Embedding problem solving in teaching and learning at KS2

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Embedding problem solving in teaching and learning at KS2. Dr Ray Huntley Brunel University, London September 2, 2013. How to be good. Most learners make good progress because of the good teaching they receive Behaviour overall is good and learners are well motivated - PowerPoint PPT Presentation

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Embedding problem solving in teaching and learning at KS2

Embedding problem solving in teaching and learning atKS2Dr Ray HuntleyBrunel University, LondonSeptember 2, 2013How to be goodMost learners make good progress because of the good teaching they receiveBehaviour overall is good and learners are well motivatedThey work in a safe, secure and friendly environmentTeaching is based on secure subject knowledge with a well-structured range of stimulating tasks that engage the learnersThe work is well matched to the full range of learners needs, so that most are suitably challengedTeaching methods are effectively related to the lesson objectives and the needs of the learners

Assessment for LearningEnsure that every learner succeeds: set high expectationsBuild on what learners already know: structure and pace teaching so that they can understand what is to be learned, how and whyMake learning of subjects and the curriculum real and vividMake learning enjoyable and challenging: stimulate learning through matching teaching techniques and strategies to a range of learning needsDevelop learning skills, thinking skills and personal qualities across the curriculum, inside and outside of the classroomUse assessment for learning to make individuals partners in their learningPersonalisationTeaching is focused and structuredTeaching concentrates on the misconceptions, gaps or weaknesses that learners have had with earlier workLessons or sessions are designed around a structure emphasising what needs to be learntLearners are motivated with pace, dialogue and stimulating activitiesLearners progress is assessed regularly (various methods)Teachers have high expectationsTeachers create a settled and purposeful atmosphere for learning Main part of a lessonIntroduce a new topic, consolidate previous work or develop itDevelop vocabulary, use correct notation and terms and learn new onesUse and apply concepts and skillsAssess and review pupils progressThis part of the lesson is more effective if youMake clear to the class what they will learnMake links to previous lessons, or to work in other subjectsGive pupils deadlines for completing activities, tasks or exercisesMaintain pace, making sure that this part of the lesson does not over-run and that there is enough time for the plenaryWhen you are teaching the whole class, it helps if you:Demonstrate and explain using a board, flipchart, computer or OHPHighlight the meaning of any new vocabulary, notation or terms, and encourage pupils to repeat these and use them in their discussions and written workInvolve pupils interactively through carefully planned and challenging questioningAsk pupils to offer their methods and solutions to the whole class for discussionIdentify and correct any misunderstandings or forgotten ideas, using mistakes as positive teaching pointsEnsure that pupils with particular needs are supported effectivelyWhen pupils are working on tasks in pairs, groups or individuals it helps if youKeep the whole class busy working actively on problems, exercises or activities related to the theme of the lessonEncourage discussion and cooperation between pupilsWhere you want to differentiate, manage this by providing work at no more than three or four levels of difficulty across the classTarget a small number of pairs, groups or individuals for particular questioning and support, rather than monitoring them allMake sure that pupils working independently know where to find resources, what to do before asking for help and what to do if they finish earlyBrief any supporting adults about their role, making sure that they have plenty to do with the pupils they are assisting

Fishy ProblemA fish has a head that is 9cm long.Its tail is the same length as its head plus half its body.Its body is the same length as its head and tail together.How long is the fish?

A Fishy Solution Head = 9cmTail = Head + Body, so Body = Tail 9Body = Head + Tail, so Body = Tail + 9

Body = Tail 9, so Body = 2 Tails 18So Tail + 9 = 2 Tails 18, so Tail = 27And Body = 36, so fish is 72cm longEqual SetsTake a set of digits, say 1 to 8. Can you split them into 2 sets with the same total?What about other sets of digits, say 1 to 5? 1 to 7? 1 to 20?How can you decide whether it can be done?

Equal Sets SolutionNeed total of the set to be an even number.Each set totals to a triangle number.So it can be done for any set that totals to an even triangle number.1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, These are the 3rd, 4th, 7th, 8th, 11th, 12th, etc..So it can be done if the number in the set is a multiple of 4, or 1 less than a multiple of 4.QuadrilateralsStart with a circle marked with 8 points evenly spaced on the perimeter.What different quadrilaterals can you draw by joining 4 points?How many are there? How do you know you have them all?Can you sort the quadrilaterals by some criteria?Quads solutionThere are 8 different shapes that can be made.Denoting each shape by the number of spaces between the points round the circle, they are:1,1,1,5 - trapezium 1,1,2,4 trapezium (different one) 1,1,3,3 - kite 1,2,1,4 another trapezium1,2,2,3 - irregular 1,2,3,2 another trapezium 2,2,2,2 - square 1,3,3,1 - rectangleHousesThere are some houses arranged around a square green. There is the same number of houses on each side of the square. Number 9 is opposite number 47.How many houses are there around the square?

Houses solutionWith 9 houses in each row, 9 is opposite 19With 10 in each row, 9 is opposite 22With 11 in each row, 9 is opposite 25

Continuing this pattern,With 18 in a row, 9 is opposite 46With 19 in a row, 9 is opposite 49So 9 can never be opposite 47!! (Sorry!) Thank you!Please try these activities with your children and your teaching colleagues!

Any feedback is always welcome!

rayhuntley61@gmail.com Coordinate shapesStart with 2 points on a rectangular grid, marked by coordinates, say (2,1) and (4,3).Can you find 2 more points to make a square (rhombus, trapezium, etc) ?Can you do it in different ways? How many can you find?

HalftimesIf a sporting match (football, hockey) has a final score of 3-1, what are the possible half time scores? If the fulltime score is a-b, what is the connection between a and b and the number of halftime scores possible?

FractionsCan you find a fraction between and ?Can you find a fraction between any two fractions? Can you devise a rule that will always do this? How can you show why it works (not algebraic proof!)

9s to make 1000Use a dice to generate 9 digits, each in the range 1-6.Arrange them into three 3-digit numbers. Add them. Largest/Smallest/Closest to 1000 wins!

Magic square patternsDraw a 3x3 magic square, where each row, column and diagonal adds to 15 using 1-9.Find pairs of numbers in the square that have the same totals. Record this on a blank square colouring the positions of one pair in one colour and the other pair in another.How many different coloured relationships can you find?

5 presentsThere are 5 presents, labeled A, B, C, D, E.A and B together cost 6B and C cost 10C and D cost 7D and E cost 9.All 5 presents together cost 21. How much is each present?

Digit SumsWithout 0, write down as many 2-digit numbers as you can where the digits add to 6. Now do the same for 3-digit numbers. How many 4-digit numbers do you think there might be? Try it. Now 5-digits, and finally 6-digits.

15 cardsFrom a set of cards numbered 1 to 15, put down 7 cards in a row, face down.Cards 1&2 add to 15, 2&3 add to 20, 3&4 add to 23, 4&5 add to 16, 5&6 add to 18 and cards 6&7 add to 21. From this information can you work out what numbers are on the cards?How many solutions are there?

Numbers of trianglesTake an integer number for the perimeter of a triangle, say 12.What integer sides are possible?Find all permutations.How many possible permutations are there? Is it always a triangle number?

IRATsStart with an isosceles right-angled triangle (IRAT). Fold along the line of symmetry. Open and cut along the fold line, what do you get? (Predict first!)Now start with a new IRAT, fold along the line of symmetry and then again.Open just the last fold and cut along the fold line. What do you get? (Predict first!)

IRATsNow do 3 folds along lines of symmetry and cut along the 2nd fold line what do you get? What about 4 folds and cut along the 3rd fold line?How does the pattern continue?