ALEX Classroom Resource

Students:

• Model and solve real-world problems involving sums and differences of fractions (including mixed numbers) with unlike denominators.
• Use visual models to illustrate the problem situation involving fractions.
• Use fraction understanding and estimation strategies to assess the reasonableness of answers.

Students know:

• The meaning and magnitude of fractions expressed in units of halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, and hundredths.
• Strategies to find sums of two or more fractions with like denominators.
• Strategies to find the difference of two fractions with like denominators.
• How to decompose a fraction greater than 1 and express as a mixed number.
  Example: 7/3 = 3/3 + 3/3 + 1/3 = 2 1/3.

Students are able to:

• Solve real-word problems involving addition and subtraction of fractions with unlike denominators.
• Represent problems using fraction models or equations.
• Assess reasonableness of answers using estimation and benchmark fractions.

Students understand that:

• solving word problems involving addition and subtraction of fractions with unlike units
• Require strategies to find equivalent fractions in a common unit, and the sum or difference will be expressed in the common unit.
• Can be assessed for reasonableness of answers using estimation strategies.

Learning Objectives:
M.5.9.1: Add and subtract mixed numbers with like denominators.
M.5.9.2: Recognize that comparisons are valid only when the two fractions refer to the same whole.
M.5.9.3: Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
M.5.9.4: Recognize a fraction as a number on the number line; represent fractions on a number line diagram.
M.5.9.5: Recognize key terms to solve word problems.
M.5.9.6: Apply properties of operations for addition and subtraction.
M.5.9.7: Recall basic addition and subtraction facts.

Students:

• Use a variety of strategies and fraction equivalence to find sums and differences of fractions and mixed numbers with unlike denominators.

Students know:

• Strategies to determine if two given fractions are equivalent.
• How to use a visual model to illustrate fraction equivalency.
• Contextual situations for addition and subtraction.

Students are able to:

• Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.

Students understand that:
Addition and subtraction of fractions and mixed numbers with unlike units,

• Require strategies to find equivalent fractions in a common unit, and the sum or difference will be expressed in the common unit.
• Can be assessed for reasonableness of answers using estimation strategies.

Learning Objectives:
M.5.10.1: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
M.5.10.2: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
M.5.10.3: Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
M.5.10.4: Recognize and generate simple equivalent fractions.
M.5.10.5: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
M.5.10.6: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
M.5.10.7: Recall basic addition, subtraction, multiplication, and division facts.

Students:
Given any two or more whole numbers,

• Strategically select and apply strategies for finding the greatest common factor of the two numbers and justify that the strategy used does produce the correct value for the greatest common factor.
• Strategically select and apply strategies for finding the least common multiple of the two numbers and justify that the strategy used does produce the correct value for the least common multiple.
• Use the relationship between factors and multiples to determine prime factorization.

Students know:

• Strategies for determining the greatest common factor of two or more numbers,
• Strategies for determining the least common multiple of two or more numbers,
• Strategies for determining the prime factorization of a number.

Students are able to:

• Apply strategies for determining greatest common factors and least common multiples.
• Apply strategies for determining the product of a number's prime factors in multiple forms which include exponential form and standard form.

Students understand that:

• Determining when two numbers have no common factors other than one means they are considered relatively prime.
• Composing and decomposing numbers provides insights into relationships among numbers.

Learning Objectives:
M.6.8.1: Identify the least common multiple of a given set of numbers, with or without the use of a calculator.
M.6.8.2: List multiples of any given whole number, with or without the use of a calculator.
M.6.8.3: Identify the greatest common factors of a given set of numbers, with or without the use of a calculator.
M.6.8.4: Define prime factorization.
M.6.8.5: List common factors of given whole numbers, with or without the use of a calculator.
M.6.8.6: Identify the prime factorization of a single digit number, with or without the use of a calculator.
M.6.8.7: Identify the prime factorization of any two digit whole number, with or without the use of a calculator.