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National Curriculum Aims: Medium Term Planning Year 4 Theme 7 Theme Title: Solve problems involving position and direction KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims SIMMERING SKILLS AND ACTIVITIES within and beyond the daily Fluency The main focus of this theme is to provide varied opportunities for pupils to apply and deepen their geometrical reasoning and use the language of position and direction to describe, translate and plot shapes and points. Using a coordinate grid in the first quadrant pupils will construct both the x and y axes labelling the integers correctly. Pupils will plot coordinates presented in pairs (4,6) and be able to visualise the position of missing vertices and sides, giving the coordinates for these and applying their prior knowledge of 2D shapes and their properties (including the different types of triangles). Pupils will be able to follow instructions to translate shapes in the first quadrant: Move the shape 4 units up and 2 units left, using the vertices to translate accurately to a new position. Pupils will describe the new position in relation to patterns in coordinates: The shape has moved 3 up, so the x coordinate stays the same and 3 is added to the y coordinate. Using the coordinate grid, pupils will reflect shapes across a horizontal and vertical mirror line, giving the coordinates of the new shape and describing any patterns in the coordinates of the original and reflected shape. Pupils will begin to find the surface area of rectangles using a grid to count centimetre squares and find other rectangles with the same area. Building on prior work around the algebraic formula for calculating perimeter, and in preparation for Year 5, they could begin to reason about area, applying their knowledge of factors and linking this to arrays and multiplication. Throughout the theme, children will continue to classify and compare geometric shapes according to their properties: opposite angles of a rhombus are equal, while adjacent angles of a trapezium are equal. Pupils order and compare angles up to 180°, and compare the size of angles in shapes using the terms acute and obtuse. Can you draw a quadrilateral with 3 acute angles and one obtuse? Is it possible? N.C. Describe positions on a 2D grid as STATUTORY Reasoning Geometry: position, direction, motion coordinates in the first quadrant Describe movements between positions as Recognise and show families of common equivalent fractions Order fractions with the same denominator Compare the size of fractions with the same denominator and order on a number line Find 1/2, 1/4, 1/3, 3/4 of a quantity of money using mental strategies Order quantities of money from smallest to largest when presented in decimal notation Round any number to the nearest 10,100 or 1000 Round 2 and 3 digit numbers and quantities of money to the nearest 10p and whole pound Recall multiplication and division facts to 12 x12 and derive other facts Divide one and two digit numbers by 10 and 100 Count in multiples of 6,7,9,25 and 1000 Read the time to 5 minutes Geometry: Properties of shapes Measurement Compare and classify geometric shapes, including quadrilaterals and Measure and calculate the perimeter of a triangles, based on their properties and sizes Identify acute and obtuse angles and compare and order angles up to two right angles by size Identify lines of symmetry in 2D shapes presented in different rectilinear figure (including squares) in centimetres and metres Find the area of rectilinear shapes by counting squares orientations Complete a simple symmetric figure with respect to a specific line of symmetry NON-STATUTORY Problem-Solving translations of a given unit to the left/right and up/down Plot specified points and draw sides to complete a given polygon Approximately 3 weeks Pupils should draw a pair of axes in one quadrant, with equal scales and integer labels. They should read, write and use pairs of coordinates (2, 5), including using coordinate-plotting ICT tools © Wandsworth & Merton Local Authorities, 2014 Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (e.g. isosceles, equilateral, scalene) and quadrilaterals (e.g. parallelogram, rhombus, trapezium) Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular.. Pupils draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams including where the line of symmetry does not dissect the reflected shape. They relate area to arrays and multiplication Pupils understand and use a greater range of scales in their representations. Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit. National Curriculum Aims: Medium Term Planning Year 4 Theme 7 Theme Title: Solve problems involving position and direction EXEMPLAR QUESTIONS AND ACTIVITIES: connecting the strands and meeting National Curriculum aims KEY QUESTION ROOTS to be used and adapted in different contexts Fluency Working backwards: The co-ordinates of corners of a rectangle that has a width of 5 are (7, 3) and (27, 3). What are the other two co-ordinates? What’s the same, what’s different? What is the same and what is different about the diagonals of these 2-D shapes? Visualising: If you translated the square 4 up, what would the new coordinates be? What if…...vertex B was translated 2 right, what would your new shape look like? Can you name it? Work backwards: The steps to translate shape A to position B are 5 left, 7 down. How would you translate shape B to position A? Always, sometimes, never true….isosceles triangles can have a right angle Convince me….. that the shape you have translated is congruent to the original shape Translate the shape 4 units to the left. Translate the shape 2 units up. Give the coordinates of the acute angles...the obtuse angles. 10 9 8 Reasoning Translate the shape 2 units down and 3 units to the right. Translate the shape 1 unit to the left and 3 units down. Plot coordinates (3,6) (5,6) (6,9) and a fourth to make a trapezium. Player 1: Pick a task card and plot the shape in the first quadrant. Player 2: Pick a translation card and translate the shape on the same grid. Partners check each other’s work. 7 Reflect shapes across horizontal and vertical mirror lines. 6 Can pupils plot the coordinates of the new shape. Can they see a pattern in the coordinates? 5 4 3 Pupils choose a point and translate the point to complete the shape e.g. 2 down, 3 right. 2 1 1 2 3 4 5 6 7 Problem-Solving Is it possible to draw a shape with: 3 sides 1 obtuse angle? 8 9 Approximately 3 weeks See Wandsworth LA Calculation Policy for more detail on developing mental and written procedures! Can some of the key thematic ideas be delivered as part of a mathematically-rich, creative topic? Suggested ideas: Design a Tudor knot garden. Using a 100cm squared grid, pupils design a garden following a design brief with particular criteria: 24cm2 of gravel pathway Two symmetrical rectangular flowerbeds with an area of 16cm 2 each A paved area with an area of 20cm2 Two grassy areas with the same surface area Pupils use their knowledge of arrays and factors to create areas meeting the given measurements. Can pupils create more than one design that meets the brief? Can they fit the areas in to the 100cm squared grid without overlapping? Non-Routine Problem: Eight Hidden Squares (NRich— http://nrich.maths.org/6280 Can you find the eight hidden squares? These 28 points all mark the vertices (corners) of eight hidden squares. Each of the 4 red points is a vertex shared by two squares. The other 24 points are each a vertex of just one square. All of the squares share just one vertex with another square. All the squares are different sizes. 10 Partners challenge each other to draw shapes with the given properties. Where would these shapes fit in the carroll diagram? Why? Move one vertex to make a different triangle. What are its properties? 10 What are the properties of this shape? How many obtuse angles? How many acute angles? 9 8 7 Use Numicon shapes to create symmetrical patterns across a horizontal, diagonal and vertical mirror line and a combination of two or three. © Wandsworth & Merton Local Authorities, 2014 Is it possible to draw a shape with: 4 sides 1 pair of parallel sides 1 pair of sides of equal length? Is it possible to draw a shape with: 4 sides All acute angles? At least one line of symmetry No lines of symmetry No right angles Draw the line of symmetry. Describe how you translated the vertex. 6 5 4 What are the coordinates of the fourth vertex of this rhombus? 3 At least one right angle Draw a four-sided shape that fits these criteria. What would it be called? Join two vertices with another line to make a triangle? Describe it. What type of triangle is it? 2 1 1 2 3 4 5 6 7 8 9 10