Spring unit 9
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This document provides a unit plan for a unit on measures and problem solving for Year 6 students during the spring term. The unit objectives include using and converting standard metric units of length, mass, and capacity, as well as solving word problems involving quantities, measures, and percentages. The unit will take place over five daily lessons and utilize various teaching resources like worksheets, overhead transparencies, and calculators. Key areas of focus are using the correct units and measuring equipment, estimating measurements, and recording results to an appropriate degree of accuracy. Related test questions are also provided to assess student understanding of the concepts covered.
Spring unit 9
- 1. G Use, read and write standard metric units (km, m, cm, mm, kg, g, l, cl, ml) of length, Page 91 mass and capacity, including their abbreviations, and relationships between them. G Convert smaller to larger units (e.g. m to km, cm or mm to m, g to kg, ml to l) and vice Page 91 versa. G Know rough equivalents of lb and kg, oz and g, miles and km, litres and pints or gallons. Page 91 G Identify and use appropriate operations (including combinations of operations) Pages 83, 87 to solve word problems involving numbers and quantities based on ‘real life’, money or measures, using one or more steps, and calculating percentages such as VAT. G Suggest suitable units to estimate or measure length, mass or capacity. Page 93 G Suggest suitable measuring equipment. Page 93 G Record estimates and readings from scales to a suitable degree of accuracy. Page 95 Unit 9 Five daily lessons Measures and problem solving Year 6 Spring term Resources needed to teach this unit: G Resource sheet 9.1 G Resource sheet 9.2 G OHT 9.1 G OHT 9.2 G OHT 9.3 G OHT 9.4 G OHP calculator G Calculators G Whiteboards G Counting stick G Selection of boxes/cartons/containers G Packet of tea G Carton of orange juice G Related Key Stage 2 national test questions Unit Objectives Year 6 Link Objectives (Key objectives in bold) G Use, read and write standard metric units (km, m, cm, mm, kg, g, l, ml), including their abbreviations, and relationships between them. G Convert larger to smaller units (e.g. km to m, m to cm or mm, kg to g, l to ml). Know imperial units (mile, pint, gallon). G Suggest suitable units and measuring equipment to estimate or measure length, mass or capacity. G Use all four operations to solve simple word problems involving numbers and quantities based on ‘real life’, money and measures, using one or more steps, and finding simple percentages. G Use names and abbreviations of units of measurement to measure, estimate, calculate and solve problems in everyday contexts involving length, area, mass, capacity, time and angle. G Convert one metric unit to another (e.g. grams to kilograms). NNS Unit Plans Year 5 Year 7 This Unit Plan is designed to guide your teaching. You will need to adapt it to meet the needs of your class.
- 2. Cake Recipe for 6 Slices Toffee Apple Recipe for 8 Apples 450g sugar 50g butter 10ml vinegar 150ml water 15ml syrup 8 apples 8 sticks NNS Unit Plans Unit 9 Year 6 (Spring Term) Resource sheet 9.1 Cost 60p for 100 grams £4.80 for 1kg 90p for 200 grams £1.20 for 125 grams 75p for 1 litre Item Ham Cheese Tea Coffee Milk 5oz margarine 4oz caster sugar 2 eggs 6oz flour
- 3. NNS Unit Plans Unit 9 Year 6 (Spring Term) Resource sheet 9.2 00 10 20 30 40 50 60 70 80 90 100 110 0 10 20 30 40 50 60 70 160 140 120 100 80 60 40 20 0 Number of people Tues Wed Thur Fri October November December 0 £10 000 £20 000 £30 000 0 20 40 60 80 100 120 140 00 10 20 30 40 x x x x x x x Temperature in °C Time in minutes Distance travelled in km Time in minutes 1. 2. 3. 4.
- 4. NNS Unit Plans Unit 9 Year 6 (Spring Term) OHT 9.1
- 5. NNS Unit Plans Unit 9 Year 6 (Spring Term) OHT 9.2
- 6. NNS Unit Plans Unit 9 Year 6 (Spring Term) OHT 9.3 ? ? ? ? ? ? ? ? 5cm 8cm
- 7. NNS Unit Plans Unit 9 Year 6 (Spring Term) OHT 9.4
- 8. NNS Unit Plans Unit 9 Year 6 (Spring Term) 1 mark 22a 1 mark 22b How much more money was spent in the shop in December than in November? Stepan says, ‘In November there was a 100% increase on the money spent in October’. Is he correct? Circle Yes or No. Explain how you can tell from the chart. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ✎ The chart shows the amount of money spent in a toy shop in three months. 2001 Test A ✎ £ ✎ Yes / No October November December 0 £10 000 £20 000 £30 000 Related Key Stage 2 national test questions: Total 22
- 9. NNS Unit Plans Unit 9 Year 6 (Spring Term) This recipe is for 8 people. Josie makes enough raspberry ice cream for 12 people. How much cream does she use? Fred makes raspberry ice cream in the same way. He uses 2 kg of raspberries. How much sugar does he use? Here is a recipe for raspberry ice cream. 2001 Test B ✎ g ✎ litre 1 mark 19a 2 marks 19b Total raspberry ice cream for 8 people litre of cream 1kg raspberries 250g sugar 1 2 19 1 2 Show your method. You may get a mark.
- 10. NNS Unit Plans Unit 9 Year 6 (Spring Term) Estimate the number of people who went there on Thursday and Friday altogether. Each person paid £2.25 for a ticket to get in. How much ticket money was collected on Wednesday? This bar chart shows how many people went to a school play. 2000 Test B ✎ £ ✎School Play £2.25 160 140 120 100 80 60 40 20 0 Number of people Tues Wed Thur Fri 1 mark 10a 2 marks 10b Total 10 Show your method. You may get a mark.
- 11. NNS Unit Plans Unit 9 Year 6 (Spring Term) 2001 Test B A hot liquid is left to cool in a science experiment. This graph shows how the temperature of the liquid changes as it cools. Read from the graph how many minutes it takes for the temperature to reach 40°C. Read from the graph how many minutes the temperature is above 60°C. 00 10 20 30 40 50 60 70 80 90 100 110 0 10 20 30 40 50 60 70 Temperature in °C Time in minutes 1 mark 25a✎ minutes 1 mark 25b✎ minutes Total 25
- 12. NNS Unit Plans Unit 9 Year 6 (Spring Term) 2000 Test B Carol went on a 40-kilometre cycle ride. This is a graph of how far she had gone at different times. 1 mark 19c Carol says, ‘I travelled further in the first hour than in the second hour’. Explain how the graph shows this. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ✎ Total 0 20 40 60 80 100 120 140 00 10 20 30 40 x x x x x x x Distance travelled in km Time in minutes How many minutes did Carol take to travel the last 10 kilometres of the ride? Use the graph to estimate the distance travelled in the first 20 minutes of the ride. 1 mark 19a✎ minutes 1 mark 19b✎ km 19
- 13. NNS Unit Plans Unit 9 Year 6 (Spring Term) 2000 Peanuts cost 60p for 100 grams. What is the cost of 350 grams of peanuts? ✎ g 2 marks 15b Total ✎ 2 marks 15a Raisins cost 80p for 100 grams. Jack pays £2 for a bag of raisins. How many grams of raisins does he get? 15 Test A Show your method. You may get a mark. Show your method. You may get a mark.
- 14. NNS Unit Plans Unit 9 Year 6 (Spring Term) 2000 Test A 16 Kim has some rectangular tiles. Each one is 4 centimetres by 9 centimetres. She makes a design with them. Calculate the width and height of her design. 4cm 9cm width height 1 mark 16a ✎ cmwidth = ✎ cmheight = Total 1 mark 16b
- 15. NNS Unit Plans Unit 9 Year 6 (Spring Term) Mr Singh buys paving slabs to go around his pond. Mr Singh says, ‘It would cost more to use square slabs all the way round.’ He buys 4 rectangular slabs and 4 square slabs. 11 2002 Test A Total 2 marks 11a PAVING SLABS £1.95 each Square slabs 50 cm by 50 cm £3.50 each Rectangular slabs 100 cm by 50 cm Pond 50 cm 100 cm ✎ ✎ £ 1 mark 7 Show your working. You may get a mark. What is the total cost of the slabs he buys? Explain why he is correct. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- 16. Unit 9 Year 6 (Spring Term) NNS Unit Plans Mina has two cartons of juice. Each carton contains 220ml. She empties them both into this jug. Draw an arrow ( ) to show the level of the mixture in the jug. 7 2002 Test B ✎ 2 marks 10b Total 500ml 400ml 300ml 200ml 100ml
- 17. Unit 9 Year 6 (Spring Term) grams kilos Complete the table. This table shows the weight of some fruits and vegetables.15 ✎ 2 marks 15 13b 1 mark 1 mark 13a potatoes 3500 3.5 apples 1.2 grapes 250 ginger 0.03 1 2 3 4 5 6 kg 0 Here is a pencil sharpener, a key and a rubber. What is the length of all three things together? Give your answer in millimetres. 13 Actual size 0 1 2 3 4 5 6 7 8 9 cm ✎ mm What is the length of the key? Give your answer in millimetres. ✎ mm 2002 Test A 2002 Test A NNS Unit Plans Total
- 18. NNS Unit Plans Unit 9 Year 6 (Spring Term) 2 marks 21 2002 Test B21 A B 60cm C Not drawn to scale The distance from A to B is three times as far as from B to C. The distance from A to C is 60 centimetres. Calculate the distance from A to B. ✎ cm Show your working. You may get a mark. 2002 Mental Arithmetic 6 Look at the table of prices on your answer sheet. What is the cost of two kilograms of apples? £
- 19. NNS Unit Plans Planning sheet Day One Unit 9 Measures and problem solving Term: Spring Year Group: 6 Oral and Mental Objectives and Vocabulary Count on or back in different increments related to mass/ capacity. G Show a carton of orange juice and a packet of tea. Establish that capacity (the orange juice) is measured in litres while mass/weight is measured in grams. G Write on the board: 1l = 1000ml 1kg = 1000g G Remind children that: kilo means thousand milli means thousandth. G Use the counting stick to count in increments of 100g from different starting points and crossing the kg boundary. G Change to kg and count in 0.1kg. G Count in 10g intervals, change to kg and count in 0.01kg intervals. G Repeat this for measures of capacity, 100ml, 200ml, 0.1l, 0.2l. G Make the links between the conversions by pointing to any one point and expressing it as ml and l. Q What units are used on these packages? Use, read and write standard metric units and know their abbreviations. Know imperial units. Suggest suitable units and equipment to estimate or measure length, mass or capacity. G Show the children a selection of boxes and cartons (cereal, sugar, milk, fizzy drink ...etc.) Discuss whether the units represent mass, capacity ... G Write on board/OHT the list: – milk in a bottle – distance from Sydney to Paris – diameter of a strand of hair – thickness of the page of a book – length of a running track – strength of the wind – strength of an earthquake – weight of a child – volume of petrol in a tanker. Allow children a few minutes to discuss in pairs then collect responses. G Collect responses. Use opportunities to consolidate relationships between units as appropriate. G State some imperial units of measurement such as pint, gallon, pound, mile, ounce ...In pairs, the children are to identify three things that would be measured in that unit. G Take brief feedback, e.g. pint (milk, blood, drinks). Q How could we measure the following and what units would we use? Q What units of measurement would we find on these containers? Teaching Activities Objectives and Vocabulary Teaching Activities Teaching Activities / Focus Questions Main Teaching Plenary G Show the children a range of boxes; cartons and containers. Take brief feedback and discuss the reasons for the children’s answers. G On the board, draw a capacity number line from 0 to 2l. Mark different values and ask the children to identify the capacities on the number line, e.g. 1.5l, 300ml. G Ask them to place the capacity of different containers on the number line. Ensure the placements are reasonably accurate and that the class agrees with them. G Ask the children to solve the following problem: G Compare the methods the children use. Draw attention to units and conversion to l. Repeat posing other simple problems. Q There is 320ml of juice in a carton: a big bottle holds five and a quarter times as much. How much juice does the bottle hold? Q What units are the contents measured in? Q What would be a reasonable estimate of the mass or capacity? Q What equipment would you need to measure this? G Write some different units of capacity on the board. Repeat for length and weight. G Pose the following: G Discuss the units and the children’s methods of solving this problem. By the end of the lesson the children should be able to: G Suggest how you could measure: the thickness of a piece of paper, etc; G Respond to oral questions like: ‘Do you think this container holds . . . ?’ G Suggest things you would measure in kilometres/ tonnes/litres/miles etc. (Refer to Supplement of examples, section 6, page 93.) Q If I cut 75cm and 1.4m lengths from a 3m length of cloth, how much cloth is left? Q What might we measure using l, cl, pints, etc? VOCABULARY capacity mass kilogram kg millilitre ml RESOURCES Counting stick Carton of orange juice Packet of tea VOCABULARY pint pt miles m gallon g ounces oz pounds lb litres l RESOURCES Selection of boxes Cartons Containers
- 20. G Show OHT 9.1. Establish it is a rectangle and confirm how to find area and perimeter. G It is useful for children to see a rectangle in a different orientation. So with the rectangle in this position, add the dimensions. Children write their answers on whiteboards. Discuss the units in m and cm. Compare the answers for area 1 × 0.5 = 0.5m2 and 100 × 50 = 5000cm2 . Using the answers confirm there are 10 000 cm2 in 1m2 , (100cm × 100cm). G Remind children the perimeter is a length and, when we find the perimeter, we are adding lengths rather than multiplying them. G On the rectangle on the OHT draw additional rectangles, e.g. Collect answers via children’s whiteboards. Repeat changing the shape, by adding or removing rectangles. Q What is the area and perimeter of this new shape? Q How many cm2 in 1m2 ? Q What is the area and perimeter of this rectangle? Q What shape is this? Q How do we find its area and perimeter? NNS Unit Plans Planning sheet Day Two Unit 9 Measures and problem solving Term: Spring Year Group: 6 Oral and Mental Objectives and Vocabulary Calculate the area and perimeter of rectangles and compound shapes. Convert smaller to larger units of capacity and mass and vice versa. G Remind the class that 1kg = 1000g. G Ask the children to convert kilograms to grams, e.g. 3kg, 0·5kg, 1 ⁄4kg, etc. Collect answers and discuss methods. Ask the class to convert grams to kilograms e.g. What would 100g, 500g, 50g, 25g, 5g, 750g, 625g, 3125g... be in kg? Collect answers and discuss methods. Repeat for l and ml. G Remind the class that in solving word problems we often need to convert from one unit to another. Pose the question: Which is better value, 3l of lemonade for £2.40 or 300ml for 25p? Ask children to answer question and discuss answers and methods. Repeat with question: G Set the class similar problems that require the conversion of units in order to make comparisons. Collect answers and correct any mistakes and misunderstandings. Q Which is cheaper, 2kg of washing powder at £5.80 or 300g for 89p? Q What information did you use? Q What units did you use to compare costs? G Collect responses and note key facts on the board. G Show the children a series of number sentences and ask them to fill in the blanks e.g. 0.6kg = 250g + g making sure the position of the empty box changes l − 280ml = 0.22l By the end of the lesson the children should be able to: G Convert a larger metric unit to a smaller; G Begin to convert a smaller unit to a larger. (Refer to supplement of examples, section 6, page 91.) Q What key conversion facts have you used in this lesson? Teaching Activities Objectives and Vocabulary Teaching Activities Teaching Activities / Focus Questions Main Teaching Plenary VOCABULARY convert units imperial VOCABULARY perimeter area cm2 RESOURCES OHT 9.1 Whiteboards 50cm 1m 25cm 50cm
- 21. G Show the top diagram on OHT 9.2. Explain that the four rectangles are identical. Say that the width of the rectangles is 6cm. Children to work this out on their whiteboards. Collect answers and discuss strategies. Repeat this twice changing the length of the rectangle to 14cm. G Show second diagram on OHT 9.2. Explain that these four rectangles are also identical. Say that area of the large shape is 48cm2 . Collect answers and discuss strategies. Discuss strategies for working this out. Q If the perimeter of large shape is 42cm what is the perimeter of each of the four rectangles? Q What are the dimensions of the four rectangles this time? Q What is perimeter and area of each rectangle? NNS Unit Plans Planning sheet Day Three Unit 9 Measures and problem solving Term: Spring Year Group: 6 Oral and Mental Objectives and Vocabulary Calculate the area and perimeter of compound shapes. Know rough equivalents of lb and kg, oz and g, miles and km and pints or gallons and litres. G Remind children that kg, g, km, m, l, cl are units within the metric system that uses multiples of 10, 100, 1 000 to convert g to kg, etc. Collect responses and record these on the boards. G Write: 1kg is about 2.2lb 16oz in 1lb Give out calculators and using an OHP calculator work through the conversion to establish: 1oz is about 30g. G Write: 4.5l is about 1 gallon 8 pints in 1 gallon Using an OHP calculator work through the conversion to establish: 1 pint is about 570ml. G Write: 8km is about 5 miles G Explain that when we are discussing miles and metres at the same time, it helps not to use abbreviations to avoid confusion. Using an OHP calculator establish there are about 1600m in 1 mile. Set conversion questions for children to use the above facts, e.g. G Collect answers and discuss strategies. Ensure children understand that the conversions are estimates, using examples to highlight when it is appropriate to round their answers to the nearest 1 or 10. Q What is half a pound in grams? Q What is 44km in miles? Q What is 3l in pints? Q How many metres in 1 mile? Q How many ml in 1 pint? Q How many grams in 1oz? Q What units are used in the imperial system? G Write on the board the cake recipe: 4oz currants 8oz raisins 2oz candied peel 10oz flour 6oz butter 9oz sugar 4 eggs Ask children to convert the recipe to metric units. Collect answers and discuss methods. HOMEWORK – Ask the children to look for packets, jars, bottles, etc. that have metric/imperial on them and note down the information. Ask them to produce a conversion line for miles and km, up to 100 miles. Remind them that 5 miles is approximately 8km. with intervals of 10 miles. By the end of the lesson the children should be able to: G Know the approximate equivalence between commonly used imperial units and metric units. (Refer to supplement of examples, section 6, page 91.) Teaching Activities Objectives and Vocabulary Teaching Activities Teaching Activities / Focus Questions Main Teaching Plenary VOCABULARY length width RESOURCES OHT 9.2 Whiteboards VOCABULARY conversion estimates rounding imperial metric RESOURCES Set of calculators OHP calculator 0 50 100 miles
- 22. G Give out calculators and work through the question on the OHP calculator with the class. Demonstrate how to find the cost of 25g by scaling down, then 200g by scaling up. Repeat and set children similar questions to answer. Collect answers and correct any mistakes and misunderstandings. G Discuss when it is appropriate to use a calculator. G Discuss the cake recipe for 6 slices. Say that you want to make enough for 12 slices, what quantity of ingredients do you need? Collect answers and discuss methods and units. Discuss answers and scaling methods and highlight the problem when planning 20 slices! Q What ingredients are needed for 9 slices? Q What ingredients are needed for 20 slices? Q What would 200g of coffee cost? NNS Unit Plans Planning sheet Day Four Unit 9 Measures and problem solving Term: Spring Year Group: 6 Oral and Mental Objectives and Vocabulary Find dimensions of compound shapes. G Show the tile on OHT 9.3. Explain that there are a number of different arrangements using this tile. Show the first arrangement. Children to record their answers on whiteboards. Encourage them to use jottings and diagrams of their own. Collect responses and discuss the strategies. G Repeat for each of the other arrangements of tiles. G If time permits, discuss finding the perimeter of each arrangement. Q What is the height and width of this arrangement of tiles? Solve word problems involving numbers and quantities based on ‘real life’, money and measures. G Discuss the homework. Collect children’s metric and imperial measures from packets, etc. Select some to check using the estimates from the last lesson. Use the OHP calculator with children using calculators and emphasise that they are approximate values. G Use a counting stick marked in 10 intervals. The stick is to represent 0 to 100 miles. Point to different intervals and ask the children to identify the value. Children to use their conversion line from the homework task to give the approximations in km. G Give out Resource sheet 9.1. Explain that the sheet has the costs of different items and two recipes. Discuss the costs of the items. Ask children to work out the costs of various quantities of the items listed. Start by scaling up the quantities, for example: Collect answers, discuss methods and correct any misunderstandings. G Ask questions that involve scaling down the quantities, for example: Collect answers, discuss methods and correct any misunderstandings. Q What would 50g of ham cost? Q What would 100g of tea cost? Q What would 250g of cheese cost? Q What would 200g of ham cost? Q What would 3l of milk cost? Q What would 500g of tea cost? Q What is 70 miles in km? Teaching Activities Objectives and Vocabulary Teaching Activities Teaching Activities / Focus Questions Main Teaching Plenary G Discuss the toffee apple recipe on Resource sheet 9.1. Say you were asked for the recipe for toffee apples for a party of 30. G Discuss methods e.g. I multiply by 3 to get quantities for 24 then divide this by 4 to get quantities for 6 and add these together. By the end of the lesson the children should be able to: G Solve ‘story’ problems involving metric and imperial measures. (Refer to supplement of examples, section 6, pages 83, 87.) Q What quantities of ingredients are needed? VOCABULARY scaling up scaling down RESOURCES OHP calculator Calculators Counting stick Resource sheet 9.1 RESOURCES OHT 9.3 Whiteboards
- 23. G Ask children to look at the remaining two graphs. Emphasise that time, temperature and distance can all be measured so that intermediate values on the axes and graph have meaning. Ask children, in pairs, to set the graphs in context. Use a context to ask questions involving the reading of values from one axes to the other. Collect answers and correct any errors and misunderstandings. Q What was the temperature after 10 minutes? Q When did the temperature first reach 30°C? Q In which 20 minute interval was the least/greatest distance travelled? Q In what ways do these graphs differ from the bar charts? NNS Unit Plans Planning sheet Day Five Unit 9 Measures and problem solving Term: Spring Year Group: 6 Oral and Mental Objectives and Vocabulary Find simple percentages. G Write on the board: 25% of £100 10% of £300 40% of £90 70% of £50 5% of £500 50% of £64 80% of £40 90% of £40 Children to work this out on their whiteboards. G Discuss answers and methods used. Agree that 40% of £90 and 90% of £40 give the same answer. G Write on the board: 171 ⁄2% of £120 is £23. Children to decide and support their view with a calculation. Encourage children to use jottings, e.g. 10%, 5%, 21 ⁄2% and add. G Repeat setting other true or false questions involving percentages. Q True or false? Q Which one of these would you rather have? Solve word problems involving numbers and quantities based on ‘real life’, money or measures. G Give out Resource sheet 9.2. Ask children to look at the first bar chart. In pairs get children to make up a ‘story’ from the bar chart. Ensure they can interpret the scales correctly and read each bar. Use one of the contexts they provide and ask questions, e.g. Collect answers and discuss other questions involving percentages. G Repeat using the second bar chart. Highlight the need to estimate as the bars do not always end on a line. Agree estimates for each day. Demonstrate how using a ruler might help. Collect answers and discuss the children’s methods. Q If the figure for Wednesday was increased by 30% would this number be greater than Tuesday’s figure? Q What might we do to help us get a better estimate? Q If 20% of December’s money is profit, how much profit was made? Q What percentage of November’s money was spent/collected in October? Q How much more money was spent/collected in December than in October and November? Q What information is shown on the bar chart? Teaching Activities Objectives and Vocabulary Teaching Activities Teaching Activities / Focus Questions Main Teaching Plenary G Show OHT 9.4 Ensure children can interpret the increase and decrease correctly. Emphasise that the graph represents data that has been collected by measuring. By the end of the lesson the children should be able to: G Interpret simple bar charts; G Interpret a graph in which intermediate values have meaning. (Refer to supplement of examples, section 6, pages 115, 117.) Q What could the two axes represent? Q What story does the graph tell us? RESOURCES Whiteboards VOCABULARY bar chart graph scales curve axes RESOURCES Resource sheet 9.2 OHT 9.4