Compare methods of one digit by double digit multiplication

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SWBAT practice one digit by double digit multiplication and look for patterns in multiplication methods.

Big Idea

Students continue to refine their methods for multiplication by one digit numbers and look for patterns among methods.

Number Hook

7 minutes

This is a great trick.  Most fourth graders eventually figure out how I am able to do this once we do several other dice tricks that work the same way. 

Dice in Water Trick!

Ask a person to drop three dice in to a glass of water. Then ask them to hold up the glass,add up the total of the numbers on the bottom faces of the dice and then put the glass back down. You then dip your finger tips in the water, mystically rub them on your fore-head and magically tell your subject the total they have.


What's The Secret?

All you do is subtract the total of the three dice's upward faces from 21. Remember opposite sides of a die total 7 and 3 x 7 is 21.


Note:  How did it go?

My students LOVED this trick.  I have several students who are very close in figuring out why it works.  I will be doing another dice trick in a future lesson and I'm sure there will be some students that figure out why it works. 

Warm Up

5 minutes

For this warm up I wanted to revisit a skill from a previous lesson and have students find all the factors for a number.  Students need to be able to find all the factors of a number as listed in CCSS 4.OA.B.4    I list the number 56 on the board and ask students to find ALL the factors for this number.  I tell them they can use a factor tree if that will help them.


This was really difficult for my students. They need more practice in finding all the factors of a number. I will design several lessons for this after our mid unit assessment.

Concept Development

40 minutes

I start this lesson by showing students this multiplication chart. Students work towards CCSS 4.NBT.5 in this lesson in their progression of multiplication. Math practice standard 7 is prevalent in this lesson as students attempt o make connections between strategies.  Math practice standard 1 is also developed in this lesson as students mentally wrestle with the various methods and how those lead up to the standard algorithm.  This is an exciting time in mathematics for fourth grade students.  They are so eager to learn how to multiply large digits.  I find that pointing out their perseverance whenever possible adds to the classroom climate of valuing challenges and mistakes. 

I give them about one minute of silent thinking time to look at the chart and make mental observations about what they notice about the various methods listed.  Then after that one minute, I give them 3 minutes to talk with the learning partner about what they noticed.  

A key to making this lesson successful is to stress the vocabulary of the digits place value when multiplying it with another digit.  I want all my students to take away that the values of the digits are important. For example, when students build the the number 28, nine times, they can see the two tens, or twenty being built nine times which results in 20 x 9.  It is important for students to make the connections that in each method, each digit is being multiplied to each other, but the value of the digits is important in determining the partial products and total products. 

Comparing six methods at once is a task of great complexity and many students will struggle to make sense of all six methods. I don't expect students to master each method, rather simply be presented with various methods in order to make connections about how multiplication works.  By seeing the various methods, I want students to deepen their understanding of multiplication using strategies based on place value and the properties of operations. CCSS 4.NBT.5 states that is what students will know and be able to do.

Students will spend about the next 25 minutes using one or more of these methods to solve 8 multiplication problems. I have them divide a piece of paper into fourths. On the first side, students solve 36 x 4 in each rectangle using a different method in each square. This really pushes them to think critically about how all the methods are similar and connect to each other.  On the back side of the paper, students solve four different multiplication problems and choose a method or several methods of their choice to use in order to find the products.

 The following video shows a student talking about the "shortcut method" or the standard algorithm.   This student has not been shown the shortcut before by teachers or parents and he is just now making sense of the algorithm and why it works.  I especially love the  end of this video when I ask this student to use the algorithm with a three digit number. He responds by asking if he can practice it first before I video him.  You can see that he is truly attempting to understand this method. 

Some students will be very comfortable with the area model and need guidance and support in trying a numeric method.  Students who are not at an abstract level in their thinking at this point are allowed to use strictly the area model, but this would only be a scaffold for a few students based on previous lesson observations.

After the 25 minutes, I then show an area model for a three digit by one digit multiplication problem.  I ask students what similarities they see between the area model for double digits by one digit,  and the area model for triple digits and one digit.  Once students are able to verbalize patterns they see with the area model, I then ask students about using a numeric methods to calculate the product. We do several together in our math notebooks.

If students did not finish the 8 problems, I assign it as homework.


Student debrief - Wrap Up

5 minutes

Student will complete an exit ticket today and place it into the exit door holder as the leave.  Students will find the product for one problem on their exit ticket.  I ask students to find the product for 6 x 63 using a method of their choice.