Pattern, algebra and number sequences SCITT Day 8 2012/13 Pattern, algebra and number sequences

Today we will… develop algebraic thinking as a way expressing generality; understand how work with pattern in key stage 1 and lower key stage 2 provides the foundation for algebraic thinking; review aspects of measures with practical materials and estimation.

Associated issues for teaching Promoting mathematical thinking with appropriate and challenging questioning. Marking children’s work. Measures work provides lots of opportunities for pupil questioning and data handling

Day 8 Session 1 Session 2 Session 3 Session 4 Assignment groupings, Questioning and planning aids for the New Curriculum Session 2 Number Sequences Session 3 Measures Session 4 Marking and Tasks

Starter – Frames of reference Estimate How many ‘giant footsteps’ to the door? How many hands high is the IAW? How long is a table in cms? How much liquid does a mug hold? How much does a shoe weigh? How far is it to Birmingham? Set other examples for your group… What helped you to estimate?

Planning Aids Long Term Medium Term A3 overview NC2014 Medium Term Planning – Autumn term How could you use these plans to support the requirement to plan a series of lessons? What else do you use to help you plan? How could they work together?

Assignment Hand in / post to Carole W by Fri 25th April 2 copies In groups of 3/4 Discuss your focus Your reading so far – share? Plans for/ reflection of lessons

Questions Why do we ask questions? Benefits? Share your experiences with Questioning Reading/ research Observing good practice What are your next steps?

Strengthening the Power of Talk How we facilitate feedback; How we respond to pupils; Ensure pupils use correct mathematical vocabulary; Develop mathematical talk through sorting; Develop the pupils’ vocabulary of reasoning; Use discussion of errors to deepen thinking; Change the nature of the tasks we provide; Use proof to deepen thinking.

‘Seeing’ and ‘saying’ On the next screen you will see some number sequences… Look at each pattern carefully. Can you see how the pattern is made? Can you describe it to a friend? What will the next number be? And the next one…?

Patterns 1,3,5,7,9,……. 1,4,7,10… 25,50,75,100… 27, 31, 35, 39… 32, 28, 24,…

Your turn… Make up a number sequence for your partner to solve They must find the rule and the next two numbers

From DAY 7… ‘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 ?

Growing Patterns Watch this pattern grow…

Square Numbers Term (t) Dots Added (a) Total Dots (d) 1 2 3 4 6 9 10 16 5 15 25 21 36

Another pattern to explore Challenges: Can you describe what is happening? Can you draw the next two steps of the pattern? Can you find the rule?

In year group pairs… explore PNS examples Use the ideas to draft a lesson plan or a series of lessons to allow children to build, play, reason, predict and generalise about patterns. How will you enable their thinking? What questions will you ask?

Measures Where do we measure? What do we need to measure for? Subjects / contexts What do we need to measure for? How do we measure? Measuring instruments Scales Units

Nrich Article - Measures Subjects – sciences, social studies, history, geography, art and literature Measuring distance, weight, mass, volume, capacity, rotations, position, movement, time, money… What do we need measurement for? Recording change, comparing, evaluating, constructing, trading ...   How do we measure? The variety of ways both standard and non-standard created by which to measure documents man's technological advances. Already we can see that measurement permeates just about everything and everywhere.

The Man is much smaller than you and me The Man is much smaller than you and me. Here is a picture of him standing next to a mug.  KS1 example     How tall do you think the Man's mug might be? Can you estimate how many "Man mugs" of tea might fill one of our mugs? Can you estimate how tall he is? Can you think of something that you have at school or home that is approximately twice as tall as the Man? What about something that is about half as tall?

Olympic Starters In 1896 Thomas Burke from the USA won the 100m in 12  seconds. I wonder how far you could run in 12  seconds. In 1924 Jackson Scholz from USA won the 200m in just over 21  seconds. I wonder if you could run the 100  metres in that time? Or you could see how far you could run in 22  seconds…

Olympic Starters In 1906 Ray Ewry from the United States jumped 1  metre 56  centimetres. How high is 1 metre 56  centimetres? How high can you jump? The triple jump is a hop, step and a jump. In 1906  it was Peter O'Connor from Ireland who won a silver medal. He jumped [about] 15  metres. What's your best hop, step and a jump?

Software to Support Measuring Cylinder Thermometer Measuring Scales Ruler Others online?

Marking A ‘real’ example to discuss

TASKS Task 4 (Hand in Day 9 – 27/28 Mar 2014) Deliver a Problem Solving lesson to a group, or class, of children. Focus on one set of skills that you wish to make explicit to learners. Evaluate the lesson – how & when did you make the skills explicit? How successful were the learners in acquiring them, what do they need to do next? Task 5 (Bring to Day 10 – 19/20 May 2014) Identify a learning objective that requires consolidation. Create a game (or other practical activity) for your learners to use in class (& at home?)