Shape Draw translate reflect polygons Objectives Day 1
Shape Draw, translate, reflect polygons Objectives Day 1 Plot points and draw polygons in all 4 quadrants. Day 2 Work out new co-ordinates after a translation. Day 3 Work out new co-ordinates after a reflection. © hamilton-trust. org. uk 1 Year 6
Shape Draw, translate, reflect polygons Starters Day 1 Coordinates in 4 quadrants (1) (pre-requisite skills). Day 2 Coordinates in 4 quadrants (2) (pre-requisite skills). Suggested for Day 3 Find lines of symmetry (simmering skills). © Hamilton Trust 2 Year 6
Shape Draw, translate, reflect polygons Starter Coordinates in 4 quadrants (1) © Hamilton Trust 3 Year 6
Shape Draw, translate, reflect polygons Starter Coordinates in 4 quadrants (2) Co-ordinates © Hamilton Trust 4 Year 6
Shape Draw, translate, reflect polygons Starter Find lines of symmetry http: //www. crickweb. co. uk/ks 2 num eracy-shape-and-weight. html#Symm © Hamilton Trust 5 Year 6
Shape Draw, translate, reflect polygons Objectives Day 1 Plot points and draw polygons in all 4 quadrants. © hamilton-trust. org. uk 6 Year 6
Day 1: Plot points and draw polygons in all 4 quadrants. y Do you remember which axis is which on the co-ordinate grid? x The x-axis goes across. When reading and plotting, the x co-ordinate goes first and then the y. Walk before you fly! © hamilton-trust. org. uk 7 Year 6
Day 1: Plot points and draw polygons in all 4 quadrants. y What co-ordinates have been plotted on the grid? 2 nd quadrant 1 st quadrant The y -coordinate is negative each time as it is below the horizontal axis, a bit like being below ground! Today we are going to use all four QUADRANTS… x + (-4, -2) 3 rd quadrant © hamilton-trust. org. uk 8 + (6, -2) 4 th quadrant Year 6
Day 1: Plot points and draw polygons in all 4 quadrants. y These are three of the four vertices of a rectangle. (-4, 4) + + x + Talk to a partner… What are the co-ordinates of the missing vertex? © hamilton-trust. org. uk 9 + Year 6
Day 1: Plot points and draw polygons in all 4 quadrants. y (-5, 8) + + (-7, -1) © hamilton-trust. org. uk + (4, 6) x + What are the co-ordinates of the vertices of this square? (2, -3) 10 Year 6
Day 1: Plot points and draw polygons in all 4 quadrants. y What shape is this? (1, 5) + Sketch the shape (not the grid) and label the co-ordinates of its vertices… (-7, 2) (9, 2) + (-4, -3) + + x + (6, -3) Tell your partner how you remember which order to plot and read coordinates… © hamilton-trust. org. uk 11 Year 6
Challenge © hamilton-trust. org. uk 12 Year 6
Shape Draw, translate, reflect polygons Objectives Day 2 Work out new co-ordinates after a translation. © hamilton-trust. org. uk 13 Year 6
Day 2: Work out new co-ordinates after a translation. y What shape is this? (-4, 3) Now, let’s use our paper, pencils and rulers to sketch the shape (not the grid) and label the co-ordinates… Don’t rub off the co-ordinates when we finish! + + (3, 3) x + (-6, -3) + (1, -3) This parallelogram moves 3 squares to the right. Work with a partner to agree the coordinates of its new position… © hamilton-trust. org. uk 14 Year 6
Day 2: Work out new co-ordinates after a translation. y This shape has been translated; this means that it has moved but kept its original shape and orientation. (-1, 3) + Look at the new co-ordinates. What is the same; what is different? x + (-3, -3) © hamilton-trust. org. uk + (6, 3) 15 + (4, -3) Year 6
Day 2: Work out new co-ordinates after a translation. y This time, move the parallelogram up four squares… Sketch the shape on your whiteboard, labelling the new coordinates. (-4, 3) (3, 3) + + x + (-6, -3) © hamilton-trust. org. uk 16 + (1, -3) Year 6
Day 2: Work out new co-ordinates after a translation. y Look at the new co-ordinates. What is the same; what is different this time? (3, 7) (-4, 7) + + (1, 1) (-6, 1) + © hamilton-trust. org. uk 17 x + Year 6
Day 2: Work out new co-ordinates after a translation. y Watch carefully… Then discuss how to describe this translation…. FINISH x The rectangle has moved ___ squares up and ___ squares to the right. START © hamilton-trust. org. uk 18 Year 6
Challenge © hamilton-trust. org. uk 19 Year 6
Shape Draw, translate, reflect polygons Objectives Day 3 Work out new co-ordinates after a reflection. © hamilton-trust. org. uk 20 Year 6
Day 3: Work out new co-ordinates after a reflection. y Sketch this parallelogram and write the co-ordinates of its vertices. The new shape must be the same distance away from the y -axis as the first one, but ‘flipped’ over. x If we reflect this parallelogram across the y-axis, where will the new shape be? Sketch it… © hamilton-trust. org. uk What are the co-ordinates of the new shape? 21 Year 6
Day 3: Work out new co-ordinates after a reflection. y Now reflect this new shape in the x-axis. original shape What do you notice about the shape itself compared with the original one? What about its position? Is this different from a translation? x What are the co-ordinates of the new shape? © hamilton-trust. org. uk 22 Year 6
Day 3: Work out new co-ordinates after a reflection. y Now reflect the new shape in the y-axis; again record the new co-ordinates. original shape x What would happen if it was now reflected again in the x-axis? IT’S BACK WHERE IT STARTED! © hamilton-trust. org. uk 23 Year 6
Challenge © hamilton-trust. org. uk 24 Year 6
Shape Draw, translate, reflect polygons Well Done! You’ve completed this unit. Objectives Day 1 Plot points and draw polygons in all 4 quadrants. Day 2 Work out new co-ordinates after a translation. Day 3 Work out new co-ordinates after a reflection. © hamilton-trust. org. uk 25 Year 6
Shape Unit 2 Problem solving and reasoning questions Without drawing a co-ordinate grid and plotting the points, say what each of these shapes are. Be as specific as you can. (a) (2, 1) (2, 5) (6, 1) (6, 5) (b) (1, 1) (5, 1) (3, 6) (c) (– 1, – 1) (– 1, – 3) (– 3, 0) (– 5, – 2) (– 3, – 4) Now plot each set of co-ordinates and join to create each shape to check your answers. A triangle is translated so that it has moved 4 squares up the grid. Its co-ordinates are now: (2, 0) (5, 2) and (3, 7). Draw it in its original position. (0, 0) (5, 5) (0, 5) are the co-ordinates of four vertices of a shape. When it is reflected in the y-axis, two pairs of co-ordinates do not change. Why not? Sketch it to explain. © hamilton-trust. org. uk 26 Year 6
Problem solving and reasoning answers (1 of 2) Without drawing a co-ordinate grid and plotting the points, say what each of these shapes are. Be as specific as you can. (a) (2, 1) (2, 5) (6, 1) (6, 5) It’s a quadrilateral as it has 4 vertices. The difference between both the x- and y-values of the pairs of coordinates is 4 (6 - 2 and 5 - 1). This means that the 4 sides are the same length – the shape is a square. (b) (1, 1) (5, 1) (3, 6) It’s a triangle. It has a horizontal side as two of the vertices have a y-value of 1. The third vertex is half-way between the other two (its x-value of 3 is half way between 1 and 5), making this an isosceles triangle. (c) (– 1, – 1) (– 1, – 3) (– 3, 0) (– 5, – 2) (– 3, – 4) It’s a pentagon, having 5 vertices. It sits in the 3 rd quadrant, as all co-ordinate values are negative. One vertex sits on the x-axis, having a y-value of zero. Two pairs of coordinates are vertically in line with one another as they share the same x-value: (-1, -1) and (-1, -3); (-3, 0) and (-3, -4). Now plot each set of co-ordinates and join to create each shape to check your answers. Look for accurately plotted shapes. Common misconceptions include plotting x and y values in the wrong order, and becoming confused with the negative co-ordinates in example (c). © hamilton-trust. org. uk 27 Year 6
Problem solving and reasoning answers (2 of 2) A triangle is translated so that it has moved 4 squares up the grid. Its co-ordinates are now: (2, 0) (5, 2) and (3, 7). Draw it in its original position. (2, -4) (5, -2) and (3, 3). As it has moved up, each of the y co-ordinates must have originally been 4 less than those given. The x- values are unchanged by the move. (0, 0) (5, 5) (0, 5) are the co-ordinates of four vertices of a shape. When it is reflected in the y-axis, two pairs of coordinates do not change. Why not? (0, 0) and (0, 5) do not move as they are located on the y-axis itself. Sketch it to explain. As before, look for accurately plotted shapes. © hamilton-trust. org. uk 28 Year 6
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