Using Division to Find Unknown Factors Worksheets
This is the next natural progression for building up our algebra skills. Of all the basic operations, I find that division gives students the most trouble. If you start with a visual approach and show students that division is simply putting a fixed value (the dividend) into equal groups (divisor) they will catch on much quicker. I also spend a good deal of time showing how multiplication and division can be used to balance one another. I encourage all teachers and students to take their time learning this topic. It is a foundational skill that you will need to succeed with a great deal of different operational based problems. Also ease this skill into word problems. If you sail through that topic too fast, it is super to be a sticking point toward further progress. These worksheets and lesson concentrate on finding unknown factors of various values. The focus is on counteracting or using division as the operation in the process.
Aligned Standard: Grade 3 Operations - 3.OA.6
- Missing Parts of a Product Step-by-step Lesson- I provide a 64 block matrix to help you solve the problem.
- Guided Lesson - We extend into the use of word problems and pictures to help us understand the skill.
- Guided Lesson Explanation - In this one I breakdown the problem into every factor leading to the answer.
- Practice Worksheet - Find the missing part of the product.
- Matching Worksheet - I think this was a neat way to do it. I saw a similar problem on a practice core exam and that sparked me into this problem.
- Answer Keys - These are for all the unlocked materials above.
We mix a few coordinated word problems in here too.
- Homework 1-A city planner organizes the garbage collection for the city into 64 areas. He breaks the blocks into 8 areas. How many blocks are there in each of these areas?
- Homework 2- A baker can fit 3 muffins in each plate. How many plates should he use to create an order of 18 muffins?
- Homework 3- John made 6 equal pillars of blocks. How many blocks did he put in each pillar, if he used 42 blocks in all?
It is finally time to kick off our career with algebra!
- Practice 1- Complete all the problems. These types of exercises require you do two steps.
- Practice 2- Match the related math facts / equations. I encourage students to replace the unknown with the variable "x".
- Practice 3- A little fast facts for you. This is nice to start off with or go back to if students are having difficulty.
Math Skill Quizzes
Over the course of all the quizzes, I'm pretty sure that I covered every question type I have seen.
- Quiz 1-Kenny owns and rents 8 fleets of 6 different types of RVs. How many total RVs does Kenny own?
- Quiz 2- Jacob is 20 years old. His grandpa is 60 years old. How many times older is Jacob's grandpa?
What Are Unknown Factors of Division Problems?
First, you need to understand what a factor is. A factor is a whole number that gets divided into another number exactly (evenly). That means that there are no remainders as a result of this quotient. So, when we multiply the numbers 3 and 5, we know the final product of these two factors will be 15.
Let's see that in the form of an equation. 3 x 5 = 15
The commutative property of multiplication allows us to also say that: 5 x 3 = 15
Lets apply this to the counter operation of multiplication (division). We can state this equation: 15 / 3 = 5 as 15 / 5 = 3
So, what if there was a number missing from the above equations? When we have a unknown value in an equation we refer to that unknown as a variable. The most common symbols that are used for variables in equations are the letter x or y.
Work on this example: 3(y) = 15
Given the equation above, can we determine the value of y? Yes, we can by understanding that we can perform any operation of our choosing to an equation, as long as we apply it to both sides of the equal sign. In this case, the unknown (y) is being multiplied by 3. To undo that we can divide both sides by 3. This would mean the value of y is 5. In this case, 5 was an unknown factor. Let's take another example.
8 / x = 2
This is a more complex problem because the dividend is 8 and the unknown variable (x) is the divisor. We can solve this problem in 2 steps. First, multiply both sides by x. This leaves us with 8 = 2x. This now looks just like the last problem. If we divide both sides by 2, we free up the unknown (x). The answer is 4. Let's check the answer.
2 x 4 = 8 or this can be restated as: 8 / 4 = 2
Remember, these are basic factor problems, and with practice, you will be able to solve these equations faster. This simple approach can be used to solve problems that contain much larger factors. Your focus just needs to on freeing up the variable by getting it by itself.