Groups and Arrays up to 99

A group is simply a collection of objects that all belong together, like a bag of 5 apples or a shelf of 5 books. When several groups have the same number of items, they are called equal groups. Once you line those equal groups up neatly in straight rows and columns, you get an array. An array is just an organized way of showing equal groups, and it makes counting large totals up to 99 much faster and less error prone.

Before jumping into arrays, it helps to be comfortable with counting equal groups up to 99, since an array is really equal groups arranged in a grid.

Every array has rows (the lines going left to right) and columns (the lines going up and down). To describe an array, we say how many rows it has and how many objects are in each row, which is the same as the number of columns. For example, an array with 4 rows and 5 columns has 4 groups of 5 objects.

Notice that reading an array this way is really just repeated addition: \( 5 + 5 + 5 + 5 = 20 \). Once you can see the rows and columns, you are ready to turn that picture into a multiplication statement instead of adding one row at a time.

Multiplication is the shortcut for finding an array's total. If an array has \( r \) rows with \( c \) objects in each row, the total number of objects is found with \( r \times c = t \). For the array above, that means \( 4 \times 5 = 20 \).

You can find this total in more than one way:

• Skip count by the number in each row: 5, 10, 15, 20 (this uses the same idea as multiplying by skip counting up to 99).
• Add each row's amount together with repeated addition: \( 5 + 5 + 5 + 5 = 20 \).
• Write the array directly as a multiplication statement, \( 4 \times 5 = 20 \), which is the fastest method once you're confident with your facts.

To see exactly how a picture like this becomes a number sentence, check out multiplication statements.

If you rotate an array so its rows become columns and its columns become rows, the total stays exactly the same. This is called a turnaround, and it shows that \( r \times c \) and \( c \times r \) always give the same product.

This idea appears again when you study turnarounds in more depth, where you'll practice spotting turnaround facts across many multiplication problems.

A gardener plants flowers in 6 rows with 9 flowers in each row. How many flowers are there in total?

Step 1: Identify the rows and columns. There are 6 rows and 9 columns, so \( r = 6 \) and \( c = 9 \).

Step 2: Multiply rows by columns: \( 6 \times 9 = 54 \).

Step 3: Check with repeated addition or skip counting by 9: \( 9 + 9 + 9 + 9 + 9 + 9 = 54 \).

There are 54 flowers in the garden, and since totals here stay below 99, this method works comfortably for any array you'll meet at this level.

Arrays give you a visual bridge between counting, repeated addition, and multiplication. Once you can see equal groups arranged in rows and columns, you can quickly find totals up to 99, write a matching multiplication statement, and recognize when two arrays are turnarounds of each other. These skills carry directly into faster mental multiplication and later work with larger numbers.

Related lessons

• Math 2