Math Strategy: Using 5 X / 10X

Math strategy: Using 5 X / 10X
Math strand: Number Sense and Numeration - Multiplication and Division







Overview:
Students often learn to skip count by five and ten quite easily because of the wide variety of songs, poems, and storybooks based on fives and tens. It is important for students to connect the skip counting rhythm to concrete materials as they count. It is recommended to start with the ten times tables, then move to the five times table to help students see relationships between the products. For example, 5 is half of 10, so if you want to know what 5 x 6 is you could multiply 6 by 10 and then half the product to get 30.


How this supports student learning:
One way to think about multiplying by 10 is to think in terms of using place value units that are 10 times as big.


Another way to think about multiplying by 10 is to think in terms of a place value chart model. Where the numbers would shift one column to the left.




Notice that after multiplying a whole number by 10, there is always a 0 in the ones place of the product. This happens because after all the digits have moved left one place you end up with 0 ones. You can extend the same thinking to multiplying by 100 and 1000.

It may be tempting to simply give students rules about adding a zero to the end of the number when multiplying it by 10. However, it is important to focus on why adding zeros makes sense. With a firm foundation in why we add zeros, students will understand when it is appropriate to add zeros or when it isn't. For example, you don't add a 0 to the end when you multiply a decimal by 10 (4.2 x 10 = 42).

The 10 X strategy is an essential building block as many strategies for multidigit multiplication depend on decomposing numbers into their place value to multiply by 10, 100, or 1000. This strategy will support students’ understanding of multiplying decimals and measurement conversions. It will also support students’ understanding of dividing by 10.


Where to next?
Consider using The Big Race, an open worksheet, for targeted practice for 5X / 10X, as well as many other strategies, which can be found on page 69 in A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 Volume 5

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