Unknown Numbers – Multiplication/Division


With our Unknown Numbers – Multiplication/Division lesson plan, students learn how to solve multiplication and division problems for an unknown number. Students solve practice problems and practice using lesson vocabulary.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to use games at the beginning and end of the lesson to reinforce the importance of memorizing multiplication facts.

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What our Unknown Numbers – Multiplication/Division lesson plan includes

Lesson Objectives and Overview: Unknown Numbers – Multiplication/Division teaches students strategies for solving for unknown numbers in multiplication and division problems. At the end of the lesson, students will be able to determine the unknown whole number in a multiplication or division equation that relates three numbers. This lesson is for students in 3rd grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The supplies you will need for this lesson are paper, scissors, and glue.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. If you have students who haven’t memorized their multiplication facts, you can let them use a multiplication chart. You can use games at the beginning and end of the lesson to reinforce the importance of memorizing multiplication facts. Finally, you could create flash cards that students could use to find unknown numbers or play a relay game with.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. It notes that the lesson includes many practice problems to help solidify students’ understanding of the material. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.


Unknown Numbers – Multiplication/Division

The Unknown Numbers – Multiplication/Division lesson plan includes four pages of content. The lesson begins by defining an equation as a number sentence that shows two values are equal. Some equations have a missing part, called an unknown number. We can use an empty box, a letter, or another symbol to show where an unknown number is. Learning how to find unknown numbers is the first step towards learning algebra. To do this, we first have to learn the vocabulary.

When solving multiplication problems, we’re solving for an unknown product. In the example problem 3 x 5 = ?, we’re trying to find the product. In this case, the unknown number is 15, because 3 x 5 = 15. The unknown number will not always be the product. Sometimes we have problems where the unknown number is one of the factors. In the example problem 4 x ? = 8, we need to find the unknown factor. The missing number is 2, because we know that 4 x 2 = 8. We can also switch the order of the problem around to make it a division problem: 8 / 4 = ?. The answer is 2.

If you can’t easily find the unknown number using the multiplication and division facts you already know, you can try guessing, checking, and revising. For the example problem 12 x ? = 60, you can try some numbers that might make sense to see which is right. You might try 12 x 3 = 36, which isn’t right, and then 12 x 4 = 48, which is closer but still not right, and then 12 x 5 = 60, which is correct! The unknown number was 5. If your first guess is too high, try a lower number. If it’s too low, try a higher number. This is a great method to use to find an unknown number. The lesson includes another example problem to help reinforce this concept.

Division is the inverse of multiplication, which means that, to solve a division problem, you can simply create a multiplication fact to find the answer. You can multiply the quotient by the dividend or divisor to find the unknown number. The lesson includes several examples.

In the example problem 5 = ? / 3, we need to find the dividend. We can do this using drawings, using three groups of five objects each and counting the total number of objects. In this case, the unknown number is 15. This method works with smaller numbers like these, but becomes much more difficult when dealing with larger numbers. Instead of using a drawing, we can simply use multiplication. For the problem 5 = ? / 3, we can multiply 5 x 3 to get 15. Therefore, the unknown number is 15. This method is a lot faster.

The lesson closes with several more examples that show how to find the unknown number in a division problem by using multiplication.


The Unknown Numbers – Multiplication/Division lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.


For the activity worksheet, students will cut out and match words, definitions, and examples.


The practice worksheet asks students to solve practice problems to find the unknown number.


For the homework assignment, students will solve a word problem.

Worksheet Answer Keys

This lesson plan includes answer keys for the activity worksheet, the practice worksheet, and the homework assignment. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

Additional information


3rd Grade



State Educational Standards


Lessons are aligned to meet the education objectives and goals of most states. For more information on your state objectives, contact your local Board of Education or Department of Education in your state.