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Year 5 Block D - Calculating, measuring and understanding shape Unit 3

Objectives Children's learning outcomes	Assessment for learning
Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use I can use the most efficient method of solving a problem, including using a calculator	Write instructions for a friend to solve the 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.
Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations I can use rounding of whole numbers and decimals to estimate and check calculations I can round numbers to the nearest whole unit	Round these measurements to the nearest whole unit: 4275ml 3.25kg 5.85km What is the approximate perimeter and area of this rectangle? About how heavy are 8 boxes of apples weighing 5.6kg each? About how many 185ml glasses of water can you pour from a 2 litre bottle?
Use efficient written methods to add and subtract whole numbers and decimals with up to two places I can add and subtract whole numbers and decimals with up to two places in columns	Show me your method for solving these problems: Max jumped 2.35 metres on his second try at the long jump. This was 68 centimetres longer than on his first try. How far in metres did he jump on his first try? Nasreen made some fruit punch. She poured 2.4 litres of water, 1.35 litres of pineapple juice and 780ml of mango juice into a large bowl. How much fruit punch did she make? Did you make any estimates? Explain how you worked out the answers.
Refine and use efficient written methods to multiply and divide HTU × U, TU × TU, U.t × U and HTU ÷ U I can use efficient methods to multiply U.t by U and divide HTU by U I can recognise when to round up or down, depending on the problem	Show me your method for solving these problems: I fill 6 jugs with water. Each jug holds 2.3 litres. How much water do I have altogether? 5 boxes of chocolates weigh 645g. How much does each box of chocolates weigh? What is the total mass of 235 screws each weighing 6 grams? What estimates did you make? Explain how you worked out the answers.
Use a calculator to solve problems, including those involving decimals or fractions (e.g. to find of 150g); interpret the display correctly in the context of measurement I can use a calculator to solve a measurement problem and interpret the display correctly	Show me how you used your calculator to solve these problems: I use 2.4kg of apples to make 4 pies. How many grams of apples are there in each pie? What mass of apples would I need to make 3 pies? A piece of wood is 3.25m long. I use all the wood to make five shelves of equal length. How long is each shelf in metres? In centimetres? What key sequence did you use?
Read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre); convert larger to smaller units using decimals to one place (e.g. change 2.6kg to 2600g) I can choose and use the correct metric unit to estimate and measure capacity I can use benchmark objects to help me to estimate capacity I know how many millilitres there are in a litre	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 millilitres 20 millilitres 120 millilitres 220 millilitres 420 millilitres
Interpret a reading that lies between two unnumbered divisions on a scale. I can interpret a reading between two unnumbered divisions on a scale on measuring cylinders and jugs I can read accurately the number of millilitres in a litre jug	50 millilitres of water are poured out from this container. How much water is left in the container? 180ml of water are added to the water in this container. Draw a line to show the new level of the water in the container.
Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals. I can solve problems using a timetable written in 24-hour clock notation	Here is part of a train timetable. 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?
Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle's area I can find the area of a rectangle using the formula length × width I know that area is measured in cm²	Tell me a rule for working out the area of a rectangle. The area of a rectangle is 24cm2. What are the lengths of the sides? Are there other possible answers? Tell me something that has an area of approximately 30m². What did you use to help you? Estimate the area of the front cover of this exercise book. How did you go about doing that?
Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides I can use a set-square and ruler to draw shapes with parallel and perpendicular sides	How would you check if two lines are parallel? How would you check that two lines are perpendicular? On plain paper, use a ruler and set-square to construct: a square with sides 56mm a rectangle with length 6.3cm, width 4.9cm Construct a right-angled triangle with the two shorter sides measuring 3.5cm and 4.2cm. What is the length of the third side?
Complete patterns with up to two lines of symmetry; draw the position of a shape after a reflection or translation I can complete a pattern with one or two lines of symmetry I can draw where a shape will be after it has been reflected or translated	The heavy lines are lines of symmetry. Complete the pattern. This triangle is translated two squares the left. Draw the triangle in its new position. The shaded triangle is a reflection of the white triangle in the mirror line. Write the coordinates of point A and point B.
Estimate, draw and measure acute and obtuse angles using an angle measurer or protractor to a suitable degree of accuracy; calculate angles in a straight line I can draw angles less than 180 to within 5 I can calculate angles on a straight line	Estimate then use a protractor to measure these angles to the nearest 5 degrees Use a protractor to draw an angle of 35 . PQ is a straight line. Calculate the size of angle x
Understand different ways to take the lead and support others in a group I can lead a group and make sure that tasks are shared fairly I can support others in a group by helping them with their tasks when I have finished mine	I want you to plan an itinerary for a journey around the world. You will have one week to do your research and make your plans. Start by deciding on your roles in the group and what tasks you need to carry out.

Learning overview

Children continue to develop their problem-solving skills in the context of measurement. They now focus on capacity, and on using the 24-hour clock to measure time. They continue to solve real-life problems involving one or two steps and any of the four operations. They use efficient written methods for all four operations and are able to explain the methods they have used. They change the units of measurement to the same unit before doing any calculations. They estimate their answers and check them by using an alternative calculation method. They interpret their answers in the context of the problem. For example, they recognise when to round up or down after a division in problems such as:

256 children attend a summer camp. They sleep in tents that hold 7 children. How many tents are needed? [round up]
A farmer's chickens lay 152 eggs. How many boxes of 6 eggs can he fill? [round down]

Children also interpret the calculator display after division in problems such as:

The twins have saved save £ 356. A computer game costs £ 42. How many computer games can the twins buy?

Children divide 356 by 42 and interpret the calculator display of 8.4761904. They give the answer of 8 computer games.

When they estimate and measure capacity, children compare the sizes of containers using a benchmark such as a 1 litre bottle or jug. They put a range of containers in order of capacity from smallest to largest, estimate the capacity to the nearest 100ml and then measure the capacity to see how accurate their estimates were. They solve problems such as:

How many cups of water do you think it would take to fill this jug?
How many teaspoons of water can I put in this coffee cup?

Children read scales such as measuring cylinders with divisions of 10ml numbered every 100ml, or with divisions of 25ml numbered every 100ml.

Children reflect on the units that they are familiar with. They suggest suitable units to measure, say, the area of the school hall, the amount of liquid in a tablespoon or the mass of a baby. They 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 like the one below.

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

They answer questions such as:

How long does Dr Who last?
If I turn over to ITV 1 at the end of Dr Who, what programme is on?
I switch the TV on at 8:00 pm. What programme is on BBC 1?
I switch on the TV at 10:25 pm. How long do I have to wait for Match of the Day?
Planet Earth lasts 45 minutes. At what time does it finish?
Which is longer: Film Special on BBC 1 or Movie Special on ITV 1?

Children know that a right angle is equal to 90 degrees . They recognise that a straight line can be formed from two right angles and is equivalent to 180 degrees . They use this to calculate angles on a straight line. They draw and measure angles using a protractor. For example, children take 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 using 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.

Children consolidate their understanding of perimeter and area, appreciating the difference between the two. They solve problems such as:

Create different T-shapes which have an area of 26cm². Do they all have the same perimeter?
Find as many rectangles as you can with whole-number sides and an area of 36cm2. Which has the smallest perimeter?
A picture frame is created from a narrow length of wood 60cm long. Suggest some possible measurements for the frame. Work out the area inside each frame.
A rectangle drawn on a centimetre coordinate grid has three vertices at (1, 5), (1, 3) and (5, 3). Complete the rectangle and find its perimeter and area.
A rectangular mirror has a perimeter of 1.7m. It is 50cm long. Work out its area.

Children construct shapes that have parallel or perpendicular sides. For example, they 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. They draw a rectangle with a perimeter of 28cm and a longest side of 8cm. They measure the length of the diagonal, again to the nearest millimetre.

Children develop their ideas of reflection and symmetry to complete patterns and reflect and translate shapes. They reflect shapes in a mirror line where not all the sides of the shape are parallel or perpendicular to the mirror line. They translate shapes in directions parallel to the axes of a coordinate grid, giving the coordinates of the new position.

Resource links to existing published material

Mathematical challenges for able Key Stages 1 and 2

Activities	PDF 1MB
Activity 67 - Franco's fast food
Activity 70 - A bit fishy

Intervention programmes

Objectives for Springboard intervention unit	Springboard unit
Multiply and divide whole numbers by 10 and 100 and understand the effect	Springboard 5 Unit 6 (PDF 305KB)
	Springboard 5 Unit 6 supplementary (PDF 57KB)
Develop and refine written methods for subtraction, building on mental methods. Reinforce the fact that subtraction is the inverse of addition	Springboard 5 Unit 8 (PDF 245KB)
	Springboard 5 Unit 8a Part 1 supplementary (PDF 77KB)
	Springboard 5 Unit 8a Part 2 supplementary (PDF 75KB)
Know the three- and four-times tables Begin to know the six-times tables	Springboard 5 Unit 9 (PDF 269KB)
	Springboard 5 Unit 9 supplementary (PDF 110KB)

Supporting children with gaps in their mathematical understanding (Wave 3)

Diagnostic focus	Resource
Has an insecure understanding of the number system resulting in addition and subtraction errors and difficulty estimating	1 Y4 /- DfES 1128-2005 (PDF 101KB)
Does not make sensible decisions about when to use calculations laid out in columns	3 Y4 /- DfES 1130-2005 (PDF 101KB)
Has difficulty with adding three numbers in a column	4 Y4 /- DfES 1131-2005 (PDF 95KB)
Does not apply partitioning and recombining when multiplying and confuses the value of two digit numbers	4 Y4 ×/÷ DfES 1153-2005 (PDF 104KB)
Assumes the commutative law holds for division also	5 Y4 ×/÷ DfES 1154-2005 (PDF 85KB)
Writes a remainder that is larger than the divisor	6a Y4 ×/÷ DfES 1155-2005 (PDF 76KB)
Discards the remainder; does not understand its significance	6b Y4 ×/÷ DfES 1156-2005 (PDF 93KB)
Does not recognise when the remainder is significant when rounding up or down	6c Y4 ×/÷ DfES 1157-2005 (PDF 65KB)
Continues to subtract 2s without using knowledge of times tables	7 Y4 ×/÷ DfES 1158-2005 (PDF 89KB)

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Primary Framework for literacy and mathematics

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