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.