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:

• Use visual models to create equivalent fractions.
• Explain the generalized pattern, a/b = (n x a) / (n x b).
• Use the generalized pattern to create equivalent fractions.

Set models (parts of a group) are not models used in grade 4.

Students know:

• Fractions can be equivalent even though the number of parts and size of the parts differ.
• Two fractions are equivalent if they are at the same point on a number line or if they have the same area.

Students are able to:

• Use area and length fraction models to explain why fractions are equivalent.
• Recognize and generate equivalent fractions.

Students understand that:

• equivalent fractions are fractions that represent equal value.

Learning Objectives:
M.4.13.1: Identify fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts and size 1/b.
M.4.13.2: Identify a fraction as a number on the number line; represent fractions on a number line diagram.
M.4.13.3: Recognize a fraction as a number on the number line.
M.4.13.4: Represent fractions on a number line diagram.
M.4.13.5: Recognize fractions as numerals that may represent division problems.
M.4.13.6: Label numerator, denominator, and fraction bar.
M.4.13.7: Identify parts of a whole with two, three, or four equal parts.
M.4.13.8: Distinguish between equal and non-equal parts.
M.4.13.9: Define area, length, equivalent, fraction, numerator and denominator.