ALEX Classroom Resource

Students:
When given any fraction in form a/b,

• Create an area model to represent the fraction.
• Use a number line to represent the fraction.
• Explain the relationship between the fraction and the model including the corresponding number of unit fractions.
  Example: 3/4 is composed of 3 units of 1/4 or 3/4 is the same as 1/4 + 1/4 + 1/4.
• Identify a point to represent the fraction when given on a number line labeled with multiple points.

Note: Set models (parts of a group) are not models used in grade 3.

Students know:

• Fractional parts of a whole must be of equal size but not necessarily equal shape.
• Denominators represent the number of equal size parts that make a whole.
• The more equal pieces in the whole, the smaller the size of the pieces.
• The numerator represents the number of equal pieces in the whole that are being counted or considered.

Students are able to:

• Use an area model and length model to show a unit fraction as one part of an equally partitioned whole.
• Explain that given a fraction with a numerator greater than one, the numerator indicates the number of unit fraction pieces represented by the fraction.
  Example: 3/4 is the same as 3 units of 1/4 size, or three 1/4 pieces, 3 copies of 1/4, or 3 iterations of 1/4.
• Identify and describe the fractional name given a visual fraction model.
• Identify and demonstrate fractional parts of a whole that are the same size but not the same shape using concrete materials.

Students understand that:

• Given the same size whole, the larger the denominator, indicating the number of equal parts in the whole, the smaller the size of the pieces because there are more pieces in the whole.
• Fractions are numbers that represent a quantity less than, equal to, or greater than 1.
• Fractions represent equal partitions of a whole.

Learning Objectives:
M.3.13.1: Define fraction, numerator, and denominator.
M.3.13.2: Identify the parts of a fraction.
M.3.13.3: Label numerator, denominator, and fraction bar.
M.3.13.4: Identify parts of a whole with two, three, or four equal parts.
M.3.13.5: Distinguish between equal and non-equal parts.
M.3.13.6: Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.

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.