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Intermediate Math Scope & Sequence.Pdf Grade Four Grade Five Grade Six Grade Seven Grade Eight number concepts to 10 000 number concepts to 1 000 000 number concepts: small to large numbers (thousandths to billions) ◦ counting: ◦ counting: ◦ place value from thousandths to ▪ multiples ◦ multiples billions, operations with ▪ flexible counting strategies ◦ flexible counting strategies thousandths to billions ▪ whole number benchmarks ◦ whole number benchmarks ◦ numbers used in science, medicine, ◦ Numbers to 10 000 can be arranged ◦ Numbers to 1 000 000 can be technology, and media and recognized: arranged and recognized: ◦ compare, order, estimate ▪ comparing and ordering ◦ comparing and ordering numbers numbers ◦ estimating large quantities ▪ estimating large quantities ◦ place value: ◦ place value: ◦ 100 000s, 10 000s, 1000s, 100s, ▪ 1000s, 100s, 10s, and 1s 10s, and 1s ▪ understanding the ◦ understanding the relationship relationship between digit between digit places and their places and their value, to 10 value, to 1 000 000 000 ◦ First Peoples use unique counting systems (e.g., Tsimshian use of three counting systems, for animals, people and things; Tlingit counting for the naming of numbers e.g., 10 = two hands, 20 = one person) Decimals: to hundredths & addition and Decimals: to thousandths and addition and subtraction of decimals to hundredths subtraction of decimals to thousandths ◦ Fractions and decimals are ◦ estimating decimal sums and numbers that represent an amount differences or quantity. ◦ using visual models such as base ◦ Fractions and decimals can 10 blocks, place-value mats, grid represent parts of a region, set, or paper, and number lines linear model. ◦ using addition and subtraction in ◦ Fractional parts and decimals are real-life contexts and problem- equal shares or equal-sized based situations portions of a whole or unit. ◦ whole-class number talks ◦ understanding the relationship between fractions and decimals ◦ estimating decimal sums and differences ◦ using visual models, such as base 10 blocks, place-value mats, grid paper, and number lines ◦ using addition and subtraction in real-life contexts and problem- based situations ◦ whole-class number talks Fractions: Comparing and ordering Fractions: Equivalent fractions and Fractions: Fractions: Fractions: fractions whole-number, fraction, and decimal ◦ improper fractions and mixed ◦ relationships between decimals, ◦ percents less than 1 and greater benchmarks numbers fractions, ratios, and percents than 100 (decimal and fractional ◦ introduction to ratios percents) ◦ whole-number percents and ◦ numerical proportional reasoning percentage discounts (rates, ratio, proportions, and percent) ◦ operations with fractions (addition, subtraction, multiplication, division, and order of operations) ◦ comparing and ordering of ◦ Two equivalent fractions are two ◦ using benchmarks, number line, ◦ conversions, equivalency, and ◦ A worker’s salary increased 122% fractions with common ways to represent the same amount and common denominators to terminating versus repeating in three years. If her salary is now denominators (having the same whole). compare and order, including decimals, place value, and $93,940, what was it originally? ◦ estimating fractions with ◦ comparing and ordering of whole numbers benchmarks ◦ What is ½% of 1 billion? benchmarks (e.g., zero, half, fractions and decimals ◦ using pattern blocks, Cuisenaire ◦ comparing and ordering decimals ◦ The population of Vancouver whole) ◦ addition and subtraction of Rods, fraction strips, fraction and fractions using the number line increased by 3.25%. What is the ◦ using concrete and visual models decimals to thousandths circles, grids ◦ ½ = 0.5 = 50% = 50:100 population if it was approximately ◦ equal partitioning ◦ estimating decimal sums and ◦ birchbark biting ◦ shoreline cleanup 603,500 people last year? differences ◦ comparing numbers, comparing ◦ ◦ Beading ◦ estimating fractions with quantities, equivalent ratios ◦ two-term and three-term ratios, benchmarks (e.g., zero, half, ◦ part-to-part ratios and part-to- real-life examples and problems whole) whole ratios ◦ A string is cut into three pieces ◦ equal partitioning ◦ using base 10 blocks, geoboard, whose lengths form a ratio of 10x10 grid to represent whole 3:5:7. If the string was 105 cm number percents long, how long are the pieces? ◦ finding missing part (whole or ◦ creating a cedar drum box of percentage) proportions that use ratios to create ◦ 50% = 1/2 = 0.5 = 50:100 differences in pitch and tone ◦ paddle making ◦ includes the use of brackets, but excludes exponents ◦ using pattern blocks or Cuisenaire Rods ◦ simplifying ½ ÷ 9/6 x (7 – 4/5) ◦ drumming and song: 1/2, 1/4, 1/8, whole notes, dot bars, rests = one beat ◦ changing tempos of traditional songs dependent on context of use ◦ proportional sharing of harvests based on family size Addition and Subtraction: to 10 000 Addition and Subtraction: of whole numbers to 1 000 000 ◦ using flexible computation ◦ using flexible computation strategies, involving taking apart strategies involving taking apart (e.g., decomposing using friendly (e.g., decomposing using friendly numbers and compensating) and numbers and compensating) and combining numbers in a variety of combining numbers in a variety of ways, regrouping ways, regrouping ◦ estimating sums and differences to ◦ estimating sums and differences to 10 000 10 000 ◦ using addition and subtraction in ◦ using addition and subtraction in real-life contexts and problem- real-life contexts and problem- based situations based situations ◦ whole-class number talks ◦ whole-class number talks Multiplication and Division: of 2 or 3 Multiplication and Division: to three Multiplication and Division: Multiplication and Division: digit numbers by a one digit number digits, including division with remainders ◦ order of operations with whole ◦ operations with integers numbers (addition, subtraction, ◦ factors and multiples — greatest multiplication, division, and order common factor and least common of operations) multiple ◦ operations with decimals ◦ multiplication and division of (addition, subtraction, decimals multiplication, division, and order of operations) ◦ understanding the relationships ◦ understanding the relationships ◦ includes the use of brackets, but ◦ addition, subtraction, ◦ between multiplication and between multiplication and excludes exponents multiplication, division, and order division, multiplication and division, multiplication and ◦ quotients can be rational numbers of operations addition, division and subtraction addition, and division and ◦ prime and composite numbers, ◦ concretely, pictorially, ◦ using flexible computation subtraction divisibility rules, factor trees, symbolically strategies (e.g., decomposing, ◦ using flexible computation prime factor phrase (e.g., 300 = 22 ◦ order of operations includes the use distributive principle, commutative strategies (e.g., decomposing, x 3 x 52 ) of brackets, excludes exponents principle, repeated addition and distributive principle, commutative ◦ using graphic organizers (e.g., ◦ using two-sided counters repeated subtraction) principle, repeated addition, Venn diagrams) to compare ◦ 9–(–4) = 13 because –4 is 13 away ◦ using multiplication and division in repeated subtraction) numbers for common factors and from +9 real-life contexts and problem- ◦ using multiplication and division in common multiples ◦ extending whole-number strategies based situations real-life contexts and problem- ◦ 0.125 x 3 or 7.2 ÷ 9 to decimals ◦ whole-class number talks based situations ◦ using base 10 block array ◦ includes the use of brackets, but ◦ whole-class number talks ◦ birchbark biting excludes exponents ◦ Fact Fluency: Fact Fluency: Fact Fluency: Fact Fluency: ◦ addition and subtraction facts to 20 ◦ addition and subtraction facts to ◦ multiplication and division facts to ◦ multiplication and division facts to (developing computational 20 (extending computational 100 (developing computational 100 (extending computational fluency) fluency) fluency) fluency) ◦ multiplication and division facts to ◦ multiplication and division facts to 100 (introductory computational 100 (emerging computational strategies) fluency) ◦ Provide opportunities for authentic ◦ Provide opportunities for authentic ◦ mental math strategies (e.g., the ◦ When multiplying 214 by 5, we practice, building on previous practice, building on previous double-double strategy to multiply can multiply by 10, then divide by grade-level addition and grade-level addition and 23 x 4) 2 to get 1070. subtraction facts. subtraction facts. ◦ flexible use of mental math ◦ applying strategies and knowledge strategies of addition and subtraction facts in ◦ Provide opportunities for concrete real-life contexts and problem- and pictorial representations of based situations, as well as when multiplication. making math-to-math connections ◦ building computational fluency (e.g., for 800 + 700, you can annex ◦ Use games to provide opportunities the zeros and use the knowledge of for authentic practice of 8 + 7 to find the total) multiplication computations. ◦ Provide opportunities for concrete ◦ looking for patterns in numbers, and pictorial representations of such as in a hundred chart, to multiplication. further develop understanding of ◦ Use games to provide opportunities multiplication computation for authentic practice of ◦ Connect multiplication to skip- multiplication computations. counting. ◦ looking for patterns in numbers, ◦ Connecting multiplication to such as in a hundred chart,
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