Multiplying by Multiples of Ten

To teach students to multiply by 10, 100, 1,000, and other multiples of 10, begin with a two-digit number to be multiplied by 10, for example, 45 x 10. Students draw a place value mat with places for the hundreds, tens, and ones. Having students draw their own place value mats rather than working on a perfectly printed one helps to build number sense. Divide the class into groups of ten students each. One group builds the number 45 on their place value mats. The other group builds the number 32 on their place value mats. 

When each student has completed building his number, invite students to put the base ten blocks used to build their number on one mat in the group to model 45 x 10. The other group will place their base ten blocks on a mat to model 32 x 10.  

Then each group works together to regroup the ones into the tens place, and regroup the tens into the hundreds place. 

Guide students to record the two equations in their math journals.      45 x 10 = 450 and 32 x 10 = 320

Using a calculator, write several more equations with a factor of 10. Ask guiding questions to help students see the pattern that when one of the factors is 10, you can multiply the two digits in the tens place, then simply put a zero in the ones place for the complete product. Then, use a calculator to generate several equations with a factor of 100, then 1,000, and other multiples of 10. As the class discusses the pattern, refer them back to the two equations they built. 

A note about base ten blocks:  Students work best if they are manipulating the base ten blocks themselves, rather than one person in the group handling the materials. The problem is that base ten blocks are expensive, so there are rarely enough for each student to have his own set. I solve that problem by printing pictures of base ten blocks on colored construction paper. I cut them out and distribute to each student a set that includes enough flats (representing 100), rods (the 10s) and units (the ones) to build the numbers.  

If you would like a free set of base ten blocks you may download a free set from my Teachers Pay Teachers store by clicking here.
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