familiar structures of our base-ten place value system i.e. 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day, 7 days  = 1 week etc.
• It can be displayed in analogue and digital forms and, furthermore, digital times can use a 12 or 24 hour system.
• It is not uniform around the globe; each country belongs to a time zone and the time is different in each time zone.

Furthermore, there is a distinct difference between identifying a particular instant/moment in time (i.e. the skill of reading or telling the time) and understanding the concept of duration and the passage of time. In many cases, children may know how to tell the time, without having any real understanding of the concept of duration. Remember, that just because a child can read the digits on a digital clock/watch, or even read time from an analogue clock/watch, this does not mean they understand time as a concept.

As explained in all of the previous Digging Deeper posts, Operation Maths is based on a CPA approach. And, while we acknowledge that given the abstract nature of time is can be difficult to represent it concretely, Operation Maths does introduce the empty number line as a way to pictorially represent elapsed time (see below in post).

### Telling Time

Telling time requires the children to:

• develop an understanding of the size of the standard units of time eg days, weeks, hours, minutes
• be able to estimate and measure using units of time
• read and tell the time using both analogue and digital displays (12 hr & 24 hr).

The analogue clock has its own features that can further complicate matters; there is a “past” half and a “to” half; when reading times on the hour, the hour is said first (eg 3 o’clock) but when reading all other times the hour is said last (eg half past 3). Other valid questions that a child might have about the conventions of reading time include:

• Why do we only say half past; why not half to? (Interesting point: the German for half past three, translates literally into English as half to four)
• Why do we say half past; why not 30 past?
• Why do we say quarter past/to; why not 15 past/to?

More often than not, when teaching analogue time, teachers tend to get the children to focus on the position of the long/minute hand and to use that to tell the time eg “if the minute hand is at 12, it is o’clock”, “if the minute hand points at 6, it is half past” etc. However, this type of explanation can in itself be very confusing, with many children interpreting half past any time as 6 o’clock, quarter past any time as 3 o’clock etc.

In fact, the first thing a child should be able to read is the bigger unit of time i.e. to identify the hour (hence, the first mention of telling time in our Primary Mathematics Curriculum is telling time to the hour, in senior infants . To do this, the children should, logically, look at the hour hand, which, although it is shorter than the minute hand, can often be wider on real analogue devices, emphasizing its significance. When the hour hand points straight at a number, then it is that time; when it points half way between two numbers, it is half past the previous hour (also the lesser number). In this way, the children will be enabled to tell time in relation to the hour eg “it’s nearly 2”, “it’s just gone past 7”, “it’s around half 5”, etc. Consider also how many children, when drawing hands on a clock to show time, will often have the hour hand pointing straight at the number even if it is half past, quarter past or a quarter to the hour. Focusing initially on the hour hand rather than the minute hand, highlights the fact that the hour hand also travels around the clock as the hour passes, and doesn’t jump from one hour to the next. A real or made clock with only the hour hand can be very useful here to teach this concept. Or use the Operation Maths Clock eManipulative (pictured below), and ask the children to look only at the red hour hand. The Two Clocks problem from NRICH can also be used to reinforce the importance of the hour hand.

Next, draw the children’s attention to the blue minute hand and to the blue minute markings around the edge of the clock. Logically, the minute hand has to be the longer hand because it points, beyond the numbers, at the minute markings which are furthest out from the centre, whereas the hour hand points to the hours (numbers) which are typically closer to the centre, and thus the hour hand is shorter. Emphasise that the minute hand enables us to become more accurate in our measurement of time. “O’clock” is actually an abbreviation of “of the clock”, so then when the minute hand points to the top of the clock , it is o’clock. Avoid saying “when the minute hand points to 12 it is o’clock” as the minute hand is actually pointing to the minute markings around the edge and not to the hours, which instead is the purpose of the hour hand.

At this point, it can be useful to use a cut-out paper circle (see below) to represent the clock and fold it in the centre to show both halves of the clock. Thus we can explain that when the minute hand points at the bottom/base of the clock, it is half past, as the minute hand has now passed through half of the clock. In a similar way, use the paper circle to make quarters and emphasise that when the minute hand has passed a quarter way through the hour, it is a quarter past, and when the minute hand is a quarter away from the next hour, it is quarter to. However, it should be acknowledged that, while it would be mathematically correct to say it is three quarters past the last hour (which prepares them for digital time), the convention used is to describe time in terms of how it relates to the next hour once it has passed the half-way point, at the bottom of the clock. Return to the paper circle at this point and label each half “past” and “to”. “Past” and “to” are also clearly labelled on the Operation Maths Clock eManipulative (see above), along with arrows to indicate the clockwise direction in which the hands travel.

When the children are ready, they should begin to measure time in minutes also (reading time in 5 minute intervals is on the curriculum for third class). Again, focus their attention on the blue minute hand and on the blue minute markings around the edge. In this way, the children may initially begin counting  the minutes in ones around the edge before realising that it is more efficient to count in groups of five, which co-incidentally, are also marked by the hour numbers. Creating and using peek-a-boo clocks can help reinforce this idea.

It is essential that when teaching digital time that the connection between analogue and digital is emphasised from the start. The Operation Maths Clock eManipulative is very useful in this regard as both clock types can be shown concurrently (see below). It is also includes the feature to hide/reveal the time in word form, as well as the feature to produce a random time on either clock, which can then be displayed manually on the other clock to match. For ease of use the teacher can also select the options that best suits the class level and ability eg hours only, time to half hours, quarter hours, five minutes, individual minutes.

Equally customisable is the What Time is it Mr. Wolf game from Teachers Pet. A free version can be played online and there is also a paid app available to download from the iTunes store for iPads.

### Time as Duration

It is very important that the concept of time as duration is emphasised from the start. Duration of an event requires noting the starting and finishing points of time.
Developing a solid understanding of duration develops from a child’s experience  and understanding of:

• Sequencing activities (eg pictures  of familiar/daily events, seasons etc)
• The language of time such as before, after, soon, now, earlier, later, bedtime and lunchtime
• The standard cycles of time (seconds, minutes, hours, days, months, seasons etc ) which in turn follows from the sequencing of daily events.
• Measuring duration (using non-standard units initially, and then standard units)
• How long does it take to …..? Estimate & measure
• How many ….can you do in …? Estimate & measure
• What if you do it faster/quicker…? (this in turn develops an understanding of the relationship between speed and time)
• Comparing the duration of two events, (using non-standard units initially, and then standard units) eg what takes longer/shorter? How much longer/shorter is ….. than …..?

Developing an understanding of duration also requires the ability to visualise the passage of time in some way. For this purpose, empty number lines, one of the key problem solving strategies used in Operation Maths, are extremely useful. This can start with drawing an empty number line on the IWB or on the Operation Maths MWBs, to which class/question appropriate details can then be added:

• What hour is after 9 o’clock? 11 o’clock? 12 o’clock?
• Ann’s school starts at 9 o’clock. What time is it 2 hours later? 2 hours earlier? 5 hours later?
• If Ann’s school finishes at 2:30 for how long is she at school?
• Umair’s school starts at 9:30 and finishes at 3:00. For how long is he at school?
• How long is it from the start of the 11 o’clock break to the start of the next break?

In Operation Maths, empty number lines are presented as a viable alternative, to the traditional column method approach, for calculating time. In many other countries, the traditional column method used for calculations involving units, ten, hundreds etc., is not encouraged, or not used at all, for calculations involving hours, minutes etc. However, as our Primary Mathematics Curriculum here in Ireland, still specifies the use of subtraction to solve elapsed time problems, Operations Maths has opted to present both ways in the books.

To view an excellent video of students solving elapsed time problems using an empty time line, please click here.

### Other tips and suggestions for teaching time

• Refer to, and use, aspects of time as much as possible during the school day, as appropriate to the class level e.g.:
• Assign times for tasks and show interactive count-down timers on the IWB. This loop timer is particularly useful for timing stations in class.
• Reference calendar facts such as the current, previous and next day, date, month, season, etc every morning.
• Have a calendar visible in the classroom, marked with significant dates eg school play, outing, pupil birthdays etc. Ask the children to tell you how long it will be (in hours, days or weeks) until certain events.
• Encourage the children to wear watches themselves, with a preference for analogue, as an awareness of analogue time better develops the children ability to appreciate the passage of time.
• When writing time in digital format always use a colon (as seen on digital displays) as opposed to a dot i.e. 10:30 as opposed to 10.30. Using a dot, which is identical to a decimal point, doesn’t help the child to recognise that the system of measuring time is inherently different from our base-ten place value system.

## Maths Week Project: #MathsAroundUs

Category : Competitions

For Maths Week, we want you to observe your surroundings and look for signs of Maths around you.

From the 14th of October until the 22nd of October, we invite teachers, students, children and everyone to tweet us photos/video of any sign of Maths that you see in your classroom, school or locality with #MathsAroundUs. Make sure to include a caption of the sign of Maths you discovered in your post.

At the end of Maths Week, we will select an entry to WIN a €50 One4All voucher.

Project Conditions
Please note that by participating in this project, you agree to have your photo/video used by Edco for promotional purposes.
You can enter as many times as you like.
Winner will be picked at random and announced on 23rd of October.

## Maths by Month – October

Category : Uncategorized

Welcome to the second installment in a new 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.

In each monthly overview, there will be links to other 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.

### Operation Maths Jr Infs to 2nd classes:

• Junior Infants will spend most of this month comparing and ordering objects according to length, width, height, weight, thickness or size, before extending this to comparing equivalent and non-equivalent sets. The key is to have the children engaged in activities using a wide range of concrete materials, ranging from mathematical equipment (such as Cuisenaire rods, attribute bears, attribute shapes, cubes etc) to real objects in the classroom (pencils, crayons, etc) and from the environment (leaves, twigs, shells, stones etc).  They will also begin to identify, copy and extend simple patterns.
• The TRB has lots of suggestions for practical activities and stations using a concrete materials.The Ready Set Go Maths programme also has a whole suite of suitable activities.
• Don’t forget to use the Sorting eManipulative on edcolearning.ie. Drag out images onto the blank work space to compare (there are attribute bear images, shapes of different sizes etc), to create simple patterns and use the Venn diagram background for comparing sets.
• You could also use the Bar Modelling eManipulative to create bars of different lengths, similar to Cuisenaire rods. Other very useful interactive resources for representing Cuisenaire Rods include this one from NRICH and  this one from the Maths Playground
• Senior Infants will spend the first week of the month doing activities similar to that of Junior Infants, ie  sort and classify sets of objects as part of Data and identify, copy and extend simple patterns as part of Algebra. Thus, the Junior Infant suggestions above will also be relevant here.
• Senior infants will also be exploring the sequencing of daily and weekly events, stages of development and the seasons as part of the strand unit Time.
• Weeks 3 and 4 are largely concerned with counting and analysis of number and, in particular, using the Operation Maths ten frames for this purpose. If you are not overly familiar with ten frame and their purpose, you could read this post. Ten Frame images are also a core component of the Number Talks for Junior and Senior Infants, which are all accessible by scrolling down to the Junior and Senior Infants sections in this post.
• First Classes will continue with Number, counting and numeration to cover all the “teen” numbers to 19. Teen numbers are widely acknowledged as common hurdles for children and so time spent now will be time well spent for the future.
• As mentioned in September, the Operation Maths frames are invaluable tools for this topic.
• Similar to infants, Ten Frame images are also a core component of the Number Talks for First classes, which are all accessible by scrolling down to the First class section in this post.
• Recommended reading also includes these two blog-posts: Count on Me and Show Me.
• Second Classes will start the month by consolidating their understanding of ordinal numbers, from the activities completed on the last week of September. As mentioned in Maths by Month September, there is a list of online interactive games here that could be used.
• In comparing equivalent and non-equivalent sets, the children will use the inequalities symbols (<, >) for the first time. Many children will struggle with selecting the correct symbol to use, even if they can identify the larger or smaller quantity. Interactive quizzes like this one from That Quiz or this one from ixl.ie can provide opportunities for extra practice. However, it is preferable for there to also be a visual representation of the number, for example using stacks of cubes, base ten blocks, straws or base ten money (10c and 1c coins). As well as using the actual concrete materials, the Sorting eManipulative can be used to demonstrate how to do this using images of base ten materials; see Ready to go activities 2.3 and 2.4 as examples.
• In Operations, the children will use and develop their strategies of doubles, bonds of ten and making 10. Worthwhile resources to accompany this include the addition Number Talks for second class, which are all accessible by scrolling down to the second class section in this post.
• Another objective is to solve problems involving addition to 20. While bar models do not appear until Operation Maths 3, the children could use and explore simple bar models to achieve this objective. Thinking Blocks Jr are based on simple bar models and could be shown to the class on the IWB while the children suggest answers and labels on their Operation Maths MWBs.  Then the children could draw simple models in their books to help solve the word problems there. The Bar Modelling eManipulative could also be used to create bars of different length.
• Also recommended viewing (if you didn’t view them last month) is the following videos, from Origo One, listed below:
• 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 for your class level.
3. Click on the Edco Resources icon (on book cover image on left-hand side)
4. Select Weblinks from list of categories and then click to download the document.
• 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.

### Operation Maths 3rd to 6th classes:

The October plan for these classes has deliberately allowed for a free week, to enable teachers to engage with Maths Week, held every year at this time. If you would like some suggestion for Maths Week activities, scroll down to the next section.

The topics for this month are:

Click on each link above to access more in-depth information and links on each of the topics for this month.

### Other suggestions for October:

• As mentioned above, with every October comes Maths Week. This year, Maths Week will run from 14-22 October. Make sure to register your school at the link above and then organise some fun maths activities for your class or school. You can follow the links in the site to find out more about Maths mazes, Maths Art (which coincidentally links very well with October Operation Maths for 3rd and 4th classes ie tessellations in 2D shapes), Maths and historycode breaking and lots more.
• You could also make Maths Week become a game-themed week in your class. Teachers of third to sixth classes could use the Games Bank in the Operation Maths TRB. Teachers of infants to second classes can use any of the games listed in the short-term plans in their TRBs.
• Another option for Maths Week, if you didn’t already do it in September,  is Jo Boaler’s  Week of Inspirational Maths. Click on the link for an overview of the activities in Week of Inspirational Math, and scroll down to the bottom of the page to access all the resources; K-2 roughly align with Infants to 2nd and Grades 3-5 roughly align with 3rd-6th classes.