In our place value system, students have been taught the power of ten since primary grades. They start by adding and subtracting by tens and work up to multiplying and dividing with powers of 10. The foundation for this concept begins in 3rd grade when students multiply numbers by multiples of 10 and build from there.

This skill is critical, so let’s explore some ideas to help students grasp this concept. Even though this is a specific 5th-grade standard, 3rd—and 4th-grade teachers will find helpful tips on teaching multiplying and dividing by ten and multiples of ten.

## Multiplying and Dividing with Powers of 10: Reinforce Vocabulary

Vocabulary is the cornerstone of teaching multiplying and dividing with powers of 10. Reinforcing vocabulary is a great place to start. Go back to the beginning. Review words such as place value, digits, tens, ones, and more with your students. You will use these words nonstop, so ensure everyone understands their meaning.

Once you feel students are comfortable with the essential words, you can introduce and discuss words like “multiples of ten,” “powers of ten,” “ten times as many,” and “exponents.” Students need to understand the difference between each word. Here is a breakdown you can use…

- Multiples of 10 are the product of a number multiplied by ten
- Ten times as many is when we multiply a number by ten
- The exponent of a number shows how many times the number is multiplied by itself
- Powers of 10 are ten multiplied by itself over and over again and written using exponents

Reinforcing the vocabulary you will use with students before you dive into teaching multiplying and dividing with powers of ten will help students throughout the unit.

## Multiplying and Dividing with Powers of 10: Use Manipulatives

Manipulatives are a great teaching tool for upper-grade students. They allow students to explore math hands-on. Here are some manipulatives to teach multiplying and dividing with powers of ten.

Base Ten blocks: These manipulatives don’t just belong in primary classrooms; we can use them with big kids, too. They are a great visual representation of powers of ten.

- A unit cube is 1. It represents 10⁰.
- A rod is 10. It represents 10¹
- A flat is 100. It represents 10².
- A cube is 1,000. It represents 10³.

Students can represent numbers and equations using these base ten blocks. They serve as an excellent visual reminder to students of what the power of ten means. For example, they can see that 10² is not 20 but 10×10, which is 100.

Place Value disks are round chips representing our base ten systems. They can be found in multiple values (.1,1,10,100, etc.), which works well for more significant numbers. They can be helpful when students are building numbers on place value charts.

Place Value disks are also great for representing powers of 10. These disks can help students show a number in multiple ways and can help build their foundation of understanding the powers of 10.

## Multiplying and Dividing with Powers of 10: Visual Representations

Visual Representations are also helpful when teaching students to multiply and divide with powers of 10. Along with providing a hands-on experience with manipulatives, using visual representations can help students grasp multiplying and dividing with powers of 10.

Visual representations allow students to start making connections about how the number increases or decreases based on the equation. Here are some helpful visual representations…

- Place value charts: students can use these with place value disks and see the patterns emerging when they move them.
- Number lines: These are a great visual representation for students. Most older students are familiar with number lines and how they work, so making the connection between the number line and the powers of 10 can be easy for them.

Are you looking for some helpful visual representations to use with your students? Download this free place value toolkit with visual tools to help your students multiply and divide with powers of 10 and various other place value skills.

## Multiplying and Dividing with Powers of 10: Pattern Recognition

Once your students understand that the numbers will increase or decrease by powers of 10 when you multiply or divide them, you can help them discover the happening pattern. Simply put, each time you multiply by 10, the digits shift one place to the left, and a zero is added. Each time you divide by 10, the digits shift one place to the right.

Students must understand what is happening before they jump to the pattern, but once they have that basic understanding, pattern recognition makes it even easier.

An excellent way to start this is by having students act it out. The easiest way to do this is to go outside and use chalk.

Draw a place value chart on the ground and have various numbers written on paper. Then, give students a digit and have them make the number by standing on the chalk place value chart. Give your students an equation that requires them to multiply or divide by powers of 10. They must work together and physically move to represent the new number.

In this activity, students will see that they sometimes need to add a zero to the number or that the value of their digit has changed. After they do this, talk with your students about the patterns they notice. This is an excellent opportunity to segway into the pattern recognition of multiplying and dividing with powers of 10.

Once students have mastered pattern recognition and understand that the digit values increase or decrease by units of ten, you can teach them to move the decimal point. But you do not want to jump to this too early. You must ensure students understand what is happening before giving them the shortcut!

## Multiplying and Dividing with Powers of 10: Real-World Math

One of my favorite ways to ensure math skills stick with my students is to show them how the concept connects to the real world. This provides relevance and meaning to students. When students see that they will use this math skill, they will be more motivated to learn it. Here are some real-world examples you can give your students…

- Converting units of measurement
- Using scientific notation
- Money transactions
- Making models or scaled items

With this real-world Math City Bank project, students can practice multiplying and dividing with powers of ten (along with other place value skills). In this math project, students will solve money problems like bankers.

This activity provides relevance and practice in a skill that your students need. Check out the Math City Bank here.

## Multiplying and Dividing with Powers of 10: Practice

Provide plenty of practice opportunities for your students. The more students practice, the more they will start to quickly apply the patterns of multiplying and dividing with powers of 10 until they become automatic. Check out these engaging, no-prep, and standards-based color-by-number activities.

- Multiplying and Dividing with Powers of 10 (without exponents)
- Multiplying and Dividing with Powers of 10 (with exponents)

Check out these color numbers for the 4th and 3rd grades if you want some prerequisite skills to practice.

By reviewing the vocabulary needed for the skill, using manipulatives and visual representations, and providing real-world connections and practice opportunities, we can help our students master the concepts of multiplying and dividing with powers of 10. So, which strategy are you going to use with your mathematicians today?

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