2.8 Equal Groups

Unit Goals

  • Students work with equal groups of objects to gain foundations for multiplication.

Section A Goals

  • Determine whether a group of objects (up to 20) has an odd or even number of members.
  • Write an equation to express an even number as a sum of two equal addends.

Section B Goals

  • Find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns using addition.
  • Partition rectangles into rows and columns of equal-size squares, and count to find the total number of squares.
  • Represent the total number of objects in an array as a sum of equal addends.
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Glossary Entries

  • a third

    One piece of a shape split into 3 pieces that are the same size.

    A third of the rectangle is shaded.

  • 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.
  • centimeter

    A length unit in the metric measurement system. There are 100 centimeters in a meter.

  • column
    In an array, a column goes up and down.
  • compose
    To make a new unit from 10 of the next smallest unit. For example, compose a ten from 10 ones.
  • data
    Information about the things or people in a group.

    Example: If you have a box of colored pencils, then the lengths and colors of each of the pencils are data about the pencils in the box.
  • decompose
    To break a unit into 10 of the next smallest unit.  For example, decompose a ten into 10 ones.
  • even
    A number is even if that number of objects can be split into two equal groups or made into pairs without any objects left over.
  • 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 \(400 + 80 + 2\) .

  • face
    A flat side of a solid shape.
  • foot

    A length unit in the U.S. customary measurement system.

    There are 12 inches in a foot.

  • hexagon

    A shape with 6 sides and 6 corners.

  • inch

    A length unit in the U.S. customary measurement system. 

    There are 12 inches in a foot.

  • line plot
    A way to show how many of each measurement using an x for each measurement.
  • meter

    A length unit in the metric measurement system. 

    There are 100 centimeters in a meter.

  • number line

    A diagram that represents numbers as lengths from 0 using equally spaced tick marks or points.

  • odd
    A number is odd if that number of objects cannot be split into two equal groups or made into pairs without any objects left over.
  • pentagon
    A shape with 5 sides and 5 corners.
  • picture graph
    A way to show how many in each group or category using pictures of the objects or symbols.
  • quadrilateral
    A shape with 4 sides and 4 corners.
  • row

    In an array, a row goes side to side. 

  • thirds

    The pieces created when a shape is split into 3 pieces that are the same size.

    This circle is split into thirds.