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**W**

*‘Raising pupil outcomes in both written and mental arithmetic strategies, in order that they can make connections and apply reasoning to a range of problems’*

Intent: Through the use of Number Talk and Fluent in Five we aim to develop pupils’ fluency of number, so that they can use appropriate mathematical vocabulary, apply this knowledge to other aspects of maths and explain their reasoning.

**Research **

*‘Number sense performance and growth are predictive of long-term mathematics achievement outcomes (Jordan & Dyson, 2014)’*

*Number sense is “a person’s general understanding of numbers and operations along with the ability and inclination to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for handling numbers and operations” (McIntosh, Reys, & Reys, 1992,p. 3).*

* ‘How a person chooses to use mental calculations and computation strategies to solve problems is referred to as their number sense. “Number sense denotes an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations” (Toll, Kroesbergen, & Van Luit, 2016, p. 431; Gersten, Jordan, & Flojo, 2005). Number sense is a “person’s general understanding of numbers and operations along with the ability and inclination to use this knowledge in flexible ways to make mathematical judgments and to develop useful strategies for handling numbers and operations” (McIntosh, Reys, & Reys, 1992, p. 3).’*

* *

**Implementation**

‘Number Talk’ is a teaching strategy that focuses on developing pupils’ fluency, deepening their understanding of numbers, the connections between them and other concepts. It works on supporting pupils to become efficient, accurate, and work flexibly at the same time developing pupil’s mathematical vocabulary and reasoning skills. Number Talk is about pupils talking strategies rather than always recording maths or using one specific strategy. It’s not about as rapid response but about allowing pupils’ time to calculate an answer, explain their strategies, challenging each other, building on what they know and refining methods.

The session is separate from the daily maths session but the question stems and hand signals are used throughout all maths lessons and stem sentences are key. The session is about 5-15 minutes daily and starts with a problem written on the board examples are shown below:

Examples of the types of problem posed:

How would you solve 19 x 6 mentally?

How would you solve 110 – 59 mentally?

How would you solve ½ + 0.25 mentally?

Example of reasoning chains:

If I know 5 + 5 = 10

Then how would you use this to solve 5 + 6, 10 + 10, and 10 + 9, 15 + 5, 25 + 5…

If I know 12 x 4

Then how would I use this to solve 6 x 4, 24 x 2, 3 x 16, 120 x 4, and 40 x 120

Pupils are given 3- 5 minutes to consider the question and strategies. Time varies dependant of age. Pupils are encouraged to find as many different mental strategies as they can during the time given. Some pupils may use manipulatives to solve the problem. All answers are accepted and respected. Before pupils share their answers and explanations each pupil uses a hand signal to show where they are in the process.

**Hand signals for this point in the session **

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For every extra strategy the pupils will show extra fingers on the same hand.

** **

**Structure of session**

Step 1: Write a calculation on the flip chart paper e.g. 311 + 212 + 407 =

Step 2: Ask the pupils work out the answer mentally (no jottings, manipulatives for lower ability and younger pupils)

Step 3: Ask all the pupils who has got an answer, ask them to use a hand sign to show if they have an answer / how many strategies ( use hand signal shown above)

* Q1: What is the answer, record the answer given*

*Q2: If correct has anyone got any different answers*

On flip chart write down all the answers, ask the pupils to show you who agrees with which answer or wishes to challenge – using the following hand signals, supported with the stem sentences ( see appendix 2 )

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*Notes for the teacher**: If they don’t agree with the correct answer then why do you disagree – remember it’s not about solving the problem it’s all about the strategy using. *

Encourage the pupils to use the language of I’d like to challenge if answer is not correct. The pupils need to use the stem sentences (see appendix) when answering for agreeing/challenging.

Step 4: Select pupils to share their strategies and accept any strategy, ask the children to be clear if they want you to write words or signs.

Notes for teacher: Write the up strategy exactly as explained by the child, don’t add the symbols use the words unless used explicitly by the pupils then record each pupil’s response and write their name next to each strategy.

**Pitfalls**

Don’t articulate the mathematical thinking of the child as you then own it not the child e.g You used partitioning or rounding, counting up etc.

* *

**Liz’s strategy **

*I add 11 and 12 which equals 23, so I would write 23 + 7 = 30 *

*Add my hundreds, so I would write 300 +200 = 500*

*Next I add the 500 to the 400, and write 500 + 400 = 900, then add on the 30 to it equals 930*

Notes for teacher: Ask a question does your strategy have a mathematical name?

** **

**Jen’s strategy **

*I added the hundreds first*

*300 and 200 which made 500 then add 400 which makes 900*

*Then I added the ones 11 and 12 and 7 which made 30*

*Then I added them together which made 930*

Notes for teacher: Ask a question does your strategy have a mathematical name?

** **

**Claire’s strategy **

* 311 + 212 + 407 = *

*I know that at 407 is close to 400 so if take the 7 off I need to add it to another number so I added it 212 to make 219. I have now got 400 add 219 which makes 619, I can now add the 11 to make 630 and I just need to add 300 to make the total of 930.*

Notes for teacher: Ask a question does your strategy have a mathematical name?

Step 5: After collecting 3 different strategies

*Q1: Ask the pupils who can tell me what mathematical calculations have been used? *

*Q2: Is there anything similar about any of the strategies used? Can the pupils name the strategies used and record these on flip chart. Does anyone wish to build on the strategies given – show using hand signal for build. *

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Note for teachers: In their explanation for building ensure that the pupils use the stem sentences for build. (See appendix 2 )

*Q3: Who used which strategy? – ask the class, hand signal to show *

*Q4: Anyone used anything different – if so add this strategy to your flip chart *

*Q5: Which is the most efficient strategy? Why? Reinforce the use of stem sentences within the answer.*

Step 6: Show the pupils a similar calculation where for this example rounding isn’t the efficient way to do it – and ask the pupils to use either Jen’s or Liz’s strategy.

**For second example – don’t make the links for the children – you have used partitioning, rounding strategies.**

Step 7: Ask class which strategy they used and which was easiest for them. Extend to ask at KS2, could they build and give you another calculation they could use this strategy for.

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