Multiplying Greater Numbers

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Objective

SWBAT multiply larger numbers using the properties of multiplication and the short cut of counting zeros.

Big Idea

The properties of multiplication and the short cut of counting zeros can be used to multiply larger numbers.

Opener

5 minutes

The students have already learned how to use a short cut to multiply by multiples of 10 and 100  In today's lesson, they will learn to multiply greater numbers by 2-digit numbers.  This aligns with 4.NBT.5 because the students are multiplying 2-digit numbers using strategies based on place value and properties of operations.  

To get the students started and excited about the lesson, I start with having the students give me examples of multiples 10 and 100.  For the greater numbers in this lesson, they will be using multiples of 1,000.  The students will use repeated reasoning and a short cut to multiply by multiples of 1,000 (MP8).  I will let them know that now we have had much experience with using multiples of 10 and 100, we are now going to something bigger.  Today, we will multiply by multiples of 1,000.  I then let the students yell out multiples of 1,000.  I find that when they have the freedom to just yell out, they seem to really enjoy themselves.  

Direct Instruction

10 minutes

At the beginning of each lesson, I like to review all relevant skills that we have learned that will help with the new skill.  The Multiplying greater numbers power point is displayed on the Smart board.  After I read each point, I ask the students to give me an example of this with a math problem.

Review:

1.  To multiply a number by a multiple of 10, multiply the facts then add the zero. 

2.  To multiply a number by a multiple of 100, multiply the facts then add 2 zeros.

3.  Identity property of multiplication says that any number multiplied by 1 equals the other number.

The students use this information to help with multiplying greater numbers.  To give some guided practice, we work a problem together.
Problem:

1,000 people went to the banquet.  They each paid $35.00.  How much did they pay altogether?

 

Let’s find out.

1,000 x 35=

 In order to make the problem simpler, multiply 1x 35 = 35.  The identity property of multiplication can help you.  Any number times 1 equals that number. 

Next, count the total number of zeros. 

How many zeros do you see?

Yes, there are 3 zeros.

 Add the zeros behind 35.  The answer is $35,000.

 

I like for my students to interact with me during our whole group discussion.  I like to ask questions of them to make sure they are understanding the skill.  I feel that these are 3 essential questions that must be asked during the lesson to help the students learn the skill:

1.  Why did we add 3 zeros behind the number? 

2.  What property of multiplication helps us?

3.  How does working simpler problems help solve greater problems?

 

I feel that all answers should not be given to students.  During whole class discussion and group activity, students should have to "think" to come up with some information.  I feel that when they discover some things on their own, then this information stays with them.

 

 

 

 

Group or Partner Activity

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others (MP3).

 

For this activity, I put the students in pairs.  I give each group an activity sheet of word problems.  The students must decontextualize the problem and represent them symbolically (MP2).  The students must work together to find the product of the greater numbers. They must communicate precisely to others within their groups (MP6).  The students must explain how solving simpler problems help them solve greater problems.  They must justify their answers, as well as critique the reasoning of their partner (MP3).

Independent Activity

10 minutes

To give me a clear understanding of what each student knows, the students complete an independent assignment (Multiplying Greater Numbers).  Group activities are great, but as a teacher I need to assess students independently to make sure they are all receiving the help they need.  I put a problem on the Smart board for the students to work (see attached resource).  The students use paper and pencil to solve the problem.  I walk around to visually assess the students understanding, keeping track of all students who I will work with in small group for remediation.

 

Problem:

1500 students all received 3 books each.  How many books did they receive all together?

 

What strategy did you use to help you solve this greater problem?

 

 

Closure

5 minutes

To close the lesson, I have one or two students share their answers.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples, as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during student independent and partner sharing will be addressed whole class.  

Misconception(s):

I still have a few students not counting the zeros correctly.  If the product for the basic facts ends with a zero, then some students are getting the answer wrong.  For example, with the problem 4,000 x 15, some of the students had the answer as 6,000 instead of 60,000.