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.