Multiplication and Division

Operations with Fractions: Multiplication and Division

Fraction Learning Pathway

Curriculum Connections

OP F Use models to recognize that any fraction is a multiple of its unit fraction
Grade Curriculum Expectations
2
  • regroup fractional parts into wholes, using concrete materials (e.g., combine nine fourths to form two wholes and one fourth)
4
  • represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of fractional parts being considered;
6
  • represent, compare, and order fractional amounts with unlike denominators, including propoer and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation
6
  • determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions, decimal numbers and percents.
7
  • divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials;
7
  • use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals;
7
  • add and subtract fractions with simple like and unlike denominators, using a variety of tools and algorithms;
7
  • demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number;
7
  • determine, through investigation, the relationships among fractions, decimals, percents, and rations;
8
  • represent, compare, and order rational numbers;
8
  • translate between equivalent forms of a number;
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions;
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9P
  • solve problems requiring the expression of perecnts, fractions, and decimals in their equivalent forms

Curriculum Connections

OP G Recognize division is the inverse of multiplication and vise versa
Grade Curriculum Expectations
5
  • describe multiplicative relationships between quantities by using simple fractions and decimals (e.g., "If you have 4 plums and I have 6 plums, I can say that I have or 1.5 times as many plums as you have.");
6
  • determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions, decimal numbers and percents.
7
  • divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials;
7
  • determine, through investigation, the relationships among fractions, decimals, percents, and ratios;
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigaion, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9D
  • identify, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

OP H Use models to decompose fractions using unit fractions as a form of division
Grade Curriculum Expectations
1
  • divide whole objects into parts and identify and describe, through investigation, equal-sized parts of the whole, using fractional names (e.g., halves; fourths or quarters).
3
  • divide whole objects and sets of objects into equal parts, and identify the parts using fractional names (e.g., one half; three thirds; two fourths or two quarters), without using numbers in standard fractional notation.
6
  • represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation;
6
  • determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions, decimal numbers, and percents.
7
  • divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials;
7
  • use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals;
7
  • add and subtract fractions with simple like and unlike denominators, using a variety of tools and algorithms;
7
  • determine, through investigation, the relationships among fractions, decimals, percents and ratios;
8
  • represent, compare, and order rational numbers;
8
  • translate between equivalent forms of a number;
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.

Curriculum Connections

OP I Multiply any fraction by a whole number using models and symbols
Grade Curriculum Expectations
6
  • represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation;
6
  • determine and explain, through investigation using concrete materials, drawings and calculators, the relationships among fractions, decimal numbers, and percents.
7
  • use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals;
7
  • add and subtract fractions with simple like and unlike denominators, using a variety of tools and algorithms;
7
  • demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number;
7
  • determine, through investigation, the relationships among fractions, decimals, percents, and ratios;
8
  • represent, compare, and order rational numbers;
8
  • translate between equivalent forms of a number;
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

OP J Divide a fraction by a like-denominator unit fraction using models and symbols
Grade Curriculum Expectations
6
  • represent, compare, and order fractional amount with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation;
7
  • use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals;
7
  • add and subtract fractions with simple like and unlike denominators, using a variety of tools and algorithms;
8
  • represent, compare, and order rational numbers;
8
  • translate between equivalent forms of a number;
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

Op K Divide a fraction by a like-denominator fraction, with a whole number result
Grade Curriculum Expectations
7
  • use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals;
7
  • add and subtract fractions with simple like and unlike denominators, using a variety of tools and algorithms;
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

OP L Multiply fractions where the numerator of one fraction is the denominator of the other using models
Grade Curriculum Expectations
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

OP M Divide a fraction by a smaller friendly denominator fraction with a whole number result
Grade Curriculum Expectations
8
  • represent, compare, and order rational numbers;
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

OP N Multiplfy fractions using models and symbols
Grade Curriculum Expectations
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

OP O Divide a fraction by a like denominator fraction a non-whole number result
Grade Curriculum Expectations
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

OP P Divide fractions with unlike-denominators with a visually recognizable result using models
Grade Curriculum Expectations
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Curriculum Connections

OP Q Divide fractions with unlike-denominators with a visually recognizable result using models
Grade Curriculum Expectations
8
  • use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
8
  • represent the multiplication and division of fractions, using a variety of tools and strategies;
8
  • solve problems involving addition, subtraction, multiplication, and division with simple fractions.
9D
  • simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
9D
  • solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
9D
  • determine, through investigation, various formulas for the slope of a line segment or to determine the slope of a line segment or a line;
9P
  • solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms