In fourth grade, the main focus of instruction should be on three key areas: mastering multi-digit multiplication and division with multi-digit dividends, understanding equivalent fractions, adding and subtracting fractions with the same denominators, and multiplying fractions by whole numbers, and recognizing properties of geometric shapes like parallel and perpendicular sides, specific angles, and symmetry. Students extend their comprehension of place value up to 1,000,000, grasping the relative magnitudes of numbers in different place positions. As they work on multiplying multi-digit whole numbers, students use their knowledge of different multiplication models like equal-sized groups, arrays, and area models, along with concepts like place value and the distributive property, to create, talk about, and implement efficient, precise, and adaptable strategies for finding products. Students gain knowledge of how fractions are equal to each other and how to perform operations with fractions. They understand that it is possible for two fractions to be equal (e.g., 15/9 = 5/3), and they create techniques for creating and identifying equivalent fractions.

During third grade, the main focus of teaching time should be on four key areas: (1) building comprehension of multiplication and division, as well as tactics for multiplication and division up to 100; (2) building comprehension of fractions, specifically unit fractions (fractions with a numerator of 1); (3) building comprehension of the patterns in rectangular arrays and area; and (4) describing and examining two-dimensional shapes. Students gain insight into the concepts of multiplication and division of whole numbers by participating in tasks that focus on equal-sized groups, arrays, and area models. In these scenarios, multiplication involves identifying a mystery product, while division involves determining a mystery factor. Students can understand the connection between multiplication and division by examining different solution methods. Students start learning about fractions by first focusing on unit fractions. Students can utilize fractions to signify numbers that are equivalent to, smaller than, and larger than one. They address issues by analyzing fractions through visual models and strategies that identify equal numerators or denominators. Students identify area as a characteristic of two-dimensional areas. Students connect area to multiplication by breaking rectangles down into arrays of squares, and they support using multiplication to find the area of a rectangle. Students talk about, examine, and contrast characteristics of two-dimensional shapes. Shapes are compared and categorized based on their sides and angles, and then linked to shape definitions. Students connect their fraction work to geometry by representing the area of a portion of a shape as a unit fraction of the entire shape.

During Kindergarten, the main focus of instructional time should be on two important areas: (1) comparing and representing whole numbers using sets of objects; (2) explaining shapes and space. Kindergarten should focus more on teaching numbers than other subjects with additional learning time. Students utilize numbers, including written numerals, to symbolize amounts and address quantitative issues, like tallying objects in a group; tallying out a specified amount of objects; contrasting sets or numerals; and simulating basic combining and separating scenarios with sets of objects, or later on with equations like 5 + 2 = 7 and 7 - 2 = 5. Kindergarten students can be shown addition and subtraction equations, and it is recommended that they practice writing equations, although it is not mandatory. Students select, merge, and utilize efficient methods for solving mathematical problems, such as promptly identifying the quantities of small groups of items, counting and generating sets of specific sizes, totaling objects in merged sets, or determining the remaining objects in a set after some are removed.

When we refer to things that will happen in the future, we often use something known as the Simple Future tense. When we talk or write about plans, expectations, schedules, and predictions, we often use the Simple Future tense. The Simple Future tense helps convey an action or state that will begin and end in the future. We use the Simple Future tense in declarative sentences to state that something is scheduled or planned. It communicates willingness and expresses an expectation, a prediction, or a guess. This highly practical ebook contains detailed explanations on how the Simple Future is formed, when to use it, and there are plenty of activities in the end for your students to practice and master it. Anwer key is also included.

When we describe an action in the Future Perfect Continuous tense, we are projecting ourselves forward in time and looking back at the duration of that activity. The activity will have begun sometime in the past, present, or in the future, and is expected to continue in the future. For example: “In November, I will have been working at my company for three years.” There are similarities and differences between the Future Continuous and the Future Perfect Continuous tense, which might cause confusion. The main difference is that we use the Future Continuous to predict the future, while we use the Future Perfect Continuous to talk about an ongoing action that will finish before another. This practical ebook will explain how the Future Perfect Continuous is formed, when it is used, and it will also provide plenty of examples and exercises. The relevant answer key is provided at the end as well.

The Future Perfect is a verb tense used for actions that will be completed before some other point in the future. For example: “The parade will have ended by the time Chester gets out of bed. At eight o’ clock I will have left.” The Future Perfect tense is used for talking about an action that will be completed between now and some point in the future. On the other hand, the Future Perfect tense is only for actions that will be complete before a specified point in the future. In other words, the action you’re talking about must have a deadline. If you don’t mention a deadline, use the Simple Future tense instead of the Future Perfect tense. In this ebook, you will find detailed explanations on how to form the Future Perfect tense, when it should be used, and many exercises for your students to practice. There is also the relevant answer key at the end.

The Future Continuous tense is a verb tense that shows an action happening over a period of time in the future. “I will be driving all night” is an example of the Future Continuous tense, as it indicates an action continuing over a specific future period of time. Compare it to this sentence, written in the Simple Future tense: “I will drive.” Although this example indicates an intention to drive in the future, it does not refer to a continuous action over a specific period of time in the future. The Future Continuous tense can be confusing because it sometimes seems interchangeable with other future tenses. This ebook sheds light to all the uses of the Future Continuous tense. It describes how it is formed, when it is used, and has ample practice for students, with plenty of exercises and examples. The relevant answer key to the activities is also included.

This is the first book of the Practical English Grammar series, on the Simple Present Tense. Understanding and using the Simple Present correctly is essential for clear and effective communication in English. The Simple Present tense is one of the most fundamental tenses in English grammar. It is primarily used to describe habitual actions, general truths, and fixed arrangements. This book contains all the uses of the Simple Present tense, along with examples. They are followed by formation rules, and also some activities. You can use these activities in your class to teach or reinforce the use of the Simple Present Tense. It is one of the most widely used tenses of the English language, and it is very easy to use and to teach. Even younger students can easily master it and use it in no time. We hope you enjoy teaching the Simple Present Tense to your students.

The Present Perfect Continuous tense is a unique case and poses certain difficulties for English language learners. It is unique in the sense that it has an easy aspect and a difficult aspect. The difficult aspect is its formation. It needs the auxiliary verb ‘to have’ in its perfect form plus the main verb in its continuous form. This is too complicated for most students, and they usually struggle to get it right. On the other hand, the easy aspect is its usage. It is used in very specific situations that connect the past with the present, and almost always with specific time expressions like ‘for’ and ‘since’. Hence it is virtually impossible to mix it up with another tense. This ebook offers clear explanations about both the formation and the usage of the Present Perfect Continuous tense, along with examples. Students who master them can move on to the activities at the end of the book.

This is the second ebook from the highly successful Practical English Grammar series. The Present Continuous Tense is probably the most commonly used tense in English. It is used to describe an action that is happening now, at the moment of speaking, and it is therefore one of the first tenses that young students learn, as it is very easy to understand. It is also called Present Progressive. The first part of the ebook focuses on theory: the correct formation and usage of the Present Continuous tense, followed by examples. The second part of the ebook contains exercises that will help your students practise and consolidate their knowledge of the tense. Finally, there is the key to the activities, which makes the book ideal for both classroom use and self study as well. We hope that both you and your students will enjoy teaching and learning about the Present Continuous tense.

This consice ebook is about the Present Perfect tense. It is one of the tenses that cause most difficulties to English language learners, both because of its formation and because of its usage. The formation is tricky because it involves a modal verb and the past participle of the main verb. The usage is not as clearcut as other tenses in English, since it refers to an action that has started in the past, but its effects are still visible in the present. Hence, many students consider the Present Perfect tense to be a past tense and confuse it with the Simple Past tense. However, as its name suggests, the Present Perfect is a present tense. Read on to find out how this tense is formed and when it is used. At the end of the book there are some very useful practice activities to consolidate your students’ knowledge, and the relevant answer key.

This ebook provides essential information about the Past Perfect Tense, its formation and usage. We use the past perfect to talk about the past, but not just any situation in the past; we use the Past Perfect when we’re talking about two events that happened in the past and when one event happened before the other event. So it helps you to order the actions in your story. Think about the Past Perfect as helping us to create a timeline. If your students have mastered the Present Perfect tense as they should, it will be easy for them to form the Past Perfect as well. We create the Past Perfect by using the verb ‘had’ the auxiliary verb ‘had’, followed by our main verb in past participle form. Students usually confuse the Past Perfect and use the Simple Past instead. Hopefully, this ebook will help them clarify these two distinctive tenses.

The Past Continuous Tense is essential in communicating in English. It provides clarity and depth to descriptions of past events. It establishes the background, highlights the atmosphere, and illustrates interrupted actions. This tense is also useful for describing parallel actions, and multiple events that happen simultaneously. In narratives, it establishes the background, adds nuance to storytelling, and allows speakers and writers to convey the progression and interaction of past actions with greater precision and detail. Overall, the past continuous tense enriches communication in English. This practical ebook contains all the essential information on the Past Continuous Tense. You will find details about its formation and all the various cases when it is used. Finally, there are 20 exercises, so that your students will practise and familiarize themselves with the Past Continuous Tense, and of course the relevant answer key to the activities. Enjoy teaching the Past Continuous Tense to your students!

We use the Past Perfect Continuous tense, also referred to as the Past Perfect Progressive tense, to describe an action that started some time in the past and continued until another point in the past. In our daily lives, we frequently employ the past perfect continuous tense. However, there are instances when we use it improperly. In essence, this tense conveys the “past in the past.” You will thus learn about the composition and application of the Past Perfect Continuous tense from this page. It will make learning about it easier and more detailed. You will then be given questions to answer in order to assess your comprehension of this tense. This ebook contains all the information you need about the Past Perfect Continuous tense, including usage, formation, examples, and meaning. There are also extensive exercises and the relevant answer key in the end. We hope you enjoy teaching it to your students!

Grade 2 Common Core Math Standards Overview With forty-one states adopting the common core curriculum, there is a very good chance your child is following the common core state standards. There are four main topics covered in the second-grade common core math standards: Operations & Algebraic Thinking - Students learn to represent and solve problems involving addition and subtraction, add and subtract within 20, and work with equal groups of objects to gain foundations for multiplication. Numbers & Operation in Base Ten - Students learn to understand place value, and use place value understanding and properties of operations to add and subtract. Measurement & Data - Students learn to measure and estimate lengths in standard units, relate addition and subtraction to length, and work with time and money. Geometry - Students learn to reason with shapes and their attributes. If you want to help your students boost their math scores, this ebook will give you some practical activities.

43 states have embraced a new set of academic standards called the Common Core State Standards. The purpose of the standards is to increase academic competitiveness in the US, while also preparing pupils for careers and college. These serve as benchmarks for what knowledge and skills in math and language arts kids should possess from kindergarten through their senior year of high school. Many of the benchmarks are included in the Common Core at every grade level, but there are certain commonalities. Language arts standards emphasize using evidence to support arguments. Pupils will write more viewpoints and fewer personal stories in their writing. They will be required to read more nonfiction as well. The arithmetic standards cover fewer topics in more detail. The idea behind the Common Core curriculum, also referred to as Common Core State Standards, was straightforward: if all kids were held to the same high academic standards, achievement and college preparation would increase. This ebook will give you a practical description of the Common Core and the basic concepts behind it.

A solid command of verb tenses is necessary for effective communication in English. However, why do verb tenses matter so much in English? One cannot accurately convey their meaning if the past, present, and future are not used appropriately. The verb’s indicated time of action is indicated by the tense. The primary tense in English for discussing the past is the simple past tense. Although its meaning is fairly clear-cut and easy, language learners may find it challenging to form. The primary challenge is the abundance of irregular verbs in the Simple Past Tense. All of these verbs must be learnt by heart by the students. Use this ebook to teach your students about the Simple Past Tense. You can teach them how the tense is formed correctly, when it is used, and most importantly, how not to confuse it with other past tenses of the English language. Happy teaching!

The Common Core Standards don’t give equal emphasis to every topic within a grade level. Instead, some concepts require more focus due to their depth, the time needed to master them, their importance for future math learning, or their relevance to college and career readiness. Students need to dedicate more time to these areas to meet the Mathematical Practice Standards. In Grade 1, teaching should concentrate mainly on these four key areas: (1) developing strategies for addition and subtraction within 20; (2) understanding place value and the relationships between whole numbers, including grouping by tens and ones; (3) developing skills in linear measurement and using length units to measure; and (4) reasoning about the properties of geometric shapes and how they can be composed and decomposed. This worksheet provides plenty of practice on these topics through brief and straightforward activities for your classes. We hope you enjoy them with your students!

Bridges are among the most impressive human constructions. Marvels of engineering and architecture, they take advantage of the latest technology of each era to provide solutions for the movement of people and goods. Some suspended in the air and others on the water, each one is unique in its category and causes many photo clicks. But they are not only tourist sights; bridges connect pieces of land, connect countries and civilizations, they allow the faster commuting of people and goods, so their usefulness is immesurable. We have singled out and present in this ebook the longest and biggest bridges in the world. Take some time with your students to explore these bridges in all their colossal beauty, and learn about their history, construction, importance etc. At the end, you will find as usual 20 exercises to practice your knowledge, and of course the relevant answer key. We believe you and your students will really enjoy this!

Caves are empty spaces inside the rocks, they have an entrance that allows communication with the surface and dimensions such that human entry is possible. Each cave can be completely or partially filled with sediments, that is, with materials brought there mainly by the erosion of rocks, by water or ice. When caves present a complex development – ​​such as a combination of vertical shafts and horizontal chambers – they constitute cave systems. The shape and size of caves varies greatly due to a large number of factors related to the structure and composition of the rock, the geometry of the cracks it presents, the relief of the area in which it is located, the hydrological conditions and many other factors of lesser importance. What you will find in this ebook Information about the largest caves in the world Follow up questions to check students’ knowledge Answer key