Primary Standards:
MAFS.2.OA.3.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by 2s; write an equation to express and even number as a sum of two equal addends (doubles).
MAFS.2.OA.3.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
MAFS.2.G.1.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Content Knowledge:
Students have been exploring addition and subtraction since kindergarten. In third grade they will begin to study multiplication and division. In order to prepare them for multiplicative thinking, 2nd grade students benefit from opportunities to explore and observe equal groups of objects. They explore groups with even and odd numbers of objects, recognizing even numbers as numbers that can be represented with paired objects. In addition, they explore rectangular arrays and use addition to find the total of the equal rows of objects.
When asked what an even number is, many people reply, “A number that ends in 0, 2, 4, 6, or 8.” Those are examples of even numbers, but they do not tell what an even number is. Students develop an understanding of even and odd numbers by using concrete materials to determine if a number can be broken into two parts, with the same number of objects in each part, or by pairing objects and looking to see if there are leftovers (odd) or not (even). They make connections from concrete materials to pictorial representations and later relate this concept to doubles addition facts.
2nd graders use rectangular arrays and rectangular area models. These two models are used as examples of repeated addition, but will become important models to represent multiplicative thinking starting in 3rd grade. By exploring repeated addition and building addition equations, 2nd graders are becoming familiar with models that will transition to multiplication models in the future. Experiences with skip counting, pairs and equal groups, and models that capture key ideas about multiplication provide the foundation for the introduction to multiplication and division.
GCG 1 – Learning Goal: Identify odd and even numbers
- Step 1: Determine if a number of objects is even or odd by separating the objects into groups of two OR two groups (even – none left over; odd – one left over)
- Step 2: Write an equation to show an even number as a doubles fact or an odd number as a doubles plus one fact
- Step 3: Identify patterns of even and odd numbers. Determine if a number (less than 1,000) is even or odd
GCG 2 – Learning Goal: Make rectangular array models
- Step 1: Identify rows and columns
- Step 2: Find the total number of objects in an array using repeated addition of the number of objects in each row or column
- Step 3: Determine which values can or cannot be formed into rectangular arrays (up to 25 and excluding 1 × n rectangles)
GCG 3 – Learning Goal: Decompose rectangles into rows and columns
- Step 1: Partition rectangles into equal rows and columns (using tiles, graph paper, and quick draws)
- Step 2: Use repeated addition to find the total number of square units created by partitioning a rectangle into rows and columns
- Step 3: Decompose a rectangle in more than one way using different sizes of square units