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Fractions  Proportional Reasoning Across the Grades (68)
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Concept
Grade 6
Grade 7
Grade 8
fractions
Addition
Subtraction
Represent, compare, order with unlike denominators
Proper, improper, mixed numbers
Addition
Simple like and unlike denominators
Subtraction
Simple like and unlike denominators
Multiplication
Fraction by fraction
Relationship of repeated addition to multiplication
Division
whole number by simple fraction
Represent/compare/order
Solve problems (+, , x, / of simple fractions)
Addition
Subtraction
Multiplication
Division  fraction/whole number
Represent, compare, order positive and negative fractions
Represent multiplication and division
decimals
Add
to thousandths
Subtract
to thousandths
Multiply
to tenths by whole numbers
whole numbers by tenths, hundredths, thousandths
decimal numbers by 10, 100, 1000, 10 000
Divide
to tenths by whole numbers
decimal numbers by 10, 100, 1000, 10 000
Place value
.001 – 1 000 000
Read/represent/compare/order to thousandths
Add
Subtract
Multiply
to thousandths by whole numbers
Divide
to thousandths by whole numbers
whole numbers by decimal numbers to hundredths
Represent, compare, order positive and negative decimals to thousandths
x, / decimal numbers by powers of 10
Real life problem solving
percent
How percents relate to fractions and decimals
Problem solving using whole number percents
Real life problem solving using percents expressed to one decimal place and whole number percents greater than 100
ratio
Represent (including standard fractional notation)
Rate is a ratio of two measurements with different units
Real life problem solving
Positive square roots of whole numbers (differentiate between perfect square numbers and those that are not)
rate
Represent relationships using unit rates
Rate is a comparison of two measurements with different units
Problemsolving by calculating unit rates
Real life problem solving
linear relationships
Real life situations where two quantities are directly proportional
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Subtraction
Represent, compare, order with unlike denominators
Proper, improper, mixed numbers
 Simple like and unlike denominators
Subtraction Simple like and unlike denominators
Multiplication Fraction by fraction
 Relationship of repeated addition to multiplication
DivisionRepresent/compare/order
Solve problems (+, , x, / of simple fractions)
Subtraction
Multiplication
Division  fraction/whole number
Represent, compare, order positive and negative fractions
Represent multiplication and division
 to thousandths
Subtract to thousandths
Multiply to tenths by whole numbers
 whole numbers by tenths, hundredths, thousandths
 decimal numbers by 10, 100, 1000, 10 000
Divide to tenths by whole numbers
 decimal numbers by 10, 100, 1000, 10 000
Place value .001 – 1 000 000
Read/represent/compare/order to thousandthsSubtract
Multiply
 to thousandths by whole numbers
Dividex, / decimal numbers by powers of 10
Real life problem solving
Positive square roots of whole numbers (differentiate between perfect square numbers and those that are not)
Problemsolving by calculating unit rates