Written multiplicationSome reminders for written multiplication
When you are multiplying numbers you need to decide whether to use a mental method (doing calculations in your head) or a written method (writing the numbers down).
A reminder about place value
Have a look at the number 623.
6 is the hundreds digit. 2 is the tens digit. 3 is the units digit.
Multiplication vs. Division
With whole numbers when you multiply the number gets bigger. When you divide the number gets smaller.
There is always a link between multiplication and division sums. Have a look at these three numbers in multiplication and division sums:
Multiplication and division are opposites or 'inverses'. If you multiply by an amount and then divide the result by the same amount you end up back where you started.
Timesavers x10 and x100
Multiplying by 10
When you multiply by 10 you move all the digits one place to the left and then numbers become 10 times bigger. Remember to add a zero in the empty place.
Remember: If you multiply a number by 10 the answer is the same number with a zero at the end.
Multiplying by 100
When you multiply by 100 you move all the digits two places to the left and then numbers become 100 times bigger. Remember to add two zeros in the empty places.
Remember: If you multiply a number by 100, the answer is the same number with two zeros at the end.
To learn more about multiplying and dividing by 10, 100 and 1 000 visit the Multiply and divide by 10, 100 and 1 000 module.
Multiplying large numbers by splitting
Have a look at the question: 255 x 5
First split the number into hundreds, tens and units.255 splits into 200, 50 and 5
Then, multiply each of the numbers by 5.
5 x 200 = 1 0005 x 50 = 2505 x 5 = 25
This method can be represented in a grid, as shown below.
Finally, add the three numbers together to get your answer.
So 255 x 5 = 1 275
Remember: check the answer by doing the opposite!1 275 ÷ 5 = 255
Now have a look at this question:255 x 25
First, split the numbers up and put them in the table:255 splits into 200, 50 and 5. These go along the top.25 splits into 20 and 5. These go down the sides.
Then, multiply each number in the column by each number in the row. Have a look at the grid below.
Add up each column, then add the resulting numbers together.
255 x 25 = 6 375
Try this method out in the game!
Multiplying large numbers - traditional method
If this method seems familiar it might be because you were encouraged to use it in school. Talking through the method is far easier than trying to follow written instructions. Have a look at the examples.
Have a look at how the sum 235 x 5 can be worked out using this method.
Step 1: 5 x 5 = 25. Put the 5 in the units column, and carry the 2 to the tens.Step 2: 3 x 5 = 15. Add the 2 makes 17.7 goes into the tens column and carry the 1 to the hundreds column.Step 3: 5 x 2 = 10. Add the carried 1 makes 11.
235 x 5 = 1 175 Look below to see how it is done. Remember to line up the units, tens and hundreds underneath each other.
Now have a look at the sum:255 x 25
First, multiply 255 by the unit digit 5.Step 1: 5 x 5 = 25. Put the 5 in the units column, and carry the 2 to the tens.Step 2: 5 x 5 = 25. Add the 2 makes 27.7 goes into the tens column and carry the 2 to the hundreds column.Step 3: 5 x 2 = 10. Add the carried 2 makes 12.
Then multiply 255 by the tens digit 2.Remember to add a zero first when multiplying the tens.
Step 1: 2 x 5 = 10. Put the 0 in the tens column, and carry the 1 to the hundreds.Step 2: 2 x 5 = 10. Add the carried 1 makes 11.1 goes into the hundreds column, with 1 carried to the thousands. Step 3: 2 x 2 = 4, add the carried 1 makes 5. The total is 5 100.
Finally, add down the columns down to get the total. Have a look below to see how it is done.
255 x 25 = 6 375
Remember:
Keep the numbers in columns - units, tens, hundreds etc When multiplying the tens digit add a zero first.
Multiplying large numbers - lattice method - 1
This method is also called Napier's bones. In some ways it is similar to the grid method as it involves multiplying rows and columns, but it gives you a better way to add the results at the end of the calculation.
With this method, you multiply each number in the column by each number in the row. Then you add along the diagonals to get the answer.
Have a look at this sum:25 x 5
Step 1: Make a grid with diagonal lines as shown below. Split the 25 into a 2 and a 5, putting each digit at the top of a column. Put the 5 by the top row.
Step 2: Multiply the columns by the rows, splitting the digits up on either side of the diagonal as shown here.
Step 3: Finally, add along the diagonals to get your answer.
25 x 5 = 125
This method is a bit complicated. Talking yourself through each step as you do it can be useful - someone is sure to ask you what you're doing and you'll end up explaining to them!
Multiplying large numbers - lattice method - 2
Here's another multiplication sum worked out using the lattice method. With this method, you multiply each number in the column by each number in the row. Then you add along the diagonals to get the answer.
Have a look at this sum:25 x 5
Step 1. Make a grid with diagonal lines as shown below. Split the 255 into 2, 5 and 5, putting each digit at the top of a column. Split the 25 into 2 and 5, putting each digit by a row.
Step 2: Multiply the columns by the rows, splitting the digits up on either side of the diagonal as shown here.
Step 3: Finally, add along the diagonals to get your answer.
255 x 25 = 6375
This method is a bit complicated. Talking yourself through each step as you do it can be useful - someone is sure to ask you what you're doing and you'll end up explaining to them!
'Written multiplication' tutor notes
This module can be used as a starting point for: learning different methods of written multiplication.
Please let us know what you think of the factsheets, worksheets and game at [email protected]
Students might like to look at the Times tables section before starting this module.
How does this tie in with the new curriculums?
England N1/L1.3 - Add, subtract, multiply and divide using efficient written methods.N1/L1.4 - Multiply and divide whole numbers by 10 and 100.N1/L1.5 - Recall multiplication facts up to 10 x 10 and make connections with division facts.
Wales As England.
Northern Ireland As England.
Scotland See www.aloscotland.com for details of the Scottish curriculum.
In the Skillswise module you'll find:
Written multiplication factsheets There are seven sheets in this section which can be printed out and kept.
Factsheet 1 - Some reminders for written multiplication. Factsheet 2 - Timesavers x10 and x100. Factsheet 3 - Multiplying large numbers by splitting. Factsheet 4 - Multiplying large numbers - vertical method / traditional long
multiplication. Factsheet 5 - Multiplying large numbers - lattice method - 1. With an easy sum. Factsheet 6 - Multiplying large numbers - lattice method - 2. Another lattice
example with a harder sum. Factsheet 7 - A glossary of terms for multiplication.
The Amoeba Multiplication Game In this game learners can practise the multiplication grid method shown in Factsheet 3.Learners fill gaps by typing in. At each stage they are shown where they went wrong and get a second try. At the end of the game they are given a summary of how they got on in each section and an overall score.
If they get 75% or more, they get a bonus game - 'Shoot the Amoebas'.
TOP TIP! To see the game completely full screen, press the F11 key on the keyboard. This takes away the distraction of the top browser bar. To bring the browser bar back, just press F11 again!
Written multiplication quiz The learner can choose their level. Level A is the easiest, level C the hardest. The method shown in the feedback on the answer page is long multiplication.Students can print out a certificate if they score 50% or more in the quiz. This will appear as a link on the results page - click on the link and the certificate will appear in a new window. Once printed students can write their name on the certificate.
Written multiplication worksheets There are six printable worksheets in this section for learners to carry on the work done online.
Worksheet 1 - Short multiplication. Worksheet 2 - Long multiplication. Worksheet 3 - Grid method multiplication. Worksheet 4 - Lattice method multiplication. Worksheet 5 - Puzzle 1. A crossword style multiplication puzzle. Worksheet 6 - Puzzle 2. A larger crossword style multiplication puzzle.
Technical help:
To get the most out of this topic area you need the following 'plug-ins':
Flash The game in this topic section uses Flash. This is free to download and should only take a few minutes. You can follow the BBC WebWise instructions to download it to your machine.Find out more.
If you don't have Flash the same learning points are covered in the quiz and in the worksheets and factsheets.If you are new to the web, why not try the BBC WebWise online course, Becoming WebWise? It's free, you can do it in your own time from any computer and it will take you through everything you need to know to use the web successfully in your teaching.Get WebWise.
You can find out more about the technical requirements for Skillswise in our Help - Technical Information section.
Taking it further:
Here are a few suggestions of other places on the web where you might find useful resources that you can adapt for teaching written multiplication.
Multiplication.com A site with games, activities, techniques, tips and secrets for teaching times tables.
AAA Math - multiplication An American site containing many pages demonstrating different multiplication skills, with interactive activities and games.
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