## Multiplication as Repeated Addition

#### Aligned To Common Core Standard:

**Grade 3 Operations** - 3.OA.A.1

How to Present Multiplication as Repeated Addition - Imagine you are asked to add the following numbers; 3+3+3+3+3+3+3+3+3+⋯+3+3+3+3. It will take forever for you to add these numbers. The practice is termed as repeated addition. When you have to add a number, again and again, you are carrying out repeated addition. The other name for repeated addition is multiplication. Yes, multiplication and addition are two different arithmetic operations but you can use multiplication in place of repeated addition. You can present multiplication in the form of repeated addition. Consider a product expression; 10×2. The particular equation says that we are adding 2s, ten times. You can also write this product expression in an addition expression; 2+2+2+2+2+2+2+2+2+2. Multiplication is basically a number being added n times. Students, at this level, are so proficient with addition operations that it is almost an involuntary mental process for them. This is why it is a nice way to tiptoe to the next logical operations progression which is multiplication. These worksheets and lessons show students how to transition to multiplication by using the concept of repeating addition.

### Printable Worksheets And Lessons

- Keys Step-by-Step Lesson- Represent the problem as both a multiplication and addition statement. Write how many keys that you see.
- Guided Lesson - No guides here, make your own problems up. Write the groupings of images that you see below as both an addition and multiplication problem.
- Guided Lesson Explanation - This is more of an answer key than an explanation. The process of how to position yourself with this will definitely help students get going.
- Matching Sheet - Match the pictures to the sum or product statements. Write the letter of the answer that matches the visual problem.
- Practice Worksheet - A really great practice set that kids seem to like a lot. This is a three page visual set of ten problems for you to work on this skill with.
- Multiplication as Repeated Addition 5 Pack - A prompted worksheet set for students to work with. Each worksheet is set over two pages. There are five version, so it is ten pages in all.
- Using Multiplication Arrays Lesson - Give us words, than sums, and finally products. Count the number of dogs in the two groups. There are 5 dogs in each row. When we count all the dogs together, we get the total as 10.
- Visual Arrays Worksheet - This is truly just the lesson expanded. Fill in the missing numbers to all of the operations in here.

#### Homework Sheets

You should start to see light bulbs go off as students see this skill more.

- Homework 1 - Write it as both an addition and multiplication problem.
- Homework 2 - Write the groupings of images that you see below as both an addition and multiplication problem.
- Homework 3 - Convert each addition problem to an equal multiplication problem.

#### Practice Worksheets

I revert back to using pictures to reinforce all the skills.

- Practice 1 - Write how many bugs that you see.
- Practice 2 - Count the ice cream cones and mice.
- Practice 3 - Hippos and the fish that they eat.

#### Math Skill Quizzes

I start to use less space on the paper to give students more room to work with.

- Quiz 1 - Write an equal multiplication statement for each problem.
- Quiz 2 - Write an equal addition sentence for every multiplication problem.

### Concerns When Teaching This Skill

There are few considerations that teachers should have when teaching this concept to students. The target grade level for this topic is the perfect to time to present this concept because it builds upon something that they have already mastered. It makes a nice mental progression for students. There are times that you will need to caution students on thinking of this operation as adding in a continuous manner. This will really only present as they move up in grade levels. This concept only applies directly to natural numbers. It will certainly work every time when working with those integers, but as students start to work with fractions and non-real number applications, this concept falls flat. So, our advice to teachers is that this is a great way to introduce the concept, but you will want to ensure that students eventually progress to mastering times tables and multiplication charts. Flashcards and consistent repetition is a great way to help students achieve this. I have personal worked with several students that never progressed to those levels and then came across fractions for the first time and had a great deal of difficulty.