I can’t claim to have all the answers. At the end of the day I am one of many primary school teachers who are doing their best in the classroom with the programme of study we currently have. However, the idea of mastery is integral to the new curriculum yet there has been very little FREE training for teachers on how to teach a mastery curriculum. Surely the government needs to ensure their vision for the future of education is implemented to their standard. After all, as talented as teachers are, we are not mind readers, even if we have eyes in the back of our head.

However, I feel as though I have been in a privileged  position during my time as a teacher. I was one of the last cohort of students that completed master credits in Education with a specialism in Mathematics. I have spent 2 years, completing essays, researching theologians and taking part in workshops which all result in a greater understanding of mastery mathematics.

So….Please don’t assume that mastery is only for your advanced students. The new POS states that virtually every child (85%) should be reaching the required level of mastery by the end of Year 2 and Year 6.

Below you will hopefully discover a few different ideas on how you break down one concept of mathematics so that children understand it to a mastery level? The important thing to take from this is that we require a revolution in the way were teach mathematics. Move away from teaching a different mathematical concept every week. The downfall in this way of teaching is that children only receive a superficial understanding. That is why we have to constantly review previous learning before moving onto the next concept. The new POS ideally wants children to have a deep conceptual understanding of what they are learning. They should be able to conjecture and convince (see Mason’s, 5 powers) each other as well as reason. Children should be completing concepts with fluency and solving problems with resilience.

Chris Quigley said something interesting the other day at his conference on assessment without levels

“Word problems are not problem solving. they are just calculation where you give the child a context”

So no word problems will be found in my ideas for teaching a mastery unit of work

Numberbonds to 10

Year 1 – learning your numberbonds

Intial lessons: lets not forget that these children are very young and therefore require plenty of concrete learning. Please don’t worry if you have very little in the children’s books at this stage. If anyone asks you about the lack of work in books you can simply say, “My planning is on the server, please feel free to have a look and see what we have been doing.” If you feel more comfortable, you can always take pictures or print labels to stick in books as a form of documenting. EYFS are in a great habit of documenting in this way.

Concrete

Give children a bar with 10 written on it. Ask children to tell you what they notice? This is the conjecturing and reasoning part of the lesson.

Could children find objects that make this number?

How many of each object have they got?

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Children could reason that they have 2 pencils and 8 coloured pencils or they could have 2 pencils, 2 purple pencils, 2 green pencils, 3 brown pencils and 1 black pencil. The list could go on but it certainly gets the children thinking about amounts to a given number.

Children may not even realise they have been making ten. They are just grabbing objects .

Next we replace the objects for something like multilink:

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Here is a bar with 10 as its whole and I have two sets of 10 multilink blocks. Hopefully children will be able to make 10 using the two colours.

The above examples are ways to make 10 using multilink and as before you can see the Singapore bar where the 10 represents the whole and the green and yellow multilink represents the parts.

Pictorial

Children should now be at the stage to move on to pictorial representations and this means they can write in their book.

Use the idea of the multilink blocks and allow children to draw them in their books to represent the concrete objects.

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My drawings are basic (just coloured in blocks) but the children will probably draw objects that look like blocks. You can see that the bar method is still used.

Abstract

After pictorial representations come the abstract. Once children have an understanding of the value of the numbers they should be able to write down the calculations associated with this.

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This one is an example

Problem solving and investigations

Mastery elements

Finally comes the sections that the new POS asks for, mastery!

To master the concept of numberbonds (for example) the children need to apply their learned skills in other contexts. Below are a couple of ways in which this can be done.

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Partitioning the number is the first way. Have a look at the top two, they are your basic representations. Now look at the example below, this is more complex and requires more problem solving skills. Children could inevitably work up to this.

The applying section of the picture is where we would ideally need children to be at by the time they reach year 3. Can children use their knowledge of numberbonds to add to make the next 10. eg know 17 + 3 = 20 and so on.

Finally, really challenge the children to think beyond the literal and ensure children gain fluency.

Try the following questions:

–True or false (8+2 = 10 so 80 + 20 will equal 100 and 800 + 200 = 1000)

-sometimes/always/never (eg if I add 6 to any number that ends in 4 I will reach the next 10)

–What’s the same and What’s different?  – give children a range of calculations that involve numberbonds and ask them what is the same and what is different (12 + 8 = 20, 2 + 8 = 10, 38 + 2 = 40, 40 – 2 = 38)