REDBRIDGE VERSION 2014
Year 5 Block D: Three units
Calculating, measuring and understanding shape
Objectives / Units /1 / 2 / 3 /
• 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 / ü / ü
• Use knowledge of rounding and place value to estimate and check answers to calculations, including rounding decimals with 2 decimal places to the nearest whole number and to 1 decimal place / ü / ü
• Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) / ü / ü
• Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000 / ü
• Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers / ü / ü
• Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context / ü / ü
• Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed / ü / ü
• 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 and around a point / ü / ü / ü
• 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) / ü / ü / ü
• Interpret a reading that lies between two unnumbered divisions on a scale / ü / ü / ü
• Solve problems involving numbers up to 3dp / ü
• Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals / ü / ü
• Read Roman numerals to 1000 (M) and recognise years written in Roman numerals / ü
Vocabulary
problem, solution, answer, method, strategy, compare, order, explain, predict, reason, reasoning, pattern, relationship
operation, calculation, calculate, calculator, equation, add, subtract, multiply, divide, sum, total, difference, plus, minus, product, quotient, remainder, calculator, memory, display, key, enter, clear
place, place value, decimal, decimal point, decimal place, estimate, approximate, approximately
measure, measurement, measuring scale, scales, balance, metre stick, tape measure, ruler, measuring cylinder, metric unit, standard unit, length, distance, perimeter, area, surface area, mass, weight, capacity, units of measurement and their abbreviations
days of the week, months of the year, second (s), minute (min), hour (h), day, month, calendar, timetable, 12-hour clock, 24-hour clock, am and pm
angle, degree (°), angle measurer, protractor, set-square, acute, obtuse, right angle
position, direction, parallel, perpendicular, reflection, reflective symmetry, line of symmetry, mirror line, translation, coordinates, x-coordinate, y-coordinate, origin, x-axis, y-axis
Building on previous learning
Check that children can already:
• talk about their methods and solutions to one-step and two-step problems
• partition, round and order four-digit whole numbers and decimals to two places, and use decimal notation to record measurements, e.g. 1.3m or 0.6kg
• multiply and divide numbers to 1000 by 10 and 100 (whole-number answers)
• use written methods to add and subtract two-digit and three-digit whole numbers and £.p, and to multiply and divide two-digit numbers by a one-digit number, including division with remainders, e.g. 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-step 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.
• read and plot coordinates in the first quadrant
• describe translations
Year 5 Block D: Calculating, measuring and understanding shape
Extracts from the New National Curriculum
The national curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Number – Number and place value
Pupils should be taught to:
read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
whole numbers, including through zero
round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
solve number problems and practical problems that involve all of the above
read Roman numerals to 1000 (M) and recognise years written in Roman numerals / Notes and guidance (non-statutory)
Pupils identify the place value in large whole numbers. They continue to use number in context, including measurement. Pupils extend and apply their understanding of the number system to the decimal numbers and fractions that they have met so far.
Number – Addition and subtraction
Pupils should be taught to:
add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
add and subtract numbers mentally with increasingly large numbers
use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why. / Notes and guidance (non-statutory)
Pupils practise using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see Mathematics Appendix 1). They practise mental calculations with increasingly large numbers to aid fluency (for example, 12 462 – 2300 = 10 162)
Number – Multiplication and division
Pupils should be taught to:
multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
multiply and divide numbers mentally drawing upon known facts
divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates / Notes and guidance (non-statutory)
Pupils practise and extend their use of the formal written methods of short multiplication and short division (see Mathematics Appendix 1). They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations. Pupils interpret non-integer answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (for example, 98 ÷ 4 = 4 98 = 24 r 2 = 242 1 = 24.5 ≈ 25). Pupils use multiplication and division as inverses to support the introduction of ratio in year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1000 in converting between units such as kilometres and metres. Distributivity can be expressed as a(b + c) = ab + ac. Pupils use and explain the equals sign to indicate equivalence, including in missing number problems (for example, 13 + 24 = 12 + 25; 33 = 5 x ).
Measurement
Pupils should be taught to:
convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes
estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]
solve problems involving converting between units of time
use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling. / Notes and guidance (non-statutory)
Pupils use their knowledge of place value and multiplication and division to convert between standard units.
Pupils calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically, for example 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter of 20cm.
Pupils calculate the area from scale drawings using given measurements.
Pupils use all four operations in problems involving time and money, including conversions (for example, days to weeks, expressing the answer as weeks and days).
Geometry – Properties of shape
Pupils should be taught to:
identify 3-D shapes, including cubes and other cuboids, from 2-D representations
know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
draw given angles, and measure them in degrees (o)
identify: angles at a point and one whole turn (total 360o)
angles at a point on a straight line and 2 1 a turn (total 180o)
other multiples of 90o
use the properties of rectangles to deduce related facts and find missing lengths and angles
distinguish between regular and irregular polygons based on reasoning about equal sides and angles. / Notes and guidance (non-statutory)
Pupils become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles. Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools. Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems.
Year 5 Block D: Calculating, measuring and understanding shape
Unit 1
• 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 identify the steps I need to take to solve problems
I can decide whether to do a calculation using mental methods, written methods or a calculator / What information did you use to solve the problem?
How did you decide what calculations to do?
Solve a problem such as:
Three jugs hold 850L altogether. The biggest jug holds 378L. The smallest jug holds half the volume of the biggest jug.
What is the volume of the middle-sized jug?
How did you work out your answer?
• Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000
I can multiply and divide whole numbers by 10, 100 and 1000 / Tell me a quick way of multiplying/dividing a number by 10. By 100. By 1000.
Explain what happens to the digits when you multiply or divide a whole number by 1000. What do you notice about the digits in your answer?
How many times larger than 60 is 6000?
The product is 400. At least one of the numbers is a multiple of 10. What two numbers could have been multiplied together? Are there any other possibilities?
· 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 2.6 kg to 2600 g).
I can measure capacity using appropriate instruments.
I know how many millilitres there are in a litre / Suggest some objects whose capacity could be measured using a 1-litre measuring jug. Suggest a sensible estimate for the capacity of a kettle. How did you decide on this estimate?
Which measurement is equivalent to 1.3 litres: 130ml, 1003ml, 1300ml or 103ml?
How do you know?
REDBRIDGE VERSION 2014
Objectives Unit 1 / Assessment for Learning• Interpret a reading that lies between two unnumbered divisions on a scale
I can interpret a reading between two unnumbered divisions on a ruler, tape measure or metre stick / What is the distance between the two arrows?
How many of these cherries weigh between 85g and 90g?
• 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 estimate and measure angles less than 180°