3.5 Fractions as Numbers

Unit Goals

  • Students develop an understanding of fractions as numbers and of fraction equivalence by representing fractions on diagrams and number lines, generating equivalent fractions, and comparing fractions.

Section A Goals

  • Understand that fractions are built from unit fractions such that a fraction $\frac{a}{b}$ is the quantity formed by $a$ parts of size $\frac{1}{b}$.
  • Understand that unit fractions are formed by partitioning shapes into equal parts.

Section B Goals

  • Understand a fraction as a number and represent fractions on the number line.

Section C Goals

  • Explain equivalence of fractions in special cases and express whole numbers as fractions and fractions as whole numbers.

Section D Goals

  • Compare two fractions with the same numerator or denominator, record the results with the symbols >, =, or <, and justify the conclusions.
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Glossary Entries

  • algorithm
    A set of steps that works every time as long as the steps are carried out correctly.
  • area

    The number of square units that cover a flat figure without gaps or overlaps.

  • array

    An arrangement of objects in rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number of objects as the other rows.

  • bar graph
    A way to show how many in each group or category using the length of rectangles.
  • denominator
    The bottom part of a fraction that tells how many equal parts the whole was partitioned into.
  • division
    Finding the number of groups or finding the size of each group when we share into groups of equal size.
  • divisor
    The number we are dividing by which can represent the size of the groups or the number of groups.
  • equation

    A statement that includes an equal sign (=). It tells us that what is on one side of the sign is equal to what is on the other side.

  • equivalent fractions
    Fractions that have the same size and describe the same point on the number line. For example, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent fractions.
  • expanded form

    A specific way of writing a number as a sum of hundreds, tens, and ones.

    Expanded form writes a number as a sum of the value of each digit. Example: 482 written in expanded form is \(400 + 80 + 2\) .

  • expression

    An expression has at least 2 numbers and at least one math operation (such as addition, subtraction, multiplication and division).

  • factor
    When we multiply two whole numbers to get a product, each of those numbers is a factor of the product.
  • fraction
    A number used to describe the parts of a whole that has been partitioned into equal parts.
  • key
    The part of a picture graph that tells what each picture represents.
  • multiplication
    The operation that tells you the total number of objects when you have a certain number of equal groups.
  • numerator

    The top part of a fraction that tells how many of the equal parts are being described.

  • parentheses
    Grouping symbols that can be used in expressions or equations, such as: \((3 \times 5) + (2 \times 5), (24 \div 2) + 5 = 17\).
  • picture graph
    A way to show how many in each group or category using pictures of the objects or symbols.
  • product
    The result of multiplying some numbers.
  • quotient
    The result in a division equation.
  • rounding

    A formal way to say which number a given number is closer to. For example, for 182, the number 180 is the closest multiple of ten and 200 is the closest multiple of a hundred. We can round 182 to 180 (if rounding to the nearest ten) or 200 (if rounding to the nearest hundred).

  • scaled bar graph
    A bar graph marked in multiples of some number other than 1.
  • scaled picture graph
    A picture graph where each picture represents an amount other than 1.
  • square centimeter

    A square with side lengths of 1 centimeter.

  • square foot

    A square with side lengths of 1 foot.

  • square inch
    A square with side lengths of 1 inch.
  • square meter
    A square with side lengths of 1 meter.
  • unit fraction
    A fraction with 1 in the numerator.