Multiplying decimals can be straightforward if students grasp a simple trick: remove the decimal place and multiply the whole numbers. But is it enough for them to just follow steps, or should they truly understand why these steps work?
In my teaching approach, efficiency is key, but so is building a solid foundation. Imagine a house—without a strong foundation, any extensions will be shaky in a storm. Similarly, without a strong grasp of foundational concepts like place value and decimals, students may struggle with more complex problems.
This is true for when we are teaching our students to multiply decimals. Do your students understand place value, or what decimals are?
Lesson Plan – Multiplying Decimals
Activating Prior Knowledge
Start with a warm-up to refresh students’ understanding of decimals and place value. This primes them to build upon existing knowledge.
Explicit Teaching of Steps to Success
Introduce the shortcut of temporarily removing decimals, multiplying the whole numbers, and then replacing the decimal. I humorously tell my students that mathematicians are lazy—they aim for the quickest solutions. However, it’s crucial to delve into the mathematics behind this trick to ensure understanding.
In my resource, “Everything Decimal,” I include a video that demonstrates the mathematical reasoning behind this efficient strategy:
- Decimal places as Powers of 10
Decimal places represent a division by 10, 100, 1000 depending on the place value of the last digit! For example, 2.5 is actually and 3.46 is actually . When you multiply 2.5 by 3.46, you are multiplying x , which is .
- Combining the multiplication of Division
By multiplying the whole numbers, we get 8650. This must then be divided by 1000 (10×100), to account for the decimal places. Therefore, = 8.65
After Students understand this foundation, I then teach the explicit steps to success, as follows:
Guided Practice
Provide opportunities for students to work alongside you on simple multiplication problems involving decimals. Using whiteboards allows them to experiment freely without fear of mistakes.
Independent Practice and Application
As students gain confidence, introduce more complex problems, including worded scenarios. Group work encourages peer discussion and reinforces learning in a cooperative setting
Lesson Review and Exit Ticket
Allow 5-7 minutes to review learning and provide students the opportunity to reflect on their new knowledge. I return to the lesson Intent and students can assess their own level of understanding.
Exit Ticket Ideas
Error analysis: On the board, write a solved equation with an error. Students need to identify the error and correctly solve the problem to leave the classroom!
Buddy Questions: Each student writes a multiplication question on a sticky note for their buddy to solve. The original author of the question must ensure their buddy has answered it correctly, if they have made a mistake, they must identify the error and teach their buddy the correct answer.
