The Arithmetic simulation from PhET is a game where you practise multiplication, division and factoring, with no calculator allowed. You can use an array model to see how multiplication tables help with all three skills. It is free, runs in any browser on a phone, tablet or laptop, and it is a great fit for the multiplication, division and factors lessons in Tamil Nadu State Board (Samacheer Kalvi) Maths.
What is the Arithmetic simulation?
This interactive game helps you get faster and more accurate at multiplying, dividing and factoring. It uses an array model, which is a grid of rows and columns, to show how the three skills are connected. Because it runs on HTML5, there is nothing to install, and it works on phones, tablets, Chromebooks and computers.
Elementary and middle school
Multiplication, division and factoring
Phone, tablet, Chromebook, PC
English
PhET’s learning goals are to explain how multiplication tables help with multiplication, factoring and division, to use an array model to understand all three, to become more accurate at multiplying, factoring and dividing, and to develop more than one strategy for arithmetic problems.
Launch the Arithmetic simulation online
Tap or click inside the player and start playing. Use the full-screen button in the player for a bigger view.
Credit: University of Colorado Boulder
How to use the Arithmetic simulation, step by step
- Warm up with the array. Look at a grid of rows and columns and count how many items it has.
- Multiply. Use the number of rows and columns to find the product, and check it against the multiplication table.
- Divide. Start with the total and one side of the array, and find the missing side.
- Factor. Find the pairs of numbers that multiply to give a target number.
- Play the game. Answer without a calculator and try to get more answers right, faster.
Tip for students: if you forget a fact, build the array in your head. Break a big array into smaller ones that you already know.
The idea behind the simulation: the array model
rows × columns = total
An array shows a number as rows and columns of dots. The total number of dots is the product. If you know the total and the number of rows, dividing gives the number of columns. Every pair of numbers that makes the same array total is a factor pair of that number. Turning an array on its side swaps rows and columns, which is why a × b = b × a.
Worked example: An array has 3 rows and 4 columns. The total is 3 × 4 = 12. Turn it around and you get 4 rows of 3, which is also 12. Dividing, 12 ÷ 3 = 4 and 12 ÷ 4 = 3. The factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4.
Multiplication and factoring key terms explained
These are the words you will meet while using the Arithmetic simulation, with simple meanings.
Multiplication
Finding the total of equal groups, such as 3 rows of 4.
Product
The answer to a multiplication.
Factor
A number that divides another number exactly. 3 and 4 are factors of 12.
Factor pair
Two numbers that multiply to give a target number.
Division
Sharing a total into equal groups. It undoes multiplication.
Quotient
The answer to a division.
Array
A grid of rows and columns that shows a multiplication.
Multiplication table
A chart of products that helps you remember facts for multiplying, dividing and factoring.
Common mistakes: Mixing up the number of rows with the number of columns, forgetting that 1 and the number itself are always factors, and stopping after one factor pair when there are more.
Try the array and factor calculator (practice what you explore)
Enter a number of rows and a number of columns from 1 to 100. The calculator draws a small array and shows the product, the division facts and all the factor pairs. Then tap a “what if” button.
What happens when you change a number
| Change | Effect |
|---|---|
| Swap rows and columns | The product stays the same |
| Add one more row | The product goes up by the number of columns |
| Double the rows | The product doubles |
| Divide the total by the rows | You get the number of columns |
| A prime number as the total | Only one array shape (1 row), so only 1 and itself as factors |
Classroom activities for teachers
The Arithmetic simulation fits a single 40-minute period.
- Predict and test (10 min): students say the product of an array before they check it.
- Break it apart (10 min): students split a big array into two smaller ones they know and add the products.
- Factor hunt (10 min): students find every factor pair of a target number.
- Exit ticket (10 min): students explain in two sentences how an array shows both multiplication and division.
Looking for the matching chapters? Browse the Maths books on TN SchoolBooks and download the Samacheer Kalvi PDFs, then use this game to make multiplication and division lessons visual. More free simulations and textbook PDFs are on the home page.
Quick quiz: test your understanding of multiplication and factors
Score: 0 / 5
Arithmetic simulation: frequently asked questions
Is the Arithmetic simulation free?
Yes. PhET simulations are free to run online in a browser. Check PhET’s licensing page for reuse terms.
Does it work on a mobile phone?
Yes. It is built with HTML5 and works on phones, tablets and Chromebooks. Use landscape mode or the player’s full-screen button for a bigger view.
What is an array model in multiplication?
An array model shows a multiplication as rows and columns of dots. The number of rows times the number of columns gives the total, so it helps with multiplication, division and finding factors.
How do I find all the factors of a number?
Try dividing the number by 1, 2, 3 and so on. Every number that divides it exactly is a factor, and each one has a partner. For 12 the pairs are 1 and 12, 2 and 6, and 3 and 4.
The Arithmetic simulation turns times tables into a game you can play, picture and win. Explore it, take the quiz above, and keep playing until multiplying, dividing and factoring feel easy.