Year 5 Book 2 of 2 2014 Curriculum PRIMARY MATHS Resources and teacher ideas for every objective of the 2014 Curriculum
Foreword Primary Maths is a photocopiable, six-level, year specific series designed to address the Primary National Curriculum for Mathematics objectives of: number measurement geometry statistics. Each book in the Primary Maths series includes: at least one activity page for each objective comprehensive teachers notes to accompany each activity additional teachers notes on activities and games assessment checklists additional photocopiable resources interactive whiteboard resources available to download. The Year 5 books in the Primary Maths series are: Primary Maths Number Primary Maths Measurement, Geometry and Statistics Contents Teachers notes: How to use this book... iv v Setting up a maths classroom... vi Activities and games... vi vii Assessment checklists... viii x Additional resources... xi xv Pupil activities with accompanying teachers notes: Measurement... 2 39 Metric measures... 2 13 Imperial measures... 14 15 Perimeter... 16 19 Area... 20 25 Volume... 26 27 Capacity... 28 29 Time... 30 33 Money... 34 37 Word problems... 38 39 Geometry... 40 73 3-D shapes... 40 49 Angles... 50 59 Rectangles... 60 61 Polygons... 62 65 Reflections and translations.66 73 Statistics... 74 99 Line graphs... 74 81 Tables... 82 95 Timetables... 96 99 Primary Maths Prim-Ed Publishing www.prim-ed.com iii
The Primary Maths series provides teachers with a number of varied and challenging activities. At least one activity, often more, is provided for each objective of the Primary National Curriculum for Mathematics. Suggestions for using the activities in this book: Objective: Decide which curriculum objective you wish to address and choose the appropriate activity page(s). Oral work and mental calculation starter: Choose which oral and mental activities you will use, from the list provided, to introduce the lesson or sharpen pupils skills. Some of the activities have accompanying interactive whiteboard activities to help introduce the lesson and capture pupils attention. These activities should occupy the first 5 10 minutes of the lesson. Main teaching activity: Decide how much teacher input you will provide for the main activity and whether pupils will be working individually, in pairs or as a group. Depending upon the abilities of the pupils in your class, decide whether any additional activities will be needed, from the list provided, or whether these can be used during subsequent lessons. This activity should occupy approximately 40 minutes. Teachers notes How to use this book Plenary: Decide what opportunities will be provided during the plenary session. Will pupils be given the opportunity to share and explain work, compare strategies used or summarise the key facts they have learnt? Think about how you can use the plenary session to assess pupils progress and therefore inform your future planning. The plenary should occupy the final 15 minutes of the lesson. Pupil activity pages: The pupil activities follow a common format: Title explanation An icon denotes the curriculum strand for each activity. After initial discussion, some activities can be completed individually, and others in small groups or as a whole class. The Challenge activity can be completed by early finishers or those pupils requiring extension of the task. Pupils may need to complete the activity on the back of the worksheet or investigate an activity further by using concrete materials or creating their own ideas linked to the objective. The objective provides the teacher with the focus of the activity. It is written in the form of a general objective. N Number M Measurement G Geometry S Statistics Number Measurement Geometry Statistics iv www.prim-ed.com Prim-Ed Publishing Primary Maths
Teachers notes How to use this book Teachers pages A teachers page accompanies each pupil worksheet. It provides the following information: The objective tells the teacher which strand and objective from the Primary National Curriculum for Mathematics is being covered. Oral work and mental calculation activities are suggested, for introducing the lesson or sharpening/developing oral and mental skills. The activities should occupy the first 10 minutes of the lesson. Some activities have interactive whiteboard activities available to download. If an interactive activity is provided it is listed here. Suggestions for additional activities are provided. They can be completed during the lesson, or in subsequent lessons. They can be used to aid differentiation. Answers to all activities are provided. The title of the main teaching activity is given. The photocopiable activity is on the page facing the teachers notes. The main activity should occupy approximately 40 minutes. Assessment Assessment checklists have been included for the Year 5 Measurement, Geometry and Statistics objectives. See pages viii x. These can be used to assess each pupil s understanding of the key objectives covered. Use the key to write the appropriate code next to each task the pupil completes. A summary of the tasks pupils will complete. Teaching notes for the Measurement, Geometry and Statistics objectives have been included on pages vi vii. These comprise background information and suggested activities and games. Extra teacher resources have been included on pages xi xvii. These can be enlarged if necessary and used in appropriate activities or as display posters. Interactive whiteboard activities have been provided to help teach the objectives. These can be downloaded from www.prim-ed.com. Primary Maths Prim-Ed Publishing www.prim-ed.com v
Teachers notes Setting up a mathematics classroom By having the following materials and visual representations around them, pupils can better engage in mathematical learning. Allow room to move so pupils can investigate things around the room. Organise desks and floor space appropriately. Display a Numbers chart. Display a number line with positive and negative numbers. Display numbers, number words and a visual representation of numbers. Display a place value chart, from hundred thousandths to hundredths. Display addition and subtraction facts. Display a 100 square. Ensure you have a good range of maths games and use them regularly. Provide calculators. Display times tables charts. Have an analogue and digital clock in the classroom (12-hour and 24-hour). Provide a thermometer. Display pictures of labelled 2-D and 3-D shapes. Provide construction materials such as cardboard boxes, cylinders, paper, scissors and so on. Provide protractors, rulers and set squares. Ensure you have adequate concrete materials to teach each strand (refer to pages vi vii). Allow pupils opportunities to investigate outside the classroom in the school environment. Display a chart showing simple equivalent fractions, decimals and percentages. Display or make various graphs such as pictograms, bar charts, block graphs, Venn diagrams and Carroll diagrams. Display a class birthday chart which includes the months of the year. Display and use a calendar. Have computer software related to mathematics available for use on the classroom computer(s) or in the computer room. Display a poster showing all coins and notes. Provide a range of measuring equipment for length, mass and capacity. Display the eight compass directions. Display a poster showing different angles. Ensure you have a good selection of interactive maths resources for use on a whiteboard (available to download from www.prim-ed.com). Statistics Activities and games Make various graphs using data gathered about the pupils in the class; e.g. hair colour, eye colour, favourite sport/colour/tv show. Pupils prepare questionnaires with a partner on given topics, concentrating on the questions needed to collect appropriate data. Search for timetables (bus, train) on the Internet. Ask a friend questions about them. Materials required grid paper graph paper (see page xv) various graphs for reference; e.g. bar chart, pictogram computer with graphing software vi www.prim-ed.com Prim-Ed Publishing Primary Maths
Teachers notes Measurement Activities and games Collect a number of cardboard packages cereal boxes, cake mix etc. and record the capacity of each box by filling the box with sand, rice or beans. Measure the capacity by cupfuls. Cut the boxes open and compare their surface areas. Check to see whether the box with the largest surface area also has the largest capacity. Use a geoboard to make shapes using different numbers of squares. Record the shapes made on either square dot paper or square grid paper. Check the perimeter and the area for each set of shapes made from the given number of squares. Write the perimeter and area on each shape; for example, a diagram of the shape on square dot paper, with area and perimeter marked. Use a trundle wheel to mark a one-kilometre distance around the school field. Estimate how long it will take to walk one kilometre. Pupils record their estimate, then record the actual time taken. How accurate were they? Estimate how long it will take to run one kilometre. Pupils time themselves and record their results. How accurate were they? Pupils use balance scales (commercial or self-made) to compare and order the mass of a variety of self-chosen objects. Compare to see if larger objects are heavier. Pupils measure the mass of given objects against readily available materials; for example, sealed container of rice, nails, 2-cm cubes or other materials. Record results. Measure the mass of objects using a spring balance. Repeat the measure with the object suspended in water. Record the results each time. Measure a number of other objects the same way. What conclusions can be drawn from the two measures of each object? Use a piece of wool, cotton or string 24 cm long. Join the ends to make a loop. Use a sheet of grid paper to find the smallest and largest area you can cover using the loop. Draw outlines on the grid paper. Record the perimeter and area of each. Materials required rulers/metre ruler containers of varying capacity trundle wheel 1-cm cubes grid paper stop watch balance scales bathroom scales spring balance tape measure analogue and digital clocks (24-hour) Geometry Activities and games Use an assortment of 2-D shapes to see which tessellate. Using a shape that tessellates, make a pattern to cover a page. Estimate how many shapes it will take. Using a variety of 3-D shapes, classify them according to their attributes. Do the same with 2-D shapes. It may help to have headings on sheets of paper to assist in initial classification. Alternatively, use a Venn diagram. Use a protractor to measure angles in regular 2-D shapes. Classify the shapes according to whether they have acute, right or obtuse angles. Use three-dimensional shapes to see if a relationship among edges, faces and vertices can be determined. Results may be recorded on a table such as this. Make models of three-dimensional shapes using modelling clay. Using fishing line, make cross-sectional cuts. Try to determine what the cross-section will look like before the cut is made. Alternatively, have the pupils make a cut that will give a predetermined shape for example, triangle, rectangle, square from a given shape. Use the three-dimensional shapes, or models, to show axes of symmetry and planes of symmetry. Three-dimensional axes of symmetry will display rotational symmetry, as shown below. A plane of symmetry will effectively slice the model into two identical halves. Pupils draw all the possible nets of a cube using grid paper. Materials required 2-D and 3-D shape pictures (see pages xii and xiii) 2-D shapes for tessellation/symmetry construction material for 3-D models tangrams toothpicks mirrors grid paper pattern blocks modelling clay/plasticine fishing line protractors rulers and set-squares Primary Maths Prim-Ed Publishing www.prim-ed.com vii
A Assessment Year 5 Measurement assessment checklist Key D = Demonstrated NFO = Needs further opportunity Pupils names Convert between different units of metric measure. Understand equivalent metric and imperial measures. Measure and calculate perimeters of composite rectilinear shapes in cms and ms. Calculate and compare the area of rectangles. Estimate the area of irregular shapes. Estimate volume. Estimate capacity. Solve problems involving converting between units of time. Use all four operations to solve problems involving measures and decimals. viii www.prim-ed.com Prim-Ed Publishing Primary Maths
Year 5 Geometry assessment checklist A Assessment Key D = Demonstrated NFO = Needs further opportunity Pupils names Identify 3-D shapes 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. Identify angles at a point and one whole turn, 1 2 turn, multiples of 90. Use properties of rectangles to deduce related facts and find missing lengths and angles. Distinguish between regular and irregular polygons. Identify, describe and represent the position of a shape following a reflection. Identify, describe and represent the position of a shape following a translation. Use appropriate reflection and translation language. Primary Maths Prim-Ed Publishing www.prim-ed.com ix
A Assessment Year 5 Statistics assessment checklist Key D = Demonstrated NFO = Needs further opportunity Pupils names Solve comparison, sum and difference problems using information presented in line graphs. Complete, read and interpret information in tables. Complete, read and interpret information in timetables. x www.prim-ed.com Prim-Ed Publishing Primary Maths
Teachers notes 24-hr clocks 23 11 22 10 00 13 12 1 2 14 23 11 22 10 00 13 12 1 2 14 21 9 3 15 21 9 3 15 20 8 7 19 6 18 5 17 4 16 20 8 7 19 6 18 5 17 4 16 23 11 22 10 00 13 12 1 2 14 23 11 22 10 00 13 12 1 2 14 21 9 3 15 21 9 3 15 20 8 7 19 6 18 5 17 4 16 20 8 7 19 6 18 5 17 4 16 Primary Maths Prim-Ed Publishing www.prim-ed.com xi
Teachers notes 2-D shapes xii www.prim-ed.com Prim-Ed Publishing Primary Maths
Teachers notes 3-D shapes rectangular prism (cuboid) Primary Maths Prim-Ed Publishing www.prim-ed.com xiii
Teachers notes Angles xiv www.prim-ed.com Prim-Ed Publishing Primary Maths
Teachers notes Bar/Line graphs Primary Maths Prim-Ed Publishing www.prim-ed.com xv
M Measurement TEACHER INFORMATION MEASUREMENT Objective Calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm 2 ) and square metres (m 2 ) and estimate the area of irregular shapes. Oral work and mental calculation Use the vocabulary: perimeter, distance, edge, area, surface, covers, centimetres, square centimetres (cm 2 ), square metres (m 2 ), square millimetres (mm 2 ). Demonstrate how to measure the area of a small object (e.g. book) using the formula length x breadth. Discuss whether you would use square millimetres, centimetres or metres to measure the area of given objects; for example, the area of a garden, maths book, postage stamp. Respond to oral multiple-choice questions; for example, Would the area of a playing card be about 5 cm 2, 50 cm 2 or 100 cm 2? Main teaching activity Square centimetres (page 21) Additional activities suitable for developing the objective Draw simple shapes on squared paper. Count the squares inside the shape to discover the area. Write the formula when finding the areas of rectangles. Work out the area of given rectangles by using the formula length x breadth. Order areas from smallest to largest, and vice versa. Draw a range of different shapes, all with an area of 20 cm 2, onto squared paper. Measure the perimeter of each shape, and write it in the centre of the shape. Answers 1. (a) 12 cm 2 (b) 8 cm 2 (c) 15 cm 2 (d) 10 cm 2 (e) 12 cm 2 (f) 11 cm 2 2. (a) 5 cm x 2 cm = 10 cm 2 (b) 6 cm x 3 cm = 18 cm 2 (c) 4 cm x 4 cm = 16 cm 2 (d) 7 cm x 4 cm = 28 cm 2 Challenge: 30 cm x 21 cm = 630 cm 2 20 www.prim-ed.com Prim-Ed Publishing Primary Maths
SQUARE CENTIMETRES M Measurement 1. Find the area of each shape below. The area of quadrilaterals can be calculated by multiplying the length by the breadth. Area = L x B 2. Measure the sides of each shape to the nearest whole centimetre. Multiply the length by the breadth to find the area. CHALLENGE Calculate the area of this sheet of paper by first measuring the length and the breadth in centimetres. x Area = cm 2 Objective Uses appropriate resources and methods to measure area. Primary Maths Prim-Ed Publishing www.prim-ed.com 21
M Measurement TEACHER INFORMATION MEASUREMENT Objective Calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm 2 ) and square metres (m 2 ) and estimate the area of irregular shapes. Oral work and mental calculation Use the vocabulary: perimeter, distance, edge, area, surface, covers, centimetres, square centimetres (cm 2 ), square metres (m 2 ), square millimetres (mm 2 ). Demonstrate how to measure the area of a large object (e.g. classroom) using the formula length x breadth. Discuss whether you would use square millimetres, centimetres or metres to measure the area of given objects; for example, the area of a garden, maths book, postage stamp. Respond to oral multiple-choice questions; for example, Would the area of a bedroom be about 1 m 2, 10 m 2 or 100 m 2? Interactive whiteboard activity Interactive whiteboard activity available to support this copymaster. Visit www.prim-ed.com. Main teaching activity Square metres (page 23) Additional activities suitable for developing the objective Draw simple shapes on squared paper. Count the squares inside the shape to discover the area. Write the formula when finding the areas of rectangles. Work out the area of given rectangles by using the formula length x breadth. Order areas from smallest to largest, and vice versa. Start to work out the areas of shapes that can be split into two separate rectangles. Answers 1. Teacher check 2. Teacher check 3. (a) 4 m x 3 m = 12 m 2 (b) 7 m x 2 m = 14 m 2 (c) 5 m x 5 m = 25 m 2 (d) 6 m x 3 m = 18 m 2 add 3 m x 3 m = 9 m 2. 18 m 2 + 9 m 2 = 27 m 2. Challenge: Teacher check 22 www.prim-ed.com Prim-Ed Publishing Primary Maths
SQUARE METRES M Measurement 1. Make a square metre by measuring and cutting sheets of newspaper to measure 1 m x 1 m. (a) Name five things in the classroom that are smaller than your square metre. (b) Name five things in the classroom that are larger than your square metre. 2. Work with a partner to measure the area of the following, using your square metre. (a) the cloakroom Area = m 2 (b) the library Area = m 2 (c) a netball court Area = m 2 3. (a) 4 m 3 m (b) 7 m 2 m A = x A = m 2 A = x A = m 2 (d) (c) 5 m 3 m 6 m 5 m 3 m 3 m A = x A = m 2 A = x A = m 2 A = x A = m 2 CHALLENGE Work out the area of the classroom in metres by measuring its length and breadth with a tape measure or trundle wheel. Objective Uses appropriate resources and methods to measure area. Total area = + = m 2 Area = x Area = m 2 Primary Maths Prim-Ed Publishing www.prim-ed.com 23
M Measurement TEACHER INFORMATION MEASUREMENT Objectives 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 (cm 2 ) and square metres (m 2 ) and estimate the area of irregular shapes. Oral work and mental calculation Use the vocabulary: perimeter, distance, edge, area, surface, covers, centimetres, square centimetres (cm 2 ), metres, square metres (m 2 ). Demonstrate how to measure the perimeter and area of a small object (e.g. book) using centimetres and square centimetres. Demonstrate how to measure the perimeter and area of a larger object (e.g. dining hall) using metres and square metres. Main teaching activity Finding area and perimeter (page 25) Additional activities suitable for developing the objectives Draw simple shapes on squared paper. Count the squares inside the shape to discover the area and count the squares around the outside of the shape to discover the perimeter. Estimate, measure and record the areas and perimeters of small objects using square centimetres and centimetres. Record results in a simple table. Order perimeters and areas from smallest to largest, and vice versa. Draw a range of different shapes, all with a given area, onto squared paper. Measure the perimeter of each shape, and write it in the centre of the shape. Draw a range of different shapes, all with a given perimeter, onto squared paper. Measure the area of each shape, and write it in the centre of the shape. Answers 1. (a) P = 8 cm, A = 4 cm 2 (b) P = 12 cm, A = 5 cm 2 (c) P = 14 cm, A = 6 cm 2 (d) P = 12 cm, A = 5 cm 2 (e) P = 10 cm, A = 4 cm 2 (f) P = 12 cm, A = 6 cm 2 2. (a) The following pairs of shapes should be coloured the same colour: a and e, b and d, c and f. (b) Shapes b, d and f have the same perimeter. 3. (a) P = 12 cm, A = 9 cm 2 (b) P = 14 cm, A = 10 cm 2 (c) P = 14 cm, A = 12 cm 2 Challenge: Teacher check 24 www.prim-ed.com Prim-Ed Publishing Primary Maths
FINDING AREA AND PERIMETER M Measurement Remember 1. Find the area and perimeter of these shapes. Area is the space inside a shape. Perimeter is the distance around the edge of the shape. 2 (a) Colour the shapes above that have the same area in the same colour. (b) Which shapes have the same perimeter? 3. Use your ruler to measure and find the perimeter and area of the shapes below. Remember to add all sides to find the perimeter and multiply the length by the breadth to find the area. CHALLENGE Measure and find the perimeter and area of a dictionary. Perimeter: + + + = cm Area: x = cm 2 Objective Uses appropriate resources and methods to measure area and perimeter. Primary Maths Prim-Ed Publishing www.prim-ed.com 25