Author Archives: Operation Maths

Maths by Month – February (updated 2019)

Category : Uncategorized

Welcome to the February 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.

HINT: To ensure you don’t miss out on any future Maths by Month blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

 

Operation Maths for Junior Infants to Sixth Class:

Teachers of Infants to Second Class: before you administer, score and record the results of the Operation Maths End of Februaury Assessments please check out the Excel Record Spreadsheets to accompany the rest of 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. 

  1. Log into your edcolearning account
  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)
  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.

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 February:

  • Lá ‘Le Bríde, is Friday February 1st. The story of St. Bridgid’s Cloak could be used as springboard into a pattern activity, or a discussion on exponential growth with older students.
  • Ireland’s first game in the 2019 Six Nations (against England in the Aviva Stadium) is on Saturday 2nd February. Some mathematical possibilities:
    • With older children, use the opportunity to explore the rugby union scoring system, and to identify what scores (up to 30, for example) are possible (how?) or impossible.
    • Calculate the number of games to be played; what if the competition had less or more teams, how many games would need to be played then?
    • Use the language of chance to discuss the possible outcomes for each nation in the competition and recognise that while it is impossible to predict the actual outcomes, we can use of knowledge of the teams performances to make informed predictions.
    • Calculate the dimensions of the pitch
    • Run a Fantasy Rugby League in your class
    • Make score predictions for each match and plot how these scores would be recorded on the Six Nations Table
  • Valentine’s Day is Thursday 14th February. Try out these themed problems  and challenges (suitable from first class up) from Mashup Math

 

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 


Maths by Month – January (updated 2019)

Category : Uncategorized

Happy New Year!

And welcome to the fifth 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.

HINT: To ensure you don’t miss out on any future Maths by Month blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

 

Operation Maths for Junior Infants to Sixth Class:

Psst! Teachers of Infants to Second Class: if you have not yet scored and recorded the Operation Maths End of December Assessments please check out the Excel Record Spreadsheets to accompany the rest of 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. 

  1. Log into your edcolearning account
  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)
  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.

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 January:

  • Storytelling Week runs from Sunday 27th January to Sunday 3rd February. While this is primarily a UK based event, it does serve as a timely reminder of the rich role that mathematical stories can play in the early years.  For teachers of infants to second class, be sure to check out the Literacy suggestions within the Integration section of each short term plan in the TRB.

 

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 … Comparing and Ordering (infants to second class)

Category : Uncategorized

Of all the strand units in maths, this topic is one that is very close to the hearts of almost all young children:

  • “She’s got more than me! That’s not fair!”
  • “I want to be first!”
  • “I want to be the biggest!”

This strand unit evolves from the separate strand units of comparing and ordering that, along with the other two strand units of classifying and matching, make up the strand of early mathematical activities. The content objectives for this strand unit are quite similar across the four junior classes, with the main difference being the specific number limits for each class level:

Number > Comparing and Ordering >The child shall be enabled to:

  • compare equivalent and non-equivalent sets (to include the symbols <, >, = in second class)
  • order sets of objects by number (infants to first only)
  • use the language of ordinal number

 

Comparing

As mentioned above, even from when they are very young, most children are quite adept at comparing what he/she has with that of another.

As part of the strand early mathematical activities (i.e. pre-number) the children will already have had experience comparing sets by quantity (but without counting) i.e. identifying which of two sets has an obvious amount more (or less) than another. They will also have been identifying two sets/objects as being the same or different.

In Junior Infants, once children are comfortable establishing the cardinality of sets up to five, the next step is comparing and ordering sets of objects up to five. Since the amount of these sets may often only differ by just one or two, then it is not very obvious, from a visual point of view, which one has more or less. Comparing two similar sized sets requires that the child:

  • Can identify (and, later, write) the correct numeral for that set
  • Understands one-to-one correspondence, and using this can match the items in the two sets, so as to establish which one has more or less
  • Understands the conservation of number i.e. that a short line of five objects situated close together still has more than a longer line of four objects further apart.
  • Does not assume that the quantity of a set with objects bigger (or smaller) in size must be greater (or less) than the other set.

 

How many more?

Once a child is able to identify the greater set, the next step is to be able to state the difference between the sets i.e. how many more plates than cups? This can be a very difficult concept, with which children can struggle for many years.

As with the entire Operation Maths programme, a CPA approach is recommended when teaching this concept and, in particular, to use that which is most familiar to the children:

  • Use items that typically go together eg knives and forks, cups and saucers/plates, children and chairs/coats/school bags. Take a number of each and ask the children to suggest how we could ascertain the number of each. If not siggested by the children, the teacher should demonstrate how to set out the items in groups toegther eg the first knife with the first fork, the second knife with the second fork etc. If the quantities of each are not equal/the same, ask the children to explain how many more of the lesser quantity is required AND to explain how many extra items there are in the larger amount.
  • In a mixed classroom, use girls and boys. Call up a random group of children, ask the boys to line up at the top of the room, and the girls to line up in separate line beside them, so that, where possible, each child is adjacent to one other child in the other line (if you are lucky enough to have square tiles on your floor, ensure that there is a child standing in each square space). Ask the children to identify the children who have a match/partner on the other line and the number of children who do not have a match/partner on the other line. This activity could also be repeated using dolls and teddies, toy farm or zoo animals, attribute bears etc.
  • Use concrete manipulatives and pictures. Start with only two sets initially. Impress up on the children that the easiest way to see the comparison is to “line up” the objects, was done with the children previously. Use a grid of squares* to help with this. Once again, ask the children to identify where there is a “partner” fruit on the other line and the number of fruit that do not have a “partner” on the other line. These are the extras. How many more (extra) bananas than  apples? How many more (extra) bananas than  strawberries?  *The 5×5 grid on  the Operation Maths Sorting eManipulative is very useful here. The Operation Maths 100 Square eManipulative can also be used; select to show counters only and line up two (or more) rows or columns of different colours.
  • Ultimately, it is hoped that the children realise that it is not necessary to establish the exact amount of each set to be able to establish the difference between each set. In the example above, there are two more bananas than strawberries, and it is not necessary to identify the number of each fruit to establish this. This encourages the children to develop efficiency and flexibility in their approaches.
  • As the children move into first and second class, they should still be encouraged to “line up” the sets. If comparing the number of items in two static sets that cannot be lined up, eg an image in their books, the children can represent the number of items in each set using cubes and these cubes can then be lined up to make it easier to identify the difference between each set. This would link very well with their experiences of comparing quantities in pictograms and block graphs from the strand of Data.

It is important that teachers are aware that establishing the extra number in the larger/greater set and establishing how many less/fewer in the smaller/lesser set requires the children comparing the amounts in two different ways. In the example above, to identify how many more bananas there are than strawberries, requires identifying the number of bananas for which there are no corresponding strawberries. However, to identify how many fewer strawberries there are than bananas, requires identifying the number of empty spaces in the strawberries that there are, opposite the extra bananas. While the answer is the same both time, the route to the answer is different, and the latter approach requires the children to count empty spaces, which is more challenging due to its abstractness.

In second class, the children will begin to use the inequalities symbols (<, >). Many children will struggle with selecting the correct symbol to use, even if they can identify the larger or smaller quantity. Thus flashcards or reference cards such as the ones at this link can be very useful to connect both the language and the symbol. Interactive quizzes like this one from That Quiz or this one from ixl.ie can provide opportunities for extra practice. However, as emphasised previously, it may still be necessary to use a visual representation of both numbers being compared, for example using stacks of cubes, base ten blocks, straws or base ten money (10c and 1c coins). In this way, the children are now beginning to use their place value understanding also to compare quantities. 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 (screenshots below).

 

Hint: Developing the children’s ability to compare, will also be of benefit when they encounter the concept of subtraction as difference (as opposed to subtraction as deduction/take-away) and of further benefit when they are introduced to comparison bar models in third class up

 

Ordering

As part of a early mathematical activities, the children will already have experienced ordering objects by length, size etc. Now, they are extending this understanding to order by quantity.

In Junior Infants, once the children are able to count individual sets of up to five objects, this enables them to start ordering the sets of objects.

Counting and numeration are both very important when it comes to ordering:

  • The children are beginning to understand how higher numbers correlate with greater numbers of objects and vice versa.
  • When ordering sets we must also consider the number word sequence i.e. number five comes after the number four so five must be a greater amount than four.

 

Ordinal numbers

The nature of the English words for the ordinal numbers (first, second, third, fourth etc) and the nature of their abbreviated forms (1st, 2nd, 3rd, 4th etc) can pose significant difficulties for children as, at first glance, there appears to be little correspondence between the forms, and the abbreviations may not appear to follow any rule or pattern. Another difficulty lies in the apparent contradiction between ordinal numbers and cardinal numbers; it is typically better to have 10 rather than 1 of anything, but it is typically better to be 1st rather than 10th in any competitive activity.

  • Initially the focus should be on the spoken words only and the activities used should reflect this eg lining up children at the classroom door, asking the rest of the class to identify who is first, who is second, third, last etc.
  • When ready, flashcards of the ordinal words should be introduced and these can be incorporated into the familiar activities eg the flashcard with “first” can be given to a child who must give it to the child in that position in the line.
  • It is better to avoid using the abbreviations until first class and it is also better to start with the words, fourth, sixth seventh and tenth. Write the word fourth on the board and establish that the children can read and understand the word. Explain that for speed we want to find a quicker way to write/indicate this position and ask them to suggest what might be written to replace the underlined part of the word (ie 4th). Repeat this with the ordinal words sixth, seventh and tenth. Ask the children to suggest how fifth, eighth and ninth might be abbreviated and then finally ask for suggestions for the words first, second and third; ultimately, tell them the correct answers if they do not arrive at them themselves. In this way, the children are being prompted to discover the system of abbreviations that we use, as opposed to being just told.

Hint: For first and second classes, there is a list of online interactive games here which will help as extra practice. There are also lots of useful videos on YouTube etc; just search for “ordinal numbers”.

 

Further suggestions:


UPDATED! Operation Maths Assessment Records (infants to second class) on Excel

Category : Uncategorized

At Operation Maths we are constantly looking for ways to improve the usability of our programme, and to make it even more teacher-friendly. The most recent additions included long term plans for various combinations of multi-classes as well as excel versions of our Assessment Records. Following on from feedback from teachers, we have now expanded the original version of the latter, released in October last, to include all the assessments for the entire school year, as well as incorporating extra features designed to make them even more teacher-friendly.

 

 

 

 

While there are already word versions of these assessment records available to download from Edco Learning, as well as the hard copy photocopiables in the Teacher’s Resource Books (TRBs), these excel versions provide teachers with a more efficient and flexible way to both record and analyse the results from the Assessment Booklets:

  • Quickly get a total attainment score for each child (Assessment of Learning)
  • Use these attainment scores to compare the attainment of various individuals and/or groups of children and identify children in need of further support (Assessment for Learning).
  • Quickly get a score for each learning outcome, use these scores to identify the strengths and weaknesses of the class as a whole, while also being able to identify which learning outcome(s) require further consolidation (Assessment for Learning).

And this is all achievable in a very teacher-friendly way:

  • Each of the five assessments ( eg End of October, End of December etc ) has a dedicated page; click the tab at the bottom to move between them.
  • Teachers need only enter the children’s names once only on the first page; the inbuilt formulas then copy these names to the other pages in the document.
  • Under each child’s name, the teacher can enter a score for each question (or page in junior infants); see more below for a suggested scoring system.
  • The score for each individual question (or page) will be automatically totaled (horizontally across bottom) to give an attainment score for each child.
  • When all the scores have been entered for each child, these will also be totaled along the right-hand side vertically to give a total for each learning outcome.
  • After the five assessment tabs, there is a tab entitled “All”. Here all the scores from each assessment will be automatically replicated, once entered on the original assessment tab. This allows the teacher to easily view all the data in one screen. The scores for each child will also be totaled here to give you an overall score.
  • Other useful information provided includes the specific strand and strand unit (S.SU) to which the learning outcome relates. These are abbreviated and a full explanation of the abbreviation is given on the last tab.

HINT: If you already used the version of this document released last October, it is now recommended that you download and use these documents for the remaining assessments. They also include a page for the End of October Assessment, allowing teachers to copy and paste in the October Assessment scores, so as to have all the information in the one document.

Suggested Scoring System

While teachers can devise and use any system which they prefer, one option would be to try the following:

  • 4 = Question answered fully and correctly
  • 3 = Question answered fully but without full accuracy ie almost all correct
  • 2 = Has a majority of correct responses but a number of errors also
  • 1 = Some correct responses but a majority of errors
  • 0 = Not attempted or incorrect responses

Obviously, teachers will have to apply any scoring system in a flexible way; for example if there is a question that requires just one response and is therefore is either correct or incorrect, then only 0 or 4 will be awarded.

Once the appropriate score has been entered for each question then the teacher will have:

  • a total attainment score for each child; the higher the score the more learning outcomes achieved.
  • the means to sort and/or compare the attainment of various individuals and/or groups of children using these total attainment scores and identify those children with the lowest scores as needing further support.
  • the means to to identify the strengths and weaknesses of the class as a whole by sorting/comparing the total scores for the learning outcomes, while also being able to identify which learning outcome(s) would benefit from further teaching.

Downloading and using

The excel documents for each class level are available to download by clicking on the links below:

Operation Maths Jnr Infants Assessment Record BETA

Operation Maths Snr Infants Assessment Record BETA

Operation Maths 1 Assessment Record BETA

Operation Maths 2 Assessment Record BETA

You may notice that these are still BETA versions only. This is because we would welcome more feedback on the usability of these documents.

Feedback can be left on this Edco Primary Maths facebook post or messaged to Edco Primary Maths.

Some questions you might consider answering:

  • Did you find the excel document(s) useful?
  • Did you find the scoring system useful?
  • What suggestions would you make to improve them?

We welcome all feedback!
And it doesn’t have to be specific to these assessment records. Remember, that if you have any suggestions or any questions on Operation Maths, Number Facts or anything related to primary maths, please PM or contact Edco Primary Maths via Facebook and/or Twitter 


Digging Deeper into … Spatial Awareness

Category : Uncategorized

Spatial awareness…being able to describe the position of something/someone in relation to another using words and/or gestures, and being able to represent spaces and locations using models and/or drawings, may, at first glance, appear to have more in common with communication and geography, than with maths. However, the concepts of spatial awareness lay the foundations for all geometric thinking, be it at upper primary, secondary or an even higher level.

Essentially the children need to develop an understanding that:

  • The spatial relationships between objects and places can be described and represented.
  • These relationships may be viewed, described and represented differently depending on the perspective of the viewer (in particular, consider left and right).
  • Developing the ability to mentally visualise the representations will enhance a person’s ability to picture how a shape will look when rotated when turned, flipped etc.

A synopsis of the curriculum objectives for infants to second class, state that the children should be enabled to:

  • explore, discuss, develop and use the vocabulary of spatial relations (describing both position and direction/movement)
  • explore closed shapes and open shapes and make body shapes
  • give and follow simple directions (first and second class), including turning directions using half and quarter turns (second class only)
  • explore and solve practical problems (first and second class)

In the case of the practical problems, this could include completing a jigsaw or a tangram puzzle, using mazes, grids, board games and or exploring basic coding eg via coding programs and apps, such as Lightbot, and more hand-on devices such as BeeBots.

Moving through space

Since spatial awareness requires an understanding of using  space and moving through space, the majority of the activities should be active ones, where the children are moving around. This is where the suggested activities in the Operation Maths Teachers Resource Book (TRB) become extremely useful, such as the examples below.

Much of the language development in this strand unit can be reinforced via activities in PE (Orienteering) and Geography (mapping).

Digital Resources

While activities incorporating physical movement are preferable, the Operation Maths digital resources on edcolearning, provide a worthwhile alternative and add variety. The Ready to Go activities below, as the phrase says are “exactly what they say on the tin”; the teacher need only click on the relevant icon in the digital version of the pupil’s book to open the activity, and the accompanying suggested questions are quickly viewable along the side menu. A full description of the activity, including the questions, is also given in the TRB.

 

 

 

Further Reading


Maths by Month – December (updated 2018)

Category : Uncategorized

Welcome to the fourth installment in this year’s 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.

HINT: To ensure you don’t miss out on any future Maths by Month blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

 

Operation Maths for Junior Infants to Sixth Class:

 

Psst! Teachers of Infants to Second Class: work is well underway on the Excel Record Spreadsheets to accompany the rest of 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. 

  1. Log into your edcolearning account
  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)
  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.

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 December:

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 


Maths by Month – November (updated 2018)

Category : Uncategorized

Welcome to the third installment in this year’s 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.

 

HINT: To ensure you don’t miss out on any future Maths by Month blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

 

Operation Maths for Junior Infants to Sixth Class:

HINT: Teachers of Infants to Second Class – if you have yet to collate the results of your “End of October” Assessments, please check out this useful new addition to the Operation Maths resources that will make this process even more teacher-friendly and informative.

  • 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. 
    1. Log into your edcolearning account
    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)
    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.

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 November:

 

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 … Representing and Interpreting Data (infants to second class)

Category : Uncategorized

Data analysis, whether at lower primary, upper primary, or even at a more specialised level of statistics, is essentially the same process:

  • It starts with a question, that doesn’t have an obvious and/or immediate answer. Information is then collected relevant to the question.
  • This collected information or data is represented in a structured way that makes it easier to read.
  • This represented data is then examined and compared (interpreted) in such a way as to be able to make statements about what it reveals and, in turn, to possibly answer the initial question (if the question remains unanswered it may be necessary to re-start the process again, perhaps using different methods).

Thus, every data activity should start with a question, for example:

When choosing a question it is worth appreciating that some questions might not lend themselves to rich answers. Take, for example, the first question above; once the data is collected, and represented, there is not that much scope for interpretation of results other than identifying the most common eye/hair colour and comparing the number of children with one colour as being more/less than another colour. However, other questions might lead to richer answers, with more possibilities to collect further information, to make predictions and to create connections with learning in other areas. Take, for example, the question above about travel; the children could be asked to suggest reasons for the results e.g. can they suggest why they think most children walked/came by car on the day in question, whether weather/season/distance from school was a factor and to suggest how the results might be different on another day/time of year. Even in a very simple way, the children are beginning to appreciate that data analysis has a purpose i.e. to collect, represent and interpret information, so as to answer a question.

From Operation Maths Jr Infs TRB p. 147

Sets and Data

Data is very closely related to sorting and classifying sets:

  • The initial question may focus on a particular set in the classroom e.g. identifying the most common/frequent occurring item in the set of farm animals, the set of buttons in our button box, the shoes that the children are wearing, the nature items collected on the walk etc
  • Information is then collected by sorting and classifying the items in the original set according to the target attribute.
  • This collections of items are represented in a structured way that makes it easier to compare e.g. items put in lines of same type, use cubes or drawings to represent the actual items.
  • This represented data is interpreted to answer the question and to make other statements about  relationships e.g. which group has more, less etc

Thus sorting and classify activities should be viewed as potential springboards into data activities and it is important that the children realise that they can represent and compare the size of the sets within each sort by graphing them.

CPA Approach

Even as the children move into first and second classes, it is important that their data activities continue to follow a CPA approach:

Concrete: Continuing to use real objects initially to sort and classify ) e.g. the number of different colour crayons in a box, the different type of PE equipment in the hall , the different fruit we brought for lunch etc), progressing towards using unifix cubes, blocks, cuisinere rods etc to represent the same data. Indeed, the children themselves could be used at this stage; sort the children into groups according to eye colour, hair colour,  age etc and get them to organise themselves into lines that represent the same criterion. This is turn can be very useful for the children to realise that how they are lined up is crucial to being able to interpret the data easily and correctly. If you have visible tiles/markings as flooring on the classroom/hall/corridor, these can be used to organise the “data” accurately!

The children can build block graphs using cubes or blocks, laid flat on a piece of paper or their Operation Maths MWBs.

Pictorial: using multiple copies of identical images to make pictograms and/or using identical cut out squares/rectangles of paper on which the children draw an image that represents the data as it relates to them (e.g. how I traveled to school today). These can then be collected and organised into lines, so that it is easier to read the data. As a development, identical cut out squares/rectangles of paper of different colours can be used with the children taking the correct colour as it relates to them (e.g. choosing the colour for their eyes/hair colour etc.) while also progressing towards using a specific colour for a specific criterion (“Take a blue square if you walked to school today”). Thus, the children should begin to appreciate the need to label the graph, axes etc so that the meaning of the represented data can be correctly interpreted.

HINT: A common confusion among children when making vertical graphs of any type is that the pictures/blocks start at the top and go down; an understandable misconception when you consider that in most other activities we work from the top down! A simple way to show how vertical graphs are formed, is to demonstrate, using a concrete Connect 4 type game, how the first counter in each column falls to the bottom and subsequent counters in that column build up from there. If you don’t have an actual Connect 4 game in your classroom you could use an interactive type such as this one here

Abstract: the final stage, where the focus is primarily on numbers and/or digits e.g. identifying how many, how many more prefer this than that etc.

 

Further suggestions:

 

 


Thinking Strategies for Multiplication and Division Number Facts

Category : Uncategorized

What are number facts?

Number facts are the basic number facts that, it is hoped, children could recall instantly, so as to improve their ability to compute mentally and use written algorithms. Traditionally referred to as tables, the multiplication and division number facts typically include all the multiplication facts up to 10 x 10 and their inverse division sentences.

Some of the big ideas about number facts:

  • Some facts are easier than others to recall – which ones, do you think?
  • The easier facts can be used to calculate other facts – which ones, do you think?
  • The same fact can be calculated using various approaches – these approaches are often referred to as thinking strategies – see more below.
  • Using thinking strategies means that the children can apply the understanding, to facts beyond the traditional limits of “tables”.

 

What are thinking strategies?

A thinking strategy is a way to think about a process to arrive efficiently at an answer. For example, if asked to multiply a number by 2, one could double the number. Doubling is a very effective thinking strategy for the multiplication facts of 2, 4 and 8, as can be seen in the video below.

 

Halving is the opposite to doubling. And halving is a very effective thinking strategy to use for the multiplication facts of 5; if asked to multiply a number by 5, one could think of 10 times the number and then halve that amount (see below).

The Operation Maths  and Number Facts books for third and fourth classes repeatedly emphasise (among other thinking strategies) the strategy of doubling and halving known facts to derive unknown facts, eg through doubling I can work out 2 times, 4 times and 8 times a number; if I know 10 times the number I can work out 5 times, etc. 

From Operation Maths 3, possible thinking strategies for 2x, 5x, 10x.

The 100 dots grids on the inside back covers of Operation Maths 3 and 4 and Number Facts 3 and 4 can be extremely useful for the pupils to model various arrangements/arrays, while the teacher can use the Operation Maths 100 square eManipulative to replicate (and label) the children’s arrangements on the IWB.

Using doubling to model 2 x 6, “2 rows of 6”, 4 x 6, 8 x 6 (left) and trebling to model 3 x 7, 6 x 7, 9 x 7 (right)

Furthermore, multiplication and division are taught together throughout the Operation Maths series, so that, rather than compartmentalising each operation, the children develop a better understanding of how both concepts relate to each other. In this way, the basic division facts are easier to acquire, as they are understood to be the inverse of the more familiar multiplication facts. However, it is important that within each group of facts, the children explore the multiplication facts first; the better their understanding of these, the more likely they are understand the inverse division facts. Indeed, “think multiplication” is in itself, a thinking strategy for the division facts (see video below).

 

Traditionally, learning “tables” had been by rote, but current research suggests that this is ineffective for the majority of children. In contrast, children should be taught to visualise numbers and to use concrete materials, images and thinking strategies to use what they know to solve what they do not know. Below are examples of some useful thinking strategies for the basic multiplication and division facts (taken from Number Facts 3 & 4, Edco, 2018)

There can often be different ways to think about the same fact (or groups of facts), and the children should always be encouraged both to identify alternative approaches and to choose their preferred strategy. For example, consider 5 x 9:

5 times is half of 10 times: 10 × 9 = 90, so 5 × 9 = half of 90 = 45
9 times is one set less than 10 times: 10 × 5 = 50, so 9 × 5 = 50 − 5 = 45
9 times is treble 3 times: 3 × 5 = 15, so 9 × 5 = treble 15 = 45

Once the children understand how to arrive at an answer via a thinking strategy, they can then apply this thinking strategy to more complex calculations that are beyond the traditional 10 x 10 ceiling of “tables”; for example if I understand 5 times any number is half 10 times the number, then I can use this to mentally calculate 5 x 18, 5 x 26 etc (see more on this below).

 

Computational Fluency:

‘Fluency requires the children to be accurate, efficient and flexible.’ (Russell, 2000).

The primary aim of both the Operation Maths and Number Facts series (see more information on Number Facts below) is to enable the children to become computationally fluent. To achieve computational fluency, the children must be accurate, efficient and flexible:

  • Accurate: the children must arrive at the correct answer, e.g. 6 x 8  =48.
  • Efficient: the children must calculate the answer in an efficiently. A child who produces an answer of 48 in response to the question 6 × 8 by counting in jumps of six or eight may be accurate but is not efficient.
  • Flexible: children must be able to visualise and mentally manipulate numbers in order to see how they might be broken down and recombined to get an accurate and efficient answer (as shown with the various ways to consider 6 x 8 below).

Thus, flexibility is the key to fluency. A child who only knows that 6 x 8 = 48 becasue they have memorized that fact, is missing out on all the various possible connections between those numbers, subsequently hampering future connection-building. In contrast, a child who is flexible with number facts is one with a well-developed number sense, who can see the connections both between and within numbers, i.e. they can partition and/or combine numbers into more compatible (friendly) amounts and can apply their strategies to numbers beyond those they have dealt with. Therefore, a thinking strategies approach will not only be effective for aiding understanding and recall of the basic facts up to 10 x 10, a thinking strategies approach can enable children to apply these mental computation skills to numbers beyond this traditional ceiling, as shown below.

From Number Facts 4

 

The Number Facts Series from Edco

Number Facts is latest addition to the Edco Primary Maths stable, and it is a series of activity books designed to foster fluency in number facts for primary school children from First Class. The series features an innovative approach to the acquisition of basic number facts, and, like Operation Maths, teaches children to understand, not just do, maths.

Image result for number facts edco

In contrast to the more traditional drill-and-practice workbooks, which just test whether the answer is known, Number Facts teaches children to visualise numbers pictorially and to use these images and thinking strategies to become more adept at manipulating numbers. The specific focus of Number Facts will be to develop children’s thinking strategies and apply these to the basic number facts in such a way as to promote the child’s ability to visualise and recall these facts, thereby achieving fluency.

Both this rationale, and the suggested teaching approaches to the teaching of the basic multiplication and division facts for third and fourth classes, are clearly outlined in the Teachers Resource Book (TRB) which accompanies the series, and which is downloadable here. This TRB also includes a Long Term Plan for both third and fourth classes (see extract below), outlining a logical progression for the various fact groups throughout the school year. To view sample pages from the pupils Number Facts books please click here. Sample copies of all the books are also available from your local Edco reps.

 

Further reading and viewing:

 

 


Maths by Month – October (updated 2018)

Category : Uncategorized

Welcome to the second installment in this year’s 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.

HINT: To ensure you don’t miss out on any future Maths by Month blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

Operation Maths for Junior Infants to Sixth Class:

  • 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. 
    1. Log into your edcolearning account
    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)
    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.

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 October:

  • The October plan for third to sixth classes has deliberately allowed for a free week, to enable teachers to engage with Maths Week, held every year at this time. This year, Maths Week will run from 13-21 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 i.e. 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.

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 


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