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 a fraction a/b (with denominators of 2, 3, 4, 6, 8),

• Use a number line and partition the interval between 0 and 1 into b equal parts, specified by the denominator.
• Use a number line and partition the interval between 0 and 1 into b equal parts and mark off a lengths of 1/b unit fractions.
• Model a fraction with a point on a number line and recognize the length of the fraction as the distance from the fraction point to 0.
• Extend the number to include fractions greater than one as a continuation of counting unit fractions.
• Given a fraction, draw a model to represent the fraction using a number line.
• Given a fraction and a number line with labeled points, identify the labeled point that represents the fraction.
• Given a point on a number line, identify the fraction modeled by the point.

Students know:

• How to use fraction strips as a model to connect to finding fractional parts on a number line.
• Fractions are numbers that can be represented on a number line.
• Fractions can be placed on the number line by marking off equal parts between two whole numbers.
• Fractions equal to 1 have the same numerator and same denominator.
• Fractions greater than 1 have a numerator that will be greater than the denominator.

Students are able to:

• Represent fractions on a number line.
• Locate fractions on a number line.
• Use a number line and partition an interval from 0 to 1 into equal parts as specified by the denominator of a fraction.
• Represent a non unit fraction on a number line by marking off unit fraction lengths as specified by the numerator from zero.
• Extend the number line to include fractions greater than one as a continuation of counting unit fractions.

Students understand that:

• A number line is a length model.
• Fractions are numbers that represent a quantity less than, equal to, or greater than 1 and can be placed on a number line.
• A number line can be partitioned to represent equal parts of a whole.

Learning Objectives:
M.3.14.1: Recognize fractions as lengths from zero to one.
M.3.14.2: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
M.3.14.3: Identify a number line.
M.3.14.4: Recognize whole numbers as lengths from zero to one.
M.3.14.5: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
M.3.14.6: Identify a number line.
M.3.14.7: Label the fractions on a pre-made number line diagram.
M.3.14.8: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
M.3.14.9: Recognize a number line diagram with equally spaced points.

Students:

• Use a variety of area models and length models to identify equivalent fractions.
• Use a variety of area models and length models to illustrate equivalent fractions.
• Use visual representations to find fractions equal to 1.
• Illustrate and explain fractions equivalent to whole numbers (limited to 0 through 5).
• Compare two fractions by reasoning about their size and use <, >, or = to record the comparison.
• Compare two fractions using visual fraction models.
• Use symbols <, >, or = to record the comparison between two fractions.

Note: Tasks in grade 3 are limited to fractions with denominators 2, 3, 4, 6, or 8.

Students know:

• Fractions with different names can be equal.
• Two fractions are equivalent if they are the same size, cover the same area, or are at the same point on a number line.
• Unit fraction counting continues beyond 1 and whole numbers can be written as fractions.
• Use a variety of area models and length models to show that a whole number can be expressed as a fraction and to show that fractions can be equivalent to whole numbers.
• Comparing two fractions is only reasonable if they refer to the same whole.
• The meaning of comparison symbols <, >, = .
• Reason about the size of a fraction to help compare fractions.
• Use a variety of area and length models to represent two fractions that are the same size but have different names.
• Use a fraction model to explain how equivalent fractions can be found.
• Use a variety of area models and length models to demonstrate that any fraction that has the same nonzero numerator and denominator is equivalent to 1.
• Use models to show that the numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater numerator is the greater fraction.
• Use models to show that the denominator of a fraction indicates the size of equal parts a whole is partitioned into, and that the greater the denominator, the smaller the parts. -Determine when two fractions can not be compared because they do not refer to the same size whole.

Students are able to:

• Explain equivalence of two fractions using visual models and reasoning about their size.
• Compare two fractions with same numerators or with same denominators using visual models and reasoning about their size.
• Express whole numbers as fractions.
• Identify fractions equivalent to whole numbers.
• Record comparisons of two fractions using <, >, or = and justify conclusion.
• Explain that the whole must be the same for the comparing of fractions to be valid.

Students understand that:

• A fraction is a quantity which can be illustrated with a length model or an area model.
• Two fractions can be the same size but have different fraction names.
• A fraction can be equivalent to a whole number.
• Any fraction that has the same nonzero numerator and denominator is equivalent to 1.
• The numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater number of parts is the greater fraction.
• The denominator of a fraction indicates the size of equal parts in a whole, so the greater the denominator, the smaller the size of the parts in a whole.

Learning Objectives:
M.3.15.1: Define equivalent.
M.3.15.2: Recognize pictorial representations of equivalent fractions.
M.3.15.3: Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
M.3.15.4: Recognize that equal shares of identical wholes need not have the same shape.
M.3.15.5: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
M.3.15.6: Label a fraction with multiple representations.
M.3.15.7: Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).
M.3.15.8: Partition circles and rectangles into two and four equal shares; and describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
M.3.15.9: Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.
M.3.15.10: Label a pictorial representation.
M.3.15.11: Recognize that a fraction is a part of a whole.
M.3.15.12: 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.