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Unit 10 Five daily lessons Shape and space; Position, movement and scales, and solve problems Year 6 This Unit Plan is designed to Autumn term guide your teaching. Unit Objectives You will need to adapt it to Year 6 meet the needs of your class. Read and plot co-ordinates in all four quadrants. Page 109 Recognise where a shape will be after two translations. Page 107 Resources needed to teach this unit: Identify and use appropriate operations (including combinations of operations) to solve Page 83-89 word problems involving numbers and quantities based on ‘real life’ or measures (including time), using one or more steps. Resource sheet 10.1/OHT 10.6 OHT 10.1 Choose and use appropriate number operations to solve problems and appropriate ways of Page 75 OHT 10.2a calculating (mental, mental with jottings, written methods, calculator). Explain methods OHT 10.2b and reasoning. OHT 10.3 Page 95 OHT 10.4 Record estimates and readings from scales to a suitable degree of accuracy. OHT 10.5 Know imperial units, know rough equivalents of lb and kg, oz and g, miles and km, litres and Page 91 OHT 10.6 pints or gallons. OHT 10.7 OHT 10.8 OHT 10.9 Counting stick Link Objectives Squared paper Year 5 Year 7 Calculators Read and plot co-ordinates in the first quadrant. Use conventions and notation for 2-D co-ordinates Rulers with cm and mm in all four quadrants; find co-ordinates of points Tape measures with cm and inches Recognise where a shape will be after a determined by geometric information. Whiteboards translation. Related Key Stage 2 national test questions Recognise and visualise the transformation and Use all four operations to solve simple word symmetry of a 2-D shape translation. problems involving numbers and quantities. Choose and justify the use of an appropriate Choose and use appropriate number operations and efficient method for solving problems. to solve problems, and appropriate ways of calculating (mental, mental with jottings, written Solve problems and puzzles in a variety of contexts. methods, calculator). (Key objectives in bold) NNS Unit Plans Planning Day One Unit 10 Shape and space: Term: Autumn Year Group: 6 sheet Position, movement and scales, and solve problems Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Vocabulary Vocabulary Questions Order a set of positive Hold a counting stick Read and plot co- Show the first quadrant on OHT 10.1 Draw the diagram: Write (4, 2), (8, 2), (–2, 4), (–2, 8) and negative integers. horizontally and count from ordinates in all four (cover the other 3 quadrants). y-axis on the board. Explain that these negative five through zero quadrants. Remind children that both axes begin should be the vertices of a square. to positive five in steps of at zero and identify the x-axis and the Plot the points on OHT 10.1. Ask one. y-axis. Say that if they forget, it might 2 1 the children to suggest where help to remember that the x-axis goes x-axis mistakes have been made in the Remind the children of the across. 3 4 co-ordinate notation. symmetry involved. Ask them to identify the biggest Mark a point on the grid. Q What must we remember number on the stick and The Four Quadrants when we plot co-ordinates? the smallest. Quickly point Q What are the co-ordinates of this to various divisions on the point? Ask the children to give you Establish that the first number in a stick asking which numbers instructions to plot (2, 5), (–2, 5), pair of co-ordinates always refers lie there. (It is helpful to Discuss and remind children about (–2, –5) and (2, -5), start from (0, 0) to the x-axis, the second to the y- keep your thumb on zero.) the notation, e.g. (3, 2). each time. Ensure that they are axis. confident with this. Repeat holding the Q If I move the cross 2 squares down HOMEWORK – Give the children counting stick vertically so what will the co-ordinates be? Tell the children to draw axes (each squared paper on which to plot points that negative five is at the from –10 to 10) on the squared paper that make up 4 different shapes. For bottom. Record the co-ordinates on the board. and plot the following co-ordinates each shape the children are to name (–1, 1), (2, 5) and (5, 2). Tell the the shape. Explain that the stick now Q What if I move it 5 squares down? children that these are 3 of the 4 represents the range –25 vertices of a square. Ask them to plot Shape 1 - (–4, 6), (–3, 10), (5, 8), (4, 4) to 25. Repeat the counting Establish that the cross would be off the fourth vertex and check this with a Shape 2 - (–8, –4), (–8, 1), (–5, 4), (0, 4) activity from –25 to 25 in the grid. partner. Shape 3 - (–5, –5), (–2, 1), (–2, –8), steps of 5, first with the (–1, 0) counting stick horizontally Uncover the other 3 quadrants. Give the children other groups of co- Shape 4 - (2, 4), (9, 1), (3, –3). and then with the counting ordinates to plot which are vertices of stick vertically. Refer to the use of negative numbers triangles and different quadrilaterals on the stick in the oral/mental e.g. parallelogram. Get the children By the end of the lesson children Remind the children that so session. Explain that this is like two to identify and plot the missing should be able to: far the zero has been in the counting sticks crossing at zero which vertices. Explain that there may be middle. Ask them to form four sections, or quarters. Say more than one answer if only two Read and plot points beyond identify the zero on the that these are called quadrants. vertices are given. the first quadrant; stick for different ranges of VOCABULARY Identify the co-ordinates of the numbers, e.g. –10 to 40, quadrant Collect children’s results and correct Plot points in each quadrant of the 4th vertex of a square. –40 to 10, –20 to 30, –30 x-axis any mistakes and misunderstandings. grid, stress the (x, y) convention. Say to 20, –15 to 35 etc. For y-axis (Refer to supplement of examples, that if they forget which comes first, it each range get the children origin Q A square has vertices at (–1, 0) and section 6, page 109.) may help to remember that x comes VOCABULARY to identify the step size for vertex (1, –2). What are the positions of before y in the alphabet and so they positive the divisions and as a vertices the other two vertices? should read along the x-axis first. negative whole class count forwards Label each quadrant (first, second, and backwards to confirm third and fourth) pointing out that the On the board or OHT show the 3 this and the position of order is anti-clockwise around the possible squares that have vertices at zero. RESOURCES (-1, 0) and (1, -2). origin (0, 0). RESOURCES OHT 10.1 Counting stick Squared paper NNS Unit Plans Planning Day Two Unit 10 Shape and space: Term: Autumn Year Group: 6 sheet Position, movement and scales, and solve problems Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Vocabulary Vocabulary Questions Read and plot co- Ask the children to give you Recognise where a Collect names of shapes from Discuss with the children how to Give the children the co-ordinates ordinates in all four quickly the pairs of numbers shape will be after two homework. Correct any errors and describe the translation C to D. of the trapezium after a two-step quadrants. which total 5. As they give translations. misunderstandings. Emphasise the 2 translations, C to A translation. Ask children to these to you, write them in then A to D and write on the board: describe the translation of shape A this order: Use OHT 10.2a with trapeziums A to to this new position. G. Ask for the co-ordinates of C to D is translation +9 in x direction 5+0 trapezium A. Using an overlay, OHT and +5 in y direction. Ask children to Compare answers, drawing 4+1 10.2b, move shape A to shape B. describe G to B, C to E, F to C. attention to the fact that the 3 + 2… movements could be described Q How has the shape moved? Give the children squared paper. Get differently. so that they can see the them to draw axes (–10 to 10), and to pattern. Discuss and establish that it has draw the trapezium in the same Q Why do we sometimes need two moved 5 squares to the right. position as Shape A on OHT 10.2a. instructions for moving a shape? Ask what pair would come Emphasise they must give direction Tell them you are going to give them next in the pattern after 0 + 5, and distance and refer to the axes for some translations of shape A, e.g. +4 Establish that a translation involves e.g. -1 + 6, -2 + 7… help. Emphasise it is the movement in x direction and –2 in y direction. a movement along a straight line in of each corresponding vertex that They are to draw the shapes after the one direction. It is simplest to Using OHT 10.1 ask children they are giving. Tell them this translations and identify the co- describe a translation by to come up and plot the movement keeps the shape in the ordinates of the vertices. Give single movements parallel to the graph points represented by these same upright position i.e. its and two-step translations and collect axis we need two instructions for pairs as co-ordinates, i.e. orientation stays the same, and its results. Check for errors and correct moving a shape. (5, 0), (4, 1)… area does not change. mistakes. (–1, 6), (–2, 7)… Q What do we call a movement in a Q What do you notice about straight line? By the end of the lesson the the position of the points? children should be able to: Establish that it is a translation. Discuss and establish that Sketch the position of a simple they lie on a straight line. Explain that in this case A is shape after it has been translated 5 places forward in the x translated. Join the points up with a direction. Write +5 in the x direction straight line. Ask if the on the board. Discuss how this (Refer to supplement of examples, intermediate points on the recording explains the translation. section 6, page 107.) lines have meaning e.g. (3½, 1½). Ask the children to describe the translations of A to C, A to D, A to E Ask what you think will and write on the board: happen if you started with totals of 3 or 6? Repeat using VOCABULARY A to C is translation –9 in x direction 3 and 6. Highlight the fact trapezium A to D is translation +5 in y direction VOCABULARY that the points are on parallel translation A to E is translation –11 in y direction. parallel lines and identify where they orientation intercept cut the axes. Get children to do the same for translations B to C, B to F, D to E, G to F etc. RESOURCES RESOURCES OHT 10.2a OHT 10.1 OHT 10.2b NNS Unit Plans Planning Day Three Unit 10 Shape and space: Term: Autumn Year Group: 6 sheet Position, movement and scales, and solve problems Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Questions Vocabulary Vocabulary Convert between Ask the children to give quick Use all four operations to Write on the board: Collect the results and discuss the Collect answers to problems. km, m, cm, mm. responses to questions: solve measurement word solutions. Correct any errors and Emphasise steps and methods of problems, including time. A farmer buys 2.5 km of wire for misunderstandings. recording. Remind children to How many metres in 1 km? fencing. He uses 850 m in one field decide whether to use a mental, How many cm in 0.5 m? etc. Choose appropriate and 1.25 km in another. How much Write on the board: written or calculator method. They operations and calculate wire has he left? Ask the class to should always ask: ‘Can I do this in Write calculations on the methods. Explain identify the key information. Cars are about 1700 mm wide. The my head?’ board such as the following: working. width of a parking space adds 25% to Q What calculations are needed? the width of the car. How many Q If 24 million people watch TV for 3.6 km + 550 m = spaces could be made along a school 150 minutes each day, how many 7 m – 240 cm = Discuss the methods suggested and playground 35 m long? minutes of watching TV does this 0.3 m + 45 cm = record, e.g. total? 1 km – 725 m = 2.5 km – (1.25 km + 850 m) Work out and record the calculations or needed and the conversions of units Get the children to do the Ask the children to work out (2.5 km – 1.25 km) – 850 m. with the class. Estimate the answer, calculation on the calculator, the answers to these and then give out calculators and use discuss what happens to the then share their strategies Emphasise that it is important to write them to find the solution, recording display. Then solve the problem with a partner. down the calculations to help with steps and interpreting the display. mentally keeping the unit in checking solutions. Ask children to Highlight the need to round the millions i.e. 24 x 150 million Collect answers. Check that estimate the answer, then work answer to make it sensible. minutes. children can convert between through the calculation with the class, units and deal with decimal converting units and showing how to Set other problems which the children points correctly. set out the solution. Emphasise the use the calculator to solve. need to give the answer using the By the end of the lesson the Give five other calculations units. children should be able to: for children to do on their own. Review the stages used to solve the Solve ‘story’ problems problem. Show OHT 10.3 step-by- involving: step guide. Emphasise that the km, m, cm, mm, miles; calculation can be done mentally or seconds, minutes and using a written method or with a hours calculator, but the calculations must and explain and record how be recorded. the problem was solved. Work through another problem (Refer to supplement of examples, following the step-by-step guide, section 6, pages 87 and 89.) discussing each stage with the children, and showing them how to record the solution. Set the class problems to do. Ensure these include mixed units, the four operations and time; no calculators at this stage. RESOURCES Calculators OHT 10.3 NNS Unit Plans Planning Day Four Unit 10 Shape and space: Term: Autumn Year Group: 6 sheet Position, movement and scales, and solve problems Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Questions Vocabulary Vocabulary Count on in steps of Hold the counting stick Record estimates and Ensure that each child has a ruler Write on the board: Collect children’s responses. 0.1, 0.2, 0.25, 0.5… horizontally and say that one readings from scales to with cm and mm scales. Ask each and then back. end represents 1 kg and the a suitable degree of child to measure their hand span, 1 litre is about 1¾ pints Write the following on the board: other 2 kg. Point to various accuracy. the length of their middle finger points asking what and the width of he nail on their Get the class to say ‘A litre of water Measuring your waist for a new pair of measurement lies there. Know imperial units little finger. Check that everyone is about a pint and three quarters’. jeans. and rough metric measured from 0. Ask for the Use this to calculate that: Measuring out a dose of medicine. Q What does each division equivalents. measurements in cm and mm. Putting petrol in the car. represent in kg? Ask if their measurements are 2 litres is about 3½ pints Weighing flour to make a cake. likely to be accurate to the nearest 5 litres is about 8¾ pints. Measuring the bedroom floor before Establish that each tenth is cm, the nearest mm. Ask how ordering a carpet. 0.1 kg. many times longer their finger is Remind the class that there are 8 Telling someone the distance from than their nail, and their hand span pints in 1 gallon or 5 litres is just where you live to the nearest Q What do they represent in than their finger. Agree a over 1 gallon. Show the class OHT supermarket. grams? representative set of values for the 10.6 the litre/gallons scale. Give Measuring the amount of tread on a class and explain that this is an out copies (Resource sheet 10.1) tyre. Establish the answer as 100 g. estimate rather than an accurate for pairs to refer to. Ask: measure. Q These are all situations where we use Q What does half a division Q How many litres in 3 gallons? some form of measurement. Can you represent? Give pairs of children measuring How many gallons and pints in 15 suggest some others? tapes which have both metric and litres? Establish 0.05kg or 50 g. imperial units (cm and inches). Q How accurate do we need to be in Discuss the two scales and ask Write on the board: each case? Can you think of any Count from 1 kg in steps of children to convert from one to the situations where we need to be really 0.1 kg. Then use grams other. Ask: 1 litre of water weighs 1 kg. accurate? counting from 1000 g in steps of 100 g. Q 4 inches is about how many mm? Reshow OHT 10.5. Suggest that in many cases, approximate measurements are Repeat with one end Ask the children to measure their Q If the watering can was full could sufficient. Accuracy could be critical in: representing 0.1 kg and the hand spans in inches. Ask for this you lift it up to water the plants? – dispensing powerful drugs, other 0.2 kg, and 0 g to 500 g, VOCABULARY length to the nearest inch, the – measuring engine parts for inches nearest ¼ inch, 1/8 inch etc. etc. Discuss how to use the litre/gallon aircraft, feet Discuss other imperial units for – adjustments to car engines, scale to answer these questions yards – measuring accurate temperatures in Show the class the OHT 10.4 of length and establish that there are and to check the values on the pints 12 inches in 1 foot and 3 feet in 1 certain manufacturing processes like the scales with the central board. Use calculators to convert gallons yard. Discuss metric equivalents brewing beer. needle/pointer missing. Ask the and discuss the degree of scale and establish that 1 metre is about class what this might be used to accuracy. degree of accuracy 3 feet and 3 inches, or one yard By the end of the lesson the children measure and in what units. Point to 0.4 and ask for this in and 3 inches, or 39 inches. Set litres to gallons questions for should be able to: kg and g. Repeat with different pairs to answer. measurements including Read measuring scales, converting RESOURCES between indicated values. the unit to an equivalent metric unit; OHT 10.6 Emphasise the accuracy that Read both metric and imperial units RESOURCES Resource sheet 10.1 can be obtained. from measuring scales that show Counting stick Rulers with cm and both units. OHT 10.4 mm Show OHT 10.5 of the can for OHT 10.5 Measuring tapes with measuring litres and repeat the (Refer to supplement of examples, cm and inches exercise. section 6, pages 91 and 95.) NNS Unit Plans Planning Day Five Unit 10 Shape and space: Term: Autumn Year Group: 6 sheet Position, movement and scales, and solve problems Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Questions Vocabulary Vocabulary Solve problems Write on the board: Record estimates Remind children that miles are Write on the board: Remind the children that they have been plotting points based on measures. and readings from imperial units. Discuss the other and drawing shapes and graphs on different axes, using Bath 44 scales to a suitable imperial units used in the last 1 litre = 1¾ pints different scales. Emphasise that it is important to plan Bristol 28 degree of accuracy. lesson and record on the board. 1 m = 40 inches carefully how the scales on the axes are to be arranged Exeter 150 and to draw them carefully. Taunton 84 Know imperial units Q What are the imperial units Explain that these are Gloucester 64 and rough metric used for weight? approximations. Give out squared Hold up the counting stick. Explain to the class that the Plymouth 230 equivalents. or graph paper and say that you divisions on the stick are like the divisions on the scales. Write on the board; pounds, want to be able to use the graphs The size of each division depends on the numbers at the Explain this ounces. Discuss these units. to convert up to 10 l, 10 kg and start and end of the stick. There are 10 divisions so represents the return 10 m to imperial units. each is worth one tenth of the length. Remind the journeys in miles Get the class to say: children some scales are wrapped around a circle; some made by a salesman. Give the children time to work out span negative and positive numbers. The important He gets 12p per mile ’Two and a quarter pounds of how the axes are to be arranged. thing is to look at the first and last numbers, count the from his firm. jam is round about one Discuss these with the class and divisions and work out what each division is worth. kilogram.’ ensure they know how the axes Ask children to are to be scaled and which points Draw on the board: choose a journey and Explain that a better conversion to plot to make the graphs. work out the amount is: 1 kg = 2.2 pounds. Write this A he should receive. on the board. Ask children to draw their graphs. 10 20 Collect methods and Explain that children are going When children have completed solutions. Compare to construct their own their graphs, display OHT 10.7. B methods and the conversion graphs. They can Remind the class that the 20 40 recordings made. choose whether to construct a equivalents are approximate and graph for converting between: discuss the statement 10 litres ≈ Ask: 17.5 pints. litres and pints Q How many divisions are there on each scale? What is VOCABULARY metres and inches Ask the children to give one or two each division worth? Where are the arrows pointing? approximately equal kg and pounds further approximate equivalents to (≈ ) and demonstrate how to use the Collect responses and discuss methods used. Correct imperial graph to find them. any misunderstandings. pounds ounces Repeat with OHT 10.8, then OHT pints 10.9. By the end of the lesson the children should be able inches to: divisions Ask children to use their own scales graphs to find other approximate Read measuring scales, converting the unit to an equivalents, recording them using equivalent metric unit; the ≈ sign. Know the approximate equivalence between VOCABULARY commonly used imperial units and metric units; miles RESOURCES Read metric and imperial units from measuring per mile Counting stick scales that show both units. Squared or graph paper (Refer to supplement of examples, section 6, pages 91 OHT 10.7 and 95.) RESOURCES OHT 10.8 Whiteboards OHT 10.9 NNS Unit Plans