Multiplying multiples of ten - Not your Daily Grind

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SWBAT practice making area models to find products of one-digit by two digit multiplication problems.

Big Idea

Students continue to deepen their understanding of multiplication and look for patterns in structure as they multiply by multiples of ten.

Warm Up

4 minutes

I start this warm up by playing this song for students. 


These songs never get old for my students and it's one of the things they look forward to.  

Now that we have defined the terms multiple and factor, I explicitly point out that we are saying multiples of 7 each time we say a number in this song.

I want students to start making the connection that when we count by a number, we are listing a product and a multiple.  Students begin to realize that they can look at the multiplication chart hanging on the wall and see all the multiples in the song by following along on the chart; 7 x 1, 7 x 2, 7 x 3, etc. Skip counting can also be a powerful way for students who have not mastered their multiplication facts to practice. 

Concept development

45 minutes

I find the information in this lesson to be a critical step for my students to master in order to be successful with CCSS 4.NBT.5.  When students are able to find products of a number and a multiple of ten, they are often more successful when using an area model to solve double digit by double digit multiplication problems.  When students use large amounts of time and brain power to solve a problem that is multiple of ten, in past experiences, these students often lose sight of what the intended problem is asking.  They forget that they might be solving a problem like 22 x 36 because they are stuck trying to compute 20 x 30 or the tens in this problem.

I start this lesson with this Khan academy video.

While I don't love the part in this video when the instructor points out that you can "just add a zero", I do like the way he is rewriting the equations. This is a skill my students definitely need practice in. After watching the video, students practice this skill on their whiteboards.  I list a problem on the smartboard for students to calculate, and they show their work on their whiteboard.  When they have found the product, they show their whiteboards by holding it above their heads.  I have them do this several times until it appears that most students are able to do this.

For the remainder of the lesson, students participate in what I call coffee klatch.  I usually use this formative assessment with vocabulary words, but decided to use it for math problems today. 

I give each students a cup filled with multiplication number sentences, a single digit multiplied with a multiple of ten, to solve.  For this lesson, all problems in the cup are numbers sentences in which a multiple of ten is multiplied to a single digit number.  When the music plays, students walk around the room to find a partner. When the music stops, students sit with a partner. They reach into the cup and pull out one problem to solve. They then solve this problem and practice their math talk while solving the problem. One students is writing the problem and solution while talking about it to their partner while the other person listens. The partner should watch, and listen intently while the student explains how to solve the problem and solves the problem.  Then, partners switch roles.

While students are discussing and solving, I am constantly walking around listening to students and making notes about students who seem to struggle and which students are understanding the concept. If both partners share and solve before the music begins again, they are allowed to continue conversing about math. An important piece to this lesson is MODELING!  I model what is appropriate conversation, pace in walking (although the music helps with this as well) and what to do when the music stops.

In the following video, two students continue a math conversation as they were waiting for the music to begin.


When it looks like most students have solved and shared, I start the music again for students to find new partners.  I use a jazz channel from to play as students mingle around the room. 

This is what my classroom looked like as students participated in the coffee klatch.   I love how they are pretending to drink coffee.  :)



Student debrief - Wrap up

15 minutes

Instead of a traditional "pop quiz,"  I gave the students a "coffee quiz."  I posted the coffee quiz on the board for students to complete.  I asked students to show in numbers or write in words how they computed their product.  For most students, finishing the sentence for question 4 on this quiz confused them.  I find that students are still very reluctant to write in math.  I have my work cut out for me this year to get my students to realize that writing in math is about communicating or Math Practice 3.  When it comes time for a quiz or test, my students still have in their mindset that they should compute a page of problems for an assessment.

Math Practice 7 is a math practice standard that is always in the back of my mind.  Maybe it's a favorite!  You can see from this student's response: number 4 from coffee quiz, I am always pushing students to tell me more and be more specific.  I love this response that this student feels good about multiplying by multiples of ten, but I always try to give constructive feedback as well.  While I can probably guess the pattern this student is talking about, I strive for them to communicate specifics.

This is another response that made me chuckle: similie number four coffee quiz.  Again, this student feels very confident about his/her multiplication by multiples of ten skills.  The simile truly made my heart happy.  You can see the CCSS language standards for fourth grade here.  Explaining the meaning of simple similes and metaphors is context is asked of fourth graders.  I think she's got the simile down!