Category Archives: Uncategorized

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.

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

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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:

 

 


NEW! 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.

 

 

 

 

Now, we are also adding excel versions of our Assessment  Records. While there are already word versions of these 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.
  • Use these attainment scores to compare the attainment of various individuals and/or groups of children and identify children in need of further support.
  • 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.

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

  • Teachers need only enter the children’s names once.
  • 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.
  • 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 second tab.

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 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 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 BETA versions only, (ie they are still works in progress), and currently they only include the learning outcomes covered on the end of October assessments on the pupils’ Assessment Booklets. This is because we would like some feedback on the usability of these documents, before incorporating the rest of the learning outcomes for all of the assessments from the Assessment Booklets.

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?
  • When adding the learning outcomes for the end of December, February, April and June assessments, would they be better placed on separate tabs or directly below the end of October learning outcomes?

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 


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 


Digging deeper into … Addition and Subtraction (infants to second class)

Category : Uncategorized

A quick look at the maths curriculum for junior and senior infants will reveal that, within the strand of number, there are no strand units entitled operations, addition or subtraction, as are evident in the curriculum for first and second classes. However both operations are there – under the guise of combining, partitioning and comparing.

Addition and subtraction are two of the four basic mathematical operations (multiplication and division being the other two):

  • Addition involves the joining/combining of two or more quantities/sets/parts to get one quantity/whole/set, typically referred to as the sum or total. There are two main types: active (2 children at a table and 3 more join them) or static (2 boys and 3 girls at a table, how many children in all?)
  • There are three types of subtraction:
    • take-away (active) which involves the removal/deduction of one quantity/part from a whole amount/quantity
    • comparison (static) which involves identifying by how much one quantity/set is more or less than another (the difference)
    • missing addend (active) which involves identifying the amount needed to combine with a known part to make a whole.

In each type of subtraction we know the total/whole and a part and we need to find the missing part, which could be the amount left, the difference or the missing addend.

The types of addition and subtraction are explained very clearly and succinctly in the Origo One videos below.

 

Relationship between addition and subtraction

As shown in the videos above, addition and subtraction are inverse operations; we can demonstrate addition by adding more to an existing amount; the reverse action would involve removing an amount, thus demonstrating subtraction as take away. In contrast to traditional maths schemes, which often have separate chapters for each of these operations, Operation Maths predominantly teaches addition and subtraction together, as related concepts. Teaching the operations in this way will encourage the children to begin to recognise the relationships between addition and subtraction.

Beginning in first and second classes, the children are enabled to understand addition and subtraction as being the inverse of each other, which will progress towards using the inverse operation to check calculations in higher classes.

 

CPA Approach within a context

As mentioned repeatedly in previous posts, both the Operation Maths and Number Facts series are based on a CPA approach. Furthermore, as was referenced in the videos above, for the children to develop a deep understanding of the different types of addition and subtraction, there has to be some context or story, with which they can identify. This, in turn, should be explored via progression through concrete, pictorial and abstract stages.

This context can be simply made up by the teacher or be inspired by a picture book that the class is reading. It can be modeled using the concrete materials available in the classroom (eg plastic animals, toy cars, play food etc. ) and/or using the Operation Maths Sorting eManipulative (see below) and the extensive suite of inbuilt images; the images can be shown either with or without a background (background options include five and ten frames, set outlines and various grids).

 

HINT: To find out more about how to use the 5, 10 and 20 frames that accompany the Operation Maths series please read on here: http://operationmaths.ie/youve-been-framed-closer-look-ten-frames/

As the children progress, the need arises to record the operations using some graphic means. Initially, this can include representing each of the items in the story with counters and/or cubes. In turn, bar models could also be used to represent number relationships, while bearing in mind that different types of bar models will be required to model different context and types of subtraction (even though the subtraction sentences, if using them, might look exactly the same). Using the examples below, the first bar model (a part-whole bar model) could be used to model this story: Snow White had seven dwarfs. If four of these went to work, how many were left at home? Whereas, the second bar model (a comparison bar model) would better suit this story: the seven dwarfs all wanted to sit down at the table but there were only four chairs. How many dwarfs had no chair?

While bar models do not specifically appear until in the pupils books until Operation Maths 3, the children could use and explore simple bar models. Thinking Blocks Jr is 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. Furthermore , as shown above, the Bar Modelling eManipulative could also be used to create bars of different length.

Before rushing too quickly into abstract recording (using only digits and symbols), an alternative intermediary stage could be to represent the relationships, using a branching bond (opposite). Similar to the part-whole bar model earlier, this branching bond structure encourages the children to appreciate that two sets/parts ( 4 and 6) can be combined to make a larger set/whole (10). Inversely, when a part (4) is removed from the whole (10), a part is left (6). This bond structure can also represent the missing addend type of subtraction: if a part was hidden (6), the question could be asked  what must be added to 4 to make 10.

Both branching bonds and simple bar models are used throughout the Number Facts series to represent relationships and demonstrate strategies. They are also used throughout the Operation Maths 3-6 books, but in increasingly more complex situations.

 

The meaning of the equals sign

With the formal introduction of addition number sentences in senior infants (ie the recording of relationships using the plus and equals sign), followed by the formal introduction of subtraction sentences (using the minus sign) in first class, comes the need to correctly interpret the purpose of the equals sign as identifying equivalence; ie that the value on one side of the equals sign is the same as the value on the other side. It is essential at this stage that the children don’t interpret the equals signal incorrectly as being a signpost indicating that the answer is coming next. A pan or bucket balance is an extremely valuable resource to help demonstrate equivalency, as can be seen in the video below.

Calculations in the Operation Maths book are often shown vertically and horizontally. When presented horizontally, it is often misinterpreted that the children must now rewrite the calculation vertically, to be solved using the traditional column method (see more on the column method in the next section). Rather, presenting calculations horizontally is a deliberate effort to encourage the children to explore how to solve the calculation using a concrete based approach and/or using a mental strategy, as opposed to always tackling these calculations in a written way.

 

Looking at more complex numbers

In first and second classes, once introduced to operations using two-digit numbers, children can often have tunnel vision (or column vision) regarding addition and subtraction calculations: they “do” the units, and then the tens, without really looking at the whole numbers or the processes involved.

One way in which you can encourage the children to look at and understand these operations better is by using a CPA approach. This means that the children’s initial experiences should involve groupable base ten concrete materials (e.g. bundling straws or lollipop sticks, ten-frames and counters, unifix or multi-link cubes arranges in sticks of ten, see below), where a ten can be physically decomposed  into ten units and vice versa, before moving on to pregrouped base ten materials (eg base ten blocks/Dienes blocks, base ten money and/or Operation Maths place value discs) which require a swap to exchange a ten for ten units and vice versa.

When children are comfortable with the manipulating the concrete materials, they can move on to a process whereby these materials are represented pictorially and/or demonstrate the process using a suitable the visual structure eg an empty number line and/or bar model. Abstract exercises, where the focus is primarily on numbers and/or digits, should only appear as part of the final stage of this process.

When exchanging tens and units (or tens and hundreds in second class), reinforce that a ten is also the same as 10 units, and that a hundred is the same as 10 tens and is the same as 100 units. The use of non-canonical arrangements of numbers (e.g. representing 145 as 1H 3T 15U or  14T 5U), as mentioned in Place Value, can also be very useful to children as they develop their ability to visualise the regrouping/renaming process. The Operation Maths Place Value eManipulative, accessible on edcolearning.ie,  is an excellent way to illustrate this and explore the operations in a visual way.

 

Mental strategies are as important as written methods

In first and second classes, the traditional, written algorithms for addition and subtraction, i.e. the column methods, are important aspects of these operations. However, in real-life maths, mental calculations are often more relevant than written methods. Also, as mentioned previously, children can often have tunnel vision (or column vision) regarding addition and subtraction calculations; they ‘do’ the units, then the tens, without really looking at the entire numbers or the processes involved. Therefore, while the column method for addition and subtraction is an important aspect of this topic, equally important is the development of mental calculation skills, via a thinking strategies approach.

From Number Facts 1 & 2

Thus, one of the main purposes of the operation chapters in Operation Maths is to extend the range of strategies that the children have and to enable them to apply the strategies to numbers of greater complexity i.e. for the children to become efficient and flexible, as well as accurate. As the same calculation can often be done mentally in many different ways, the children have to develop their decision-making skills so as to be in a position to decide what is the most efficient strategy to use in each situation.

To find out more about using a thinking strategies approach to teach the basic addition and subtraction facts please read on here.

When meeting new calculations, ask the children, as often as possible, can they do it mentally, and how, so that they become increasingly aware of a range of mental calculation skills and approaches. In this way the children will also be developing their decision-making skills, so as to be in a position to decide the most efficient strategy/approach to use.

HINT: Number Talks are a fabulous resource to use alongside the Operation Maths and/or Number Facts series, as they complement their thinking strategies approach. Read on here to find out more about where both Operation Maths and Number Talks overlap.

 

Key messages:

  • There are different types of addition and subtraction and children need to explore the different types to gain a deep understanding of the concepts
  • As children encounter new numbers and new number ranges, be it numbers to ten in infants, teen numbers to 199 in first and second classes, they should be afforded ample opportunities to combine to make these amounts, partition these amounts and compare these amounts using concrete materials and via some story-like context.
  • Initial recording of these relationships should be via counters and cubes etc, before moving on to pictorial representations of the same and/or using frames, maths rack, bar models, branching bonds etc.
  • Addition and subtraction number sentences, that use only digits and symbols, should be avoided until the children demonstrate readiness for this more abstract stage.
  • Encourage the children to use and develop mental strategies and avoid focussing almost exclusively on the formal, traditional ways of doing addition and subtraction ie column method.

This short video from Graham Fletcher showing the progression of addition and subtraction from the infant classes to the formal written algorithm, with three and four-digit numbers, is very worthwhile viewing and summarises the key messages well.

 

 

Further reading and viewing:

  • Mental Maths handbook for Addition and Subtraction from the PDST
  • Thinking Blocks: an interactive resource that enables you to build bar models to solve problems. This is a great way to practice the different types of bar models for addition and subtraction when you are unfamiliar with this visual strategy.
  • Hit the button: Can used to play various games involving doubles and number bonds of whole and decimal numbers
  • Balloon Popping Game: Can be used to practice number facts from +1 to +10 and the -1 to -10
  • Addition & Subtraction Board on Pinterest

Thinking Strategies for Addition and Subtraction 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 addition and subtraction number facts typically include all the addition facts up to 10 + 10 and their inverse subtraction 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 add 9 to a number, one could think of moving 1 from the other addend to the 9 so as to make a 10, which therefore becomes an easier calculation (see below)

      

 

The Operation Maths books for first and second classes emphasise three specific thinking strategies throughout: counting on from the biggest number, using doubles and near doubles and using the number bonds for ten (see image below). The doubles facts and bonds of ten are also included on the pull-out flap at the back cover to the pupils books, both for quick reference and to emphasise their importance.

From Operation Maths 2 At School Book

In the case of doubles, near doubles and bonds of ten, these key sets of number facts tend to be easier for children to understand and recall. These facts also make up a core section of the total addition facts to 10 + 10, as highlighted below on the addition square. When these become known facts, they can then in turn be used to calculate unknown facts (eg if 7 + 3  = 10, then 7 + 4 = 11), thus covering an even greater number of the total addition facts.

Furthermore, addition and subtraction 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 subtraction facts are easier to acquire, as they are understood to be the inverse of the more familiar addition facts.

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 addition and subtraction facts (taken from Number Facts 1 & 2, Edco, 2018)

From Number Facts 1 & 2

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:

8 + 6 = (5 + 3) + (5 + 1) = 10 + 4 (make a ten) = 14
8 + 6 = 10 + 4 (move 2 from 6 to 8 to make a ten) = 14
8 + 6 = 7 + 7 (move 1 from 8 to 6 to make a double) = 14

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 + 10 ceiling of “tables”; for example if I understand different ways to calculate that 8 + 6 = 14, then I can use these ways to mentally calculate 18 + 6 , 18 + 16 etc.

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. 8 + 6 = 14.
  • Efficient: the children must calculate the answer in an efficiently. A child who produces an answer of 14 in response to the question 8 + 6 by ‘counting all’ (eg have to count up to a total using using counters, fingers, etc.) 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 8 + 6 above).

Thus, flexibility is the key to fluency. A child who only knows that 8 + 6 = 14 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. Thus, a thinking strategies approach will not only be effective for aiding understanding and recall of the basic facts up to 10 + 10, a thinking strategies approach can enable children to apply these mental computation skills to numbers beyond this traditional ceiling e.g. 19+ 5, 29 + 6 etc (see below).

       

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 addition and subtractions facts for first and second 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 first and second 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:

  • Are you compensating? A closer look at the thinking strategy of compensation.
  • Number Talks : this is a maths methodology centered around the development of  strategies and mental calculation skills. As such, it really complements both the Operation Maths and Number Facts series. For more information on where Operation Maths and Number Talks overlap, please read on here.
  • Mental Maths handbook for Addition and Subtraction from the PDST
  • Number Facts Board on Pinterest
  • The Origo One videos below are a great way to get an overview of some various thinking strategies, each in 60 seconds or less!

 

 

 

 


Maths by Month – September (updated 2018)

Category : Uncategorized

It’s a new school year! And with it comes the first in this year’s series of posts designed to support teachers 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 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 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 September:

  • Check out the “Maths and me” attitudes questionnaire, situated after the last assessment in the Operation Maths Pupil Assessment booklet for 3rd to 6th classes. Suggest to the children that they fill this using a particular colour on one of the first days of the school year to be then revisited later in the year. At this point, the children can again record their attitudes in a different colour and reflect upon any changes they made, if any.
  • Maths about me: another great activity for the start of a new school year. The children write facts about themselves that are appropriate to their ability eg height, age, shoe size, telephone number, distance from school (use google maps), time that they get up or go to bed etc. This can be recorded on the inside front cover of the discovery book, filled in on a pre-made template from the internet, used to make a large class display or even become a more complex problem solving activity in the more senior classes.
  • Inspire your class for the year ahead: 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 and followed that up with a Week of Inspirational Maths 2 and 3 in 2016 and 2017 respectively. The latter two have lessons and activities aimed at infants to 6th, as well as second level. 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.
  • New year, new initiative! Number Talks is an excellent maths methodology that is gaining traction globally, and more recently, nationally thanks to the promotion of the PDST. Better still, the rationale behind it aligns itself very closely with the underlying principle of Operation Maths, that is teaching children to understand maths, not just do maths. To find out more about number talks and to access a whole suite of ready-made resources for all class levels just click on the link above.

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 … Counting and Numeration

Category : Uncategorized

Counting and numeration are listed as strand units in the strand of number for Junior Infants, Senior Infants, First and Second Class in the Primary Maths Curriculum (1999) and counting and numeration at each of these classes require similar skills, although the range of numbers will differ. However, while counting and numeration is specified as strand units only in infants to second, the understanding required is just as relevant and as important in the higher classes e.g. counting with larger numbers, counting fractions, decimals, percentages, etc.

Learning to count: rote versus rational counting

You are probably all familiar with the scenario: a parent declares that their pre-school age child can count because they can rattle off numbers to ten! As we all know, counting involves much more that just listing off numbers (rote counting). Watch this one minute video, which synopsises the difference between rote and rational counting.

While rote counting is relevant when learning to count, to count with understanding (i.e. rational counting) depends on the child developing an appreciation of rational counting, via the five counting principles, (briefly outlined in the video above); each of these counting principles are explained further in these follow-on videos from Origo Education:

HINT: For more information on the Counting Principles, including suggestions on what to look out for and what to ask/do, check out this blog post.

Apart from rattling off numbers, a child’s main interest in counting is to identify the quantity of objects in a set. “How many cars do you have? I have six cars”. Cardinality is using counting to find out “how many”.  And, since most of the sets that children will encounter, and will want to count, will be randomly arranged, then teaching the order-irrelevance principle will probably be most relevant to the children themselves. Therefore, the children must develop some strategies to ensure that they count every object, once only:

  • Count and tag: as each item is counted it is touched (this works quite well if the set to be counted is already in a line, or a rectangular array, but doesn’t work as well with scattered sets .
  • Count and push/put: as each item is counted it is pushed to the side or put into a pot, tray etc.
  • Count and mark: put a mark beside each item as it is counted; this works well for pictorial representations that cannot be physically moved.
  • Count and group: in the case of large collections (for example in first and second classes), rearrange the objects into “friendly” groups (eg two, tens or fives) that the children can easily skip-count. Using the Operation Maths frames and structures to help to reorganise the objects can be of particular benefit.

This ability to demonstrate one-to-one counting should not be taken for granted; while it seems quite a simple concept, many children can struggle. Therefore, when the focus is on the cardinality of counting (establishing how many), all counting activities should be counting something; lining toys up and counting how many by tagging each one, etc.

When observing children as they count, check:

  • Do they “tag” each object as they count (eg pushing them aside)?
  • Can they count regular arrays or rows?
  • Can they count random groups in some sort of systematic way so that they don’t miss or double up on objects?
  • Can they count the same set several times, starting with a different object each time?
  • Can they show how rearranging the objects does not change the quantity?

HINT: use relevant number rhymes and stories to reinforce counting and number word sequence. Many of the short-term plans (STPs) in the Operation Maths TRBs list various possibilities; see the Literacy suggestions in section on Integration

Counting without counting!

When can you count without counting? When you subitise! Subitising is the ability to recognise a quantity at a glance, without counting. When you throw a five on a die, usually it is not necessary to count the individuals dots; we recognise that there are five dots from their shape. So, while it is very important that we spend significant time practising one-to one counting initially, this is not the most efficient approach, and we do want the children to progress to a point where they do not need to count each item/object individually.

Ways to promote subitising:

  • Play lots of dice and domino games; the Operation Maths TRBs have game suggestions and station activities in every STP plan, many of which are based around dice etc.
  • Use the Operation Maths frames: the visual layout of various numbers in the frames (see image below) encourages the children to internalise a picture of how the numbers look and to recognise this in other situations.
  • Play dot flash: briefly show the children dot cards in various arrangements and ask them to tell you what they saw. There are photocopiable dot cards at the back of the Operation Maths TRBs for this purpose.
  • Use other structures that have a definite layout eg rekenreks (or maths rack) can also be used. This visual structure features quite strongly in the Number Talks presentations for junior infants, senior infants and first class, all available at the link above.
  • Arrangements of Base Ten blocks, bundled sticks and/or place value discs can also be used.
  • Use online games (eg Number Flash from Fuel the Brain) and/or suitable apps (such as this free one)

HINT: For more suggested subitising activities read this blog post Counting With Your Eyes

Numeration

Numeration involves the children being able to match a numeral and its matching number word to each other and to various different arrangements of objects (both identical and non-identical) of that amount eg 3 = three = 🏀⚾⚽ = 🚗🚗🚗.

As the children move into first and second classes, numeration will move beyond the numbers to ten, through the teen numbers and all the way up to 199. Numeration in these classes involves much more than just matching a quantity to the numeral and to the number word:

  • The children need to appreciate the visual pattern of numbers in sequence: 20, 21, 22, 23, 24, 25, 26…
  • The children need to recognise the patterns in the number word sequence when spoken: “twenty one, twenty two, twenty three, twenty four…”
  • From this understanding the children should be able to count forwards and backwards from various starting points. They should also be able to identify the number before or after a given number.

Visual structures, such as the Operation Maths 100 Square e-Manipulative (see below), can be very useful, as:

  • they provide the numbers in order
  • the patterns can be easily identified
  • individual squares and/or large sections can be hidden and then revealed for the children to test their ability to identify preceding and subsequent numbers in a sequence.

HINT: Particular attention should be given to the multiples of ten ie the “ty” numbers and a deliberate distinction should be made between the “ty” numbers and the “teen” numbers, especially when being verbalised i.e. there is little difference verbally between eighteen and eighty, but there is a significant difference between these numbers in value . Like the “teen” numbers, “ty” numbers are also widely acknowledged as common hurdles for children and so time spent now will be time well spent for the future. 

 

Further reading:


Digging Deeper into … Early Mathematical Activities

Category : Uncategorized

Early Mathematical Activities (EMA) is a strand in the Primary Mathematics Curriculum (1999) for children in junior infants only, although the activities might also be suitable for children in senior infants as revision, as well as being suitable for many children in their final preschool year.

It includes the strand units of:

  • Classifying
  • Matching
  • Comparing
  • Ordering

While comparing and ordering appears as a strand unit also in the strand of Number, for EMA the emphasis should not be on using number or counting to describe relationships, rather on the attributes themselves. However, once the children have been introduced to the numbers,  the early mathematical activities can be repeated, but now to include using the opportunities presented to incorporate numbers or counting to describe relationships.

Sets

EMA is fundamentally all about sets; a set is any collection that has been grouped together in some meaningful way. Sets are all around us, and much of a young child’s exploration of the world involves the child seeing things in terms of sets e.g. my toys, the set of toys that belong to me as opposed to all other toys. Sets are also fundamental to developing an understanding of number and operations: numbers are used to describe the quantity in a set;  a quantity will be removed from a set to model subtraction etc.

Matching

Although classifying is listed before matching in the Primary Mathematics Curriculum (1999), matching is actually less complex, as typically we understand matching as completing a pair, whereas classifying is typically interpreted as organising a collection into two or more subsets. For this reason, in Operation Maths for junior infants, the children first match pairs of identical objects (reinforcing one-to-one correspondence), using the language same for those that match and different for those that don’t match.

 

  • Start with a limited amount of objects e.g. eight, where each has a match that is the same (ie fully alike). This can be demonstrated using real objects and/or on the class IWB, using a representation of real objects, using the Operation Maths Sorting e-Manipulative (see image above).
  • Working with a small group of children, isolate one of the objects and ask a child to “find the match/find the one that is the same” i.e. identify the other that is fully alike, and most importantly, to verbalise why it is the same and therefore the correct match. In this way, you are asking them to justify their choice using the language of the attributes.
  • The children can also be asked to orally justify why certain objects are not the same/are different.
  • Initially, you can use objects where each pair is completely unlike the other pairs e.g. four different shapes, in four different colours. Then, progress towards collections where, while there are like objects, there is only one match that is fully alike/exactly the same (see example above).
  • To make this task more complex:
    • introduce more attributes (e.g. size) and a larger range of attributes (e.g. more shapes and colours).
    • increase the size of the collection
    • remove/conceal an object and ask the children to identify the object which now has no match and to use this to be able to describe the object that has been removed/concealed.
    • See also the Clothesline activity in the Junior Infants TRB (p 16). The materials could be expanded to include gloves as well as socks. Initially try to ensure that there is two of everything (in order to make complete pairs). When the children locate the matching items, they should explain why they are the same, before hanging them up using clothes pegs (clothes peg activities have the added advantage of developing pincer grip and fine motor skills necessary for correct pencil grip). A development of this activity if the teacher deems it suitable: include odd socks/gloves and observe how children react. Use questioning to elicit their own “rules” for dealing with these and how they might describe them. If appropriate, use the opportunity to discuss and introduce language such as even, odd etc., if the children do not suggest this terminology themselves.
    • For further experience using one-to-one correspondence, the children should also have opportunities to match pairs of related objects,  i.e. objects that are not the same, but that purposely go together,  e.g. putting out knives and forks, buttoning coats, putting lids on boxes/tubs. Again, many of these activities, using objects from the children’s daily lives, will also be useful for developing and strengthening fine motor skills.

HINT: Commercial products such as attribute bears, shapes and people are very useful for all EMA and may appear to even be the most suitable material because the attributes, and therefore the “rules” that govern a set can be deciphered clearly. However, they can also be limited, in that there is little negotiation required. Thus more arbitrary materials, such as items from nature (stones, rocks, leaves etc), children’s own clothing items (socks, shoes, gloves) and assorted toys (threading beads, toy cars, soft toys etc) and indeed any objects in the classroom for which there is at least one other that is fully alike, can provide greater opportunities for mathematical discussion and thinking, as the children have to come up with their own ways to group them. In particular, see the Aistear play suggestions in the Operation Maths TRB for Junior Infants.

 

Classifying

Classifying (or sorting) is different from matching as classifying involves reorganising a collection into two or more subsets. When presented with a large set of objects e.g. toys, children will often isolate a certain group of objects e.g. take out all the toy cars. In this way they have made a set of cars and (by default) a set that is not cars. This is referred to as a binary sort, where two subsets have been created: one which has the chosen attribute and one which does not. In mathematical terms this “opposite” set is the complement of the chosen set.

  • The children should have lots of opportunities to explore various collections of objects from which they will likely create their own sets. Through questioning, elicit from the children an explanation (ie rule) for their set.
  • The teacher can also isolate objects to create sets and then ask the children to identify the rule of the set: “What’s my rule?” (see image above). This is more complex than matching since, while the objects are all the same shape, they are not all the same size or colour. The children can also be encouraged to play the “What’s my rule?” game in groups.
  • Initially, the isolated objects should only have one attribute in common, e.g. in the image above, there is the set of all the shapes that are square and all the shapes that are not squares.
  • Ultimately, it is hoped that the children appreciate that while the collection above has been classified according to  a certain attribute (i.e. whether it is a square or not a square), that the same collection can be sorted in various other ways  e.g. triangles/not triangles; pink/not pink; big/not big. And then for these children, they can be asked to identify the rule of a set that have two attributes in common e.g. a set of yellow squares (which then also creates by default a set of shapes that are not yellow squares).
  • The children will likely begin themselves to sort objects into multiple sets. Instead of two sets of yellow shapes and non-yellow shapes (i.e. a binary sort) they will produce a set of yellow shapes, red shapes, blue shapes etc. The production of multiple sets will naturally lead on to comparing and ordering these sets (see next section).

HINT: The children themselves can also be used for classifying; use rope or yarn circles on the ground, and ask a small group of children up to stand at the top of the class. Point to each of the sets saying “This is for the children wearing glasses and this is for the children not wearing glasses”; “This is for the children with curley hair and this is for the children who don’t have curly hair”; “This is for the children with brown eyes and this is for the children who don’t have brown eyes” etc. 

 

Comparing and Ordering

Comparing is instinctive in humans, and children are no exception to this: “He got more than me! I have a smaller piece!”

Comparing is also intrinsically connected with matching and classifying: when a child explains that two shapes are different/not the same because one is yellow and one is red, they are already comparing according to colour. When a child classifies a set into big toys and small toys, they are already comparing the items in the sets according to size. Therefore, to compare is to measure or quantify in some way how two items or two sets are similar or different.

As well as colour and size, the children can also compare objects according to length, width, height, weight or thickness.

  • Use collections of pencils, crayons, ribbons, strings etc., to compare length. Note how the children do this; do they use a common baseline/starting point, and if not, highlight the need for the same.
  • Sort attribute shapes into sets that are thick and thin
  • Use the opportunities to introduce vocabulary that will reinforced later in the year as part of measures e.g. long/short, longer/shorter, heavy/light etc.
  • Compare sets without counting: when sorting, look for opportunities where the resulting sets are obviously different in quantity and ask the children to identify which has more and which has less. Some children may even demonstrate their ability to verify their comparison by counting; this is an added bonus, but not required from all the class at this stage.

Ordering is a development of comparing, in that the children are now comparing three or more objects and ordering them according to length, height etc. The children can compare and then order sets also; “there are more yellow shapes than red shapes, there are more blue shapes than yellow shapes, (then in desceneding order) so it’s blue shapes, then yellow shapes, then red shapes”. An important conceptual development is where the child realises that if A is more/bigger than B and B is more/bigger than C, then A has to be more/bigger than C, and thus A must be the largest and C must be the smallest.

HINT: In your materials for EMA include (real or play) coins and notes, with the  emphasis being on their attributes of material, colour, shape, size and design. Provide the children with opportunities to suggest ways to classify the coins themselves. Using money in this way is an excellent way to prepare them for the strand units of money, later in the year.  NB: While the emphasis should be on the attributes of the coins/notes, as opposed to their value and/or the numbers visible on them,  if children recognise their value and use as an attribute for matching, classifying, comparing and ordering the coins/notes, then this should be acknowledged as a valid response to the activity.

 

Further suggestions:


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