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Fractions


Created on 07 January 2014 by ncetm_administrator
Updated on 30 June 2014 by ncetm_administrator

Fractions

This suite of videos seeks to address the higher expectations in fractions that the curriculum demands, in particular the ability to develop a secure understanding and calculate with fractions.

You may find it useful to download the videos to your own device, using the links given beneath each video. If you encounter any problems, please contact us.

 

Fractions - Key Stage 1

Woodberry Y2 - adding fractions and mixed numbers

Developing fluency -  counting in fractional steps

Download the accompanying PowerPoint slides.

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Representing fractions

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Sorting and reasoning about fractions

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Reasoning about mixed numbers

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Addition and subtraction of fractions

Download the accompanying PowerPoint slides.

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Reasoning about addition and subtraction of fractions

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Practice and consolidation

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

 

Fractions - Key Stage 2

Woodberry Y4 - using an array to add fractions

Developing fluency -  counting in fractional steps

Download the accompanying PowerPoint slides.

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Preparing to add fractions with different denominators

Download the accompanying PowerPoint slides.

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Adding fractions with different denominators

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Children explore adding fractions with different denominators

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Identifying misconceptions

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

 

Fractions - Key Stage 2

Springfield Y6 - bar model dividing by fractions

Using the bar model to divide a whole number by a fraction

Download the accompanying PowerPoint slides.

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Pupils use the bar model to divide by a unit fraction

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Extending to division by non-unit fractions

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Problems involving division by a fraction

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Reasoning about division with fractions

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This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

 

Fractions - Key Stage 3

St Marylebone - fraction wall to add fractions

A fraction wall to represent equivalent fractions to support addition

Download the accompanying PowerPoint slides.

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

Students use fraction walls to add fractions

Download the accompanying PowerPoint slides.

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

 
 

 


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Comments

 


19 June 2018 16:45
By children, reminding others (fictional character) of their mistakes or misconceptions gives them the opportunity to go over rules and concepts without highlighting their own mistakes, but, allows them to be proud of what they do know. By discussing them in talk partners it also allows children to configure what they both know and may also make it clearer for one another. It also allows the teacher to listen and observe the children to assess what they know, don’t know or are unsure of and what needs to be taught again or next steps.

Misconceptions and mistakes should be celebrated as they are needed to make connections and learn. The teacher in this video has done this by allowing the children to become the ‘expert’ and gives them the chance to support others with their knowledge. By highlighting to others what they need to do next time will support them in remembering the steps themselves as well as ensuring the knowledge is embedded.
By MrsTJohnson
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18 June 2018 19:45
I think that it is really important for children to explore their own misconceptions as it helps the children to become independent learners. When children acknowledge their own mistakes, they then gain an understanding in greater depth of skills that implicate solving problems. In addition, looking at misconceptions as a way of learning from mistakes helps to provide children with a growth mid-set.

Whilst learning from mistakes can be valuable in learning, it is important for teachers to use the language regarding misconceptions to ensure that children do not follow through with these misconceptions in their own workings. In addition, I think it is important for teachers to model social skills when conducting peer-assessment so that the children can take the feedback in a constructive way.
By LucyBeer
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17 June 2018 04:07
Referring to the KS2 Identfying Misconceptions clip; I love the way that the teacher has created a relatabe context for the childre, whereby they themselves become the 'teacher', whilst at the same time recognising mistakes, and forming solutions, that they themselves can apply to their own work.
By RoryWise
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11 June 2018 20:45
Yes you are correct, the curriculum says divide a fraction by a whole number, eg 1/4 divided by 2. So this is as far as you need to go
11 June 2018 18:32
Making mistakes is an unavoidable part of life, therefore I think it is essential that children are able to make mistakes and provided with time and feedback to recognise where they went wrong. Explicitly teaching children in this way about possible misconceptions/ mistakes that can be made during maths lessons provides a valuable learning experience. It allows children to highlight where mistakes have been made, and understand that another method is needed to figure out the problem. Through assessing a piece of work that is 'made up', as was done in the video, none of the children in the class feel embarassed by having their work shared with the class if they have made an error. Allowing time for children to do these sorts of activities and practise recognising mistakes/ misconceptions may better equip them for peer and/or self assessment, potentially giving them more of a sense of ownership over their maths work.
By ebalague
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23 April 2018 16:30
Should children be exploring misconceptions? Will this confuse them?

Encouraging children to identify and explain misconceptions is an excellent activity, in particular, it would make a great plenary activity. I believe that this is an effective teaching strategy because children’s knowledge of fractions would be fresh from the main lesson. By allowing the children to work with their talk/table partners, the teacher has formed a brilliant talking setting, in which the children can bounce off one each other, as well as supporting each other with their misconceptions.

Are mistakes a valuable learning platform?

Learning from mistakes or errors suggests to children that it is acceptable to make mistakes, but also demonstrates the significance of rechecking their work once finished to make sure they are accurate and precise. I think it is essential for children to explore their misconceptions or mistakes as it enables them to understand where they may have gone wrong and how they may modify their strategy to get it right the next time.

Should we be cautious of anything?

The timing of the activity and when the activity is placed within the lesson should be carefully considered because completed at the wrong time could cause confusion. Furthermore I think the teacher needs to be sure that the children are correcting the work in the right manner, otherwise, misconceptions could progress further.
15 December 2017 21:26
Should children be exploring misconceptions?

Children should be exploring misconceptions because it is good to be able to identify where maths workings can go wrong. It will get children used to checking their own answers independently and reinforce their knowledge when helping a friend with a misconception (as seen by the talk partners section in the video.)

Will this confuse them?

If misconceptions are addressed quickly then it helps a child move onto the next stage of learning. However, if the children are made to address misconceptions for a longer period of time then it may confuse their thinking process.

Are mistakes a valuable learning platform?

Mistakes are a valuable learning platform because they allow for reinforcement of a topic and development of thinking mathematically.

Should we be cautious of anything?

We should make sure that children are using the correct mathematical language when explaining their workings out. The wrong language may cause a misconception or confuse another child.
13 December 2017 13:39
The use of encouraging children to identify and explain the certain misconceptions is a great plenary activity. I believe that this is an effective teaching techinique because children knowledge of fractions is fresh from the main lesson, this provides the children will secure reasoning and justification. If this was a starter activity then there would be potential for confusion, hence we should be cautious about where we would place this activity within the lesson. Furthermore, learning from mistakes suggests that to children that it is ok to make mistakes but also highlights the importance of checking back over your work and mental written processes to ensure they are correct or at least accurate. The teacher most definitely encouraged conversation by placing children in pairs, this provided the opportunity for children to reflect back on their proir knowledge and develop their mathematical vocabulary - when dealing with misconcpetions I believe talk is key, it would be a concern if children had to individually work on this activity as some may have the same misconception and this will not develop their learning.
By Cloe1803
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13 December 2017 11:35
Allowing children the chance to explore and discuss misconceptions within questions allows them to develop not only their mathematical understanding but also their use of mathematical language. The use of partner talk in this video is an excellent way for children to discover and explore misconceptions within questions. By allowing the children to work with partners, the teacher has created an excellent talking environment, in which the children can feed off one another's ideas, as well as aiding one another's understanding of misconceptions.
12 December 2017 13:01
I think that giving children time to explore misconceptions is a great way of showing them that it is normal and acceptable to not always have the right answer. Through peer-assessing, children have the chance to see that everyone makes mistakes. I also feel that through talking through answers and errors it helps children's understanding of the topic develop as they see where methods have gone wrong, and how they should be corrected.
12 December 2017 11:09
I like the way that the teacher has created a relatable context for the children, stating how she needs their help provides the children with a sense of purpose and can be an effective way of engaging the pupils. By allowing the children to explore the misconceptions they begin to cement their own understanding in the correct method, understanding both differences and similarities.

When a teacher uses this method it needs to be well set up and teacher here clearly knows her students. If the students do not have a secure understanding it can confuse them much more and lead them to further misconceptions and misunderstandings.
By jamesneal92
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12 December 2017 10:33
By encouraging children to explore misconceptions, existing knowledge can be reinforced, potential mistakes identified and it can help identify those who are still struggling with the concept. The use of talk partners in the video is an excellent example of working through the problem together and provides the opportunity to bounce ideas off each other. However, it should be noted that the majority of the class should be proficient in the use of the array strategy for fractions before asking them to identify misconceptions on their own to avoid any confusion. It is also important that you create a safe ethos within the classroom so children are not worried about making mistakes as they understand it furthers their learning.
By jbeedell
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01 December 2017 12:48
I think children should be encouraged to explore misconceptions as this is a great way for them to see the possible mistakes that could be made, and different ways to overcome or avoid these. I think, if the children have a solid understanding of the concept before looking at misconceptions, then they will not become confused by the misconceptions (because they already understand how to do it correctly). Learning from your own or other people's mistakes is key and it is a very important concept for children to learn and gain an understanding of. This will also lead t a safe environment where children feel respected and valued, even if they make a mistake in their work. Looking into misconceptions will give them an insight into how they can grasp a better understanding and achieve a higher level of learning.
22 November 2017 12:18
I think it is a good idea to allow children to explore misconceptions, as it allows them to see that people do make mistakes and that it is not necessarily a bad thing. By asking the children to come up with a target to identify the next steps, the children can hopefully grasp an understanding of the importance of doing these next steps, as they help them improve. Working in pairs works in the sense that children can work together to spot and correct the mistake rather than struggling on their own, however as demonstrated in this video, one child may take the lead, resulting in the other child partaking in passive rather than active learning. You also need to be careful that children have a secure understanding so that they do not take on the misconceptions themselves (or at least make them aware that these are incorrect).
By CDOBRIEN
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20 November 2017 21:41
I think it is very important for children to explore misconceptions as it allows them to see where they may have previously gone wrong and how they may change their method to get it right in the future. It also helps them to see that other people make mistakes and allows them to be critical of other people's work without feeling like a failure themselves. Working in pairs allows the children to learn from each other and see a method of doing the calculation that they may not have previously thought of. However, the teacher needs to be sure that the children are commenting on the work correctly otherwise misconceptions may develop further. Maybe it would be useful to go over the examples briefly at the end to make sure all of the children understand it.
By jobirt
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13 November 2017 13:53
It is a very well known concept that it is important to make mistakes as we can learn from them, so by exploring misconceptions with children it will help them identify wrong ways to do things instead of just the right way. It will also make them less scared of making mistakes if it becomes a more common classroom practice. The only problem with this method is that lines could become blurred between what is wrong and what is right, therefore perhaps by implimenting a routine where every friday you look at the things that have gone wrong that week and address them as a class in a different class format that you would in a normal lesson.
By megrobinson3
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24 May 2017 13:28
I think it is important that children should be exploring misconceptions as the children benefit from being able to identify where a person had gone wrong and use their knowledge of fractions to give a target. This also gives the children an opportunity to extend and deepen their knowledge by using their metacognition skills to work out where, and at what point, the individual has gone wrong. This activity also makes children more aware of these mistakes so they are hopefully prevented in their own work.

Nevertheless, children who are not confident with this concept may struggle to give targets to others as they may become confused and use the same methods.
By fionamundy
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19 May 2017 12:25
Children should be encouraged to explore misconceptions as this enables children to become independent learners. Learners that can acknowledge mistakes and allowing children to gain in in-depth understanding in the factors that can implicate solving problems. Learning from mistakes is a valuable learning platform, however teachers should explicitly state and use the language regarding misconceptions, and therefore children do not follow through with these misconceptions in their own workings. If taught explicitly children should not get confused as they manipulate their mathematical language to explain their thinking and reasoning.
12 March 2017 11:42
Ok will have a look there. Thanks very much for your reply. Chloe
By chloe64
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12 March 2017 11:38
I'm afraid not. I believe they were whiteboard slides. They were not shared at the time and the teacher no longer works at the school. In later videos we have sought to aquire the slides at the time of film. Please see the teaching for mastery video section
12 March 2017 11:03
Like many others have asked, is there any way to get a copy of the powerpoint slides the teacher uses in the ks1 videos? The accompanying slides are not what we are asking about as they are the NCETM slides and there's only 2 slides in them - we would like the ones that are used in the actual video.

Many thanks, Chloe.
By chloe64
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15 June 2016 17:52
Forgive me if I'm wrong but I don't think Year 4 pupils need to be able to add fractions with different denominators?!?!?
By chriskirwan
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06 June 2016 13:51
By giving children the opportunity to identify misconceptions, they are consolidating their own knowledge and are using their reasoning skills to correct the mistakes and justify why their method is correct - thus strengthening their own knowledge. It does indeed therefore seem beneficial to identify potential misconceptions. Depite this however, children who are not sucure in their understanding may easily become confused and adapt an incorrect way of completing the work. The teacher must therefore ensure that the children are ready and capable of identifying misconceptions without becoming confused.
By blythe92
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06 June 2016 13:41
I really like the strategy of showing the class some work that highlights misconceptions for them to discuss in pairs and talk through where the child has gone wrong and what they should have done. You may have certain children in a class that this would confuse but I think that if you pair the children appropriately then this will ensure that this does not add to their confusion but instead helps deal with their own misconceptions in a safe environment. Looking at mistakes is great way to help children improve both their knowledge and understanding of a topic, the teacher should however know the class well enough before engaging with this strategy as if you have children that are still really really struggling with the concept this could lead them further into the dark, knowledge of your class is key
By DaveMac78
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03 June 2016 09:30
By looking at the misconceptions made by others using arrays the children were able to revise their understanding by revisiting the processes to see where the answers had gone wrong. By giving children the opportunity to identify misconceptions it makes the children more aware of where the steps could be confused and mistakes can be made, and thus strengthens their understanding and knowledge.

However, as previously mentioned teachers must be careful to ensure that the children are correcting the mistakes made, as otherwise this misconception will prevent them from achieving the correct answer in their own work.
By CB14051480
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02 June 2016 16:42
Children's misconceptions provide learning opportunities. It enables them to explore and share their concept and ideas, aiding the process of understanding instead of using a 'spoon-feeding' teaching approach. By allowing the children to become insightful in their learning (such as in the video the children were identifying their mistakes and discussing them) provides good foundations for when they become independent learners. As identified by other commenters, the teacher needs scaffold and support children during this talk process, assessing their understanding and identifying areas that need to be supported.
By skleszcz1
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31 May 2016 15:36
In the misconceptions video the children showed a sound understanding of arrays, not only were they able to notice the mistakes that had been made but were able to explain where and how they had gone wrong. This gave the children opportunities to discuss and gain ideas from peers; which will benefit their own learning. However, I feel this task may need to be differentiated or used as an extension as I am sure there would still be some children in the class who were struggling with the concept of what an array is. The teacher needs to monitor the talk that is taking place between the partners as in some cases there was a more dominant child.
By RowenaHicks
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31 May 2016 12:41
I also agree that allowing the children to critique work and identify misconceptions will prevent them from making the same mistakes in their own work and encourage deeper conceptual understanding and further their problem- solving skills.
By KatyW13
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30 May 2016 15:59
I agree with the above commment. Allowing children to explore misconceptions is an excellent way for them to learn. Not only do they gain a deeper understanding into solving problems but they are addressing common misconceptions themselves and their peers may have.
By julimiron1
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23 May 2016 16:12
I believe that teaching children to identify misconceptions is an excellent way for them to acknowledge mistakes they may have been making previously and a way for them to gain a deeper insight into how to solve a problem. I believe it is an excellent way to gain the children's attention through talk as they can gain ideas from the other students as well as identifying any misconceptions they have. However, teachers must be assessing the children's talk regularly as they might not be on the right track. The written part of the lesson would have helped with this.
23 May 2016 15:24
Children should explore misconceptions as this will ensure that they have a full undestanding of the concept, however, some children may become confused but only if they havetn gained a full understanding and need further support. Children should not be afraid of making mistakes as these show that they are learning.
By missj93
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19 May 2016 15:36
When identifying misconceptions children have that opportunity to develop their own understanding of the topic as well as understanding the mistakes that have been made and therefore noticing if they make the same mistakes. One issue with this, is the fact that children possibly may not notice the misconception and continue to believe a problem to be fine, yet it is a mistake.
By JordanStall
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26 April 2016 20:05
As others have mentioned, when I click on the "Download accompanying powerpoint slides" at the end of each video, it only shows 2 NCETM slides, rather than the ones the teacher uses in the video. Is there a way to download the slides that the teacher uses in the Key Stage One videos?
By MissN88
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28 March 2016 12:41
Using the bar model to divide by a unit fracton video was very informative and I will definately be using the strategies. Loved the fact that the children were able to have a go and then reason their understanding with each other and develop their own further understanding at their own rate.
By Spencer1
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04 February 2016 20:07
Some other people have commented about the slides the teacher is using in the video. The accompanying powerpoints for each video aren't what they're talking about. I'd like the resources for the second and third video. The powerpoint she uses that starts with the vocab and the sorting activity.
By amygregg
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29 October 2015 14:53
The videos are all working, the issue could be one of access from within your school network.

The NCETM videos are hosted on a video hosting service called Vimeo.you may wish to try and access them at http://vimeo.com/ncetm/videos
29 October 2015 14:44
The video's don't seem to be working - is there an error on the site or is it to do with something else technical?
By markydys
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11 July 2015 15:48
1 divided by 4 using the bar would be the same as 1 divided by a quarter, no? I think for this reason alone it is not a useful tool unless it is accompanied by a better narrative than 'You look at your denominator and that's how many you fold it into.' Might it be better to say 'How many quarters in 1?' (just as 6 divided by 3 is 'How many 3s in 6'?) and then do your fold into quarters. But even then you already know the answer before you do the fold.
By zerothehero
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20 April 2015 09:16
If you click on the the link where it says "Download the accompanying PowerPoint slides." There is a link for each section.
19 April 2015 13:10
I've been looking at the Year 2 fraction slides and would like the Powerpoint slides the teacher uses. How can I access the slides the teacher uses in the lessons?
By Carolicious1
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14 February 2015 09:07
Is it possible to access the slides the teacher is using on the whiteboard in the lesson, (not the accompanying NCETM PowerPoint)? Thanks
By hld100
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19 January 2015 09:09
Suzanne - which powerpoint are you referring to? There is a different one for each video.
19 January 2015 09:05
There are only two slides on the powerpoint. Is there a link to all the slides used in the video?
By suzannecoxon
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25 October 2014 15:00
I think the lesson idea is a good one but I would also add that the children need to understand that the denominator relates to equal parts. Some of the children, particularly when dividing the bar into 5 sections, did not fold the paper equally. I'm sure the teacher would have mentioned this but I think it is worth being aware of.
By terradom
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15 September 2014 21:49
I have been trying to click on the link to the videos, but they do not load. However I have now tried copying the web addresses without the "https://" or a "www." and they work fine.
By gcooksey
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19 June 2014 21:09
They are in the Fraction materials

Click on this link https://www.ncetm.org.uk/resources/44562

half way down is a section on fraction cards
19 June 2014 19:52
Is the template for the fraction cards shown on the KS1 video 'adding fractions with different denominators' available to download from the site please? I have looked but am unable to find it. Thank you
By ruthpitt
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21 March 2014 08:52
Thank you Debbie, I agree it is a very useful example of the Bar Model and I have used it for that purpose, I just wanted to make sure I wasn't missing something in the curriculum.

Thanks again,

David
By dmorris1
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18 March 2014 19:39
Please see the note on the first PPT slide for this section. Yes you are correct re the National Curriculum. We filmed this prior to final publication of the curriculum, but thought it would be valuable to show it as an example of the use of the bar model. Also the mathematics could be valuable to KS3 colleagues
18 March 2014 09:55
The videos demonstrating division describe whole numbers being divided by a fraction, yet in the new curriculum it only talks about dividing proper fractions by whole numbers. Can anyone clear up my confusion?
By dmorris1
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