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Teacherâ€™s Guide 2

Series Editor: Peter Clarke

Authors: Caroline Clissold, Nicola Morgan, Cherri Moseley, Jo Power, Janet Rees, Louise Wallace

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Number and place value

Counting and understanding numbers Contents

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 2 Medium-Term Plans

4 5 8 9 15 16 18

Getting Started 1: Number – Number and place value 30 2: Number – Addition and subtraction 38 3: Number – Multiplication and division 48 4: Number – Fractions 56 5: Measurement 59 6: Geometry – Properties of shapes 69 7: Geometry – Position and direction 72 8: Statistics 74 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

78 112 146 180 214 248 282 316 350 384 418 452 488

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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 • 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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Year 2 Unit 6

Week 1: Number – Multiplication and division, including Number and place value Week 2: Number – Multiplication and division Week 3: Measurement (mass)

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Year 2, Unit 6

Week 1: Number – Multiplication and division, including Number and place value National Curriculum attainment targets Pupil targets Pupils should be taught to:

• Accurately count in multiples of two, five and ten, forwards and backwards

• recall and use multiplication and division facts for the 2 and 5 multiplication tables

• Recognise and use the multiplication (×), division (÷) and equals (=) signs correctly

• calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

• Recognise and recall the multiplication facts for the two and five multiplication tables

• count in steps of 2 and 5 from 0, and in tens from any number, forward and backward

• Recognise and recall the division facts for the two multiplication table • Begin to recognise that multiplication and division are related (inverse operations) • Understand the relationship between multiplication and division, applying knowledge of the two multiplication table to division

Weekly overview Children count on and back in steps of two, five and ten from and to zero, using a 1–100 number square to support their counting. They count in steps of ten from one, and then from any other number, discussing the emerging patterns. Children apply their knowledge and understanding of counting in twos and fives to multiplication. They solve multiplication problems using a number line, counting the ‘jumps’ (repeated addition). Children apply their understanding of counting in twos and multiplication to division within the two multiplication table. They are introduced to using a number line to solve division problems through ‘repeated subtraction’. Prerequisites for learning

Assessment

• Count in twos and fives from zero to at least 50, and in tens to 100, and understand the term ‘multiple’

Use the following assessments from Busy Ant Maths Assessment Guide 2:

• Recognise and write numbers from 0–100

1: C ount in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward

• Show an increasing understanding of multiplication

12: Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

• Know how to share into equal groups

13: Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs Tracking back and forward through the curriculum Year 1 • count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

Year 2

Year 3

• count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward

• c ount from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number

• recall and use multiplication and division • r ecall and use multiplication and division facts facts for the 2, 5 and 10 multiplication tables, for the 3, 4 and 8 multiplication tables including recognising odd and even numbers • solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

• calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

•w rite and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times onedigit numbers, using mental and progressing to formal written methods ve

Related Busy Ant Maths Units Y1 Units Unit 3, Week 2 Unit 6, Weeks 1 & 2

Unit 10, Weeks 1 & 2 Unit 12, Week 1

Previous Y2 Units

Future Y2 Units

Unit 3, Weeks 1 & 2 Unit 4, Week 1

Unit 6, Week 2 Unit 8, Week 1 Unit 10, Weeks 1 & 2 Unit 12, Week 1

Y3 Units Unit 2, Week 1 Unit 4, Weeks 1 & 2 Unit 6, Week 1

Unit 8, Week 1 Unit 10, Week 1 Unit 12, Weeks 1 & 2

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Year 2, Unit 6

Week 2: Number – Multiplication and division National Curriculum attainment targets Pupil targets • Recognise and use the multiplication (×), division (÷) and equals (=) signs correctly

Pupils should be taught to: • recall and use multiplication and division facts for the 5 and 10 multiplication tables

• Recognise and recall the multiplication facts for the ten multiplication table

• calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

• Recognise and recall the division facts for the five and ten multiplication tables

• solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

• Understand the relationship between multiplication and division, applying their knowledge of the five and ten multiplication tables to division

• Begin to recognise that multiplication and division are related (inverse operations)

• Solve problems involving multiplication and division using arrays

Weekly overview Children apply their understanding of counting in fives and multiplication, to division within the five multiplication table. They use a number line to solve division problems, through ‘repeated subtraction’. Children apply their knowledge and understanding of counting in tens to multiplication. They solve multiplication problems using a number line, counting the ‘jumps’ (repeated addition). They discuss the pattern in the numbers as they multiply. Children apply their understanding of counting in tens and multiplication, to division within the ten multiplication table. They use the number line to solve division problems through ‘repeated subtraction’. Children look at arrays and apply their knowledge and understanding of multiplication and division to these, finding the corresponding multiplication and division facts for the two, five and ten multiplication tables. Prerequisites for learning

Assessment

• Recognise and write numbers from zero to 100

Use the following assessments from Busy Ant Maths Assessment Guide 2:

• Show an increasing understanding of multiplication • Know how to share into equal groups • Recognise that multiplication and division are related (inverse operations)

12: Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers 13: Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs 15: S olve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

Tracking back and forward through the curriculum Year 1

Year 2

Year 3

• calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

• write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times onedigit numbers, using mental and progressing to formal written methods

• solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

• solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

Related Busy Ant Maths Units Y1 Units Unit 3, Week 2 Unit 6, Weeks 1 & 2

Unit 10, Weeks 1 & 2 Unit 12, Week 1

Previous Y2 Units

Future Y2 Units

Unit 3, Weeks 1 & 2 Unit 4, Week 1 Unit 6, Week 1

Unit 8, Week 1 Unit 10, Weeks 1 & 2 Unit 12, Week 1

Y3 Units Unit 2, Week 1 Unit 4, Weeks 1 & 2 Unit 6, Week 1

Unit 8, Week 1 Unit 10, Week 1 Unit 12, Weeks 1 & 2

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Year 2, Unit 6

Week 3: Measurement (mass) National Curriculum attainment targets

Pupil targets

Pupils should be taught to:

• Decide whether objects are heavier or lighter than one kilogram by feel

• choose and use appropriate standard units to estimate and measure mass (kg/g) to the nearest appropriate unit, using scales

• Use weighing scales to measure whether objects are heavier or lighter that one kilogram

• compare and order mass and record the results using >, < and =

• Estimate and measure the mass of different objects in kilograms and multiples of 100 grams • Convert between kilograms and grams and vice versa • Compare and order objects according to their mass • Record measurements using >, < and =

Weekly overview Children estimate and measure mass, including describing an object as being ‘more than 1 kg’ or ‘less than 1 kg’. They extend their understanding of the standard units of mass from kilograms to grams, and convert grams to kilograms and then kilograms to grams, including masses less than a whole kilogram, e.g. 3 12 kg or 1500 g. Children record and compare masses using the inequalities signs. They weigh a set of classroom objects and order them, lightest to heaviest. Children solve problems involving mass including doubling and halving – given the mass of two fruits, children work out how much one and four might weigh using halving and doubling. Prerequisites for learning

Assessment

• Estimate, measure and compare the mass of objects deciding which is heavier and/or lighter using their hands and a balance scale

Use the following assessments from Busy Ant Maths Assessment Guide 2:

• Compare, describe and solve practical problems involving mass using vocabulary such as heavy/light, heavier/lighter, heaviest/lightest • Identify items that are more or less than one kilogram using a balance scale • Make reasonable estimates

18: Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels 19: Compare and order lengths, mass, volume/capacity and record the results using >, < and =

• Measure and begin to record mass/weight • Be familiar with the symbols >, < and = • Double and halve numbers Tracking back and forward through the curriculum Year 1 • compare, describe and solve practical problems for: - mass/weight [for example, heavy/light, heavier than, lighter than] • measure and begin to record the following: - mass/weight

Year 2

Year 3

• choose and use appropriate standard units to estimate and measure mass (kg/g) to the nearest appropriate unit, using scales

• measure, compare, add and subtract: mass (kg/g)

• compare and order mass and record the results using >, < and = Related Busy Ant Maths Units

Y1 Units Unit 6, Week 3

Unit 10, Week 3

Previous Y2 Units

Future Y2 Units Unit 10, Week 3

Y3 Units Unit 2, Week 3

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Year 2, Unit 6, Week 1, Lesson 1

Counting in steps National Curriculum attainment target

Lesson objectives

• Count in steps of 2 and 5 from 0, and in tens from any number, forward and backward

• Count in steps of 2 and 5 from 0, forward and backward • Count in tens from any number, forward and backward

Previous related lessons

Future related lessons

Unit 3, Week 1, Lesson 2; Unit 3, Week 2, Lesson 1; Unit 4, Week 1, Lesson 1; Unit 5, Week 1, Lesson 1

Unit 8, Week 1, Lesson 1; Unit 9, Week 1, Lesson 1; Unit 10, Week 1, Lessons 1 & 3; Unit 10, Week 2, Lesson 1; Unit 12, Week 1, Lesson 1

Prerequisites for learning

Success criteria

Pupils need to:

Pupils can:

• count in twos and fives from zero to at least 50, and in tens to 100

• accurately count in multiples of two and five, forwards and backwards

• be familiar with counting in twos, fives and tens, and understand the term ‘multiples’

• count in tens from any number, forwards and backwards

Vocabulary zero, nought, two, four, six, eight … thirty, five, ten, fifteen, twenty … fifty, ten, twenty, thirty, forty … one hundred, count, count on, count up to, count back, count in ones/twos/ fives/tens, before, after, forwards, backwards, multiples of

Getting Started • Choose an activity from Number – Multiplication and division. • Choose an activity from Fluency in Number Facts: Y1/Y2 – Multiplication and division. 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

Year 2, Unit 6, Week 1

Resources mini whiteboard, pen and eraser (per pair); 0–9 number fan (per child) • Display: the Number Square tool. • Say: We know how to count in steps of two from zero. When we count on in twos starting from zero, we know that each number we land on is called a multiple of two. • Count on with the class in steps of two from 0 to 30, pointing to each number as you count. • Say: Tell me a multiple of two between zero and 30. • Children suggest multiples of two. Highlight the multiples of two on the number square in blue, and confirm with the class that any number that has 0, 2, 4, 6 or 8 as its ones digit is a multiple of two. • Say: Count back in twos from 30. • Count back in twos with the class, starting from 30. • Ask: If I count back in twos from 24, what will the next two numbers be? From 18? From 12? • Repeat in the same way, to count forwards and back in fives, from zero to 50, identifying multiples of five and highlighting them in red. • Again, repeat the activity to count forwards and back in tens, from zero to 100, identifying the multiples of ten and highlighting them in yellow. • Reset the number square to remove the highlighted colours. Say: We have counted on in steps of two, five and ten starting from zero each time.

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Number – Multiplication and division

• Highlight 1 and say: We are going to count in steps of ten again, forwards and back, but this time we will start from one. • Say: Use your number fan with your partner to show the next number if we count on ten from one. • In pairs, children show 11 using their number fans. Highlight 11 on the number square. • Ask: If we count on ten from here (point to 11), what is the next number we will land on? • Children show 21 using their number fans. Discuss how they decided on their answer. • Continue to ask children to identify the steps of ten up to 91, highlighting each number. • Together with the class, count forwards and backwards in tens from one. • Divide the children, as they are seated, into five groups and explain that you are going to give each group a number, e.g. 3, 5, 6, 8 and 9. • Say: Now count in tens from your number up to 100 and write down all the numbers that you land on. • Allow children, working in pairs, to record all their numbers on their whiteboards. • Discuss the results for each of the five numbers. Say: If you counted in tens from three, which numbers did you land on? • As children say their numbers, 13, 23, 33, 43 etc., highlight each one in a colour. • Repeat in the same way for the remaining four numbers. • Discuss the emerging patterns – what do the children notice about the tens and ones digits?

Individualised Learning Refer to Activity 1 from the Learning activities on page 260.

Activity Book 2B: – Page 14: Egg steps Progress Guide 2: – Extension, Year 2, Unit 6, Week 1 Lesson 1: 10 steps Resources: coloured pencils (per child)

Plenary • Display: the Number Square tool and point to a number, e.g. 40. • Ask: Which three numbers will come next if I count on in twos from here? (42, 44 and 46) Which numbers will come next if I count back in twos from 28? (26, 24, 22 etc.) • Repeat, asking children to identify the numbers that will come next if they count on and back in steps of 5 or 10. • Say: Listen to my pattern: 12, 22, 32, 42. Ask: What is my pattern? (counting forwards in steps of 10) What will be the next number? (52) Say: Listen to my pattern: 45, 40, 35, 30. Homework Guide 2 Ask: What is the pattern? What comes next? Year 2, Unit 6, Week 1, Lesson 1: • Repeat several times, asking children to identify the Counting kangaroos pattern each time.

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Year 2, Unit 6, Week 1, Lesson 2

Multiplication facts - two times table National Curriculum attainment targets

Lesson objective

• Recall and use multiplication facts for the 2 multiplication table

• Recall and use multiplication facts for the two times table

• Calculate mathematical statements for multiplication within the multiplication tables and write them using the multiplication (×) and equals (=) signs Previous related lessons

Future related lessons

Unit 3, Week 1, Lesson 2; Unit 3, Week 1, Lessons 3 & 4; Unit 3, Week 2, Lessons 2–4; Unit 4, Week 1, Lessons 2–4

Unit 6, Week 1, Lessons 2 & 4; Unit 6, Week 2, Lessons 3 & 4; Unit 8, Week 1, Lessons 2–4; Unit 10, Week 1, Lessons 2 & 4; Unit 10, Week 2, Lessons 2–4; Unit 12, Week 1, Lessons 2–4

Prerequisites for learning

Success criteria

Pupils need to:

Pupils can:

• recognise and write numbers from zero to 50

• recognise and use the multiplication (×) and equals (=) signs correctly

• be familiar with multiplication and know how to count in ‘lots of’ Vocabulary zero, nought, two, four, six … twenty-four, twos, lots of, groups of, sets of, multiplication, multiplied by, times

• recognise multiplication facts for the two times table, and write the corresponding multiplication fact for a given situation

Teach

Year 2, Unit 6, Week 1

Resources mini whiteboard, pen and eraser (per pair) • Display: the Number Line tool showing multiples of two. Count on in twos from zero to 20 with the class. • Say: Remember that each of these numbers is a multiple of two. Ask: How can we tell if a number is a multiple of two? • Encourage children to suggest that any number that has 0, 2, 4, 6 or 8 as its ones digit is a multiple of two. • Write the multiplication sign (×) on the board and ask: Can you tell us what this sign means? • Ask children for their suggestions and then say: This is a multiplication sign. Remember that multiplication is a quick way of adding up equal groups. We can sometimes call it ‘repeated addition’. Remind the class that the multiplication sign means ‘lots of’, ‘groups of’, ‘times’ or ‘multiplied by’. • Display: the Number Line tool showing the numbers 0–30. Set up the frog to start on zero. • Say: The frog is going to make jumps of two along the number line. One, two – one set of two is two. • Count: One, two… and show the frog jumping from zero to two. Place a snail 'marker' above 2 on the number line. • Show another set of two jumps from two to four, saying: Here is another set of two. One, (point to 3), two (point to 4). • Point to zero, then two and then four on the number line and say: One, two – two sets of two make four. Place a snail 'marker' above 4 on the number line. • Ask: If the frog makes another jump of two, where will I land? • Children identify that the next number in the sequence will be six. Place a snail 'marker' above 6.

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Number – Multiplication and division

• Continue in this way to identify the multiples of two up to 20. • Say: Work together to find the next two numbers in the pattern. • Children write 22 and 24 on their whiteboards. Ask them to explain their reasoning, encouraging them to say 'Eleven sets of two make 22' and 'Twelve sets of two make 24'. • All multiples of two from 2 to 24 should now be identified by having a snail 'marker' over them. • Draw a line on the board to join the first and second markers to show one jump (or one set) of two, and write: 1 × 2. Then join the markers at 2 and 4, show jumps 0–2 and 2–4 and write: 2 × 2. • Ask children to help to complete this sequence up to 12 × 2. • Remind the class that the multiplication sign (×) means ‘lots of’ or ‘times’, then point and say: One times two is two, two times two is four, three times two is six and so on, up to 12 times two is 24. • Together with the class, say the two times table, pointing to each multiplication fact along the number line as it is said.

Individualised Learning Refer to Activity 2 from the Learning activities on page 260.

Activity Book 2B: – Page 5: Skateboard multiplication facts Progress Guide 2: – Support, Year 2, Unit 6, Week 1, Lesson 2: Multiply by 2

Plenary Resources mini whiteboard, pen and eraser (per pair) • Display: the Number Line tool with the markers still showing from the Teach section. • Ask children questions relating to the two times table up to the 12th multiple, and point to the appropriate multiples on the number line. • Write on the board: 7 = 14 x 2, 4 = 8 x 2 and 5 = 10 x 2. • Point to the first set of numbers and ask children if they can suggest the correct order so that the numbers make a multiplication fact for the two times table. • Ask children for their suggestions, and then write the correct fact, i.e. 4 × 2 = 8. • Check this with the class, showing the ‘jumps’ on the number line. • Ask children to work in pairs to arrange the remaining two sets of numbers into the correct order, writing the multiplication facts (5 × 2 = 10 and 7 × 2 = 14) on their whiteboards. • Demonstrate each fact on the number line. • Remind children that, like addition, multiplication can be done in any order and the answer remains the same. • Choose one of the calculations, e.g. 5 × 2 = 10. Using the number line, show the children that five jumps of two (5 × 2) and two jumps of five (2 × 5) both have the same answer.

Overcoming Barriers • Some children may have difficulty in understanding that ‘one times two is two’ means the same as ‘one group of two makes two altogether’ and may find it hard to apply their understanding of counting in groups and multiples to the language and process of multiplication. • Provide children with opportunities to work practically using resources to make up to 12 sets of two, counting and recording the totals of these, for example: three sets of two is six altogether … five sets of two makes ten. Show how the numbers that they use are used in the multiplication facts, e.g. 3 × 2 = 6, 5 × 2 = 10.

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