Active Maths TG 2 Sampler

TEACHER’S GUIDE TEACHER’S GUIDE Stage 2 Hawa Shahbal • Penny Sim Hawa Shahbal Penny Sim The series is developed to comprehensively cover all the learning objectives of the Cambridge Primary Mathematics curriculum framework (0096). The series adopts an Active Learning approach that allows learners to actively grasp concepts on a personal level through exploration, discussion and inquiry. Learners will investigate mathematical topics like Numbers, Geometry, Measurement, Statistics and Probability. Learners are also taught to Think and Work Mathematically, which equips learners with the ability to look at Mathematical concepts from different perspectives, thus allowing learners to build a strong foundation in the subject. To encourage problem-based learning (PBL), each chapter starts by presenting learners with a case problem. As they go through the chapter, they will acquire knowledge of necessary mathematical concepts. Learners are consistently encouraged to think critically and collaborate with their peers to solve the case by the end of the chapter. Each chapter is structured in a Concrete Pictorial Abstract way, which enables learners to achieve mastery in reasoning, problem-solving and conceptual skills. They will become confident problem solvers. Most importantly, learners will gradually grow to love Mathematics as they realise its importance and relevance in their daily lives. Active Maths The series consists of: • Textbook • Workbook • Teacher’s Guide • Digital Textbook, Workbook, and Teacher’s Guide • Downloadable resources for teachers, including printables for hands-on activities, worksheets and test papers. Teacher’s Guide 2Stage 0A Active Maths TG 2 Cover.indd 1-3 16/8/22 2:01 AM © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 1 Active Maths -Teacher’s Guide – Stage 2 Note to Teachers © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 2 Introduction to Active Maths The Active Maths primary series is developed to comprehensively cover all the learning objectives of the latest Cambridge Primary Mathematics (0096) curriculum framework. In this new syllabus, the focus still remains on important Mathematical concepts, which is categorised into three main strands – Numbers, Geometry and Measurement, Statistics and Probability. Instead of teaching problem-solving skills separately from these 3 strands, each chapter is written such that problem-solving skills are integrated and weaved into the content and questions. Learners are constantly reminded of the importance of Thinking and Working Mathematically (TWM). These skills are reflected across various sections of our book via TWM indicators. We recognise that problem-solving skills is not a strand by itself, rather, it is an essential skill that learners need to cultivate as they delve into the world of Mathematics. As learners embark on their Mathematics journey, we hope that they will develop a love and interest in this subject. This is shown through achievement of mastery, in aspects such as reasoning, problem-solving, deduction and conceptual skills. By developing a comprehensive set of resources for learners and teachers, we wish to nurture every learner to be confident problem-solvers who recognize the importance and relevance of Mathematics in their everyday lives. Pedagogy This series adopts an Active Learning pedagogy. We believe that at the heart of every child is an eagerness to learn and process the world around them. To be active © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 3 learners means that learners stretch their potential and develop an ability to grasp concepts on a personal level through exploration, discussion and inquiry. Active Learning is achieved through a problem-based learning (PBL) approach. Each chapter is carefully structured such that the problem, which is first introduced at the start of the chapter, is intricately integrated together with the Mathematical concepts that learners are expected to understand. We place a strong emphasis on the themes that run through each chapter and grade, so that learners make meaningful connections between the Maths content and its relevance in many aspects of everyday life. Furthermore, having a consistent storyline sustains learners’ interest and presents them with a structured flow which is easy to follow. When learners collaborate with their peers to solve the PBL by the end of the chapter, this solidifies their understanding of the Maths concepts, allowing them to gain a sense of achievement and mastery. The series aims to break down the content for learners in a way that is easy for them to understand. To do this, we have adopted a general Concrete à Pictorial à Abstract (CPA) structure. Mathematical content can be overwhelming, and this structure helps learners process information one step at a time, such that they do not leave a lesson with misconceptions. How to use this Teacher’s Guide This Teacher’s Guide is designed to support teachers in conceptualising, developing and implementing a successful lesson. We believe that teachers should be given the resources to effectively deliver the learning objectives required to learners in an engaging, exciting and meaningful manner. As such, this guide serves as a repository of teaching ideas, instructional techniques and strategies, as well as printables and manipulatives needed to help teachers carry out a successful and meaningful Maths lesson. © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 4 Each chapter of the Teacher’s Guide is structured as such: à Overview of Stage 2 o Topics, learning indicators, prior knowledge expected, online resources à Learning Process Chart o Each lesson delivery plan is structured in the following manner using a 5E Model to instill Active Learning in learners: Engage, Explore, Explain, Extend and Evaluate. This chart includes a write-up of what each of these structures mean, such that teachers can use it to plan their lessons in an effective way. à Chapter Roadmap o Introduces the PBL scenario, themes and storyline that runs through each chapter. It is organised neatly by lessons, such that teachers have an opportunity to regularly pause at checkpoints to assess learners’ understanding of the content being taught. à Scheme of Work (SOW) o Overview of the learning indicators that are set out in each chapter, as well as a detailed breakdown of how each lesson is structured and their estimated durations. à Breakdown of TWM skills o Writeup of the 8 TWM skills and how often they appear in the textbook by chapter. à Individual detailed lesson delivery plan o Contains detailed descriptions of lesson ideas, instructional strategies, differentiated instruction, questioning techniques and TWM skills that are covered across the chapter. à Teacher evaluation reflection form o At the end of each lesson within the chapter, teachers have an opportunity to evaluate their lessons based on a variety of indicators. Guided questions in the form help teachers to reflect on different aspects of their lessons, in order to identify strengths and weaknesses, in order to suggest improvements for future lessons. • Printables o Resources for hands-on activities that can be carried out in class. These are provided to help teachers seamlessly integrate hands-on activities into their lesson delivery without having to find, create or consolidate the materials by themselves. Manipulative Icons © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 5 These manipulatives are used to help teachers conduct hands-on activities with their lessons. Learners can use these manipulatives to help them visualise counting, arranging, sorting and association. Learning Process (5E Model) Engage Explore Explain Extend Evaluate © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 6 *These learning processes can appear multiple times within a lesson. •Through a PBL approach, learners are presented with the problem scenario in the chapter, as well as its storyline, theme and learning objectives. Engage •Learners have an opportunity to actively investigate and explore Maths concepts that they will learn about in the chapter. •By forming their own conclusions, learners can make sense of the content more meaningfully when they are formally taught about it. Explore •Through a systematic, scaffolded process, learners solidify their initial knowledge about the Maths concepts they explored in the earlier stage. •Learners make meaning, build on existing concepts, explain and discuss ideas with their peers, which helps to build on existing concepts and helps to correct any misconceptions that they might have. Explain •Learners have ample opportunities to extend their Mathematical knowledge and skills through challenging questions and additional activities. This can be in the form of extended content, hands-on activities, online games, practice questions and worksheets. •This helps learners to gain a deeper understanding of Maths concepts that have been taught. Extend •Learners collaborate to solve the problem scenario presented at the start of the chapter. •Through discussions and sharing of ideas and possible solutions, learners are able to value add to the Maths concepts they have learnt about. •They also acquire important skills such as evaluation, critiquing and convincing others of the solutions they have come up with. Evaluate © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 7 Overview of Stage 2 Chapter Mathematical Strand Learning Indicators 1 Numbers to 100 Number Learners will be able to: • Estimate numbers up to 100 • Count, read and write numerals and number words from 0 to 100 • Count on and count back in ones, twos, fives and tens • Identify and complete number patterns • Recognise the value of each digit in 2-digit numbers 2 More about Numbers to 100 Number Learners will be able to: • Compare and order numbers to 100 • Round numbers to the nearest ten • Recognise even and odd numbers • Recognise ordinal numbers 3 Time Geometry and Measurement Learners will be able to: • Arrange the days of the week and months of the year in order • Read and use a calendar • Tell time to 5 minutes • Describe time using past, to, quarter past and quarter to • Compare and order units of time 4 Shapes and Solids Geometry and Measurement Learners will be able to: • Identify, describe, sketch and sort shapes and solids • Identify and draw lines of symmetry and shapes and in patterns • Sketch shapes in a mirror line • Describe a circle and its centre • Complete shape and solid patterns © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 8 5 Addition and Subtraction Number Learners will be able to: • Find number pairs to 20 and to multiples of ten • Break down 2-digit numbers into tens and ones • Estimate, add and subtract 2-digit numbers • State the relationship between addition and subtraction 6 Measurement Geometry and Measurement Learners will be able to: • Estimate, measure and compare lengths • Estimate, measure and compare masses • Estimate, measure and compare capacities • Read different measuring scales 7 Position and Movement Geometry and Measurement Learners will be able to: • Describe turns using clockwise and anticlockwise • Describe how a shape looks like when it is rotated • Give directions to move a person or an object from one place to another 8 Multiplication Number Learners will be able to: • Multiply by repeated addition • Multiply by 1, 2, 5 and 10 • Recite the 1, 2, 5 and 10 times tables 9 Money Number Learners will be able to: • Recognise coins and notes • Exchange different amounts of money • Count money 10 Division Number Learners will be able to: • Divide by repeated subtraction • Divide by sharing and grouping • Explain what a remainder is © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 9 11 Fractions Number Learners will be able to: • Find quarters of a whole and a set • Compare fractions and find equivalent fractions • Combine fractions to form new fractions • Use division to work out fractions 12 Handling Data Statistics Learners will be able to: • Conduct an investigation • Record, organise, represent and describe data in different ways • Choose and explain the best representation to use in a given situation 13 Chance Statistics Learners will be able to: • Identify patterns that are regular and random • Conduct, present and describe the results of chance experiments © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Prelims © 2022 Alston Education Pte Ltd 10 TWM Skills TWM 1 2 3 4 5 6 7 8 9 10 11 12 13 Conjecturing Characterising Generalising Specialising Classifying Convincing Critiquing Improving © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd 1 Stage 2 Chapter 1 Roadmap Numbers to 100 Lesson 1: In order to quickly find out the number of sweets and snacks they already have, the children will need to learn how to 2 count objects in different arrangements quickly. PBL Scenario: The children are preparing for a class party of 40 learners. They are not sure whether the sweets and snacks that they have bought are enough to be distributed among all the learners. They need to learn more about numbers to 100 to find out! 1 3 Lesson 2: The children learn to count in ones and tens up to 100 so that they can check if there are enough sweets and snacks for the class. 5 4 6 Lesson 3: The children are now helping Vera to count if there are enough sweets to distribute 2 to each learner in the class. They learn to estimate and count in twos, fives and tens. Checkpoint: A conclusion can now be formed on whether the biscuits Tim is holding and the muffins Cyrus is holding are enough for the class. Checkpoint: More conclusions can now be formed on counting in groups to describe and complete number patterns. A conclusion can also be formed on whether there are enough sweets to distribute 2 to each learner in class. © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd 2 7 9 8 Making conclusions: The children have learnt many things about numbers to 100. They also learnt many ways of counting and showing numbers using place values. They want to summarise what they have learnt in the reflection report to find out how many more snacks they need to buy. They can also use this knowledge of counting as they explore their school! Lesson 4: Cyrus and Tim buy more sweets for the class to ensure there are enough to distribute. They count the number of sweets they buy and use place values to show the number! Checkpoint: More conclusions can now be formed on showing a number using place values. A conclusion can also be formed on whether there are enough sweets to distribute 2 to each child in class now, after Cyrus and Tim buys more. © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd 3 Scheme of Work (SOW) Lesson Learning Indicators Resources Teaching Duration 1 Quickly count the number of objects in different arrangements Page 3: 1 hour 30 minutes Estimate numbers up to 10 2 Count, read and write numerals and number words from 0 to 100 Page 4: Ice-cream sticks Rubber bands 1 hour 30 minutes Please allocate about 30 more minutes to go through the worksheets in the workbook. Count on and count back in ones and tens 3 Estimate numbers up to 100 Pages 7, 8, 9, 10: Big jars of 60 sweets each 2 hours Please allocate about 30 more minutes to go through the worksheets in the workbook. Count on and count back in twos and fives Identify and complete number patterns 4 Recognise the value of each digit in 2-digit numbers Page 11: Page 12: 1 hour 30 minutes Please allocate about 30 more minutes to go through the worksheets in the workbook. Total time: 7 hours 30 minutes © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd 4 Helpful resources: qrs.ly/vne1tot - Number card online manipulative from 1 to 100 qrs.ly/n4e1toz - Ten-frame online manipulative qrs.ly/lqe1tp1 - Ten-frame online manipulative qrs.ly/c6e1tp3 - Place value chart online manipulative © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 5 Lesson 1: Counting objects Lesson Objectives: • Quickly count the number of objects in different arrangements • Estimate numbers up to 10 Success criteria: • Learners can quickly count the number of objects in different arrangements • Learners can estimate numbers up to 10 Keywords for this lesson: count Prior Knowledge: • Recognise and count numbers from 0 to 20 Structure (5E Model) Description / Teaching ideas TWM Skills Resources needed Structure (5E Model) Description / Teaching ideas TWM Skills Resources needed Engage Learners play an active role in identifying and solving the problem. PBL opener The children are buying some sweets and snacks for a class party. However, they are unsure whether they have enough for everyone. Learners will need to identify the problem based on what they see from the scenario given. : Let us look at the scenario on Page 2. Describe what you see. Give learners 5 minutes to discuss in pairs and tell each other their observations. Ask: • Where are the children at? How do you know? [Ans: They are at the school canteen. There is a sign that shows the school canteen.] • What do you think the children are doing? [Ans: The children are each holding on to some biscuits, muffins and sweets.] • How do you think the children in the picture are feeling? [Ans: They look unsure and puzzled.] • Textbook Page 2 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 6 • Why are they holding on to those items? What do they want to do with them? [Ans: They want to share the sweets and snacks with their friends.] • Why do you think the children look puzzled and unsure? [Ans: They do not know whether they have enough to distribute to their classmates.] • What is the problem you see in this picture? [Ans: The children are unsure if they have enough sweets and snacks.] • Why do you think the children are confused about whether they have enough food? [Ans: They are unsure of how to count the number of sweets, muffins and biscuits that they have.] • How can you estimate the number of sweets in Vera’s jar? [Ans: The jar looks the same as the jars with the blue and orange sweets! But Vera’s jar seems to have less sweets.] • How many muffins are there in each box that Cyrus is holding? How can you count the total number of muffins? [Ans: 5 in each box. We can count on in fives.] • How many packs of 10 biscuits is Tim holding? How can you count the total number of biscuits? [Ans: 3 packs of 10 biscuits. We can count on in tens.] Observe the learners’ responses to the questions above. They should share their answers until they have a clear understanding of what the problem in the scenario is. PBL conclusion Learners should be able to describe that the children are confused if they have enough food to distribute to their classmates, because they are not sure how they should count numbers above 20. Learners should also realise that the children will need to learn to count to 100 before they can find out the number of classmates. They can then find out how many sweets, muffins and biscuits they need in total. : Let us help the children find out how they can count the sweets and snacks that they are holding. They can then find out if they have enough for the whole class. © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 7 Read out the learning indicators in the yellow sticky note to the learners, so they will have an understanding of what they will learn in this chapter. Explore Learners carry out hands-on activities to find out more about quickly counting objects in different arrangements. Counting objects : Ada, Cyrus, Tim and Vera are learning how to count objects in different arrangements quickly. Let us look at their ten-frames and help them! Invite learners to work in pairs. Distribute 20 counters and ten-frames (Handout 1a) to each pair. Each learner chooses 2 mascots. Ask each learner to place the counters in the ten-frames as they see in the Textbook to represent their chosen mascots. Instruct learners to share with their partners and describe what they see in the counters. Observe if learners understand that the counters refer to the set of counters that Ada, Cyrus, Tim and Vera have. Ask: • What do you notice about the number of counters that each of the children have? [Ans: They each have 3 counters.] • Does it matter if the counters are arranged differently in the ten-frames? [Ans: It doesn’t matter as long as there are 3 counters.] • Are there any other ways to arrange the 3 counters? Show them to your partner. Learners have now seen how the same number of counters can be arranged differently. They will now form more numbers using different arrangements of the counters on the ten-frames. Activity (Optional): Learners are invited to come to the front of the class with their ten-frames to demonstrate how they will arrange counters given to them. 1st group of learners to show arrangement of 4 counters. 2nd group of learners to show arrangement of 5 counters. 3rd group of learners to show arrangement of 6 counters. Conjecturing Convincing Specialising • Textbook Page 3 Ten-frames template (Handout 1a) Ten-frames template (Handout 1a) © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 8 After each group of learners have demonstrated how they would arrange the counters given to them, choose one person in each group to explain his or her arrangement. As there are no right or wrong answers, learners should conclude that there are many ways to present the counters and should think of different ways to find the number of counters. They should then evaluate which might be the easiest way to count the counters quickly. Activity: In the same pairs, learners should still have 20 counters and ten-frames (Handout 1a). Instruct learners to arrange 7 counters on the tenframes individually. After learners have arranged their counters, let them compare with their partners to see if they are the same. Learners should also be guided to discuss which arrangement allows them to count 7 counters more easily. Learners may ask these questions to their partner: • How did you decide how to arrange the counters? [Ans: They could be placed anywhere on the ten-frame.] • Why did you arrange the counters in this particular way? [Ans: There is an empty slot for the counter to be placed.] • What is similar about our arrangements? [Ans: The counters take up 7 squares in total.] • What is different about our arrangements? [Ans: The counters are placed in different squares of the tenframe.] Next, learners can decide how many counters they want to place in their ten-frames. Learners will take turns to challenge their partners to guess the number of counters quickly. After getting 3 guesses each, learners should share with each other their methods of guessing and why they can correctly and quickly find the number of counters. Learners should conclude that the counters may be arranged in unfamiliar patterns, but they can still use various strategies to help them. Specialising Ten-frames template (Handout 1a) © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 9 Learners may ask these questions to their partner: • What method do you use to guess quickly? [Ans: I can quickly group the counters using my eyes into a familiar pattern for me to count / I am able to quickly count using my eyes and saying the number quickly inside my head / I am able to look quickly at the top and bottom of the ten-frame and add the numbers up.] • Are these methods faster than using our fingers to count? [Ans: Using our fingers can sometimes slow us down. In times like this, using our eyes to count for small numbers can work.] • What is the best way to find out the number of counters quickly? [Ans: There is no best way to do it. As long as we can count mentally, that should be faster than using our fingers.] Convincing Improving Explain Learners learn key concepts through activities, discussions and teacher’s explanations. Show learners the counters as shown on Page 3 of their textbooks on the visualizer and demonstrate the counting method. Demonstrate the counting of the counters quickly by counting the first row followed by the second row. So, 2 and 3 make 5 for the first ten-frame. 3 and 2 make 5 for the next ten-frame on the right. Ask: • What is the number that was counted? [Ans: 5.] • How was the counting done quickly? [Ans: Count in groups of 2 and 3.] • Will it be faster to count individually one counter at a time? [Ans: No, that will be slower. However, it should still lead us to the same answer.] Learners should fill in the answer in their textbook that there are 5 counters in each ten-frame. Show learners other arrangements of counters of 6, 7, 8 and 9. Get them to try out their methods for counting quickly. Then, invite some learners to show their counting methods with the class. Differentiated instruction: For learners who are having difficulties in their counting, encourage them to use their fingers to point to the counters as they count and say it out loud. After they become more familiar, encourage them to count mentally and in groups of two. • Textbook Page 3 Ten-frames template (Handout 1a) © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 10 Lesson 2: Counting to 100 Lesson Objectives: • Count, read and write numerals and number words from 0 to 100 • Count on and back in ones and tens Success criteria: • Learners can count, read and write numerals and number words from 0 to 100 • Learners can count on and back in ones and tens Keywords for this lesson: ones, tens, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, one hundred Prior knowledge: • Count from 0 to 20 • Read and write numerals and number words from 0 to 20 Structure (5E Model) Description / Teaching ideas TWM Skills Resources needed Explore Learners carry out hands-on activities to find out more about counting to 100. Counting to 100 : We are going to do a recap of counting numbers to 20, which we have learnt in Grade 1. Ask learners what they see in the diagram and if they recall seeing these items. Hand out 30 counters to learners to help them in the counting of the jellybeans. Instruct learners to arrange the counters like the jelly beans. Ask: • Why are the jellybeans circled and placed with a number “10”? [Ans: This makes it easier to count after 10.] • How many jellybeans are there outside of the 10? [Ans: There are 7.] • What is the numeral? [Ans: 17] • How can we spell this in words? [Ans: S-e-v-e-n-t-e-e-n] Write down the numeral and number word on the board, so learners can follow and write down their answers in the blanks. Explain to learners that similar to making 10 and counting on, we can also make 20 and count on. • Textbook Page 4 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 11 Allow learners 5 minutes to discuss how they can do so and what numbers they will get when they count on from 20. Guide them to use the counters to show each number to their partners. Learners should discuss the name of each number they come up with. Explain Learners learn key concepts through activities, discussions and teacher’s explanations. Instruct learners to look at the sticks on Page 4 of the textbook. : We shall now look at how we could count beyond 20. We saw earlier that we place 10 jellybeans into a set of 10. We shall now use ice cream sticks to represent that. Together with learners, count aloud the first 10 ice cream sticks before using the rubber band to put them together. Explain to learners that 10 ice cream sticks make a ten. Explain to learners that we can continue to bundle 10 ice cream sticks together (pre-bundled in 10s). Ask: • What do we call 2 sets of 10 ice cream sticks? [Ans: 2 tens or 20 ice cream sticks.] • What will the number be when we have 1 ice cream stick together with the 2 bundles of 10? [Ans: 21.] Ensure learners understand that 2 tens make 20. Explain to learners that now that we have 20, we can count on to get larger numbers. Take out another 1 individual ice cream stick and place it next to the 2 bundles of tens. Guide learners to look at the numbers 22 and 23 on Page 4 of the textbook. At the same time, keep adding individual ice cream sticks to the 2 bundles of tens. Get learners to discuss with their partners what they notice about the numbers. Learners should conclude that they can count on in ones from 21 to get these numbers. Guide learners to conclude that there are already 2 bundles of 10 ice cream sticks which represent 20. We can count another one, two and three sticks to get 21, 22 and 23 sticks respectively. : In the arrangement of jelly beans, we can see that 10 and 7 make 17. Look at the number • Textbook Pages 4 - 5 Ice-cream sticks (individual sticks and some prebundled in groups of ten) Rubber bands © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 12 23. How would you describe it? [Ans: 20 and 3 make 23.] Continue counting aloud the remaining numbers on Page 5 of the textbook along with learners. Add an additional ice cream stick each time. After reaching 30, invite a learner to make another bundle of 10 ice cream sticks and tie them up with a rubber band. For the numbers 21 to 29, invite learners to circle the 2 bundles of tens on Pages 4 and 5 of the textbook. Get learners to discuss how this helps them see the numbers more easily. Ask: • What do you notice about the number of ice cream sticks as you count on? [Ans: As we count on from one number to the next, the number of ice cream sticks increases by 1.] • Are we able to continue counting on in tens after 30? How? [Ans: Yes. We can add another bundle of 10 ice cream sticks.] • As we count on in ones, should we bundle less than 10 sticks together? Why? [Ans: No. It would make it more difficult to count if we bundle less than 10 sticks together.] Remind learners that after the bundles of 10 are counted, we can start counting in ones until another bundle of 10 is formed. Explain to learners that we can also count on by looking at only the bundles of 10. Show learners 1 bunch of 10 and count “10” together with them. Add another bunch of 10, and count “20” together with them. Add another bunch of 10, and count “30” together with them. Ask: • What do you think we are counting on in by using only the bundles of 10? [Ans: We are counting on in tens.] • Can you continue counting on in tens? What do you think is the next number? [Yes, we can continue counting on in tens. The next number is 40.] Add another bundle of 10 to show learners that the next number is indeed forty. Inform learners © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 13 that we will be looking at that shortly after we learn to count back. Extend Learners extend the key concepts learnt through discussion and activities. : We have used the bundles of 10 ice cream sticks to help us count on in tens. Let’s see if we can count back in tens as well. Show learners the 3 bundles of 10 ice cream sticks. Remove 1 bundle. Get learners to discuss what number is shown now. Then, remove another bundle and allow learners to discuss again. Get learners to write out 30, 20 and 10 on their mini whiteboards and discuss with their partners what they notice about the numbers. Guide learners to conclude that they are counting back from 3, to 2 and to 1. The ‘0’ in the numbers remain the same. Explain Learners learn key concepts through activities, discussions and teacher’s explanations. Invite 10 learners to the front of the class to take 10 ice cream sticks each. Next, invite all 10 learners with their bundles of ice cream sticks to stand in one line facing the class. : Let us look at our 10 friends in front of the class and count along to find the total number of ice cream sticks. Referring to Page 6, ask 4 learners to hold up their bundles of 10 and count aloud with the class together in tens as you point towards each learner. Learners should count in this way: ten, twenty, thirty, forty As each subsequent bundle of 10 is being counted, ask the next learner to raise up their bundle of 10 ice cream sticks until the last set of 10 is reached. At the same time, point to the numeral and words on page 6 of the textbook to ensure that learners read out loud. Ask: • What do you notice about the digit at the end of these numbers? [Ans: It is always a zero.] • Textbook Page 6 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 14 • What do you notice about the digits in front? [Ans: We seem to be counting on from 1 to 10.] To count back in tens, get the 10 learners to put down their bundles one by one as each 10 is counted all the way back to 0. Count aloud with learners. One hundred, ninety, eighty, seventy… Play a video in class to consolidate learners’ understanding and for them to gain further familiarity in counting on and back in tens. (URL 1.1) Differentiated instruction: For struggling learners, instruct them to use their fingers to point to each bundle of 10 on the textbook as they count on. Encourage them to practise counting on for every number. E.g., • Forty: Ten, twenty, thirty, forty • Fifty: Ten, twenty, thirty, forty, fifty • Sixty: Ten, twenty, thirty, forty, fifty, sixty This allows them the opportunity for more practice. Do the same for them when counting back. URL 1.1 Extend Learners extend the key concepts learnt through discussion and activities. Start a class discussion on the Maths @ Work on Page 6. Explain to learners that a hundred years is also known as a century. Allow learners 1 minute to discuss quickly with their partner where they have seen and used the word century. Explain that a person who lives to 100 years old is a centenarian. Ask the following guiding questions to help learners relate to the idea of a hundred. Ask: • What are other things that may live to 100 years old? [Ans: Giant turtles, large trees.] • What other objects or things around you can be described using 100? [Ans: The number of days, examination score etc.] Give learners 5 minutes to discuss the guiding questions with their partners. Share the following site with learners on the longest living animals that they can find in the world today. (URL 1.2) • Textbook Page 6 URL 1.2 URL 1.1: https://qrs.ly/7ie0n0e URL 1.2: https://qrs.ly/73e0n28 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 15 Invite a few learners to share their answers with the class. You may round off this segment of discussion by sharing several examples of things that can relate to the use of 100. Evaluate Learners make conclusions about what they have learnt so far. : We are going to practise how to count and write down the numeral and word in the spaces provided for us on page 6 of the textbook. Ask: • How many apples are there in 1 basket? [Ans: 10.] • How do you think we can quickly count the total number of apples? [Ans: Count on in tens first: 10, 20, 30. Then, count on in ones: 31, 32, 33.] Model the question by guiding the learners to count in tens together for the basket of 10 apples followed by the counting in ones for the 3 apples. Get learners to write down the answers in the space provided in the book, 33 and spell out thirty-three. For further practice, assign Worksheet 1 in the workbook to be completed as homework. To help them gauge their understanding, ask learners to shade either the happy, sad or neutral face of Coco at the end of each worksheet. • Textbook Page 6 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 16 Lesson 3: Counting in groups Lesson Objectives: • Count on and count back in twos, fives and tens • Complete number patterns Success criteria: • Learners can count on and count back in twos, fives and tens • Learners can complete number patterns Keywords for this lesson: estimate, twos, fives Prior knowledge: • Count from 0 to 100 • Read and write numerals and number words from 0 to 100 Structure (5E Model) Description / Teaching ideas TWM Skills Resources needed Explore Learners carry out hands-on activities to find out more about estimation and counting in groups. Counting in groups : Vera has a big jar of sweets. As she is unsure of how to count her sweets, let us find different ways that we can help her with that! Get learners to work in pairs. Give each pair a big jar of 60 sweets. If there are insufficient sweets, use counters and cubes to replace the sweets. Explain to learners that this jar of sweets has the same number of sweets as the jar of sweets that Vera is holding. Get learners to recall what they remember about what it means to “estimate”. Write on the board the word “estimate”. Explain to learners that to estimate is to make a reasonable guess based on what they see in the jar of sweets. Guide learners to look at their jars and estimate the number of sweets as a pair. Ask: • Can you use the size of your hand to make an estimate? How? [Ans: I can count how many sweets I can grab at one time in one handful. Based on the number of sweets Characterising Convincing • Textbook Pages 6 - 7 Big jars of 60 sweets each © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 17 my hand can hold, I can estimate the number of sweets in the jar.] • How else can you make an estimate? Can we make use of groups of ten? [Ans: I might be able to group the sweets mentally into groups of ten. Then, I can estimate how many groups of ten there are.] Guide learners to look at Vera’s jar of sweets on Page 2 of the textbook. Ask: • What are some things in the school canteen that can help us estimate the number of sweets in Vera’s jar? [Ans: The jar of blue sweets and the jar of orange sweets. There are 100 sweets in a full jar.] • Is Vera’s jar full? Do you think there are 100 sweets in Vera’s jar? [Ans: No. There is still some space above the sweets in the jar Vera is holding.] • What will be a good estimate of the number of sweets in Vera’s jar? [Ans: Around 60 to 70 sweets.] Give learners 5 minutes to discuss these questions with their partners. Learners should then write down their individual estimates on Page 7 of the textbook under “My estimate”. Select a few learners to say out their estimates and ask the rest of the class if they find the estimate reasonable. [A reasonable estimate will be about 60 to 70 sweets in Vera’s jar.] As an estimate is not meant to get an exact answer, give credit and encouragement to learners who make an effort to justify their estimate even if it is way off. Activity: In pairs, ask learners to pour the sweets out of the jar and practise counting the number of sweets, by first counting in ones. Take turns between themselves as one learner counts and the other observes before switching roles. Encourage learners to count aloud as they touch each sweet to count in ones while the partner observes and ensures that the counting is done correctly. Characterising Convincing Specialising © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 18 Observe the class to see what learners do with their objects as they are counting and ask learners to write down their answers for Question 2a. After learners are confident to count in ones, get them ready to count in twos. Ask: • How can you arrange the sweets or counters to count more quickly? [Ans: Arrange the sweets in groups of 2, 5 or 10.] : We are going to count the jar of sweets in twos this time. Are you ready? Get learners to look at how Vera is counting in twos on Page 7 of the textbook. Ask: • How is Vera arranging the sweets as she is counting? [Ans: She is placing the sweets in groups of 2.] • What do you notice about the numbers that Vera is saying as she is counting? [Ans: She is counting in twos. The numbers are even numbers.] • Do you think it will be faster to count in twos compared to counting in ones? Why? [Ans: It may be faster to count in twos as there are fewer numbers we have to say out.] As learners carry out the counting in twos, get the partners to listen and observe that the counting in twos is done correctly. Get learners to write down their answers for Question 2b after they have completed the counting. Explain to learners what they have just done is to count in groups of two or in twos. Invite learners to proceed with the same technique for counting in fives and to write down their answers for Question 2(c). Ask: • How should we arrange the sweets as we count in fives? [Ans: Place 5 sweets in a group as we count in fives.] • What do you say out as you are counting in fives? [Ans: 5, 10, 15, 20…] • Do you think it will be faster to count in fives compared to counting in twos? [Ans: © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 19 It may be faster to count in fives compared to counting in twos as we will need to say out even fewer numbers.] Recap with learners on how to count in tens, which they have done in the previous lesson. Get learners to arrange the sweets in tens to get ready to count in tens. Invite learners to count in tens as a class. Then, get learners to write down their answers for Question 2d. Ask: • Which is the best way to count? [Ans: Group the sweets in twos, fives or tens. There is no one correct answer. Learners’ preference may vary, depending on which way they are most comfortable with at this stage.] • Which way is the fastest? Why? [Ans: Count in tens as we there are only 3 groups to count. Some learners may find that counting in twos or fives is faster and may lead to less errors. Learners may also find that they are counting in twos to make ten, before they count in tens.] • What observations could be observed in the total number of sweets counted? [Ans: The total is always the same.] Give learners 5 minutes to discuss the guiding questions above. Learners should share with their partners their thoughts on the counting exercise. Lead learners to understand that there are various ways of counting to arrive at the same answer. Learners may also discover that they may be counting in twos or fives to form 10, before they count on in tens. Extend Learners extend the key concepts learnt through discussion and activities. : While there is no best method of counting, there are many ways to count the number of sweets in our jars! Get learners to share with their partners other possible ways of counting the number of sweets in the jar. Select learners to share their thoughts on any other possibilities that they could think of to count the number of sweets. © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 20 Ask: • Are there other ways that we could group the sweets? [Ans: We can group in threes or fours as well. Learners may also choose to group some sweets in tens and some sweets in fives. Other combinations of groups should also be accepted, as long as learners can account for all the sweets.] • How can we organize the sweets as we count? [Ans: We can place the sweets into smaller boxes as we count. We have to make sure the groups are clearly separated.] • Is there any pattern observed in the sweets as the counting takes place? [Ans: We are always counting in groups.] Help learners to understand that they can count easily as long as they account for the sweets in an orderly manner in a consistent pattern. Explore Learners carry out hands-on activities to find out more about counting in groups. This time, they start from a positive number instead of 0. Get learners to explore more methods of counting by first taking out seven sweets. : We shall now take out 7 sweets from the jar first. Then, we will continue to count in twos from there. Observe what Cyrus is saying as he counts in twos. Activity: Using the same jar, each pair will take turns to count and observe before switching roles. Ask: • What number should I start counting from after taking out 7 sweets? [Ans: Start counting from 7.] • What is two more than 7? [Ans: 9.] • Why do you think we need to learn to count in this way? [Ans: Sometimes, we may have already counted a certain number of sweets and we want to count on to find the total. Instead of starting again from zero, we can count on from that number. This will make our counting faster.] As learners carry out their counting, go around and observe that learners have separated the first 7 sweets before continuing to count in twos from 7. Listen out carefully as learners count in twos from 7. They should only be saying out odd numbers. Conjecturing • Textbook Page 8 Big jars of 60 sweets each © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 21 Ask: • What is 2 more than 7? [Ans: 9.] • What is 2 more than 9? [Ans: 11.] • What is 2 more than 57? [Ans: 59.] • What happens when there are less than 2 sweets remaining to count? [Ans: We can still count on in ones.] After each pair of learners have completed their counting, allow learners to write down the number of sweets counted for Question 3(a). : We shall now put all the sweets back and take out 7 sweets again from the jar. Then, we will count in fives this time. Similarly, as learners carry out their counting, go around and observe that learners have separated the first 7 sweets before continuing to count in fives from 7. Listen out carefully as learners count in fives. Ask: • What is 5 more than 7? [Ans: 12.] • What is 5 more than 12? [Ans: 17.] • What is 5 more than 52? [Ans: 57.] • What happens when there are less than 5 sweets remaining to count? [Ans: We can still count on in ones.] After each pair of learners have completed their counting, allow learners to write down the number of sweets counted for Question 3(b). Ask: • Does the total number of sweet in the jar change? [Ans: No.] • Why do you think it is important for us to know how to count from a number like seven? [Ans: When we already counted some sweets at the beginning, we can continue to count on from that number. This will make our counting faster! When we count on from 7, the numbers are different from when we count on from 0!] • What are the advantages of knowing many ways to count? [Ans: By knowing many ways, we can decide which way is the fastest to count in that situation.] Generalising Conjecturing Generalising © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 22 Explain Learners learn key concepts through activities, discussions and teacher’s explanations Take out some link cubes and place them on the table in front of the class for demonstration. : We shall first place ten cubes together to form 10. Take 10 cubes and put them together. Invite learners to count along to ensure that there are ten cubes in a set of 10. Without counting again, put another 10 cubes together and show learners another set of 10. Ask: • Without counting again, how do we know that this is another set of 10? [Ans: The second set of 10 cubes has the same length as the first set.] • How many sets of tens do we have now? [Ans: 2 sets of 10.] Continue by adding now one cube at a time separately and get learners to count along in ones from 20. You may wish to stop at 25. Direct learners to Page 8 of the textbook and observe what Cyrus and Tim are doing to count the sweets on the table. : Cyrus and Tim have some sweets on a table. Let us find out how we can count the total number of sweets! Look at how Cyrus and Tim separate their sweets to count. Demonstrate using the link cubes by separating 10 cubes before putting one cube at a time to represent 1 sweet. Get learners to count along in ones from 10 up to 19. Ask: • Instead of counting in ones from 10, can you think of how else we can count on from 10? [Ans: We can also count on in twos and ones. 12, 14, 16, 18, 19!] • Is there only one way we can count to 19? Which way do you like more? [Ans: There are many ways to do so! We can even count on in fives from 10. 10, 15, 16, 17, 18, 19! It is probably faster for me to count on in twos from 10! Learners may also explain a way that they like the most. As long as they can justify that their way allows them to count faster, they can be encouraged to use their own way.] • Textbook Page 8 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 23 Allow learners 3 minutes to share their answers with their partners. Separate the same 19 cubes. Take 5 cubes and put them together. Invite learners to count along to ensure that there are five cubes in a set of 5. Without counting again, put another 5 cubes together and show learners another set of 5. Get learners to discuss with their partners how they know this is a set of 5. Repeat to form 3 sets of five cubes. Ask: • How should we count in fives? [Ans: 5, 10, 15…] • When do we stop counting in fives? [Ans: When we cannot form any more fives.] • After we stop counting in fives, what do we continue counting in? [Ans: Continue counting in ones/twos.] Count along with learners the remaining 4 cubes to make up 19. (e.g., 16, 17, 18, 19) Evaluate Learners make conclusions about what they have learnt so far. For further practice, assign Worksheet 2 in the workbook to be completed as homework. Learners can consolidate this segment of the discussion as they count in groups. To help them gauge their understanding, ask learners to shade either the happy, sad or neutral face of Coco at the end of each worksheet. Explain Learners learn key concepts through activities, discussions and teacher’s explanations. Number patterns Recap with learners what they have learnt in Grade 1 on number patterns. : Let us recall how we complete number patterns using the drawing of the counters to guide us. Place 3 counters on the table to be shown on the visualizer, according to the arrangement on Page 9 of the textbook. Invite one learner to the visualizer to place the counters according to the pattern. Add 2 counters each time to see how the pattern unfolds. • Textbook Pages 9 - 10 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 24 Ask: • How many more counters should I add to get 5? [Ans: 2 more counters.] • How many more counters should I add to 5 to get the next number? [Ans: 2 more counters.] • How many more counters should I add to 7 to get to the next number? [Ans: 2 more counters.] • What is the number of counters in the missing box? [Ans: 9 counters.] Get learners to raise up their hand to share their observations on the spot to check for understanding. Learners should draw in the pattern and fill in the blank in their textbooks. : Let us now look at a number line to help us complete a number pattern! Instruct learners to pay attention to the numbers on the number line as well as the arrows that are used to count on and back. Draw a number line on the board to help learners check and verify their counting on and back in twos on the number line. Ask learners to observe the red arrows that show the counting on in twos. Then, count out loud together with learners and instruct them to use their fingers to trace along the arrows as the numbers are being read out. Get learners to fill in the answers on Page 9 of the textbook. The answers should read 22, 24, 26, 28, 30. Ask: What do you notice about the numbers on the number line? What kind of numbers are they? [Ans: They are all even numbers! We are counting on in twos from an even number. So, all the numbers will be even.] Invite learners to discuss the above question posed by Coco. Then, select some learners to share their answers. They should be able to identify that since they are counting in twos from an even number, the numbers will always be even. Similarly, for counting back, instruct learners to observe the blue arrows and count out loud with Conjecturing Generalising Generalising © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 25 learners as they use their fingers to trace along the arrows. Get learners to fill in the answers on Page 10 of the textbook. The answers should read 36, 34, 32, 30, 28. Differentiated instruction: For struggling learners, they can refer to the extra marking between 2 numbers. They should fill in the missing numbers on the number line to see how we are skip counting in twos. Explain to these learners that when we skip one number when we count, we are counting in twos. For confident learners, they can also be challenged by counting on beyond 36 and counting back beyond 20. They can choose to extend the number line to include more numbers. : Now, let us try counting in fives using the number line. Let us also observe how using the number line is similar to counting in groups. They are both number patterns! Ask learners to observe the red arrows that show the counting on in fives. Then, count out loud together with learners and instruct them to use their fingers to trace along the arrows as the numbers are being read out. Similarly, for counting back, ask learners to refer to the blue arrows as they count back in fives using their fingers to trace along the arrows while reading out loud. Learners should fill in Ada’s speech bubble of counting in groups of five. Get learners to also fill in the answers for the number patterns. The answers should read 50, 55, 60, 65, 70 and 55, 50, 45, 40, 35 respectively. Differentiated instruction: Struggling learners should refer to the extra markings between 2 numbers. They should fill in the missing numbers on the number line to see how we are skip counting in fives. Explain to these learners that when we skip these numbers when we count, we are counting in fives. For confident learners, they can also be challenged by counting on beyond 70 and counting back beyond 30. They can choose to extend the number line to include more numbers. © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 26 : Using a number line, we can also compare numbers to see which is the greater and smaller number! Ask: • How can we tell which number is greater on the number line? [Ans: Numbers on the right are larger than the numbers on the left.] • How can we tell how much larger one number is compared to another on the number line? [Ans: Check how far apart the numbers are from each other. We can count on or count back to find out!] Using the guiding questions, ask learners to fill in the answers to Ada’s questions on the use of number line for comparison. Lead learners to conclude that they could use the number line to count on or count back to make comparisons. To find out which number is 5 more than 55, we can count on in fives from 55. To find out which number is 5 less than 40, we can count back in fives from 40. Then, get learners to fill in Ada’s 2nd speech bubbles. The answers should read 60 is 5 more than 55 and 35 is 5 less than 40 respectively. Play a video (URL 1.3) in class to help learners familiarise learners with skip counting in twos, fives and tens. URL 1.3 Evaluate Learners make conclusions about what they have learnt so far. : We are going to work out the number pattern together for the 1st question. Guide learners to look at the numbers on the number line and pay attention to the helping arrows on the number line. Ask: • (Tracing the arrow from 60 to 70) How many more than 60 is 70? [Ans: 10 more.] • (Tracing the arrow from 60 to 50) How many less than 60 is 50? [Ans: 10 less.] • Textbook Page 10 URL 1.3: https://qrs.ly/8ge0sko © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 27 • So, how are we counting in this number pattern? [Ans: We are counting in groups of 10.] Allow learners to fill in the answers to Questions 1(a) and 1(b). Invite learners to share their answers as they use the number line to help them get the answers. Learners should share if they are counting on or counting back in each of the questions. Give learners 5 minutes to finish the remaining questions. For further practice, assign Worksheet 3 in the workbook to be completed as homework by the next lesson. To help them gauge their understanding, ask learners to shade either the happy, sad or neutral face of Coco at the end of each worksheet. © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 28 Lesson 4: Place values Lesson Objectives: • Recognise the value of each digit in 2-digit numbers Success criteria: • Learners can recognise the value of each digit in 2-digit numbers Keywords for this lesson: place value, digit, tens place, ones place Prior knowledge: • Count from 0 to 100 in ones, twos, fives and tens • Read and write numerals and number words from 0 to 100 Structure (5E Model) Description / Teaching ideas TWM Skills Resources needed Explore Learners carry out hands-on activities to find out more about place values in 2- digit numbers. Place values : Cyrus and Tim have decided to buy more sweets for their class party as there are not enough sweets for everyone. Let us find out how many sweets they bought! Are you ready? Help learners to think about ways of counting based on earlier lessons. Lead learners to identify which method might be the easiest. : We have already seen how grouping can help us to count the sweets easily. Let us take a moment now to look at some of the ways that we have discussed and compare the methods. Get learners to share with their partners possible ways of counting the sweets to see which way is easier to count and why. Ask: • How did we count the number of sweets in the jar in the previous lesson? [Ans: Group the sweets before counting.] • How many sweets could we place in each group? [Ans: Groups of 2, 5 or 10.] Conjecturing • Textbook Page 11 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 29 • How could we group the sweets if they are spread out? [Ans: Arrange and group the sweets or draw circles around the sweets to be grouped.] • What makes the method of counting easier? [Ans: When we can arrange the sweets in an orderly manner.] Get learners to look at the sweets laid out in the picture on Page 11 of the textbook and share with their partners their method of counting the sweets. Invite a few learners to share with the rest of their classmates how they would count the sweets. : We shall now circle the sweets in the picture together. Take out your pencils and we will circle 10 sweets. Make sure you check that exactly 10 sweets are circled. Show on the visualizer by drawing a circle around 10 sweets in the picture. Count together with learners to ensure that exactly 10 sweets are grouped. Ask: • By circling 10 sweets, what are we doing to count the sweets? [Ans: Counting in groups of 10.] • How many groups of 10 can we circle? [Ans: 1 more group of 10. Then, we will no longer have enough sweets to form another group of 10.] • Now that we have 2 groups of 10, how can we count the remaining sweets? [Ans: Count on in ones/twos.] • How many sweets did the children buy? [Ans: 25.] Distribute link cubes and a place value chart (Handout 1b) to learners. Get learners to use each cube to represent a sweet. Then, they should discuss with their partners how they would place them into the place value chart. Ask: • What do you see in the chart? [Ans: A table labelled tens and ones.] • How many ones form a ten? [Ans: 10 ones.] • How many sets of 10 cubes can we form here? [Ans: 2 sets of 10.] Critiquing Conjecturing Place value chart (Handout 1b) © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 30 • Where do you think these 2 sets of 10 cubes should be placed in the chart? [Ans: In the tens column.] • How many cubes are remaining? [Ans: 5 cubes.] • Where do you think these 5 cubes should be placed in the chart? [Ans: In the ones column.] Invite learners to use the link cubes to help them see that every time 10 cubes are being grouped together, they can combine them together and put them into the tens place. They should be able to see that a total of 2 sets of 10 sweets and 5 individual sweets can be formed. Help learners to understand that they could make their counting easier when the groups are clear and easily recognized. In addition, if there are fewer groups formed, it also reduces the amount of counting required. Next, help learners map the idea of the circling of sweets to the place value chart on Page 11. Get learners to look at the circles drawn to count the sweets again. Ask: • How many circles do you see in the picture? [Ans: There are 2 circles.] • How many sweets are not in a circle? [Ans: 5 sweets.] Guide learners to see that the 2 circles represent the 2 tens and the 5 sweets that are not circled represent the ones in the place value chart. Ask learners to draw the squares in the chart to indicate the number of tens and ones as discussed. The squares they draw should match the link cubes they have placed in their place value charts. Learners should then conclude that Cyrus has 25 sweets. Convincing Explain Learners learn key concepts through activities, discussions : We have now seen that we could count the sweets by using groups of tens very easily. Demonstrate on the visualizer by showing learners the cubes and the place value chart this time. Explain to learners that this chart is called • Textbook Page 12 Place value chart (Handout 1b) © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 31 and teacher’s explanations. the “Place value chart”, as it is a chart that tells us the value of each digit in the number. Each digit also has its own place in the number. Add 1 cube at a time to the ones place of the place value chart. When 10 cubes are counted, move the cubes to the tens place. Add the 5 remaining individual cubes to the ones place. Explain to learners that the 2 groups of tens form the tens in the place value chart, while the 5 cubes that are placed separately in ones form the ones in the place value chart. Ask: • What do you see under the “Tens” column? [Ans: There are 2 groups of 10 cubes.] • What do you see under the “Ones” column? [Ans: There are 5 cubes.] • What is the number written below the “Tens” column? [Ans: 2.] • What is the number written below the “Ones” column? [Ans: 5.] : A place value chart helps us to organize the number into tens and ones which makes it easier for us to count the number. Get learners to say along with you that 2 tens and 5 ones make 25. Activity: Get learners to work in pairs. Distribute some counters and number cards (Handout 1c) to each pair. : Let us start by forming a group of 10 counters first. Then, add 1 counter separately. Ask: • How many groups of 10 have we formed? [Ans: 1 group of 10.] • How many ones are there? [Ans: 1.] • So, how many tens and ones are there? [Ans: 1 ten and 1 one.] Using the number cards, take out the number card 10 and 1, and place them side by side. Show them to the entire class on the board. Next, place the “1” card over the “0” of the “10” card such that it reads “11”. Number cards (Handout 1c) © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 32 : We see that when we put a 10 and a 1 together, we form 11. In their pairs, learners should take turns showing numbers using counters and forming the numbers using the number cards. Learners should practice covering the “0” with the single digit card. Give learners 5 minutes to try. Get some pairs to present their understanding of the method of forming the number using tens and ones. Explain to learners that the counters counted in ones represent the ones place. The counters that are grouped in tens represent the tens place. Referring learners to the place value chart on Page 12 of the textbook, emphasise to learners that the digit 2 is in the tens place. So, 2 tens stand for 20. The digit 5 is in the ones place. So, 5 ones stand for 5. Write the number 25 on the whiteboard. Explain to learners that 25 is a 2-digit number, with the digits 2 and 5. Learners should be clear that the position of each digit is important. Ask learners if the number 52 will be the same as the number 25. Learners should conclude that the digits are in different positions and so they will have different place values. Differentiated instruction: For learners who struggle with the understanding of the place values, they should write down the values before writing the digits. For example, they should write out “20” and “5”, before writing the digits “2” and “5”. Get them to practise saying out the number several times for familiarity with the place values. Activity (optional): Ask learners to take out their mini whiteboards and draw out the place value chart with the columns “Tens” and “Ones”. Show the cube links on the visualiser to display the number of tens and the number of ones for learners to fill in on their individual miniwhiteboards. Learners will then raise up their mini whiteboards for you to verify if the answers written are correct. Mini whiteboards © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 33 Alternatively, you may choose to give out the cube link sets to learners to work on the activity with their partners. Evaluate Learners make conclusions about what they have learnt so far. : We are going to practise writing the digits in the place value chart. Guide learners to count along in tens and ones to fill in the numbers in the place value chart with 7 tens and 8 ones. Instruct learners to attempt the remaining questions on Page 13 individually. You may wish to go around to check and assist learners who are having difficulties answering. Differentiated instruction: For question 2, encourage struggling learners to draw out the place value chart and use squares to represent the number. You may also wish to provide a place value chart (Handout 1b) to them to show the number. They can then make use of the place value chart to answer the questions. For further practice, assign Worksheet 4 in the workbook to be completed in class. Go through the answers when learners are done. To help them gauge their understanding, ask learners to shade either the happy, sad or neutral face of Coco at the end of each worksheet. • Textbook Page 13 Evaluate Learners make conclusions about what they have learnt so far. To recap with learners what they have learnt in this chapter, go through the Word Wall on Page 14 with them. : In this chapter, we have learnt how to identify, read, write numbers and their number words from 0 to 100. We have also learnt how to count on and count back in groups of twos, fives and tens. Finally, we have learnt how to use the place values chart to show 2-digit numbers. Let us see how much we understood from this chapter! Are you ready? Give learners some time to individually look at the questions on the reflection page. • Textbook Page 14 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 34 You may ask these guiding questions to help learners make their conclusions about Question 1: • What is the number of apples in each bag on the table? • How many apples are not in the bag? • How many tens are there? • How many ones are there? • Can you write the number on a place value chart? Draw squares to show. • Did Cyrus and Vera write the same numbers? What is similar and different about them? You may ask these guiding questions to help learners make their conclusions about Question 2: • How many muffins are there in each box that Cyrus is holding? • How should we count on to find the total number of muffins? • How many biscuits are there in each box that Tim is holding? • How should we count on to find the total number of biscuits? • How many children are there in the class? Are there enough muffins and biscuits? • Can you count on or count back to find out how many more muffins and biscuits are needed? You may wish to use a number line to help you. Evaluate Learners make conclusions about what they have learnt so far. Assign learners Consolidation worksheet and You have a mission! to be done in class or at home. • Workbook Pages 9 - 12 © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd : Teachers say : Teachers or learners ask : Hands-on activity 35 What’s next for this chapter? Grade 2 Chapter 1 Numbers to 100 • Estimate numbers up to 100 • Count, read and write numerals and number words from 0 to 100 • Count on and count back in ones, twos, fives and tens • Identify and complete number patterns • Recognise the value of each digit in 2-digit numbers Grade 2 Chapter 2 More about numbers to 100 • Compare and order numbers to 100 • Round numbers to the nearest 10 • Recognise even and odd numbers • Recognise ordinal numbers Grade 2 Chapter 5 Addition and Subtraction • Find number pairs to 20 and to multiples of ten • Break down 2-digit numbers into tens and ones • Estimate, add and subtract 2-digit numbers • State the relationship between addition and subtraction Grade 2 Chapter 8 Multiplication • Multiply by repeated addition • Multiply by 1, 2, 5 and 10 • Recite the 1, 2, 5 and 10 times table Grade 2 Chapter 10 Division • Divide by repeated subtraction • Divide by sharing and grouping • Explain what a remainder is The learning indicators in this chapter serve as a foundation for these following chapters in higher grades. © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd 36 Reflection for teachers Answer the questions below to reflect on your lesson. What did the learners learn today? Were the learning objectives and success criteria realistic? Were there any misconceptions? What was the learning atmosphere like? Circle. Learners love the lesson Learners are interested Learners find the lesson boring Learners are confused Learners are struggling with the concepts What two things went really well? What two things would have improved the lesson? What changes did I make from my plan and why? If I taught this lesson again, what would I change? What will I teach next based on the learners’ understanding of this lesson? © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd 37 Printables Handout 1a: Ten-frames templates © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd 38 Handout 1b: Place value chart Tens Ones © 2022 Alston Education Pte Ltd

Active Maths Teacher’s Guide: Stage 2 Chapter 1 © 2022 Alston Education Pte Ltd 39 Handout 1c: Number cards 1 2 4 7 3 20 5 8 9 6 10 30 © 2022 Alston Education Pte Ltd