Arrays and repeated addition

What is this skill?

An array is an arrangement of objects in equal rows and columns, like eggs in a carton or chairs set out in rows. Second graders use arrays to find a total by adding the same number again and again. Three rows of 4 stars is 4 + 4 + 4, which is 12. They also write the matching repeated addition sentence for a picture.

Arrays are the bridge between addition and multiplication. Second graders do not need to know multiplication facts yet, but they are building the picture that makes them make sense in third grade, when 3 rows of 4 becomes 3 × 4. In the mini-quest below, the explanation mentions the multiplication sentence so that children can begin to see the link.

Why it matters

Arrays turn multiplication from a list of facts to memorize into something a child can see. Later, they explain why 3 × 4 is the same as 4 × 3 (turn the array on its side), why 6 × 4 is double 3 × 4, and how to break a hard fact into easier parts. The same rows-and-columns picture is how area of a rectangle is taught in third grade.

Repeated addition is also good practice in its own right. Adding 5 + 5 + 5 + 5 quickly, by counting by 5s, strengthens skip counting and mental addition, and it helps children notice that counting rows is faster than counting every object one by one.

Common mistakes

• Counting every object one at a time instead of using the rows. That gets the right total but misses the point. Ask "How many are in one row? How many rows?"
• Mixing up rows and columns, so a picture of 3 rows of 4 is written as 3 + 3 + 3 + 3. Both give 12, but the matching sentence follows the rows. Rows go across, like a line of words in a book.
• Writing the wrong number of addends, such as 4 + 4 for three rows. Pointing to each row while saying each number fixes this.
• Losing count of rows in a large array. Drawing a line under each row as it is added keeps track.

How to help at home

• Find arrays around the house: muffin pans, egg cartons, window panes, ice cube trays and tiles on the floor. Ask how many rows, how many in each row, and how many altogether.
• Build arrays with coins, cereal or small toys, then turn the array a quarter turn and ask whether the total changed.
• Draw dot arrays on grid paper and have your child write the repeated addition sentence for each one.
• When setting the table or arranging snacks, ask your child to lay them out in equal rows and tell you the addition sentence.

Worked examples

These are real questions from the Tutorsaurus arrays and repeated addition practice, with the answers worked out.

1. Example 1

   How many in all? 3 rows of 2.

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   Answer: 6. 2 + 2 + 2 = 6. That is 3 × 2.

2. Example 2

   How many in all? 4 rows of 4.

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   Answer: 16. 4 + 4 + 4 + 4 = 16. That is 4 × 4.

3. Example 3

   How many in all? 5 rows of 3.

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   Answer: 15. 3 + 3 + 3 + 3 + 3 = 15. That is 5 × 3.