Multi-digit Multiplication Strategies

 

Multiplication strategies-01

This past week my third grade class investigated different ways to multiply numbers.  Before diving into this concept I asked the students their thoughts on multiplication.  A few students explained to the class their view on the topic of multiplication.

  • repeated addition
  • double or triple “hopping”
  • using arrays
  • “timesing”
  • Increase the number by “a lot”

Most students were able to showcase examples of the above.  Even though their vocabulary wasn’t exactly spot-on, students were able to come to the whiteboard and show their thinking.

I received different responses from the students when asking them about multi-digit multiplication.  Actually, it was more of a lack of response.  I feel like some of this is due to exposure.  A few students raised their hands and asked to show their process to multiply multi-digit numbers. These students showcased their ability to use the traditional algorithm. The class reviewed this method with a few examples.  Although students were finding the correct product they had trouble explaining the process. Students weren’t able to communicate why it worked or another method to find a solution.

On Tuesday my class started to explore the partial-products algorithm.  Students were able to decompose individual products and find the sum.  This made sense to students.  Students were able to connect an area model with the partial-products method.  They started to write number models right next to each partial-product.

Later in the week students were introduced to the lattice method.  This method seemed “fun” for the students, but didn’t make as much sense as the partial-products method.  Students were able draw the boxes and create diagonals to find the product.  Some students had trouble with laying the boxes out before multiplying.

During the last day of the week students were asked to explain in written form how to multiply multi-digit numbers.  Even though all of the students could use the traditional, partial-products and lattice methods, they were stuck for a bit.  Soon, most students started to lean towards using the partial-products method to explain how and why this method works.  I asked one student in particular why it made sense and she said “I can see it visually and in number form.”  Although most students were able to use the other methods effectively they didn’t seem confident enough to explain why the strategies worked.

Students will be expected to multiply multi-digit numbers on the next unit assessment.  The method to multiply these numbers will be determined by the student, but I’m wondering how many will gravitate towards the strategy (not just the process) that they understand.

 

 

Exploring Subtraction Computation Strategies

During the past few weeks my second grade class has been taking apart and putting together two and three-digit numbers. In the process students have been developing a better understanding of numbers.  They’ve been exposed to using a variety of computation strategies to find the sum and differences of numbers.  Through all of this I’m finding that the students are becoming more confident in their ability to use these different computation strategies more fluently.   Although they’re confident they tend to gravitate towards using one specific strategy for computation.  The traditional algorithm is usually the primary method that they use.  Even though students can add/subtract using that method I found that they weren’t expanding their understanding of other computation strategies.  This was a bit of an issue for me because students started to look at computation as the shortcut and not delve into the understanding of why it works.

After speaking with a few other teachers I decided to use a math task found in this book.  I briefly reviewed the different strategies that we’ve learned this year and gave the students this prompt.

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I wanted to make sure that students showed two different strategies and provided some type of written explanation.  The template I copied also had fields for a number model and explanation boxes.

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The bottom of the sheet was designed for students to be able to check their work using addition.

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I gave the students about 10-15 minutes to complete the formative assessment.  Most of the students tried out the standard subtraction algorithm but had a bit of trouble with the second strategy.  After a few moments students started to dig deep and think of how to take apart numbers using different strategies.  Some of the  students truly had trouble using a different strategy and this was evident in what they produced.  I was impressed with some of the different strategies that students used.

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I wrote feedback on the papers and handed them back to the students the next day. Afterwards, I removed the names off of the papers and shared some of the results with the class.  As a class we decided on the following:

  • Students remembered many of the different computations strategies that were discussed earlier in the year
  • Some of the students invented their own strategies on this particular sheet
  • Students need to strengthen their written explanations
  • Students had some trouble explaining what regrouping means

Next week the class will be setting goals in improving our written responses.  Overall, I feel like this activity helped showcase different computations strategies while bringing awareness to areas the need improvement.  I’d like to use this template with a few other classes later in the year.  Feel free to download and edit this file for your own classroom.