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Remembering when multiplication was new

Some topics feel so foreign because it’s hard to remember a time when “5 x 7” looked like your teacher forgot how to write “+”. We have many (all?) multiplication facts memorized, but your child is just starting this journey.

There are three big phases to understanding multiplication:

  1. Initial understanding of the multiplication process based on skip counting.
  2. Using multiplicative thinking to solve problems about equal groups, areas, and arrays.
  3. Final mastery of the multiplication facts.

Beginning in Kindergarten your child has started skip counting. In fact, skip counting by 2s will be a key skill that will help unlock many multiplication ideas. Encourage your child to use their fingers to count the number of skips (and don’t forget the first number!). Children love to show how smart they are. At this stage, your student can fluently tell you facts like 1 x 8 = 8 and 7 x 1 = 7. Encourage them to show off!

As they begin to investigate other rows in the multiplication table, teachers introduce different multiplication ideas. Here are the three types of problems your child will master this year:

  1. Equal groups. For example, Eva bought 5 bags of apples, and each bag has 8 apples. How many apples did she buy?
  2. Areas. What is the total area of a rectangle that is 6 inches wide and 10 inches long?
  3. Arrays. Mr. Atu’s classroom has 5 rows of desks. Each row has 7 desks. How many desks are in Mr. Atu’s classroom?

These applications help students know “why do we have to learn this?!” In addition, well-designed problems will help students practice facts involving 2s, 5s, and 10s.

Examples of three types of multiplication situation.

5 groups of 4 apples have 20 total apples
This array uses shelves to organize the “rows”. There are 3 shelves with 10 books for a total of 30 books.
The area model is a great way to learn multiplication and practice multiplication of decimals and fractions. Here the rectangle is 10 inches wide and 2 inches long, so it’s area is 20 square inches.

Interactive games like this one help students become fast and accurate with multiplication.

By the end of grade 3, states require students to memorize all the facts in the 10×10 or 12×12 multiplication table. With practice and lots of self-testing, students can master all these facts.