CfE First Level Book 1A - Hodder Gibson · 3-D shapes (MTH 1-16a) 136 How to make 3-D shapes (MTH 1-16a) 137 Ch 25 Statistics 2 Topic overview (Book 1a pages 205–213) 138 Drawing

CfE First Level Book 1A

Gemma Meharg

TeeJay Mathsfor Mastery

Teaching

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TeachingTeeJay Mathsfor Mastery

CfE First Level

Book 1A

Gemma Meharg

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Contents

Introduction Teaching for mastery: an introduction 1

Ch 1 Whole numbers 1 Topic overview (Book 1a pages 10–21) 3Numbers 1–20 (MNU 1-02a) 5Numbers 20–30 (MNU 1-02a) 6Numbers 30–100 (MNU 1-02a) 8Word problems (MNU 1-02a) 10Reading scales (MNU 1-02a) 12Missing numbers (MNU 1-02a) 14

Ch 2 Symmetry Topic overview (Book 1a pages 22–8) 15Symmetry (MTH 1-19a) 17Symmetry in the real world (MTH 1-19a) 18

Ch 3 Whole numbers 2 Topic overview (Book 1a pages 29–36) 19Hundreds, tens and units (MNU 1-02a) 21Numbers bigger than 100 (MNU 1-02a) 23Place value (MNU 1-02a) 25

Ch 4 Time 1 Topic overview (Book 1a pages 37–46) 27Days of the week (MNU 1-10b) 29Months of the year (MNU 1-10b) 30Telling the time on the hour (MNU 1-10a) 31Telling the time: half past, quarter past and quarter to (MNU 1-10a) 33

Ch 5 Whole numbers 3 Topic overview (Book 1a pages 47–61) 35Adding (MNU 1-03a) 37Addition with carrying (MNU 1-03a) 39

Ch 6 Angles Topic overview (Book 1a pages 62–7) 41An angle (MTH 1-17a) 43A special angle – a right angle (MTH 1-17a) 45

Ch 7 Whole numbers 4 Topic overview (Book 1a pages 68–74) 46Basic subtraction (MNU 1-03a) 48

Ch 8 Money 1 Topic overview (Book 1a pages 75–80) 50Using coins (MNU 1-09b) 52Adding and subtracting money up to £1 (MNU 1-09a) 54


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Ch 9 Whole numbers 5 Topic overview (Book 1a pages 81–9) 56Subtraction with carrying (MNU 1-03a) 58

Ch 10 Money 2 Topic overview (Book 1a pages 90–7) 60Money and decimals (MNU 1-09a) 62Adding and subtracting money with decimals (MNU 1-09a) 64Money and decimals up to £5 (MNU 1-09a) 66Money and decimals up to £10 (MNU 1-09a) 68

Ch 11 Time 2 Topic overview (Book 1a pages 98–103) 69Seasons of the year (MNU 1-10b) 71Telling the time (MNU 1-10a) 72

Ch 12 Whole numbers 6 Topic overview (Book 1a pages 104–112) 732 times table (MNU 1-03a) 75Multiplying two-digit numbers by 2 (MNU 1-03a) 76

Ch 13 2-D shapes Topic overview (Book 1a pages 113–19) 78Naming 2-D shapes (MTH 1-16a) 80Sides, corners and angles of 2-D shapes (MTH 1-16a) 81

Ch 14 Whole numbers 7 Topic overview (Book 1a pages 120–9) 82Dividing by 2 (MNU 1-03a) 84Dividing by 3 (MNU 1-03a) 86

Ch 15 Algebra Topic overview (Book 1a pages 130–4) 88The missing number (MTH 1-15b) 90Simple equations with + and − (MTH 1-15b) 91Simple equations with × and ÷ (MTH 1-15b) 92Find the missing symbol in an equation (MTH 1-15a) 93

Ch 16 Fractions 1 Topic overview (Book 1a pages 135–142) 94Half of something (visually) (MNU 1-07a, MNU 1-07b) 96Quarter of something (visually) (MNU 1-07a) 97

Ch 17 Length Topic overview (Book 1a pages 143–150) 99Length (old units) (MNU 1-11a) 101Metric length – centimetres (MNU 1-11a) 102Measuring in metres (MNU 1-11a) 103


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Ch 18 Whole numbers 8 Topic overview (Book 1a pages 151–160) 104Dividing by 2 – remainders (MNU 1-03a) 106Dividing by 2 – more on remainders (MNU 1-03a) 108Dividing by 3 – remainders (MNU 1-03a) 109

Ch 19 Statistics 1 Topic overview (Book 1a pages 161–172) 111Reading from a table (MNU 1-20a) 113Reading from a pictograph (MNU 1-20a) 114Reading from a bar graph (MNU 1-20a) 115

Ch 20 Position and movement Topic overview (Book 1a pages 173–9) 116A right angle and a quarter turn (MTH 1-17a) 118Describing a journey (MTH 1-17a) 119

Ch 21 Fractions 2 Topic overview (Book 1a pages 180–5) 120A third of something (visually) (MNU 1-07a, MNU 1-07b) 122A fraction of something (visually) (MNU 1-07a, MNU 1-07b) 123

Ch 22 Weight Topic overview (Book 1a pages 186–193) 124Words used in weight (MNU 1-11a) 126Measuring in kilograms (MNU 1-11a) 127Reading scales (MNU 1-11a) 128

Ch 23 Patterns Topic overview (Book 1a pages 194–8) 129Drawing patterns (MTH 1-13a) 131Patterns with letters (MTH 1-13a) 132Patterns with numbers (MTH 1-13b) 133

Ch 24 3-D shapes Topic overview (Book 1a pages 199–204) 1343-D shapes (MTH 1-16a) 136How to make 3-D shapes (MTH 1-16a) 137

Ch 25 Statistics 2 Topic overview (Book 1a pages 205–213) 138Drawing pictographs and bar graphs (MTH 1-21a) 140Tally marks and frequency tables (MNU 1-20b) 142

Glossary 143


1

Introduction

Teaching for mastery: an introductionWhat is mastery learning?In a classroom where mastery learning is embedded, the learning outcomes are constant. A focus on aptitude, the time needed for learners to become proficient or competent, is key to the development of mastery. The expectation is that the vast majority of the class will move through content at roughly the same pace.

In a mastery classroom subject matter is broken down into blocks or units of learning with clearly delineated learning intentions. Learners work through a unit in a series of small, sequential steps. The majority of learners are expected to master the ‘fundamentals’ of the unit before moving on to the next block or unit. Working through each block sequentially ensures that learners are given opportunities to demonstrate a high level of understanding at a greater depth. Learners who struggle to reach the required level are supported through additional support, peer support or small group discussions to enable them to reach the anticipated level of understanding.

Why use this approach?By using key elements of collaborative learning and AiFL group work, for example peer tutoring or think-pair-share, mastery learning is a particularly effective vehicle for moving learners through the curriculum. Learners are encouraged to take responsibility for supporting each other’s progress. Taking a mastery approach demands a need for high expectations of all learners – a belief that all learners can and will be successful is key.

Recent analyses into mastery learning show that it may be a useful strategy for narrowing the attainment gap, particularly in relation to low attaining students.

Using this Teaching PackThis pack has been designed to support your daily teaching of mathematics. Included in the pack you will find several elements that are fundamental to learners’ understanding and progression in mathematics. They are explained below.

Topic overviewIn this section an overview of the entire chapter is provided so that it is possible for practitioners to see the ‘big picture’ of the learning over a sequence of lessons. Within this overview the big ideas – i.e. the key concepts to be taught and learned – have been identified to support teacher subject knowledge.

Potential misconceptions have also been included to support AiFL planning: it is useful to keep these barriers in mind during the daily lessons to explore misconceptions and therefore deepen understanding.

Core vocabulary that learners and teachers should be using to support the understanding of key concepts has also been identified. The vocabulary builds progressively across the full series, ensuring that learners are able to talk about their learning in the correct contexts.

Opportunities to develop non-cognitive skills have also been identified across a sequence of lessons. These skills support the development of a growth mindset and allow for opportunities to develop skills required for life, learning and work. Learning mathematics extends beyond learning concepts, procedures and their applications.


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Introduction

We want to ensure that our learners develop a positive disposition toward mathematics and see mathematics as a powerful way for looking at situations.

Disposition refers not only to attitudes but to a way of thinking and acting in a positive manner. It is an expectation that mathematical dispositions manifest themselves in the way learners approach problems – whether with confidence, willingness to explore alternatives, perseverance and interest – and in their tendency to reflect on their own thinking. Evaluating these indicators and learners’ appreciation of the role and value of mathematics is central to the evaluation of mathematical knowledge as a whole.

Within each lesson: what could it look like in the classroom?Time to get started (anchor task to hook learners in) A problem given to the whole class that hooks the learners’ interest and gives them a purpose for learning. Learners should be allowed time to explore and reflect before feeding back their findings, ideas and thoughts to the class, peer groups or teacher.

Time to learn (main modelling by class teacher) This is the main modelling part of the lesson where learners are taught the skill guided by the shared understanding shown at the start of the lesson.

Time to practise (practice guided by the teacher but learners working in pairs) Learners work in pairs to perform deliberate practice based on the problems modelled by the teacher.

Time to reflect (reflection/revisit success criteria) Learners reflect on the learning so far and identify the main success criteria for the lesson including non-cognitive attributes.

Time to work on our own (independent work) Learners work independently to practise the skill modelled with an increasing number of more difficult scenarios.

To end the lesson (overlearning) In some cases, usually with more challenging content, opportunities for overlearning have been referenced. This allows for additional content to be delivered, ensuring a deeper understanding.

Extension Advanced learners can undertake these tasks to deepen their understanding. Some extension tasks have been included in some lessons where it has been deemed appropriate.

Revision of early levelChapter 0This chapter can be used to test and evidence learners’ understanding of early level maths. The exercises in this chapter assess learners’ mathematical fluency and problem-solving skills. The exercises included in the textbooks follow the format of the other assessment opportunities seen throughout the books so that they feel familiar and provide the summative information used to inform teacher judgement.


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Topic overview (Book 1a pages 10–21)

Chapter 1: Whole numbers 1

Resources

What you need from the maths cupboard●● Unifix cubes

●● blank number tracks

●● tens frames

●● place-value arrow cards

●● base 10 materials

●● place-value charts

●● objects for counting: 1–100 number chart

●● counters

Big ideas

The key concepts for this chapter●● Magnitude (the size of a number)

●● Cardinality (the amount in a set)

●● Need for organisation and keeping track

●● Tens and units – understanding that tens and units can exist side by side.

●● Number names – knowing that instead of naming a number ‘one ten and three units’, we give it a name ‘thirteen’.

●● Numbers in different forms – the number 36 is usually thought of as 3 tens and 6.

Potential misconceptions

The barriers to learning●● Learners do not see the number of objects in each frame or image as 10.

●● Learners still count by saying 2 tens and 2 units and do not say the number name, e.g. 22.

●● Learners confuse the tens and units digits.

●● Learners still use inefficient methods such as counting all instead of counting on.

●● Learners call base 10 materials the incorrect names.

●● Learners give base 10 materials the incorrect value.

●● Learners confuse the tens with units.

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Topic overview: Whole numbers 1

Revisit, review, revise!

Activities to consolidate learningThis page can be used as an assessment tool to support teacher judgement. Ideally it would be used a week after the content in the chapter has been taught.

Fundamentals

The basic skills to be mastered●● Learners can use concrete materials to count in tens.

●● Learners can use base 10 materials to create numbers.

●● Learners can create numbers using base 10 materials.

●● Learners can determine which number is greater or smaller using base 10 materials.

Non-cognitive skills

The soft skills developed in each lessonCollaboration Resilience Flexibility Explanation Independence

Core vocabularynumber zero one, two, three, etc. none how many?count count (up) to count on (from, to) count back (from, to) moreless many few odd evenevery other how many times? pattern pair guess how manyestimate nearly close to about the same as greaterlarger bigger less fewer smallercompare order first second thirdlast before after next between


Lesson approach: Whole numbers 1


Time to get started (anchor task to hook learners in)Display an image of a street with houses, showing house numbers.

What do you notice about the numbers on the houses? Do they increase or decrease? By how many each time? Are the steps the same as the last lesson or are they different? Talk to your partners about what you notice about the sequences.Take feedback after a few minutes’ discussion.

Time to learn (main modelling by class teacher)Display the image from question 1. Allow talk partners to discuss the sequence.

How many numbers are missing this time? What could we use to help us to identify the missing house numbers?Model thinking aloud using the numbers before and after to help identify the missing numbers.

‘I’ll start at 46 and look at the next number, which is 47, so the sequence must be in steps of 1. 46 47 48 49. That must be right because if I count one back from 50 it would be 49.’

Model counting forwards and backwards to check the answers. Allow learners to support and ensure that some common errors are used as a teaching point, i.e. bridging the ten.

Time to practise (practice guided by the teacher but learners working in pairs)

Learners work in pairs at their tables to work on the number sequences shown in questions 2, 3 and 4. Circulate to ensure that learners spot the difference in the sequence in number 4 (increasing and decreasing by 2). Encourage learners to generate their own sequences if they complete the questions.

Time to reflect (reflection/revisit success criteria) Bring the class back together and showcase strategies for identifying missing numbers in sequences. Revisit the success criteria and show the sequence in question 5.

What’s the same and what’s different about these scales and the scales in the other questions? What do we need to do with these numbers first in order to identify the missing numbers?

Time to work on our own (independent work)Learners work independently to solve the number sequences in questions 5–11. Question 11 is particularly challenging because the numbers are being read from the bottom of the table up with alternate lines being read from right to left. It would perhaps be beneficial to allow learners to complete the missing numbers before attempting to solve the problems below.

Missing numbers

This section covers pages 18–20 of the TeeJay CfE Book 1a.


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Time to get started (anchor task to hook learners in)To begin this lesson, show learners the image from the yellow box on page 53.

How can we determine how many pennies there are altogether? Are there any methods we have learnt over the last few lessons that might be helpful?Allow learners some time to work out the problem. Tell learners your friend said that they ran into a problem with the following questions.

There are too many units. What do we do when we have 10 or more units? When do we rename units as a ten?Allow them to show you this using base 10 materials.

How can we write this down?

Time to learn (main modelling by class teacher)Using the example of the column method, show learners how to add the units and then add the tens and then add the two sums together. Maintain a focus on this method.

Is it important that you add the units first or can they add the tens first? Would it matter using this method?

Time to practise (practice guided by the teacher but learners working in pairs)

Learners work in pairs to solve questions 1–2 on pages 53–4, using base 10 materials, place-value charts or tens frames to support their understanding of regrouping and renaming.

Time to reflect (reflection/revisit success criteria) Bring the class back together. Show the word problem in question 3.

How would you solve this problem? How could we draw a picture to represent the problem? Can we write success criteria that we can use to help us solve similar problems?Model solving question 3 using the success criteria that learners have generated.

Time to work on our own (independent work)Learners work independently to solve questions 4–8 on page 54. Advanced learners should be encouraged to write/record their own problems for their peers to solve. Struggling learners could be supported through the use of the manipulatives on the tables.

Addition with carrying

This section covers pages 53–60 of the TeeJay CfE Book 1a.




Additional noteIt may be appropriate to explore regrouping and renaming in the units column over a sequence of lessons depending on the prerequisite understandings of the class.

Addition in tens (with carrying) and addition in hundreds (with carrying)For both of the above lessons the same sequence of learning should be followed to introduce the regrouping in different columns. You may choose to vary the materials used in the anchor task, i.e. base 10, tens frames etc. to ensure learners develop a broader understanding of the base 10 system.

Adding with a calculatorThis lesson can be taught as an additional enrichment activity to support the development of the formal written method for addition.

Learners should work through the lesson in small groups or with partners without the need for a large proportion of teacher support.

To end the lesson (overlearning)Exercise 7 on page 59 can be used to provide an insight into how well learners have grasped an understanding of column addition. It could be used as an assessment tool with the teacher observing how individuals approach the problems: do they use apparatus or not? Can they calculate in the abstract? Are they able to translate the written word problem into a calculation? Can they regroup and rename?


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Angle Angles are formed where two straight lines meet. Angles of different sizes have different names:

Acute: This is a type of angle less than 90°.

Obtuse: This is an angle larger than 90°.

Right angle: This angle is exactly 90°.

Reflex angle: An angle larger than 180° but smaller than 360°.

Area The amount of surface in a shape. Area can be measured in cm² or m².

Array A set that shows equal groups in rows and columns.

Average You can find the average of a set of numbers by adding them all together and dividing the total by how many numbers there are.

The average is also called the mean.

Axis An axis is an imaginary line through the middle of any solid shape.

An axis is also one of the horizontal or vertical lines on a graph. The axes (plural of axis) are used to measure the position of points on a graph.

Bar model The bar model method is pictorial and develops from learners handling actual objects to drawing pictures and then drawing boxes, each of which represents an individual unit to represent objects. Eventually, they will no longer need to draw all the boxes; instead, they just draw one long bar and label it with a number.

Base 10 Base 10 refers to the numbering system in common use that uses decimal numbers. Base 10 is also called the decimal system or denary system.

Brackets These are included in many maths questions and look like these ( ). You must complete the sum inside the brackets first.

Calculate This means ‘to work something out’.

Capacity The capacity of a container is the amount of water or other liquid that it will hold.

Century This means 100. A century of time is 100 years.

Circumference The circumference is the edge of a shape, especially a curved shape such as a circle.

The circumference is also the distance all the way around the edge of a shape.

Consecutive Consecutive numbers follow each other in an unbroken sequence.

Cube A symmetrical 3-D shape made up of 6 equal squares.

Cuboid A 3-D shape made up of 6 rectangular faces.

Cylinder A shape that has a pair of parallel sides and oval/circular bases.

CPA Concrete, pictorial, abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in learners.

Decade A decade of time is 10 years.

Decimal A decimal is used for a value less than 1. You use a decimal point to separate the whole number from the decimal part.

Degree A unit used for measuring angles and temperatures.

Denominator The bottom number of a fraction.

Glossary

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Documents

CfE First Level Book 1A - Hodder Gibson · 3-D shapes (MTH 1-16a) 136 How to make 3-D shapes (MTH 1-16a) 137 Ch 25 Statistics 2 Topic overview (Book 1a pages 205–213) 138 Drawing