Multiply and Divide by 10

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Students will be able to identify patterns in the multiples of 10 and represent and solve multiplication and division problems with 10

Big Idea

Counting by 10's is easy for students of this age. Knowing that base 10 can be used to help multiply and divide in the higher numbers by decomposing is critical. This lesson sets the base for future work.

Warm Up with a Journal Response

10 minutes

Today, I decide to have the students really dig into the vocabulary expression "Commutative Property."  I want to be sure the children understand how this property can help them solve problems going forward.

Boys and girls, I have placed our vocabulary card for the Commutative Property on the board.  It has an example of what this property means.  We have been discussing this idea for a few days.  Will you please copy the prompt on the board and write as much as you can about what you notice, know, or even wonder about the Commutative Property?  You may use words, drawings, and numbers to explain your thinking.

Next, the students share out what they wrote, and drew, with a partner.  You may want to walk around and choose to share the examples that best review the property.  I always allow students to edit and add to their journals when we do activities like this.  

Multiples of 10

25 minutes

Have the students write the multiples of 10 on a white board or a piece of paper. I also make the choice to have a student write them on the class white board.  When I ask her to write the multiples of 10, she asks how many.  In response to my 10, she says, "Oh, to 100"!  That is exactly what I long to hear.

Mathematicians, please write the multiples of 10, separated by commas.  Write 10 or more of them. When you are finished, please look for as many patterns as you can, while you wait for your peers.

Next, begin a conversation of the patterns the children notice.  Listen for them to know that there is always a 0 in the one's place and that they increase by 10.  I also ask them to relate the 10's to dimes, as this is a real world application that they can draw on when we multiply. 

This student disagrees with a pattern another student thinks she sees. Through this conversation, we all review the difference between the tens and ones place.

Here, the students navigate a conversation about adding on to 10 and that the zero is a place holder, which makes the digit one worth 10, not 1.

In this lesson or the next, you may choose to add the vocabulary word "multiplier" to the students' word bank.  It is a precise reference when they begin to discuss the product and the number in the 10's place and higher.  

Using 10's in Word Problems

15 minutes

Display problems such as 10 x ___ = 80 and 40 =_____ x 10.  Ask students how they solve these problems.  Some will use multiplication facts that they know, while a few may think of division.

Next, I would like you and your partner to work together on some word problems in our book.  The number ten will be one of factors in some of them. You may need to divide or multiply. Remember to talk about how you know the answer. I will walk around and listen in.  Also, remember you can and should draw representations of the story if you want to visualize it better. 

I chose to use the page from the program my district provides for this activity, as it uses 10 as a factor, as well as provides problems with factors that we have already worked with.  It is important to review as well as introduce in each lesson. 


5 minutes

What a wonderful class today boys and girls.  I really think your thinking is getting deeper and I am proud of you for using math terms like factors and products.  This helps everyone know what you are thinking about.  I also like the sketches I am seeing and the way you dissect a word problem before you work on it.  

Does anyone have wonderings about the multiples of 10?  Will you please share with your partner your favorite work in today's math class?