ASSESSING HOW DO WE KNOW WHAT STUDENTS KNOW AND HAVE LEARNED. Number- phase 3 • Learners will develop the understanding that fractions and decimals are ways of representing whole-part relationships and will demonstrate this understanding by modeling equivalent fractions and decimal fractions to hundredths or beyond. • Learners will be able to model, read, write, compare and order fractions, and use them in real-life situations. • Learners will have automatic recall of addition, subtraction, multiplication and division facts. • Learners will select, use and describe a range of strategies to solve problems involving addition, subtraction, multiplication and division, using estimation strategies to check the reasonableness of their answers Conceptual understandings • • • The base 10 place value system can be extended to represent magnitude. Fractions and decimals are ways of representing whole-part relationships. The operations of addition, subtraction, multiplication and division are related to each IBO Learning outcomes/ Objectives When constructing meaning learners: • Model numbers to thousands or •beyond using the base 10 place value system • • Model equivalent fractions use the language of fractions, for example, numerator, denominator • model decimal fractions to hundredths or beyond model multiplication and division of whole numbers • use the language of multiplication and division, for example, factor, multiple, Learning outcomes By the end of PYP year 2 students would be able to: Place Value • Represent and describe whole numbers to thousands, pictorially and symbolically. • Compare and order whole numbers to thousands. • Write whole numbers in standard, expanded and word forms. • Count within 1000; skip-count by 5’s, 10’s and 100’s • Read and write numbers to 1000 using base-ten numerals, number names and expanded form • Compare two three-digit numbers based on meanings of the hundreds, tens and ones digits, using >, =, 𝑎𝑛𝑑 < symbols to record the results of comparisons. • Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. other and are used to process information to solve problems. • Even complex operations can be modeled in a variety of ways, for example, an algorithm is a way to represent an operation. product, quotient, prime numbers, composite number • model addition and subtraction of fractions with related denominators*** • model addition and subtraction of decimals. When transferring meaning into symbols learners: • read, write, compare and order whole numbers up to thousands or beyond • Patterns and sequences occur in everyday situations. • • Patterns repeat and grow. develop strategies for memorizing addition, subtraction, multiplication and division number facts • • Patterns can be represented using numbers and other symbols. read, write, compare and order fractions • read and write equivalent fractions • read, write, compare and order fractions to hundredths or beyond • describe mental and written strategies for multiplication and division. When applying with understanding learners: • • Whole numbers exhibit patterns and relationships that can be observed and described. Functions are relationships or rules that uniquely • Add up to four two-digit numbers using strategies based on place value and properties of operations. • Add and subtract within 100, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Add and Subtract Whole Numbers • Demonstrate an understanding of addition of numbers and their corresponding subtractions (4- and 5-digit numerals), concretely, pictorially, and symbolically, by using personal strategies and using the standard algorithms. • Relate addition and subtraction: Use the inverse relationship between addition and subtraction to solve problems. • Use mental Math strategies to find sums and differences. • Round whole numbers through thousands. • Mental Math: Estimate sums and differences. • Mentally add 10 or 100 to a given number 100 - 900, and mentally subtract 10 or 100 from a given number 100 - 900. Explain why addition and subtraction strategies work, using place value and the properties of operations (Note: Explanations may be supported by drawings or objects.) Operations and Algebraic Thinking • Use addition and subtraction within 100 to solve one-step and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem. • Fluently add and subtract within 20 using mental strategies. • Determine whether a group of objects (up to 20) has an odd or even number of members, e.g. by paring objects or counting them by 2’s; write an equation to express an even number as a sum of two equal addends. associate members of one set with members of another set. • Patterns can often be generalized using algebraic expressions, equations or functions. • use whole numbers up to thousands or beyond in reallife situations • • use fast recall of multiplication and division number facts in real-life situations • • • use decimal fractions in reallife situations use mental and written strategies for multiplication and division in real-life situations • select an efficient method for solving a problem, for example, mental estimation, mental or written strategies, or by using a calculator • use strategies to evaluate the reasonableness of answers • add and subtract fractions with related denominators in real-life situations • add and subtract decimals in real-life situations, including money • estimate sum, difference, product and quotient in reallife situations, including fractions and decimals. • • • Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Select the appropriate equation to solve addition and subtraction problems Create their own addition and subtraction equations to tell a story Identify Roman numerals Connect between all four operation Solve four operations in real life. Multiplication and Division • • • • • • • Learn 2, 3,4,5,6 &10 times table Create multiplication and division equations to tell a story Apply the concept of multiplication and division using sets and groups. Model multiplication and division of whole numbers Use the language of multiplication and division, for example, factor, multiple, product, quotient, prime numbers, composite number Describe mental and written strategies for multiplication and division. Use fast recall of multiplication and division number facts in real-life situations Division of whole number by single digit. Model multiplication and division of whole numbers. • • • Fractions • Use fraction names "half", "third", "quarter", "sixth" and “eighth” to describe part and whole relationships. • Use the language of fractions, for example, numerator, denominator. • Read, write, compare and order fractions. • Read and write equivalent fractions. Patterns and functions: • • • • • understand that patterns can be found in everyday situations, for example, sounds, actions, objects, nature. understand that patterns can be found in numbers, for example, odd and even numbers, skip counting. understand that patterns can be analysed and rules identified. understand that multiplication is repeated addition and that division is repeated subtraction. understand the inverse relationship between addition and subtraction. Patterns: • • • • • • • • • • • • • • Identify patterns can be analyzed and rules identified. Identify that patterns can be found in numbers, for example, odd and even numbers, skip counting. Extend and create patterns in numbers, for example, odd and even numbers, skip counting. Identify multiplication is repeated addition and that division is repeated subtraction and is a pattern. Use equations to find unknown quantities (3 + = 20). Identify and find the missing addend in fact family. Identify and find the pattern in one and zero (1x2=2, 1x3=3). Find pattern in place value chart. Find pattern in timetable (2,5,10 and 11). Select appropriate methods for representing patterns, for example using words, symbols and tables. Describe the rule for a pattern in a variety of ways. Represent rules for patterns using words, symbols and tables. Identify a sequence of operations relating one set of numbers to another set. Use number patterns to make predictions and solve problems. Function: • • Represent the rule of a pattern by using a function. Use functions to solve problems.