Teacher’s Guide 4
Series Editor: Peter Clarke Authors: Elizabeth Jurgensen, Jeannette Mumford, Sandra Roberts
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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 4 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: Measurement 7: Geometry – Properties of shapes 8: Geometry – Position and direction 9: Statistics
26 30 36 39 42 44 49 51 53
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
56 90 124 188 192 226 260 294 328 362 396 430
Resource Sheets
466
Answers
536
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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.
HHomework o Guide
Assessment Guide 4
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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 Number and place value
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. The formative Assessment Tasks and Sheets 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, record keeping and reporting features of Busy Ant Maths.
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Year 4 Unit 1
Week 1: Number - Number and place value Week 2: Number - Addition and subtraction Week 3: Geometry - Properties of shape
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Year 4, Unit 1
Week 1: Number - Number and place value National Curriculum attainment targets
Pupil targets
Pupils should be taught to: • find 1000 more or less than a given number
• Identify the value of each digit in a four-digit number
• recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• Use the value of the digits to compare and order numbers
• order and compare numbers beyond 1000
• Count on or back in thousands
• identify, represent and estimate numbers using different representations
Weekly overview Children are introduced to place value of four-digit numbers, using Base 10 and money (£10, £1, 10p and 1p). They use and apply their knowledge of four-digit numbers to estimate. Children order four-digit numbers, focusing on the most significant digits first. They also work out thousands more or less than any four-digit number, focusing on which digit changes and which digits stay the same. Prerequisites for learning
Assessment
• Identify the value of each digit in a three-digit number • Understand that numbers extend beyond 1000
Use the following assessments from Busy Ant Maths Assessment Guide 4
• Count beyond 1000
2: Find 1000 more or less than a given number 4: Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) 5: Order and compare numbers beyond 1000 6: Identify, represent and estimate numbers using different representations
Tracking back and forward through the curriculum Year 3
Year 4
Year 5
• count from 0 in multiples of 4, 8, 50 and • find 1000 more or less than a given number 100; find 10 or 100 more or less than a given number • recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
• recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• compare and order numbers up to 1000
• order and compare numbers beyond 1000
• identify, represent and estimate numbers using different representations
• identify, represent and estimate numbers using different representations
• read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
Related Busy Ant Maths Units Y3 Units Unit 1, Week 1 Unit 5, Week 1 Unit 9, Week 1
Previous Y4 Units
Future Y4 Units Unit 5, Week 1 Unit 9, Week 1
Y5 Units Unit 1, Week 1 Unit 5, Week 1 Unit 9, Week 1
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Year 4, Unit 1
Week 2: Number - Addition and subtraction National Curriculum attainment targets
Pupil targets
Pupils should be taught to:
• Choose an appropriate mental method
• practise mental methods with increasingly large numbers to aid fluency *
• Recognise the operation needed to answer a word problem
• solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
• Write the calculation necessary to answer the problem • Write the correct answer to the problem
Weekly overview Children practise mental addition and subtraction methods using empty number lines and known number facts. They work through one-step and two-step addition and subtraction word problems, discussing the language used and writing tips for solving such problems. Prerequisites for learning
Assessment:
• Count on and back in ones from any three-digit number
Use the following assessment from Busy Ant Maths Assessment Guide 4
• Count on and back in tens from any three-digit number • Count on and back in hundreds from any three-digit number
12: Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
Tracking back and forward through the curriculum Year 3
Year 4
Year 5
• practise solving varied addition and subtraction • practise mental methods with increasingly large numbers to aid fluency * questions. For mental calculations with twodigit numbers, the answers could exceed 100.*
• add and subtract numbers mentally with increasingly large numbers
• add and subtract numbers mentally, including: – a three-digit number and ones – a three-digit number and tens – a three-digit number and hundreds • solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
• solve addition and subtraction two-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
Related Busy Ant Maths Units Y3 Units Unit 1, Week 2 Unit 3, Weeks 1 & 2 Unit 5, Week 2
Unit 7, Weeks 1 & 2 Unit 9, Week 2 Unit 11, Weeks 1 & 2
Previous Y4 Units
Future Y4 Units Unit 3, Week 1 Unit 5, Week 2 Unit 7, Week 1
Y5 Units Unit 1, Week 2 Unit 3, Week 1 Unit 5, Week 2
Unit 7, Week 2 Unit 9, Week 2 Unit 11, Week 1
* Notes and guidance (non-statutory)
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Year 4, Unit 1
Week 3: Geometry - Properties of shape National Curriculum attainment targets
Pupil targets
Pupils should be taught to:
• Identify horizontal, vertical and diagonal lines of symmetry in polygons
• identify lines of symmetry in 2-D shapes presented in different orientations
• Identify shapes with more than 1 line of symmetry
• complete a simple symmetric figure with respect to a specific line of symmetry
• Reflect shapes in vertical lines of symmetry to make a repeating pattern
• Reflect shapes in 1 and 2 lines of symmetry in different orientations
Weekly overview Practical activities introduce children to identifying shapes with 0 lines and 1 line of symmetry, which leads them to recognising that squares and rectangles have 2 lines of symmetry. They also identify lines of symmetry in different triangles. Children recognise and name half shapes and reflect each shape to make the whole shape. Pictures of paired objects and practical demonstration with paper and pin and peg boards are used to establish that equidistant points are the same distance from the line of symmetry. Paired activities give children practice in reflecting triangles and quadrilaterals to produce a range of 2D shapes and patterns. Prerequisites for learning
Assessment
• Identify a vertical line of symmetry in polygons
Use the following assessments from Busy Ant Maths Assessment Guide 4
• Complete simple symmetric patterns
36: Identify lines of symmetry in 2D shapes presented in different orientations
• Reflect a 2D shape in a line of symmetry
37: Complete a simple symmetric figure with respect to a specific line of symmetry Tracking back and forward through the curriculum Year 3
Year 4
Year 5
• identify lines of symmetry in 2D shapes presented in different orientations • complete a simple symmetric figure with respect to a specific line of symmetry Related Busy Ant Maths Units Y3 Units
Previous Y4 Units
Future Y4 Units
Y5 Units
Unit 9, Week 3
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Year 4, Unit 1, Week 1, Lesson 1
Four-digit numbers (1) National Curriculum attainment targets
Lesson objectives
• Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens and ones)
• Recognise the place of value of each digit in a fourdigit number (thousands, hundreds, tens and ones)
• Identify, represent and estimate numbers using different representations
• Identify, represent and estimate numbers using different representations
Previous related lessons
Future lessons on this objective
None Prerequisites for learning
Unit 1, Week 1, Lesson 2; Unit 5 Week 1 Lesson 1; Unit 9 Week 1 Lesson 1
Pupils need to:
Success criteria
• understand that numbers extend beyond 1000
Pupils can:
• count beyond 1000
• identify the thousands digit and its value
Vocabulary
• identify the hundreds digit and its value
place value, thousands, hundreds, tens, ones (units)
• identify the tens digit and its value • identify the ones digit and its value
Getting Started • Choose an activity from Number – Number and place value. • Choose an activity from Fluency in Number Facts: Y3/Y4 – Number and place value. The word ‘ones’ has been used throughout this lesson when referring to the least significant digit. However, children also need to be familiar with the word ‘units’.
Teach Resources
Year 4, Unit 1, Week 1
mini whiteboard, pen and eraser (per child); Base 10 thousand cube (per class) • Count on as a class from different four-digit numbers, e.g. 1389, 1995, 2601. • Ask: Are we confident counting with numbers beyond 1000? • Write three different four-digit numbers on the board, e.g. 1596, 2738, 3971. Say: These are all four-digit numbers. Ask: What can you tell me about four-digit numbers? • Establish that four-digit numbers are thousands numbers: the first digit (the digit on the left) is the thousands digit, the second digit is the hundreds digit, the third digit is the tens digit and the fourth digit is the ones digit. • Say: Let’s read these numbers together. Read the four-digit numbers as a class. As children say the number, point to the relevant digit, i.e. for 1596 point to 1 as children say “one thousand,” to 5 as children say “five hundred”, to 9 as they say “ninety” and to 6 as they say “six”.
Work on the place value of four-digit numbers.
• Say: When we say a number we can hear the place value of the digit. Write Th (thousands), H (hundreds), T (tens) and O (ones) above the digits. Point to each of the digits in turn saying thousands, hundreds, tens and ones. • Write 1000, 500, 90 and 6 underneath the relevant digits. • Repeat for the remaining four-digit numbers on the board. • Say: Write the value of each digit underneath it. • Say: Using Base 10 material to represent the numbers can help us to understand the place value of each digit. • Display: an image of a Base 10 1000 cube using the Base 10 tool. • Ask: What number does this represent? (1000) How many hundreds is it the same as? (10) • Write 1000 on the board. Then write it like this: 10 00. Say: We say one thousand but we can also see from the way the number is written that it is ten hundreds.
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Unit 1: Number - Number and place value
• Display: 2438 using Base 10 or the Base 10 tool. • Ask: What number is this? Say: Write Th, H, T and O on your whiteboard to help you. Fill them in as I tell you about my number.
• Say: Let’s count together to check our answers. • Display: 4623 using Base 10 or the Base 10 tool. • Ask: What number am I showing you now? Write it down on your whiteboards. Under the digits write the place value. • Display: 3581, 4169 and 5211 using Base 10 or the Base 10 tool. • Repeat for these four-digit numbers. • Say: I’m thinking of a number. It has four thousands, one hundred, nine tens and five ones. What is my number? Repeat several times, changing the order.
Individualised Learning Refer to Activity 1 from the Learning activities on page 68.
Pupil Book 4A: – Page 4: 4-digit numbers (1) Progress Guide 4: – Support, Year 4, Unit 1, Week 1, Lesson 1: 4-digit counting Resources: scissors (per child)
Plenary • Say: I’m thinking of a number. It has four thousands, six ones, no hundreds and no tens • Ask: What number am I thinking of? • Write 4006 on the board. Display: 4006 using Base 10 or the Base 10 tool. • Say: As there are no tens and no hundreds in this number, we just say “and” to show that. • Ask: Why do we need to write the zeros in this number? • Say the number as a class, pointing to the digits. • Ask: What would the number be if I added 100? Establish that the hundreds digit would change and it would become 4106.
Homework Guide 4
• Say: Think of a four-digit number that has no tens in it.
Year 4, Unit 1, Week 1, Lesson 1: 1000s, 100s, 10s and 1s
• Ask pairs to share their idea with the class.
Overcoming Barriers • Children will find four-digit numbers challenging if they are not really secure with three-digit numbers. Provide them with experience using Base 10 so they can understand the relative value of each of the digits.
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