Teacher’s Guide 6
Series Editor: Peter Clarke Authors: Elizabeth Jurgensen, Jeanette Mumford, Sandra Roberts, Linda Glithro
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Number and place value
Contents
Counting and understanding numbers Page number
Introduction Key Principles of Busy Ant Maths How Busy Ant Maths supports the 2014 Primary National Curriculum for Mathematics The components of Busy Ant Maths Busy Ant Maths Teacher’s Guide Busy Ant Maths on Collins Connect Other components in Busy Ant Maths Busy Ant Maths Year 6 Medium-Term Plans
4 5 8 9 15 16 18
Getting Started 1: Number – Number and place value 2: Number – Addition and subtraction 3: Number – Multiplication and division 4: Number – Fractions 5: Number – Decimals 6: Number – Fractions (including decimals and percentages) 7: Ratio and proportion 8: Algebra 9: Measurement 10: Geometry – Properties of shapes 11: Geometry – Position and direction 12: Statistics
30 35 41 46 48 51 54 56 58 67 70 71
Teaching and Learning Units 1 – 12 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 11 Unit 12 Resource Sheets
74 108 142 176 210 244 278 312 346 380 414 448 484
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Introduction
Getting Started Introduction Key Principles of Busy Ant Maths Busy Ant Maths is a mathematics course that ensures complete coverage of the 2014 Primary National Curriculum for Mathematics.
The course has at its core the following seven key principles: 1 To inspire enjoyment of maths 2 To assist in developing children’s conceptual understanding of maths 3 To help raise levels of attainment for every child 4 To provide a rigorous and cohesive scope and sequence of the primary maths curriculum, while at the same time allowing for schools’ own curriculum design 5 To promote the most effective pedagogical methods in the teaching of mathematics 6 To offer manageable strategies for effective diagnostic, formative and summative assessment, to inform planning and teaching 7 To strengthen the home/school link. In addition to these seven key principles, Busy Ant Maths offers: • a straightforward yet flexible approach to the teaching of mathematics • lesson plans following a highly effective and proven lesson structure • a weekly bank of practical hands-on Learning activities • a detailed and systematic approach to the development of mental and written calculations • extensive teacher support through materials which: – are sufficiently detailed to aid confidence – are rich enough to be varied and developed – take into account issues of pace and classroom management – give careful consideration to the key skill of appropriate and effective questioning – provide a careful balance of teacher intervention and pupil participation – encourage communication of methods and foster mathematical rigor • controlled, manageable differentiation with activities and suggestions for at least three different ability groups in every lesson • a stand-alone resource aimed at developing children’s fluency in number facts containing hundreds of whole-class, group, paired and individual games and activities • pupil materials which are enjoyable and purposeful.
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Introduction
How Busy Ant Maths supports the 2014 Primary National Curriculum for Mathematics All of the components of Busy Ant Maths emphasise, and provide guidance on, the importance of the cyclical nature of teaching in order to best promote learning and to raise pupils’ attainment.
• Promote learning • Raise pupils’ attainment
Te a c h i
ng
sment s e ss
Planning
A Planning
Busy Ant Maths supports teachers in planning a successful mathematics programme for their unique teaching context and ensures: • a clear understanding of pupils’ pre-requisite skills before undertaking particular tasks and learning new concepts • considered progression from one lesson to another • regular revisiting and extension of previous learning • a judicious balance of objectives, and the time dedicated to each one • the use of a consistent format and structure. The elements of Busy Ant Maths that form the basis for planning can be summarised as follows:
Long-term plans The 2014 Primary National Curriculum for Mathematics constitutes the long-term plan for schools to follow. By closely reflecting the Programmes of Study, the Busy Ant Maths course embodies this long-term plan.
Medium-term plans The Busy Ant Maths Medium-term Plans show termly outlines of units of work with National Curriculum Attainment Target references, and specific lesson objectives. Using the Busy Ant Maths online Planning Tool via Collins Connect, these plans can be easily adapted to meet the specific needs of individual schools.
Short-term plans Individual Lesson Plans and accompanying Learning activities represent the majority of each yearly Teacher’s Guide. The lessons provide short-term plans that can easily be followed closely, or used as a ‘springboard’ and varied to suit specific needs of particular classes. An editable ‘Weekly Planning Grid’ is also provided on Collins Connect, which individual teachers can fully adapt.
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Introduction
Teaching The most important role of teaching is to promote learning and to raise pupils’ attainment. To best achieve these goals Busy Ant Maths believes in the importance of teachers: • having high expectations for all pupils • systematically and effectively checking pupils’ understanding throughout lessons, anticipating where they may need to intervene, and doing so with notable impact on the quality of learning • generating high levels of engagement and commitment to learning • consistently providing high quality marking and constructive feedback to ensure that pupils make rapid gains • offering sharply focused and timely support and intervention that matches pupils’ individual needs.
To help teachers achieve these goals, Busy Ant Maths provides: • highly focused and clearly defined learning objectives • examples of targeted questioning, using appropriate mathematical vocabulary, that is aimed at both encouraging and checking pupil progress • a proven lesson structure that provides clear and accurate directions, instructions and explanations • meaningful and well-matched activities for pupils at all levels of understanding to practise and consolidate their learning • highly effective models and images to clearly illustrate mathematical concepts, including interactive digital resources. Each lesson in Busy Ant Maths has a specific learning objective derived from an Attainment Target from the 2014 Primary National Curriculum for Mathematics Programmes of Study, and follows the same teaching and learning sequence.
National Curriculum Attainment Target
Learning Objective
Teaching and Learning Sequence Getting Started
Teach
Individualised Learning
Plenary
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Introduction
Assessment Assessment, record-keeping and reporting continue the teaching and learning cycle and are used to form the basis for adjustments to the teaching programme. Busy Ant Maths offers manageable and meaningful assessment on four levels: • Diagnostic assessment The Assessment Tasks from the Busy Ant Maths Assessment Guide assist teachers in determining pupils’ readiness for a particular unit of work. They are designed to yield information that will directly support the teaching of individual pupils and whole-class teaching. • Short-term ‘on-going’ assessment Progress Check Questions ( ) are an important feature of every Busy Ant Maths lesson and are linked to specific learning objectives. They are designed to provide immediate feedback to pupils and to gauge pupil progress in order to adapt teaching. Shared Success Criteria are also provided in each lesson to assist pupils in identifying the steps required to achieve the learning objective. • Medium-term ’formative’ assessment As well as being used for diagnostic assessment, the Assessment Tasks, along with the Assessment Sheets, from the Busy Ant Maths Assessment Guide can be used to review and record the progress of both individual pupils and the class as a whole, in relation to the National Curriculum Attainment Targets. An End of Unit Test is provided for each of the 12 Busy Ant Maths units. Each test is designed to assess the mathematics covered during the three-week unit. The formative Assessment Tasks, Sheets and Tests provide individual and/or group opportunities to identify those pupils who are not yet reaching, or who are exceeding, national expectations. They can also be used to set individual targets for pupils. • Long-term ‘summative’ assessment The End of Year Class Evaluation document shows individual pupils’ attainment against national standards. It draws upon the data gathered throughout the year including results from Assessment Tasks and Sheets, performance in whole-class discussions, participation in group work, written evidence and any other supplementary notes. It is this document that forms the basis for reporting to parents and informing the next year’s teacher. Importantly, it also helps to determine whether pupils are on track to meet expectations at the end of the key stage. Collins Connect contains a powerful assessment tool for diagnostic, formative and summative assessments. Along with manageable and meaningful record-keeping formats it allows you to collect assessment data to store online and present digitally for class and whole school analysis. Refer to the Busy Ant Maths Assessment Guide or the Busy Ant Maths Getting Started Guide on Collins Connect for a more detailed explanation of the assessment, recordkeeping and reporting features of Busy Ant Maths.
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Year 6 Unit 1
Week 1: Number _ Number and place value Week 2: Number _ Addition and subtraction Week 3: Geometry _ Properties of shapes
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Year 6, Unit 1
Week 1: Number _ Number and place value National Curriculum attainment targets
Pupil targets
Pupils should be taught to:
• Read and write seven-digit numbers
• read, write, order and compare numbers up to 10 000 000 and determine the value of each digit
• Identify the value of each digit in a seven-digit number
• round any whole number to a required degree of accuracy
• Round any whole number to the required degree of accuracy
• Use the value of the digits to compare and order numbers
• solve number and practical problems that involve all of the above
Weekly overview Using a place value chart, children explore the value of the digits in seven-digit numbers. They read seven-digit numbers and identify the value of selected digits. Children order seven-digit numbers discussing which digits to focus on. They investigate making the highest number possible using a set of digit cards. Children round seven-digit numbers to different multiples. They recognise that the higher the multiple the number is rounded to, the less accurate it is. Children undertake an investigation involving seven-digit numbers and the place value of digits, changing the positions of the digits and discussing patterns and totals. Prerequisites for learning
Assessment
• Understand that numbers extend beyond 100 000
Use the following assessments from Busy Ant Maths Assessment Guide 6:
• Identify the place value of each digit in a five- and six-digit number • Become secure with the place value of seven-digit numbers
1: Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit 2: Round any whole number to a required degree of accuracy 4: Solve number and practical problems that involve all of the above
Tracking back and forward through the curriculum Year 5
Year 6
Key stage 3
• read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
• read, write, order and compare numbers up to 10 000 000 and determine the value of each digit
Domain: Number
• round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
• round any whole number to a required degree of accuracy
• solve number problems and practical problems that involve all of the above
• solve number and practical problems that involve all of the above
• order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
Related Busy Ant Maths Units Y5 Units Unit 1, Week 1
Unit 9, Week 1
Previous Y6 Units
Future Y6 Units
• understand and use place value for decimals, measures and integers of any size
• round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
Unit 5, Week 1
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Year 6, Unit 1
Week 2: Number _ Addition and subtraction National Curriculum attainment targets
Pupil targets
Pupils should be taught to:
• Add a multiple of 10, 100 or 1000 to a six- or seven-digit number
• perform mental calculations, including with large numbers • solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• Subtract a multiple of 10, 100 or 1000 from a six- or s even-digit number
• solve problems involving addition, subtraction, multiplication and division
• Subtract a multiple of 10 000 or 100 000 from a seven-digit number
• use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
• Add and subtract decimals with both one or two decimal places
• Add a multiple of 10 000 or 100 000 to a seven-digit number
• Add and subtract decimals with a combination of one and two decimal places
Weekly overview Children review mental addition and subtraction including adding and subtracting multiples of 10, 100 and 1000 to and from six- and seven-digit numbers. They add and subtract multiples of 10 000 and 100 000 to and from seven-digit numbers mentally. Children add and subtract decimals to one place and then decimals to two places. They then move onto calculations with a combination of one and two decimal places. Children apply mental addition and subtraction to solve multi-step problems, focussing on understanding the problem and which calculations will lead to the answer. Prerequisites for learning
Assessment
• Understand the place value of six- and seven-digit numbers
Use the following assessments from Busy Ant Maths Assessment Guide 6:
• Add and subtract mentally to and from a six-digit number • Understand the place value of decimals to two places • Add and subtract large numbers using the formal written methods of columnar addition and subtraction
8: Perform mental calculations, including with mixed operations and large numbers 11: Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why 12: Solve problems involving addition, subtraction, multiplication and division 13: Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
Tracking back and forward through the curriculum Year 5
Year 6
• add and subtract numbers mentally with increasingly large numbers
• perform mental calculations, including with mixed operations and large numbers
• solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why • solve problems involving addition, subtraction, multiplication and division
Unit 3, Week 1 Unit 5, Week 2
Domain: Number • use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative • recognise and use relationships between operations including inverse operations
• use estimation to check answers to calculations and determine, in the context of a • round numbers and measures to an appropriate degree of accuracy [for problem, an appropriate degree of accuracy example, to a number of decimal places or Related Busy Ant Maths Units significant figures] Y5 Units Previous Y6 Units Future Y6 Units • use approximation through rounding to estimate answers and calculate possible Unit 3, Week 1 Unit 7, Week 2 resulting errors expressed using inequality Unit 5, Week 1 Unit 9, Week 2 notation a<x≤b Unit 9, Week 1 Unit 11, Week 1
• use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
Unit 1, Week 2
Key stage 3
Unit 11, Week 1
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Year 6, Unit 1
Week 3: Geometry _ Properties of shapes National Curriculum attainment target
Pupil targets
Pupils should be taught to:
• Recognise, describe and build simple 3-D shapes
• recognise, describe and build simple 3-D shapes, including making nets
• Use knowledge of the properties of cubes to identify and draw different nets of cubes • Use knowledge of the properties of cubes and cuboids to construct nets of a cube and a cuboid • Construct the nets of a tetrahedron, an octahedron and a squarebased pyramid
Weekly overview Children recall the number of faces of simple 3-D shapes. They focus on using cubes to complete partially built cuboids and cubes and apply this to completing displays of products in supermarkets. The term ‘net’ is defined and children build open cubes and unfold them to reveal different nets. They investigate which nets of open cubes, with the addition of one square, will fold up to form the net for a closed cube. Pairs of children are asked to find as many different nets of a cube as they can within a fixed time. Children create the need to draw tabs on nets. They discuss where they should be drawn on nets of cubes and cuboids and the least number required. Children use interlocking equilateral triangles to find the three nets for a tetrahedron, use two nets of a tetrahedron to make the net of an octahedron and progress to finding the four nets of a square-based pyramid. They discuss the need for a protractor to construct accurate nets of a square-based pyramid. Prerequisites for learning
Assessment
• Visualise 3-D shapes from 2-D drawings
Use the following assessments from Busy Ant Maths Assessment Guide 6:
• Visualise, from the front and from the side, 2-D representations of 3-D shapes made with interlocking cubes • Identify and build different nets for a cube
42: Recognise, describe and build simple 3-D shapes, including making nets
• Know the properties of a tetrahedron, octahedron and square-based pyramid Tracking back and forward through the curriculum Year 5
Year 6
• identify 3-D shapes, including cubes and other cuboids, from 2-D representations
Key stage 3
• recognise, describe and build simple 3-D shapes, including making nets
Related Busy Ant Maths Units Y5 Units
Previous Y6 Units
Future Y6 Units
Domain: Geometry and measures • use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
Unit 1, Week 3
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Year 6, Unit 1, Week 1, Lesson 1
Seven-digit numbers National Curriculum attainment target
Lesson objective
• Read, write and order and compare numbers to at least 10 000 000 and determine the value of each digit
• Read and write numbers to 10 000 000 and determine the value of each digit
Previous related lessons
Future related lesson
none
Unit 1, Week 1, Lesson 2
Prerequisites for learning
Success criteria
Pupils need to:
Pupils can:
• understand that numbers extend beyond 100 000
• identify the millions digit and its value
• understand the place value of five-digit numbers
• identify the thousands digits and their value
Vocabulary
• identify the hundreds, tens and ones digits and their value
place value, digit, millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones
Getting Started • Choose an activity from Number – Number and place value. • Choose a game or activity from Fluency in Number Facts: Y5/Y6 – Number and place value.
Teach
Year 6, Unit 1, Week 1
Resources mini whiteboard, pen and eraser (per child) • Write 999 999 on the board. Read the number as a class. Ask: What number comes after 999 999? Write 1 000 000 on the board. • Say: After 999 999, seven-digit numbers start. A new place value column is added, thousands of thousands or millions. • Write 1 488 374 on the board. Say: To make reading seven-digit numbers easier, a space is usually left after the millions column and after the thousands column. 1
• Display: Slide 1. Read the numbers as a class. As you do, point to the appropriate digits. • Say: Write a seven-digit number and say the number quietly to yourself. • Say: Say your number out loud to your partner. Look at each other’s numbers and listen carefully to each other to check you are reading them correctly. Repeat several times.
2
• Display: Slide 2. Choose a digit and point to it. • Say: Whisper to your partner the value of this digit. • Ask several pairs for their answers and click the digit to show the value. Repeat for every digit.
3
• Display: Slide 3. Point to a digit. • Say: In your head, think of the value of this digit. • Ask several children for their answers and click the digit to show the value. Repeat for every digit. • Say: Write a seven-digit number, read it to each other and then write the value of each digit underneath. • Look at the numbers and discuss any misconceptions you notice. • Say: Write a seven-digit number and then write the value of each digit underneath. Ask children to show their number to their partner and check the place value of the digits. • Display: the Number Cards tool. Set up the cards to show random numbers 0–9 and generate a seven-digit number. Read the number as a class. • Say: I am going to point to different digits. I want you to say the value of the digit I am pointing to.
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Unit 1: Number _ Number and place value
• Repeat with different numbers. Start with whole-class responses, then ask children to think of the answer in their head. Ask just three or four children to say their answer out loud before you confirm the correct answer. • Show a new number and say: I am going to say a place value and I want you to say the value of that digit in this number. Say hundred thousands, tens, etc. Expect whole-class responses, then individual.
Individualised Learning Refer to Activity 1 from the Learning activities on page 86.
Pupil Book 6A – Page 4: 7-digit numbers Progress Guide 6 – Support, Year 6, Unit 1, Week 1, Lesson 1: 6-digit counting
Plenary • Display: the Number Cards tool. Say: Each time I show you a number, call out the value of the hundred thousands digit. Generate seven-digit numbers and expect whole-class responses. • Repeat for different place values. • Write 3 000 004 on the board. • Say: How would you say this number? Say the number as a class. • Say: When there are zeros we just say ‘and’ to show this, just saying the values of the digits that are in the number. • Repeat for different numbers with zeros, for example, 4 005 002, 7 300 010.
Overcoming Barriers • Children will find seven-digit numbers challenging if they are not really secure with six-digit numbers. Focusing on six-digit numbers will provide them with experiences with Base 10 so they can understand the relative value of each of the digits, if appropriate.
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