ALEX Classroom Resource

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.

Students:

• Compare two fractions with different numerators and different denominators using concrete models, drawings, and benchmarks (0, 1/2, 1).
• Recognize that comparisons are valid only when the two fractions refer to the same whole.
• Record the comparisons of two fractions using symbols >,<, or =, and justify the conclusions.

Students know:

• Comparing two fractions is only valid if they refer to the same whole.
• Meaning of comparison symbols,<, >, or = .
• Fractions can be represented by a variety of visual models (length and area).

Students are able to:

• Use concrete models, benchmarks, common denominators, and common numerators to compare two fractions and justify their thinking.
• Explain the comparison of two fractions is valid only when the two fractions refer to the same whole.

Students understand that:

• When comparing fractions they must refer to the same whole.
• Benchmark fractions can be used to compare fractions.
• Fractions can be compared by reasoning about their size using part to whole relationship.
• Fractions can be compared by reasoning about the number of same-sized pieces.
• Fractions can be compared by reasoning about their size when there are the same number of pieces.
• Fractions can be compared by reasoning about the number of missing pieces.

Learning Objectives:
M.4.14.1: 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.4.14.2: Identify a fraction as a number on the number line; represent fractions on a number line diagram.
M.4.14.3: Recognize a fraction as a number on the number line.
M.4.14.4: Represent fractions on a number line diagram.
M.4.14.5: Recognize fractions as numerals that may represent division problems.
M.4.14.6: Label numerator, denominator, and fraction bar.
M.4.14.7: Identify parts of a whole with two, three, or four equal parts.
M.4.14.8: Distinguish between equal and non-equal parts.