The questions in this activity use a measurement context for division rather than an equal-sharing context. You need to work with your students to correct this common error of reasoning. As the examples in the chart below illustrate, the opposite is true in many cases. This overgeneralisation is based on what happens with whole numbers.
Some may still think that “multiplication makes bigger” and “division makes smaller”. Students must be able to understand multiplication and division by powers of 10 if they are to handle more complex problems. Pages 22–27 of Book 7: Teaching Fractions, Decimals, and Percentages from the NDP resources describe how materials such as deci-mats or decimal pipes can be used to model these patterns in the place value system. Powers of 10 are created by multiplication by 10, so moving one column to the left in the table above equates to division by 10.
Students will find it helpful to create this pattern for exponents greater than or equal to 1 and then extend it to the left: Powers of 10 may also be less than 1, but their meaning will be less obvious. Powers of 10 with an exponent of 1 or greater are counting numbers. There are also 3 zeros in the product (1 000). The “3” indicates that 3 tens have been multiplied together. Powers of 10 can be written using exponents, for example, 10 3 = 1 000. Some powers of 10 are:ġ0 x 10 = 100 (ten tens equal one hundred)ġ0 x 10 x 10 = 1 000 (ten times ten times ten equals one thousand)ġ0 x 10 x 10 x 10 = 10 000 (ten times ten times ten times ten equals ten thousand)ġ0 x 10 x 10 x 10 x 10 = 100 000 (ten times ten times ten times ten times ten equals one hundred thousand). Powers of 10Īre created by multiplying tens together. The questions in this activity are about multiplication and division by powers of 10.
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