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Worksheet Maker and Multiplication Strategies

© R. Mirshahi

Instructions:

  • This resource covers a few valuable strategies that students can use. Choose the multiplication strategy you wish to practise. You can use this resource to teach these strategies. Use the pen tool to annotate right on the questions to model these strategies with the students. An interactive whiteboard is ideal for this purpose. Each time you start a practice, you will get a different set of questions custom designed for each specific strategy. You can click the eye button to reveal/hide the answers. Just click the back button and select your activity again to change the questions. You can print each activity beautifully on two pages. Make it double-sided to save paper!

Multiply by zero (x0): Any number times zero or zero times any number is always zero. For 0x8 or 8x0, you can think of zero groups of 8 or 8 groups of zero. For this reason every number in the world including zero is a factor of zero.
Multiply by one (x1): Any number times 1 or 1 times any number equals that number. For this reason, 1 is a factor for any number in the world. Prime numbers like 7 have 2 factors including themselves and 1 (1x7=7).


Multiply by two (x2): Here double facts come handy! Product of any number and 2 is always an even number. When you multiply by 2 check to make sure your answer ends with 0, 2, 4, 6, and 8.
Multiply by four: (x4): Double the number and double the answer again (x2 x2). This is the double-double method! Product of any number and 4 will also create an even number. This group of numbers are a subset of even numbers. Half of the multiples of 2 (even numbers) are multiples of 4. To find multiples of 4, you have to look at their last 2 digits. If they end with 00, 04, 08, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, they are multiples of 4. For example 136 is a multiple of 4 because it ends with 36. Remember that all multiples of 4 are even, but only half of even numbers are multiples of 4.


Multiply by three (x3): If you add the digits of multiples of 3 the sum is also a multiple of 3! You can use the double plus the number strategy here. For 3x6, you can think of double 6 and add 6 to get the final answer: (6+6) +6 = 18.
Multiply by six (x6): Multiply by 3 and then by 2 (x3 x2). Multiples of 6 are always even. Also, if you add their digits the sum is also a multiple of 3! For example, 36 is even and the sum of its digits is 9 (3+6). Therefore, 36 is a multiple of 6. Half of the multiples of 3 (even numbers) are multiples of 6. This group of numbers are a subset of multiples of 3.


Multiply by ten (x10): Just add a 0 to the end of the number you are multiplying by 10. All multiples of 10 end with zero.
Multiply by five (x5): If your number is even, find half of it and add a zero at the end. If it is odd, subtract 1, find half of it and add a five at the end. Multiples of 5 end with 0 or 5. For example for 45x5, 45 is odd. Subtract 1 (45-1=44). Find half of the number (22). Add a 5 at the end (225). When you multiply an odd number like 45 by 5 your answer must end with 5.


Multiply by seven: x7


Multiply by eight: x8 (x2x2x2 or x4x2) When multiplying by eight, you can double the number 3 times. Basically you do the multiplication in 3 steps.


Multiply by nine: Number x 9 = Number x 10 - Number (For example: 8x9---------8x10=80----------- 80-8=72)
If you add the digits of multiples of 9 the sum is 9 or a multiple of 9!


Do it in 2 or more steps: Leave the the easier step for the end. For 7x20, think of 20 as 2x10.
7x2=14 and 14x10=140 ------------- 7x2x10=140
Here, factoring is useful to break a task into smaller easier steps.


Use repeated addition to model multiplication. For example 3x6 is three groups of 6. 6+6+6=18


Basic Multiplication Facts: It is beneficial to know these basic facts by heart. This skill is necessary when multiplying any number.


Multiplying 2-Digit Numbers. There are many strategies for multiplying bigger numbers and checking your answers to make sure they make sense. For example, if you multiply any number by an even number, your answer must also be an even number. You can round your numbers before you multiply to estimate the answer.

Some methods don't make our job easier nor any faster, instead they help us gain a deeper understanding of multiplication such as the array method which involves breaking the main array into 4 sub-arrays. This can also visually explain this formula: (a+b) x (c+d) = ac + ad + bc + bd

See the examples below:


Array Subarray for multiplication.PNG

Multiplying 3-Digit Numbers.

These are just a few simple strategies. There are many more strategies and in real life, we have to choose the best one for the task at hand.

Suggested Lessons or Activities:

  • Students can print the worksheets or quizes for themselves or their peers whenever they are ready. After printing the worksheet they can click the eye button to reveal the answers and print the answer sheet. It is a good idea for students to use the
  • full screen
  • date stamp
  • annotation for showing your work and the strategies you used
  • answer sheet (Click the eye button)
  • printable (Exit Full Screen when ready to print. or when you want to type in the instructions and the name.)

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