Planning a Unit – Year 5 Block D Unit 3
This document offers you support in planning a mathematics Year 5 Unit taken from the Primary Framework. It draws on the Learning overview for the Unit, together with the assessment questions, the information and communication technology (ICT) resources and models and images materials. Further materials to support the Unit, for example vocabulary, speaking and listening objectives and links to science, can be found at www.standards.dfes.gov.uk/primaryframeworks/mathematics/planning/Year5/calculating/Unit3/
This Unit of work was prepared on the basis that before deciding where to pitch the work and which elements of the Unit to draw upon, we needed to look at the prior learning section. This was used to decide whether children had the prior knowledge, skills and understanding needed to progress through the Unit or whether they needed planned intervention.
In developing the structure of the two weeks, we worked through the following stages.
Stage 1
We started with the Unit’s Learning overview.
This Unit overview has been pasted into the first column. It has been slightly reorganised to make clear the links between the ideas and concepts in the Unit. You might incorporate elements from a previous or future Unit to support or challenge particular groups of children in response to your assessments of your children’s progress and attainment.
Stage 2
We thought about how the Unit would be taught and the range of experiences the children would need to promote and support their learning and meet the outcomes.
These examples are drawn from the Learning overview and from the resources in the Unit. As the examples are pasted into the column, connections between the different parts of the overview have been annotated in italics. This has been done to ensure that the connections in mathematics are being made across the Unit.
Stage 3
We identified ideas to support teaching and learning in this Unit, adding them to the second column.
There are models and images that you and the children might use during the Unit. The approaches and images are taken from the guidance that the Strategy offers on teaching aspects of mathematics and from the ICT resources in the Unit. Where the notes refer to ICT resources these can be accessed via the ICT resources tab of the Year 5 Block D Unit 3 page of the website.
Stage 4
We identified the questions and assessment ideas to be used during the Unit and put these into a third column.
The questions and assessment tasks are based on the Assessment for learning section of the Unit. These relate to the objectives in the Unit and the Learning overview and are planned to take place at appropriate points in the teaching of the lesson or Unit to inform day-to-day teaching.
The next stage would be to create a short-term plan for the Unit using this scaffold.
Mathematics Planning – Year 5 Block D Unit 3
Building on previous learning
Check that children can already:
• talk about their methods and solutions to one- and two-step problems;
• partition, round and order four-digit whole numbers and decimals to two places, and use decimal notation to record measurements; for example, 1.3 m or 0.6 kg;
• multiply and divide numbers to 1000 by 10 and 100 (whole-number answers);
• use written methods to add and subtract two- and three-digit whole numbers and £.p, and to multiply and divide two-digit numbers by a one-digit number, including division with remainders; for example, 15 × 9, 98 ÷ 6;
• know that addition is the inverse of subtraction and that multiplication is the inverse of division, and vice versa;
• use a calculator to carry out one- and two-step calculations involving all four operations;
• know that angles are measured in degrees and that one whole turn is 360°;
• read scales to the nearest tenth of a unit;
• measure and calculate perimeters of rectangles and find the area of shapes drawn on a square grid by counting squares;
• read time to the nearest minute, use am, pm and 12-hour clock notation, and calculate time intervals from clocks and timetables.
00390-2007CDO-ENWeb-based mathematics support materials for Year 5 and 6 teachers1
© Crown copyright 2007Primary National Strategy
Learning overview / Models, images and ideas to support planning for this Unit(Based upon the Framework website) / Assessment notes
Children continue to develop their problem-solving skills in the context of measurement.
They focus on capacity, and on using the 24-hour clock to measure time.
Within this context, they:
• continue to solve real-life problems involving one or two steps and any of the four operations;
• use efficient written methods for all four operations and are able to explain the methods they have used;
• change the units of measurement to the same unit before doing any calculations;
• estimate their answers and check them by using an alternative calculation method;
• interpret their answers in the context of the problem;
• interpret the calculator display after division problems. / Use starters to rehearse conversion of units and solve problems. For example, how many 200 g bags can be filled from 1 kg? Which is bigger: a bottle holding 300 ml or a quarter litre jug?
Use a counting stick to estimate measures at different points on the stick.
Use a converting measures spreadsheet for a starter activity to practise converting from larger to smaller units.
Vary the start number and interval size to exploit the flexibility of the ICT-based counting stick, clicking on the cells to check conversions.
Start with some problems involving measures and rounding and use these to check and confirm the children’s understanding; for example:
• I have a 3.5 m length of wood and I need some 35 cm strips to make bookends. How many bookends can we make from the original length?
• I have 3 litres of orange juice and I pour it into 330 ml cans. How many cans will I fill?
• Which is earlier, 7:30 pm or 17:30? Can you explain how you know?
• 256 children attend a summer camp. They sleep in tents that hold seven children each. How many tents are needed? [round up]
• A farmer’s chickens lay 152 eggs. How many boxes of six eggs can he fill? [round down]
• The twins have saved £356. A computer game costs £42. How many computer games can the twins buy?
Display decimal numbers on a calculator and use starters to interpret these numbers in contexts involving measures, money and time. / Check the children:
• remember the units for capacity and can change units;
• identify the correct measures and units to use for solving practical problems;
• understand why measurements must be in the same units before calculating;
• can estimate, interpret answers and round up or down after division.
Write instructions for a friend to solve a given problem.
What estimates did you make before you worked out the calculations?
How did you check your answer? Could you have checked it in a different way?
How?
Write another problem using the information in this problem.
Show me your method for solving these problems:
1. Max jumped 2.35 m on his second try at the long jump. This was 68 cm longer than on his first try. How far in metres did he jump on his first try?
2. Nasreen made some fruit punch. She poured 2.4 litres of water, 1.35 litres of pineapple juice and 780 ml of mango juice into a large bowl. How much fruit punch did she make?
Children read scales such as measuring cylinders with divisions of 10 ml numbered every 100 ml, or with divisions of 25 ml numbered every 100 ml.
They estimate and measure capacity.
Children continue to develop their problem-solving skills in the context of measurement / Use the flexibility offered by the Measuring Cylinder Interactive Teaching Program (ITP) by changing the:
• scale divisions;
• maximum amount;
• labelling of the scale
In order to assess the children’s ability to read and interpret a variety of scales. Give them opportunities to use a variety of practical equipment and read the scales.
When reading the scales, teach children first to estimate the amount of liquid using the maximum capacity as a guide.
Children answer problems such as:
• Look at liquid in a measuring jug. How many children can have a glass of squash from the jug if the glasses they are using hold 60 ml?
Ask small groups to use the internet to find out what they can about measures such as:
• How big is a tonne?
• What is a furlong?
• What are pints and gallons?
• What is a barrel of oil? / Did you make any estimates? Explain how you worked out the answers.
Show me how you used your calculator to solve these problems:
1. I use 2.4 kg of apples to make four pies. How many grams of apples are there in each pie? What mass of apples would I need to make three pies?
2. A piece of wood is 3.25 m long. I use all the wood to make five shelves of equal length. How long is each shelf in metres? In centimetres?
50 ml of water are poured out from this container. How much water is left in the container?
80 ml of water are added to the water in this container. Draw a line to show the new level of the water in the container.
The size of objects such as the:
• weight of the moon;
• length of our intestines;
• capacity of an oil tanker.
Ask children to work on investigating different measures over the summer holidays and to create a measures quiz to bring back in Year 6.
For example:
• Which is longer, a snooker table or the world’s longest long jump?
• Which contains more, a 4 litre bottle or a gallon container?
Ensure children receive practical experience of working with measures. For example, set problems such as:
• How many spoonfuls in a litre?
• What is the smallest and largest capacity of cup you can find? / Ask children to check their answers using measuring jugs.
Show me your method for solving these problems:
1. I fill six jugs with water. Each jug holds 2.3 litres. How much water do I have altogether?
2. Five boxes of chocolates weigh 645 g. How much does each box of chocolates weigh?
3. What is the total mass of 235 screws, each weighing 6 g?
What estimates did you make? Explain how you worked out the answers.
Round these measurements to the nearest whole unit: 4275 ml; 3.25 kg; 5.85 km.
About how heavy are eight boxes of apples weighing 5.6 kg each? About how many 185 ml glasses of water can you pour from a 2 litre bottle?
What unit of measurement would you use to measure the amount of water in:
• a drinking glass?
• a teaspoon?
• a bath?
Kate’s glass holds a quarter of a litre when it is full. She fills it nearly to the top with juice. Tick the approximate amount of juice she puts in the glass.
4 ml□
20 ml□
120 ml□
220 ml□
420 ml□
The children solve more problems involving time, including using the 24-hour clock. They record their work, using jottings such as time lines to support their calculations. They interpret train and bus timetables, flights of long-distance planes, and TV schedules.
Children continue to develop their problem-solving skills in the context of measurement. / Present the children with real-life timetables. For example:
BBC 1 / ITV 1
7:00 pm: / Doctor Who / 6:45 pm: / X Factor
7:40 pm: / Strictly Come Dancing / 8:00 pm: / The Bill
8:50 pm: / News and Weather / 8:45 pm: / X Factor Results
9:15 pm: / Film Special / 9:05 pm: / News and Weather
11:05 pm: / Match of the Day / 9:35 pm: / Movie Special
12:20 am: / Live Music Special / 11:15 pm: / Sport Round-up
1:10 am: / Open University / 12:20 am: / Planet Earth
Model how to use the timetable and a number line to answer questions such as: How long does Dr Who last?
1. If I turn over to ITV 1 at the end of Dr Who, what programme is on?
2. I switch the TV on at 8:00 pm. What programme is on BBC 1?
3. I switch on the TV at 10:25 pm. How long do I have to wait for Match of the Day?
4. Planet Earth lasts 45 minutes. At what time does it finish?
5. Which is longer: Film Special on BBC 1 or Movie Special on ITV 1?
Write a set of am/pm times in one column and the equivalent 24-hour clock times in another column. Ask the class to discuss in pairs how they would explain the connection between these two sets of times.
Ask several pairs to give an explanation to the class. The class should then evaluate the explanations for clarity and conciseness. Demonstrate writing an explanation and discuss its effectiveness. In a later lesson, ask children to write an explanation. Get a partner to evaluate their written explanation against the example from this lesson. / Check children can use a time line to help carry out time calculations.
Here is part of a train timetable.
Edinburgh / – / 09:35 / – / – / 13:35 / –
Glasgow / 09:15 / – / 11:15 / 13:15 / – / 13:45
Stirling / 09:57 / – / 11:57 / 13:57 / – / 14:29
Perth / 10:34 / 10:51 / 12:34 / 14:34 / 14:50 / 15:15
Inverness / – / 13:10 / – / – / 17:05 / –
How long does the first train from Edinburgh take to travel to Inverness?
Ellen is at Glasgow station at 1:30 pm. She wants to travel to Perth. She catches the next train. At what time will she arrive in Perth?
Use the Tell Time ITP to teach children to convert between am/pm and 24-hour clock times. Ensure that children have their own clock faces.
Set your analogue clock to show 21:19. Can you say that time as a 12-hour clock time?
A digital clock is displaying 5:01. What two 24-hour clock times could that be?
Set a problem involving time for pupils to answer in small groups, thinking about the range of ability and gender in order to make sure that all children contribute. Work through the problem and model how to change bits of information and vocabulary to create new problems for groups to solve. Work through solutions with the class.
Give each group a range of problems involving measures and time. They could solve them and then create a problem-solving booklet and an accompanying solutions booklet.
This will be ongoing over the remainder of the term. Children could work on it over the summer and take it to Year 6, where the booklets of problems could be distributed between groups for children to work together to solve.
Children know that a right angle is equal to 90°. They recognise that a straight line can be formed from two right angles and is equivalent to 180°. They use this to calculate angles on a straight line. They draw and measure angles using a protractor. / Model how to use a protractor using real-life protractors in guided group teaching or ICT-based tools with the whole class. Agree the degree of accuracy you are going to work to.
Set children to work in threes. Ask one child to explain to another child how to use a protractor. The third child, acting as observer, analyses how good the instructions were. Change roles and repeat. Then get children to record a set of instructions for using a protractor.
Ask groups to swap their instructions and evaluate those of another group, making suggestions on how to improve them.
Give children four card semicircles. They draw a line from the centre of each semicircle to the edge, and cut along the line to form two card ‘angles’. They shuffle the eight angles on the table top and label them randomly from A to H. They estimate the size of each angle, recording their estimates and use these to suggest which pairs will go together to form a straight line. Children then use a protractor to measure each angle, and calculate whether their predictions were correct. They check by placing the angles together to form straight lines.
Use the Calculating Angles ITP to display and estimate angles within a variety of shapes:
What are you using to help you estimate? Which of the angles of this triangle are acute and which are obtuse?
Demonstrate measuring angles using the protractor, making mistakes in its use.
Have I made an accurate measurement? What did I do wrong? / 1. Estimate, then use a protractor to measure these angles to the nearest 5°.
2. Use a protractor to draw an angle of 35°.
3. PQ is a straight line. Calculate the size of angle x.
Children construct shapes that have parallel or perpendicular sides.
Children consolidate their understanding of perimeter and area, appreciating the difference between the two. / Give the children opportunities to construct shapes accurately:
• Ask the children to draw a right-angled triangle, where they are given the lengths of the two shorter sides. They then measure the third side to the nearest millimetre.
• Ask the children to draw a rectangle with a perimeter of 28 cm and a longest side of 8 cm.
They measure the length of the diagonal, again to the nearest millimetre.
When children are working on area and perimeter and constructing shapes, take opportunities to reinforce the vocabulary of parallel and perpendicular.
Ask children to solve problems such as:
1. Create different T-shapes which have an area of 26 cm2. Do they all have the same perimeter?
2. What happens when you add one more square to each of the shapes? What different perimeters are possible?
3. Find as many rectangles as you can with whole-number sides and an area of 36 cm2. Which has the smallest perimeter?
A picture frame is created from a narrow length of wood 60 cm long. Suggest some possible measurements for the frame. Work out the area inside each frame. / How would you check if two lines are parallel? How would you check that two lines are perpendicular?