eNICLE Grade 1 & 2 programme Session 7 29th May 2018 Prof Mellony Graven, Dr Debbie Stott, Dr Pam Vale, Ms Carolyn Stevenson-Milln, Ms Roxanne Long, Ms Samu Chikiwa Unscramble these words SIUITBNISG ------I-PATT PAHR RWOLE -A-- ---- ---L- ENUIVQLEECA -Q--------E

TMN FERAE NUNSER SEEBM --- --A-- ------ ----E NOUITCNG MRAZY RXIEDUSPUN MCEB ------N- ----- --X-- -- ------AUNBERKTML ----E- ---ORUST TET CHUNT -R--- --- -----

TAT ORTDEPNS -O- -------ENIFT OTH UKSNHWN S---- --- --K---- Unscramble these words SIUITBNISG SUBITISING PATT PAHR RWOLE PART PART WHOLE NUNSER SEEBM NUMBER SENSE MRAZY RXIEDUSPUN MCEB CRAZY MIXED UP NUMBERS AUNBERKTML NUMBER TALKS ORUST TET CHUNT

TRUST THE COUNT ENUIVQLEECA EQUIVALENCE TMN FERAE TEN FRAME NOUITCNG COUNTING TAT ORTDEPNS DOT PATTERNS ENIFT OTH UKSNHWN SHIFT THE UNKNOWN Next session 14th August

Welcome To BINGO! Bingo Board Draw a quick freehand 3 by 3 grid (no ruler required) Copy 9 random words from the next CHOOSE 9 RANDOM WORDS FROM THIS LIST GROWTH MINDSET COGNITIVE CONTROL or

EXECUTIVE FUNCTIONS HAND SIGNALS SCATTERED DOT PATTERN COUNT ALL NUMBER TALKS 10 FRAME RULE SUBITISING

COUNT ON NUMBER SENSE NUMBER SYMBOL RELATIONAL UNDERSTANDI NG 10 FRAME EMPTY BOX REGULAR PROBLEMS DOT PATTERN PART-PARTWHOLE

BING O QUESTIO N Number symbol or number name? 8 BING O QUESTIO N This is a definition of: ________ _________ Five- to fifteen-minute

conversations around problems that learners solve mentally. Useful tools to include in your lessons to help learners to make sense of mathematics. BING O QUESTIO N Part-part-whole model OR 10-frame? BING O QUESTIO N

People with a ------ ------- believe that qualities like intelligence and ability are growable: they can change and flourish or wither depending on how one engages with learning opportunities BING O QUESTIO N This is a definition of ? the ability to recognise dot arrangements in different patterns

BING O QUESTIO N Name this model 8 6 2 BING O QUESTIO N Regular or alternate?

The dot patterns from 1 to 6 are the easiest to recognise. Commonly seen on dice, dominoes and playing cards BING O QUESTIO N This is a definition of The ability to work flexibly with numbers, observe patterns and relationships and make connections to what they already know, to make generalisations about patterns and processes BING

O QUESTIO N Scattered or linear dot arrangement? BING O QUESTIO N What TYPE of COUNTING is this? When you add two numbers and you begin counting from the largest number and add the second number to it.

BING O QUESTIO N Together, these are known as: ________ _______ skills SHIFTING ATTENTION WORKING MEMORY INHIBITION / SELF CONTROL BING O QUESTIO

N These problems are known as +2 6+ + 10 70 + = = = = 8 8 80 85

BING O QUESTIO N When presented with 5 + 3, some children may count from one one, two, three, four, five six, seven, eight! This is referred to as: ----- --- BING O QUESTIO N Always fill the top row first, starting

on the left, the same way you read. When the top row is full, place counters on the bottom row, also from the left. BING O QUESTIO N Relational or Operational understanding? Knowing what to do (how) and being able to explain why BING O

QUESTIO N These are _____ _______ used in Number Talks Thumbs - I have an answer Thumb and finger shake - I agree / I did the same / Me too A Number Sense Developme nt E Growth mindsets / Sessions productiv e

1 to 4 dispositio ns D Cognitive control Sessions(Executive 1 to 4 functionin g) Sessions 4 to 6 7 to 10 B Story (narrative

) Sessions approach 3&4 es to learning numeracy KEY IDEA S C Learner progressi Sessions on 2&3 C OUNTING / EARLY ARITHMETIC STRATEG IES

Tied to context tied to objects calculation by counting Counting by structuring using representations (physical & mental) 4 3 Learning to count How Many Synchronous (1-1 correspondence) 1 Counts visible items C alculating by structuring Formal calculating

Count on / Count up to / Count down To overcome counting Using number relationships & what has already been learnt (number facts) for flexible calculation without need for structured representations / materials Structure & number facts of 5 & 10 Doubles & near doubles J ump via 10 J ump of 10 Place value

2 Counts screened Items (from one: count all) 0 Cannot count visible items Count all C alculation by counting How? LEVEL 3 LEVEL 4

From calculating by COUNTING To calculating by STRUCTURING Count on / up to / down to Dot patterns (Subitising) 5 & 10-frames Number Talks Structure & number facts of 5, 10 & 20 Part-part-whole model 5 and 10-frames Part A Number Talks

Whole Part B Todays Number Talk [1] Instructions Use any combination of addition, subtraction and multiplication to make 24 You may combine 2 or more numbers Todays Number Talk [2] Instructions Work out the value of the numbers on the left. Then find other combinations of two numbers that are equal to this number Use any operation you like Addition

10 + 14 10 + 12 +2 8+8+8 20 + 4 10 + 10 + 4 12 + 12 etc Todays Number Talk: Discussion Subtractio n Multiplicati on Combinati ons

(10 x 2) + 4 (20 - 8) + 12 (14 x 2) 4 etc 34 10 26 2 etc 12 x 2 8x3 etc Do any of the addition solutions relate to a multiplication solution?

How could you explain the use of brackets to learners? Todays Number Talk: Discussion Addition 10 + 4 or 4 + 10 8+3+3 4+4+4+2 10 + 2 + 2 8 + 6 or 6 + 8 7+7 13 + 1 or 1 +13 12 + 2 or 2 + 12 Subtraction

24 16 18 20 34 - 10 2 4 6 20 Can you think of any that might use multiplication? How could you

encourage the learners to find all the combinations that add to 14? How could you do the same thing with subtraction? Number Talk Prompts These prompts can add variety to your Number Talk sessions. They are not based on any particular model or representation. To use these prompts: Select a number talk prompt from the templates below. Follow the instructions in the second column to

prepare for the talk. Draw the template on the board or on flipchart paper. Number Talk prompts [1] Page 7 Choose a target number for the number range you are working with and 7 numbers that combine to make the target number. Mathematical focus: Addition and / or subtraction in any number range you are working with Multiplication by 2, 3, 5

and 10 if the numbers are carefully selected (see 22 in the Other Examples) Number Talk prompts [2] Page 8 Choose a target number for the number range you are working with and 10 numbers that combine to make the target number. The numbers are in an ordered pattern and are easier to choose from. Mathematical focus: Addition and / or subtraction in any number range you are

working with Multiplication by 2, 3, 5 and 10 if the numbers are carefully selected (see the Other Examples) Number Talk prompts [3] Page 9 Choose a target number for the number range you are working with and 11 numbers that combine to make the target number. The numbers are in a scattered pattern, making them slightly harder to choose from. Mathematical focus:

Addition and / or subtraction in any number range you are working with Multiplication by 2, 3, 5 and 10 if the numbers are carefully selected (see the Other Examples) Number Talk prompts [4] Page 10 Choose one number for the left. Learners find 2 numbers on the right that will make the scale balance. Mathematical focus: Work with one number and

find 2 other numbers that equal the number on the left Addition and / or subtraction in any number range you are working with Multiplication by 2, 3, 5 and 10 if the numbers are carefully selected Number Talk prompts [5] Page 10 & 11 Choose two or three numbers for the left. Learners find 2or 3 numbers on the right that will make the scale balance.

Mathematical focus: Addition and / or subtraction in any number range you are working with Multiplication by 2, 3, 5 and 10 if the numbers are carefully selected Number Talk prompts [1] Page 7 Choose a target number for the number range you are working with and 7 numbers that combine to make the target number.

Mathematical focus: Addition and / or subtraction in any number range you are working with Multiplication by 2, 3, 5 and 10 if the numbers are carefully selected (see 22 in the Other Examples) Linear representations of number Page 13 Regular use of a number line can help learners to form a mental number line This can help learners to calculate mentally

BUT! Page 13 Many learners cannot use a number line very well Important to introduce number lines as early as possible One way - introduce number line work is to start with bead strings Then connect these to a counting line and then move on to a number line Bead string to C ounting line to Number line 1 2 3 4 5 6 7

Bead strings Page 13 Bead strings can be used for: Making / structuring numbers up to 10 and 20 Skip counting in 5s and 10s Early addition and subtraction Counting on / counting back 1 more / 1 less (2 more / 2 less etc) Conceptual place value Bead stings to Counting lines or number tracks Page 14

Counting line An excellent way to support learning to count. It can also be used for learning to add and subtract small numbers Over time, use a more abstract counting line - a numeral (number) track - a printed set of objects that can be counted Bead string to Number Line Page 15 Counting lines are useful, but are NOT number lines Move carefully from bead strings or counting lines to number lines, because learners find them challenging Number lines go beyond counting individual objects

They can be used to measure from a fixed point Fractions can be shown on the number line How to progress from a counting line to a number line Page 15 Important to help the learners to understand that the number marker on a number line indicates where one object finishes For example, the numeral 1 on the number line shows where bead one finishes 0 1 2 3 4 5 6 7 8 9 10

Moving onto measuring 4 0 1 2 3 4 5 6 7 8 9 10 4 0 1 2 3 4 5 6 7 8 9 10 unit unit unit unit unit

unit unit unit unit unit Page 16 Bead strings and Number Sense Number recognition Same and different More and less 1 more and 1 less Counting vertically

Bigger and smaller Doubling Pages 19 & 20 Bead Strings and Number Facts Number facts for numbers up to 10 Number facts for numbers up to 20 Page 21 Bead Strings and Ordinal Numbers Page 22 Working from left to right on the string, ask:

How many red beads are there here? [show the first red group of 5] How many white beads are there? [show the first white group of 5] Hold your bead string with the red beads starting in your left hand Using a pattern of prompts, first ask the group a question, then ask individual learners how they know type questions (see more about this on the next page) Why ask How do you know? questions When learners describe why they think that it is, for example, the 6th bead or finger Focuses on development of: mathematical language reasoning language

Some learners might point to their strings by counting in ones and say: Because look one, two, three, four, five, six. Other learners might begin to see the structure of 6 as 5 + 1 Because 6 is 5 red and 1 white or, Because the 6th is the one after the 5th and I know the last red one is the 5th. Learners dont always explain their thinking this clearly. Rephrase their explanations and share what they notice with other learners This shows other learners how seeing and using the structure is quicker than counting by ones. If learners still count in ones, encourage them to find quicker ways to know without counting for example by noticing and emphasising which beads are the 5th and 10th Bead Strings and Ordinal Numbers Page 22

Examples: One: T to group: Show me the 5th bead T to a learner: How do you know that's the 5th bead? T to group: Any other ways you know that is the 5th? Two: T to group: Show me the 11th bead T to a learner: How do you know that's the 11th bead? T to group: Any other ways you know? Bead Strings and Ordinal Numbers Page 23 Learners place both hands in front of them

Children say the order of the fingers from left to right as: 1st finger 2nd finger up to the 10th finger Use the same questioning sequence from the previous activity Stop at 10 Example of questioning sequence T to group: Wiggle your 2nd finger. T to a learner: How do you know that's your 2nd finger? T to group: Wiggle your 5th finger (yes, it's a thumb but a thumb is also a finger).

T to a learner: How do you know that's your 5th finger? T to group: Any other ways you know that's the 5th finger? (e.g. answer because there are 5 fingers on each hand and this is the last finger on my left hand) And so on