ALEX Classroom Resource

Students:

• When given any fraction or mixed number, apply unit fraction understanding to decompose the given fraction or mixed number into the sum of smaller fractions, including unit fractions.
• When given a problem solving situation involving addition and subtraction of fractions or mixed numbers with like denominators, explain and justify solutions using unit fractions, visual models, and equations involving a single unknown.

Students know:

• Situation contexts for addition and subtraction problems.
• A variety of strategies and models to represent addition and subtraction situations.
• The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.
• A fraction can represent a whole number or fraction greater than 1 and can be illustrated by decomposing the fraction.
  Example: 6/3 = 3/3 + 3/3 = 2 and 5/3 = 3/3 + 2/3 = 1 2/3.

Students are able to:

• Decompose fractions as a sum of unit fractions.
• Model decomposition of fractions as a sum of unit fractions.
• Add and subtract fractions with like denominators using properties of operations and the relationship between addition and subtraction.
• Solve word problems involving addition and subtraction using visual models, drawings, and equations to represent the problem.

Students understand that:

• A unit fraction (1/b) names the size of the unit with respect to the whole and that the denominator tells the number of parts the whole is partitioned, and the numerator indicates the number of parts referenced.
• A variety of models and strategies can be used to represent and solve word situations involving addition and subtraction.
• The operations of addition and subtraction are performed with quantities expressed in like units, and the sum or difference retains the same unit.

Learning Objectives:
M.4.15.1: Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).
M.4.15.2: Identify numerator and denominator.
M.4.15.3: Recall basic addition and subtraction facts.
M.4.15.4: Demonstrate an understanding of fractional parts.
M.4.15.5: Recall basic addition and subtraction facts.
M.4.15.6: Define mixed numbers.
M.4.15.7: Recall basic addition and subtraction facts.
M.4.15.8: Demonstrate an understanding of fractional parts.
M.4.15.9: Solve basic word problems using whole numbers.
M.4.15.10: Express parts of a whole as a fraction.
M.4.15.11: Write number sentences for word problems.
M.4.15.12: Identify key terms in word problems.
M.4.15.13: 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:

• Use a variety of strategies, including models, pictures, tables, and patterns to solve problems that provide a context for multiplying fractions and mixed numbers.

Students know:

• Contextual situations for multiplication.
• How to use an area model to illustrate the product of two whole numbers and its relationship to partial products and extend this knowledge to illustrate products involving fractions and mixed numbers.

Students are able to:

• Solve real-word problems involving multiplication of fractions and mixed numbers.
• Write equations to represent the word situation.
• Use visual fraction models to represent the problem.

Students understand that:

• A variety of strategies are used to model and solve problems that provide a context for multiplying fractions and mixed numbers.
• Solutions are interpreted based on the meaning of the quantities and the context of the problem situation.

Learning Objectives:
M.5.14.1: Define improper fraction, mixed number, fraction, equations, numerator, denominator.
M.5.14.2: Multiply proper fractions with common denominators 2-10.
M.5.14.3: Solve problems using whole numbers.
M.5.14.4: Write number sentences for word problems.
M.5.14.5: Identify key terms to solve multiplication word problems.
Examples: times, every, at this rate, each, per, equal/equally, in all, total.
M.5.14.6: Recall basic multiplication facts.