Multiplying by multiples of ten and hundred sounds like it should be an easy concept to teach, but it’s not. In fact, many students struggle with this standard. It’s such an important concept for students to understand, because students will apply this concept in their multiplication and division standards. In this post, I share some of my favorite and most effective ways to teach this challenging concept.
Before I begin this unit, I teach place value and the value of numbers. I also teach students how to represent numbers in numeral, expanded, and written form. You can read more about those lessons here.
Multiplying by Multiples of 10 and 100
The key to teaching this concept is to allow students to move back-and-forth from concrete, to pictorial representations, and abstract problems. Far too often, we skip a step or two with this concept.
One strategy to teach this concept and reinforce the value of digits is to use base-ten chips or counters. These are an inexpensive alternative to base-ten blocks.
Of course, if you have base-ten blocks available, they are a great tool.
You can also do this with virtual manipulatives. It’s not as hands-on, but it’s still effective. Students can use place value chips to analyze arrays. For example, there are 6 rows of 4 ten, which represents 6 x 4 tens. By doing this, students should realize that 6×4 tens equals 24 tens.
Students do the same type of task with hundreds, which helps to solidify the relationship of multiplying ones, tens, and hundreds.
Multiplying by Tens and Hundreds-Pictorial Models
After students have ample hands-on experience, they can then move into pictorial models. Once again, there are several options.
The easiest is to have students draw the models. However, drawing makes it incredibly hard to think about proportions. I tried my best on this example, but I struggle-I really do!
Students can also use grid paper to represent their understanding of multiplying by multiples of 10 and 100. This lesson emphasizes how the associative property allows students to multiply by multiples of 10 and 100.
You will see this concept immediately click for some students, and you’ll have others who will need additional small group instruction. Students can also complete similar activities digitally.
Multiplying by Tens and Hundreds-Games
One of my favorite ways to help students think in terms of groups of tens and hundreds is through this place value game. In this game students work with a partner and have a stack of number cards. They shuffle the number cards and place them facedown in front of each other. Students take turns drawing a card, and the student whose card has the greatest value gets to keep both cards. After all the cards have been played, the student with the most cards wins.
Multiplying by Tens and Hundreds-Common Errors
There are a few common error patterns to look for. One common error was not understanding the meaning of an equation. Students thought of 2x___=140 as 2×140=. This allowed me to teach students what the equal sign means, which is often a misconception for students.
Another issue was that some students struggle viewing 12 hundreds blocks as 12 hundreds. They limited their view to thinking of the blocks as 1 thousand, two hundreds. We were able to address that with the base-ten blocks as well.
The most concerning observation was when students were not able to count by tens, twenties, hundreds, two-hundreds, etc. For example, in the problem 6×20, one student counted: 20, 40, 60, 80, 1,000, 1,002. In 6×200, another student counted 200, 400, 600, 800, 1,000, 1,001, 1,002. I also saw some not attempting to count by two-hundreds. Instead, they counted by one-hundreds. With these students, I need to step back quite a bit. They’re not ready for this standard.
Instead, we will focus on number sense and place value remediation. You can read more about number sense here. As I work with these students, I have to remember that there is not a quick, overnight fix. Instead, it will take time. This is one of those concepts that is greatly impacted by number sense. After I feel that students are ready, I will reteach students this concept.
These students will likely need math interventions, so I will also begin implementing my place value interventions on a consistent basis. You can read more about those interventions here.
Suzie Amodio says
Hi Ashleigh, Thank you for this blog. I am an older (gulp! senior) just starting to substitute in primary grades. Of course while my daughter was growing up I would volunteer in her classroom, but teaching methods and expectations have changed dramatically since the 1980s. So having access to your blog and to some of the freebies is an absolute boon for me to try to catch up with 21st c educational modes.
Suzie Amodio
Ashleigh says
Thank you so very much!