Problem Solving and Reasoning in mixed attainment classes #mixedattainmentmaths Helen Hindle @helenhindle1 www.growthmindsetmaths.com www.mixedattainmentmaths.com

What is mixed attainment teaching? Classes that have a range of:- Prior attainment, SEN, Pupil Premium Attitude to Learning

Today’s Workshop…. Supporting all pupils with AO3 questions Encouraging reasoning Multiple Entry point tasks.

What is ‘Boxing Up’ and why do we need it.....? Last years exam results show that even our highest achieving students at GCSE struggle to cope with the problem solving and reasoning elements of the GCSE exam…. Helen

Boxing Up is a ....... Strategy for working out (for writing) Strategy for discussing (asking each other questions) Strategy for thinking (asking yourself questions) Aoife

What is the question asking me? What information do I already have? What Maths will I be using? What calculations / working out do I need to do? How can I check that my answer is correct?

A03 Question The diagram shows a garden in the shape of a rectangle. All measurements are in metres. The perimeter of the garden is 32 metres. Work out the value of x . . . . . . . . . . . . . . . . . . . . . . (Total for Question is 4 marks)

What is the question asking me? What information do I already have? What Maths will I be using? What calculations / working out do I need to do? How can I check that my answer is correct?

Perimeter is all the sides added together. What is the question asking me? What information do I already have? What Maths will I be using? Find the value of x Solve an Equation Perimeter = 32 metres Write an Equation Perimeter is all the sides added together. What calculations / working out do I need to do? How can I check that my answer is correct? 4 + 3x + x + 6 + 4 + 3x + x + 6 = 32 Substitute 1.5 for x and check that the perimeter does = 32 8x + 20 = 32 8x = 12 x = 12 8 X = 1.5

"Good teaching is more a giving of right questions than a giving of right answers."--Josef Albers What is the question asking me? What information do I already have? What maths will I be using? How can I check my answer is correct? What calculations / working out do I need to do?

Boxing Up To teach is to learn twice……….

Developing Reasoning Make a comment or ask a question…..

Class Feedback

Class Feedback

This is a regular pentagon. Find the value of the missing angle. From ‘Geometry Snacks’ by Ed Southall and Vincent Pantaloni

A square is constructed using vertices of a regular dodecagon as shown A square is constructed using vertices of a regular dodecagon as shown. What fraction of the dodecagon is shaded? From ‘Geometry Snacks’ by Ed Southall and Vincent Pantaloni

CIMT Centre for Innovation in Mathematics Teaching

Multiple Entry Point Tasks ……. “Differentiation does not happen at some spurious notion of 3 levels; it happens at as many different levels of cognition and depth of sense making as there are students in the class.” Mike Ollerton 2014

Learning Journey I can match a net to a 3D shape. Surface Area and Volume I can match a net to a 3D shape. I can identify edges, faces and vertices of 3D shapes. I can find the surface area of a cube and cuboid by counting the squares on each face. I can find the volume of a cube and a cuboid by counting cubes. I can find the surface area and volume of cuboids and triangular prisms I can find the surface area and volume of prisms I can calculate the volume of cones and pyramids.

A B C Pupil hand-out. Print this slide and the next slide two to a page. D

E G F H Pupil hand-out, print this slide and the previous slide two to a page.

The face of this sculpture has been split into 3 large squares. Each of these squares is split into four smaller squares. Each smaller square is 1m x 1m This Sculpture is a cuboid with a:- Length of 90cm Height of 88cm Width of 88cm. The circle has a diameter of 30cm

This sculpture is 93cm long across the top. This table has a semi-circular face and a rectangular top. The length across the rectangular top of the table is 160cm The width across the rectangular top of the table is 20cm. The height of the semi-circular face (without the legs) is 80cm This sculpture is 93cm long across the top. The perpendicular height of the sculpture is 76cm. The sculpture is 24cm deep. The sculpture is constructed from a solid piece of wood.

This fountain is a cylinder with a:- Diameter of 125cm Height of 300cm. This structure is a square based pyramid. The square has a side length of 5m The pyramid has a height of 8m.

These sculptures are cones. The radius of the circular face is 6m. The length of the cone (height) from the circular base to the tip is 8m. This sculpture is 3m high from the circular base to the top of the cylinder. The base has a radius of 90cm and a height of 60cm The cylinder has a radius of 50cm 3m 50cm 60cm 90cm

Match each 3D solid to its net. Name each 3D Solid. Match each 3D solid to its net. Write down the number of edges, vertices and faces for each solid. Draw the net of the cube and the cuboid on squared paper. Use the squares to calculate the surface area of the cube and the cuboid. Build a model of the cube and the cuboid using multi-link cube. Use this to calculate the volume of the solid. What is the same and what is different about the cube and the cuboid? What is the minimum information that you need to know before you can work out the volume and the surface area of the cuboid and the triangular prism? Calculate the volume and surface area of the cuboid and the triangular prism. Calculate the volume and the surface area of the cylinder. What is the minimum information that you would need to know before you could work out the volume and surface area of a cylinder? Calculate the volume and the surface area of the pentagonal prism, the hexagonal prism, and the octagonal prism. Which 2D shapes did you use to help you work them out? What is the same and what is different about each prism? Work out the volume of the pyramid and the cone. You can ask for a hint card to help you. How are the pyramid and the cone different from the prisms? How are the pyramid and the cone the same as the prisms? Main Activity – Pupils choose which task /tasks to work on.

Sequences

Sequences I can draw the next two patterns in a simple sequence I can work out the next two terms (numbers) in a sequence I can find a term to term rule for a linear sequence. I can describe a sequence in words. I can find the position to term rule for a linear sequence and explain how I worked it out. I can generate a sequence from a position to term rule. I can use a position to term rule to find any term in a sequence and also to decide whether a number is part of a sequence. I understand the difference between a linear sequence and a quadratic sequence.

Pupil hand-out. Print this slide and the next slide 2 to a page.

Pupil hand-out. Print the previous slide and the next slide 2 to a page.

Draw or build the next two patterns in the sequence. What do you notice about each sequence? Describe the sequence in words. Find the term to term rule for the sequence. What is the same and what is different about each sequence? Find the position to term rule for each sequence and explain how you worked it out. Find the 20th 50th and 100th term in each sequence. What is different about the starred sequences? Can you find the next two terms in these sequences? Can you find a nth term rule for these sequences and explain how you did it?

Types of Number. I can find multiples of any numbers up to 12. I can identify factors of two digit numbers.    I can find all the factors of number by checking for divisibility.   I can square and cube numbers. I can square root a number. I can use the concepts and vocabulary of prime numbers, highest common factor, lowest common multiple. I understand and can use powers (square, cube and higher). I understand that not all numbers will have an exact square root. I can express a number as a product of its prime factors. I can use Prime Factors to find the Highest Common Factor and Lowest common multiple of pairs of numbers. Print this slide and the next slide two to a page and give to pupils to glue into their books. These should be printed onto blue paper so that pupils can easily find them in their books. Pupils should be referring to these every lesson.

Ask a question or make a comment about the prompt. ‘The product of two numbers divided by their highest common factor is their lowest common multiple.’

Find all the factors of a number. Find the highest common factor of pairs of numbers. Find the lowest common factor of pairs of numbers. Use prime factor decomposition to find LCM and HCF of pairs of numbers.

The answer is……. Make up six questions that have the same answer. Put your questions in order from the least to the most challenging.

Make the numbers 1-20 using just four 4s and any operation?

Create an equivalent expressions spider diagram Use substitution to check that your expressions are equivalent.

Problem Solving and Reasoning in mixed attainment classes #mixedattainmentmaths Helen Hindle @helenhindle1 www.growthmindsetmaths.com www.mixedattainmentmaths.com