Using Mental Math to Multiply 2-Digit Numbers (Are You My Match?)

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Objective

SWBAT discover and understand patterns used to multiply by 10 and 100.

Big Idea

Basic facts and place-value patterns can be used to mentally multiply a two-digit number by a power of 10.

Opener

5 minutes

Rationale:  This is an important lesson because it teaches the students to look for patterns when multiplying by multiples of 10 and 100.  The students have learned to look for patterns since kindergarten because they know that patterns are everywhere.  Using patterns can help the students find the product to a multiplication problem in an efficient and accurate manner.

 

I remind the students that they have learned how to multiply a number by a 1-digit number. Also, they have learned to round numbers.  Now, you will use mental math to multiply greater numbers by multiples of 10.  I have the students count out loud the multiples of 10.  "What are some things that come in multiples of 10?"  I let the students think about the question for a few minutes.  I call on 1 or 2 students to respond to the question.  One student responds, "You can buy gum in packs of 10."  Another student responds, "You can have a lot of 10 dollar bills."  I say, "In today's lesson, you learn to multiply multiples of 10 and 100 by using a pattern."

Direct Instruction

10 minutes

To begin the instruction, I call my students to the carpet.  I will be using the Smart board to present a power point and I like for my students to be near me so that I can make sure I have all of their attention.  This will be an interactive direct instruction lesson.  My students know that when I ask a question that any of them can jump in with the answer.  All I require is that they be respectful of each other.  

To begin the lesson, we review information that we have learned from previous lessons that will be beneficial to this lesson.  

Review:

Multiply the basic facts, then count the number of zeros.
You can use an array to represent the basic facts.
Look for patterns when you multiply.
To give the students context to use for this skill, I have created a scenario that the students can relate to in their own lives.  If the students can relate to it, then they tend to see the relevance to learn it.
Problem:
At the local mall there were 200 stores having a sale.  Each store was giving away 40 coupons.  How many coupons did they give away in all?

Our multiplication problem is 200 x 40 = ___

When you are multiplying by multiples of 10 and 100, you can multiply the basic facts, then count the zeros. (I let the students know that by using this method, it gives them a way to solve the problem quickly without mistakes. I explain to the students that we have already learned about place value.  We know that the 2 is in the hundreds place and the 4 is in the tens place.  Therefore, we have 200 repeating 40 times.  Only because the numbers end with zeros, we can solve the problem using this strategy.)

Basic facts:  2 x 4 = 8

Number of zeros:  3

Therefore, 200 x 40=8,000

We can also use an array to help us find the product of our basic facts.

200 x 40=

Basic facts:  2 x 4= 8

Array:

            XXXX

 ï»¿           XXXX

 Then add the 3 zeros to get 8,000.

 

We can use patterns to help us multiply greater numbers by multiples of 10 and 100 (MP7).
200 x 4= 800
200 x 40= 8,000
During the power point, I try to address any misconceptions that I think the students will have.  One possible misconception:
1.  If the basic facts multiplies together and the products ends with a zero, the students will think that the zero in the ones place counts as one of the zeros that they must add.
(Example:  In 50 x 40, 4 x 4 = 20.  The students think that the zero in 20 counts as one of the zeros that they must add.)
To address this misconception, I include an example in the power point.  This will give students practice with this before they get into their groups.  One thing that I like for my students to do that helps with this problem is for them to underline the numbers when they multiply so that they can see what is left.  For example with 50 x 40, when they underline the 5 x 4 and write 20, then they see in their problem that there are 2 zeros that they need to add and write behind the 20.  

Group or Partner Activity

20 minutes

To let the students practice the skill, put them in groups of 6.  The group arrangement is purely for having an even number of people to pass out the numbers for the activity.  The students will  be interacting with all students in the classroom for this assignment. Rounding is a skill that is familiar to my students for smaller numbers.  Because it is familiar to them, I feel that it is appropriate to have fun with this lesson by getting them up and moving around in the class during this activity.  This is a mental math activity, so they will not need paper and pencil.  

Activity:

The activity is called "Are you my match?"  The students will each get  a multiplication problem with greater numbers.  They must estimate their number by rounding it to the greatest place and then multiplying.  (I have explained how to round to the greatest place in previous lessons.  The students know that if it does not tell them which place to round to, then round the number in the greatest place value.)  Once they have rounded their numbers mentally and solved for the product, they will have to find someone in the classroom that has the same product.   In order to know if that person has their match, the student will have to mentally round that person's number and multiply.

When they find the person who has the match, check to see if they have the winning problems.  (I have a prize for the winning pair.)  On the attached problems, the word "prize" is written on several of them, but there is only one pair that both have the word "prize" written on them.  I do not let the students know what this means until after the activity.  It may discourage the students without the word "prize" on their problem from participating.  (In the future, when I teach this lesson, I will have a small prize for all students at the end, and maybe something a little larger for the winners. This way all students will be rewarded for their efforts.)

In this activity the students are very interactive with each other.  They critique the reasoning of others because they must agree that they have matching products (MP3).  

In the Video - Using Mental Math to Multiply by 2 Digit Number.mp4, I explain how this activity helped the students learn the skill.

 

 

Independent Activity

10 minutes

After the group activity, the students will complete an independent assignment.  This will enable me to see what each student knows.  For this assignment, the student will need paper and pencil.  

On the Smart board have the following assignment:

 

Find the product

7 x 70=

60 x 80=

50 x 200=

 

Short answer:

Explain how to multiply by multiples of 10 and 100.

Closure

10 minutes

To close the lesson, I bring the class back together as a whole.  I call on 2 students to present their answers.  I will select students based upon the answers that I saw on their papers as I walked around.  If I find a student with an incorrect answer, I will select that student as 1 of my students.  The reason that I will select this student's work is because it gives the class another opportunity to critique the reasoning of others and it gives me a chance to reach any other student that has not mastered the skill.

Possible Misconception:

If the basic facts multiplies together and the products ends with a zero, the students will think that the zero in the ones place counts as one of the zeros that they must add.

Example:  In 50 x 200, 5 x 2 = 10.  The students might think that the zero in 10 counts as one of the zeros that they must add.