SCITT Day 7

Session objectives Understand how pattern provides the key to early work with algebra and generality (Understand how work with pattern in key stage 1 and lower key stage 2 provides the foundation for algebraic thinking) Use of practical equipment Access good problem solving activities Consider methods of whole class assessment and record keeping

Day 7 Session 1 Session 2 Session 3 Session 4 APP Assessing children Problem Solving Session 3 Pattern  exploring generality Session 4 Time to develop ‘Maths Matters’

Starter Probability: ‘Number Spinners’ ITP What will the total be after 10 spins?

What is the difference between Terminology What is the difference between Attainment & Achievement?

AfL – Assessment for Learning How does your school assess? Short term Medium term Long term What does your teacher count as ‘evidence’ of learning?

Primary Framework Disk APP folder APP Teachers handbook Page 19/20 Assessment Foci Page 24 Links between APP and Primary Fwk Page 31 Making judgements in APP Maths APP L1 to 2 L2 to 3 L3 to 4 L4 to 5 Guidance Documents Guidance Paper ‘Day to Day Assessment’

Assessment Consider the example ‘Standards File’ Use the APP grids to guide your Teacher Assessment of this child’s attainment

Marking linked to Assessment “Marking that leads to children being able to improve their work should be what ideally all teachers are aiming at. Children tend to ignore marking comments when a grade or a symbol is used. However when children are given information about where they achieved success against the learning intention and where they could improve against the learning intention both at the same time, the chances of the marking being effective is vastly improved. Children also need to be given time to read and respond to marking.” Shirley Clarke (1998) ‘Targeting Assessment in the Primary Classroom’

Feedback and Marking Be based on clear learning intentions/ success criteria Take account of pupil self-evaluation Highlight where success occurred and where improvement could take place Be in a form which is accessible to the learner Give strategies for improvement (often oral if this is beyond the means of the learner) Have allocated time in which to take place or be read.

Strategies for closing the gap “Highlight three places where the child has evidenced the best aspects against the learning intention and indicate with an arrow/asterisk where some improvement can be made Extend the arrow to the nearest white space and write a ‘closing the gap’ prompt for the child, to help them to be able to make a small improvement.” (Shirley Clarke, 2001)

3 types of closing the gap prompts A reminder prompt – suitable for brighter children, this simply reminds the child of what could be improved. A scaffolded prompt – most suitable for children who need more structure than a simple reminder, this prompt provides some support. This can take the form of a question, a directive or an unfinished sentence. An example prompt – very successful with all children, but especially with average or below average children, this prompt gives the child a choice of actual words [calculations] or phrases. ( Shirley Clarke, 2001)

‘Reminder’ Carry out column addition and subtraction of positive integers less than 10,000 “Estimate first by rounding, maybe use a horizontal layout to check your working?”

‘Scaffold’ Carry out column addition and subtraction of positive integers less than 10,000 “What has this person done wrong? 158 + 184 612 Now have a look at your answers I have circled. Check your working.” 4 1

‘Example’ Carry out column addition and subtraction of positive integers less than 10,000 Which one has the correct answer? 158 158 158 184 + 184 + 184+ 612 342 2142 41 11 How

Simple everyday recording LO 1 LO 2 LO 3 LO4 Pupil 1 Pupil 2 Pupil 3 Pupil 4

How can I make children think in maths lessons? Good Problem Solving… How can I make children think in maths lessons?

Using and Applying – AT1 Thinking Skills from National Curriculum Information Processing Reasoning Enquiry Creative thinking Evaluating

Information Processing One Way Out ? ? ? ? Odd Even ? Where do you think it will come out? ? ? ?

Reasoning Boxes 100 + + + =

Enquiry What questions could you ask about…?

Creative Thinking How could you find half of: A potato A piece of string A cake A pound A book A glass of water What other examples could you think of?

Evaluating 31 – 12 = ? Discuss these answers: 11, 43, 19, 20

Using and Applying – AT1 Different Types of Problem Finding All Possibilities Logic Puzzles Finding Rules and describing patterns Visual Problems

Finding All Possibilities Clown Hats - 3 colours Red Blue Yellow What different hats can be made? How would you extend this task?

Logic Problems - A mixed-up clock There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from the ten statements?

Finding Rules and describing patterns Create a repeating pattern Can you predict what the next counter will be? Can you say what the pattern is in words? Can you say what the 10th counter will be? The 20th? The 100th? The nth ?

Visual Problems How many triangles can you see?

A problem… A shepherd owns 19 sheep and 13 goats. How old is the shepherd? Answer given 32 Daniel has 8 cakes. He divides each cake into 4 parts. How many pieces does he have? Answer given 2

A word problem There are 7 shelves with 25 books on each shelf. If I remove 47 books, how many books are left? How many ‘full’ shelves would there be? What did you do to solve this problem?

Word Problems Read Underline Choose Solve Answer? Check Read Underline Decide Estimate Calculate Answer? Test it

Using and Applying – AT1 Where to find other problems… Primary Framework disk Puzzles and problems and mathematical challenges Kent Trust Web http://www.kenttrustweb.org.uk/ask8/ask8_primary_numeracy_problem_solving.cfm Nrich www.nrich.maths.org

Kent Trust Web

Nrich

Explore Kent Trust Web Nrich Find one example for your learners. http://www.kenttrustweb.org.uk/ask8/ask8_primary_numeracy_problem_solving.cfm Nrich www.nrich.maths.org Find one example for your learners.

Did we… Understand how pattern provides the key to early work with algebra and generality? Use practical equipment? Access good problem solving activities? Consider methods of whole class assessment and record keeping?