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Mathematics Belief Statement We believe mathematics is a global language that allows for all attributes of the learner profile to be developed. We believe that in a mathematical learning community, students develop, construct and communicate their understanding of mathematical concepts. Students are given time to explore and develop their understanding in a stimulating and accepting environment. Through being open-minded and using alternative models of thinking they develop efficient strategies for finding solutions. They develop skills and incorporate the appropriate use of technology through a concept-based curriculum driven by inquiry. Planning, teaching and assessing in mathematics should include engaging activities, discussions and problem solving in authentic settings. Making connections within and between strands is important for developing student’s mathematical understanding. PYP Mathematics Phases The PYP mathematics scope and sequence is based on the understanding that students construct meaning about mathematics concepts in a more developmental way rather than in fixed age bands. - Each student is a unique individual with different life experiences and no two learning pathways are the same. - Students within the same age group will have different proficiency levels and needs; therefore, teachers should consider a range of phases when planning mathematics learning experiences for a class. - Students are likely to display understanding and skills from more than one of the phases at a time. - A student may moveonto the next phase without attaining all the outcomes of a particular phase. A student does not need to be in the same phase for each strand. - VIS will use and adapt the PYP scope and sequences according to our needs. VIS will frame our mathematics scope and sequence document around the conceptual understanding outlined in the PYP document, but develop other aspects (for example, indicators and benchmarks) differently. EY 3 uses language: counting sorts items to form sets matches pairs of sets up to 5 objects EY4 use more and less; as many as use language: more, less counts to 10 matches numerals (1,2,3,4,5) to sets creates sets with one to 5 objects, not in counting order puts sets in order to show relationship 'one less than' and 'one more than' creates a matching set with 1 to 10 objects can count by 1's to 10 beginning with any number less than 10 knows what is one fewer or more than a number to 5 Counts to 10counts by 1's to 10 beginning with any number less than 10 matches numerals (1,2,3,4,5) to setsuses fraction name 'half' in real-life situations Prep use more less, first, second use language: more, less, first, second counts to 30 matches number words (one, two, three) to sets, not in counting order creates sets with one to 20 objects, not in counting order compares sets to find which has more or less states 'one' for both written one and numeral '1'; similarly up to 10 understands zero means noneidentifies the number that is one more, two more, one less, two less than a given number to 20 creates a matching set up to 20 objects rearranges a set and still understand there is the same number of objects recognizes groups of zero to five objects without countingcan count by 1's to 20 beginning with any number less than 20 knows what is one fewer or more than a number to 20 compares sets to find which has more or lesscreates a matching set up to 20 objects recognises subsets in a set of up to 10, for example a set of three is made up of a subset of one and a subset of two count to 30can count by 1's to 20 beginning with any number less than 20 matches number names (one, two, three) to sets with 1 to 10 objects, not in counting order able to say 'one' for both written one and numeral '1'; similarly up to 10 uses ordinal numbers to describe the position of things in a sequence to 10 use cardinal numbers to 'fifth' understands that '10' means one 'tens' and zero 'ones' create sets of 10 objects estimates the number of objects in a set of 6 -20 counts by 1's to 20 beginning with any number less than 20 matches number names (one, two, three) to sets of 1 to 10 objects, not in counting order interprets (retell the action and sequence) and solve combining and partitioning of sets problems creates own 'story' to match a given situation where sets are combined and partitioned uses fraction name half, quarter in real life situations uses objects (paper, ribbon) to model half and quarter uses fraction 1/2 and 1/4 in real life situations Grade 1 can count by 1's to 100 beginning with any number less than 100 knows 1, 2 and 10 fewer or more than a number to 100 recognises subsets in a set of up to 20, for example a set of three is mad up of a subset of one and a subset of two can count by 1's to 100 beginning with any number less than 100 use ordinal numbers to describe the position of things in a sequence to 100 use cardinal numbers to 20 understands what each digit in 2 digit number means up to 99 use manipulatives to model numbers up to 105 estimates the number of objects in a set to 50 counts by 1's to 105 beginning with any number less than 100 reads, writes and orders numbers to 105 in real-life situations counts by 1s, 2s, 5s, 10s, to 100 forward and backwards demonstrates fluency with addition and subtraction facts to 10 knows and applies strategies to solve addition and subtraction facts to 10 demonstrates fluency in two addend combinations to 10 finds more than one combination for two addends for a number up to 10 (ie - 7 is 4 and 3 and it's 5 and 2) knows +0's, +1s, -0's, and -1's facts to 18 demonstrates fluency in doubles to 20 (1+1, 2+2, 3+3) uses language: add, take away, plus, minus reads, writes and models addition and subtraction sentences to 20 interprets (retell the action and sequence) and solves addition and subtraction story problems creates own 'story' to tell about given number sentence solves addition and subtraction story problems with manipulatives, pictures and numbers combines 2 numbers to 20 by counting on from one quantity solves multiplication and division story problems with manipulatives and/or picturesuses language: half, equal, fourth, quarter uses objects, manipulatives or pictures to model simple fractions uses fractions 1/2, 1/3, 2/3, 1/4, 2/4, 3/4 in real life situations understands that fraction must have equal parts Grade 2 understands the value of each digit in a 3 digit number up to 999 uses manipulatives or diagrams to model numbers up 999 estimates the number of objects in a set to 100 and beyond counts to 100 by 10's starting at any point from 1 to 9 reads, writes, orders and compares numbers to 1000 in real life situations counts by 2s, 3s, 4s, 5s, 10s to 100, forwards and backwards demonstrates fluency with addition and subtraction facts to 20 knows and applies strategies to solve addition and subtraction facts to 20 demonstrates fluency in 2s, 5s, and 10 multiplication table adds columns of single digit numbers using one efficient strategy uses language: add, take away, plus, minus, sum difference reads, writes and models addition and subtraction problems to 100, without and with regrouping interprets and solves addition and subtraction story problems with number sentences creates many different 'stories' to match a given addition and subtraction sentence demonstrates at least one efficient paper/pencil method for adding any two double-digit numbers (more efficient than counting on by 1s) writes an equation to represent an addition or subtraction situation determines the difference between 2 numbers up to 99 explains the order in which numbers are added does not affect the sum but may affect the difference solves multiplication and division story problems with manipulatives, pictures and/or numbers creates many different 'stories' to match a given addition, subtraction and multiplication sentence models division situations using 'share equally into groups'models multiplication situations using 'groups of' selects and explains an appropriate method of solving a problem uses language, equal, numerator, denominator understand, model, read, write, order, compare wholes, halves, quarters, fifths finds 1/2 of a set of objects models equivalence to one whole adds and subtracts fractions with same denominator using models and pictures Grade 3 understands the value of each digit in a number up to 99,999 models numbers to 99,999 using base 10 value system estimates the number of objects in set to 1000 and beyond counts by 20s to 1000 starting at any multiple of 20 reads, writes, orders and compares numbers to 99,999 in real life situations counts by 20s to 1000 starting at any multiple of 20 reads and models decimal fractions to tenths demonstrates fluency with multiplication facts 1, 2, 3, 4, 5, 9, 10 knows and applies strategies to solve multiplication and division facts to 20 adds columns of single digit numbers using a variety of strategies uses language add, addition, plus, minus, difference, subtraction, multiplication, product, division reads, writes and models addition and subtraction problems to 1000 demonstrates more than one efficient paper and pencil strategies to add and subtract numbers models multiplication and division facts to 10 using pictures, manipulatives, arrays and sentences creates many different 'stories' to match a number sentence or array models division situations using 'shared equally' and arrays models multiplication using 'groups of' and 'arrays' uses the commutative property (3x5 = 5x3) and associative property 2x(5x4)=2x(5x4) to simplify calculations demonstrates and explains an efficient method of solving a problem solves addition, subtraction and multiplication problems with number sentences identifies the operation needed for solving a problem use language: numerator, denominator, equivalent, mixed number understands, models, reads, writes, orders, compares fractions to hundredths orders fractions with like denominators models equivalency of fractions 2/4 = 1/2 reads, writes and models mixed numbers adds and subtracts fractions with same denominator Grade 4 understands the value of each digit in a number up to 1 million models numbers to 1 million using base 10 value system reads, writes, orders, compares numbers to 1,000,000, particularly with Lao money reads, writes, compares, orders decimal fractions to tenths use diagrams to model integers in real-life situations (lifts/elevators, thermometers) model percentages using fractions, manipulatives and pictures demonstrates fluency with multiplication and division facts to 10 demonstrates strategies to multiply and divide 3 digit numbers by 1 digit numbers creates and solves double digit multiplication problem demonstrates and explains the commutative property (3x5 = 5x3) and associative property 2x(5x4)=2x(5x4) to simplify calculations demonstrates and explains many methods of solving a problem, choosing the most efficient solves addition, subtraction, multiplication, division problems efficiently choosing from a variety of strategies identifies and demonstrates the operation needed for solving a problem identifies fractional parts of a group/set orders fractions with like and unlike denominators finds lowest common denominator to model equivalency using fraction pieces reads, writes, models and compares mixed numbers and improper fractions reads, writes and models addition and subtraction of fractions with related denominators acts out division of fractions using story situations compares, simplifies and orders fractions simplifies fractions to find equivalency converts mixed numbers to improper fractions and vice versa models addition, subtraction, multiplication and division of fractions creates own stories to act out division and multiplication of fractions Grade 5 explains the value of any digit beyond a million reads, writes, orders, compares numbers beyond a million reads, writes, compares, orders decimal fractions to hundredths use number lines to find integers interchanges fractions, decimals, percents use number line to model and name integers demonstrates fluency in all basic facts (x, +, -, division) uses language: factor, multiple, product, quotient, prime number, composite number
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