SCITT Day 4 Nov 2015

532 x 4 = 672 ÷ 4 = What do you remember…? Use these examples to talk through: Short multiplication 532 x 4 = Short division 672 ÷ 4 =

Introduction “Children are born ready, able and eager to learn. They actively reach out to interact with other people, and in the world around them. Development is not an automatic process, however. It depends on each unique child having opportunities to interact in positive relationships and enabling environments.”

Talk through 4 themes, and 4 overarching principles – flag up colours same throughout card Next slide shows commitments on reverse of card 4

These are the commitment statements. There is a Principle Into Practice card for each commitment 5

There are six broad developmental stages Mathematics There are six broad developmental stages All children develop in different ways & at different rates. Birth to 11 months 8 to 20 months 16 to 26 months Notes: Each area of learning and development is organised in broad phases of development. The age ranges overlap to create broad developmental phases. This emphasises that each child’s progress is individual to them and that different children develop at different rates. A child does not suddenly move from one phase to another, and they do not make progress in all areas at the same time. However, there are some important ‘steps’ for each child to take along their own developmental pathway. Effective practice means being aware of these and supporting the child in achieving them. Note 60+ months – not all children will have met the early learning goals by the time they are five or by the end of reception class. Key Stage 1 practitioners will therefore need to be aware of how to use the EYFS and the EYFS Profile data to plan appropriate learning experiences for those children. The faces are always the same – they represent the ages and stages of development throughout the EYFS They replace previous icons of BTTM and stepping stone colours in CGFS. 22 to 36 months 30 to 50 months 40 to 60 + months 7

Numbers

“Children count reliably…” As a table… What number songs do you know?

Enabling Environments A good practitioner creates areas in the classroom that enable mathematical learning… Look at the cards on your table… Where’s the maths? Can you add to these ideas?

The numbers in alphabetland are a b c d e f g…

Alphabetland!!! a b c d e Once I caught a fish for tea f g h i and j Then I let it get away… “Why did you let it go?” “Because it bit my finger so!” “Which finger did it bite?” “This little finger on my right!”

The Skills of Counting One to one Stable Order Cardinality Abstraction There are 5 skills you need to count successfully: One to one Stable Order Cardinality Abstraction Order irrelevance (Gelman & Gallistel, 1978)

Schaffer et al (1974) Stages: ‘Recitation’ (saying the names in conventional order) ‘Enumeration’ (using those numbers to count objects in a set) ‘Cardinality’ (knowing the last number counted tells us how many are in the set.)

Numerals are arbitrary symbols representing number ideas 1 2 3 4 5 6 7 8 9 These are abstract arbitrary symbols we use to represent number ideas, there is nothing in these to tell us what they stand for -- so which one is the biggest? It is understanding the number idea that enables us to answer – not looking at the numerals. Children are given abstract ideas and arbitrary symbols to think with when they are very young, which many of them find too difficult If I say 9 what do you think of? What pictures do you have of 9? 15

Numicon is embedded into play activities Including Numicon alongside other activities in the setting …. EYFS explore shapes inside and outside. Use in play dough, sand , water. Adults shouldn’t name the shapes. Allow children to explore and find their own names for the shapes. Collect things to put in each hole outside, stones, pasta shapes. Integrate into displays Put around sand tray for children to find things and fill the holes. Use 2 sets to fill a board. 16

Include Numicon images in a Number rich environment Include Numicon images in the environment Tiles, numerals and other patterned images side-by-side 17

Constructing meaning Working with Shapes and numerals Finally introducing symbolic notation. 18

Explore Numbers and Patterns (page numbers are … of 190) p29 Observing: Aide memoire p32-33 Numbers and pattern phases p49-73 Enabling Environments Role of the Adult p79-162 Mark making extracts p180

Fractions Identifying the language, models, images and experiences children need in order to have an understanding of fractions; Considering the different concepts involved in fractions; Reviewing a range of materials which can support the learning of fractions.

This is half the house. Can you make the whole?

Halving Create an array of counters 3 x 4. Can you put a line through the array to show half? How many different ways can you find? Choose another array, try placing 1, 2, 3…. lines. Talk about what’s happening! (Use language of x, ÷ or fractions)

What fractions can you make with 1, 8, 2 and 4? Are all the fractions different? Choose a way / some ways of sorting the fractions into groups. Explain your thinking.

‘Part – Whole’ Fractional Models Area: The whole is split in to equal parts. Linear: The size of the fraction is modeled by the length of the line. 0 ¼ ½ ¾ 1 Set: The set of objects is the whole and we split in to equal subsets. ** ** ** **

Fractions Should be Thought of as… Part of a whole (proportion) A relationship between two separate things (ratio) A division operation ÷

Progression in Understanding Fractions are… 1. Part of whole – region split in two or more parts 2. Part of the set 3. Numbers on the number line 4. An operator (division) 5. A ratio Where do your learners fit into this progression? NC2014

NCETM ‘Teaching for Mastery’ Year 6

Teaching for Mastery - FDP Look at the examples in your year group. What are the Big Ideas? Which questions would you use? How would your learners respond?

NCETM ‘Teaching for Mastery’

Singapore Bar Model ‘Ben spent 2⁄5 of his money on a CD. The CD cost £10. How much money did he have at first?’

Defining terms ‘Proportion’ As a Fraction “¼ of the tiles are green” As a Decimal “0.25 of the tiles are green” As a Percentage “25% of the tiles are green”

Defining terms ‘Ratio’ So, as a Proportion “One in every four tiles is green” As a Ratio “The ratio of green tiles to red tiles is 4 to 12 or 1 to 3” or “1 green for every 3 red”