**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 **