Multiplying 2-Digit Numbers by Multiples of Ten

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Objective

SWBAT use grids and a short cut to multiply 2-digit numbers and multiples of 10.

Big Idea

Once students understand patterns when multiplying by 10, they learn a short cut that can help multiply 2-digit numbers by multiples of 10.

Opener

5 minutes

I tell the students, you have learned to estimate to find the product of numbers.  You have also learned the distributive property.  In today's lesson, you use both strategies to multiply a 2-digit number by multiples of 10.  I ask the students, "Who can name a multiple of 10?"  All of the students' hands go up.  I tell the students to call out the multiples of 10.  The students yell 10, 20, 30, 40, etc.    

Direct Instruction

15 minutes

To begin the lesson, I call all of my students to the carpet. This gives all of them an opportunity to sit close and absorb all of the information from the lesson.  We begin the lesson with a review.  

Review:
1.  When you multiply by multiples of 10, you multiply the basic facts and then add 1 zero.  For example, 10 x 5 = 50.  We know that 10 is repeating 5 times.  Based upon what we have learned about addition, we know that there will be a 0 in the ones place when we add 10 together 5 times.  Using a shortcut, we can just multiply the basic facts and add the one zero.
 
2.  ÂžWith the distributive property, you make two simpler multiplication problems by breaking apart one of the factors.  When you break apart one of the factors into two numbers, the two numbers must add back to equal that number.  (ex. 7 x 8= (6 x 8) + (1 x 8)
After the review, we go directly into guided practice.  With my guided practice, I like for my students to be interactive with me.  In our classroom environment, they know that they can just jump in to make comments or ask questions.  
For guided practice, we will use a real-world scenario.  This way the students can relate to what is going on in the problem and it feels relevant to them.
Scenario:

Tonya counted 15 bikes on her street as she roller skated.  As she passed the bikes, she noticed that they all had 40 spokes on their wheels.  How many spokes are there in all?

In this problem, they are asking us to find the total number of spokes on the bikes.  This is a multiplication problem.  Notice that one of the numbers is a multiple of 10.
žWe can use the distributive property when multiplying by a multiple of 10.
ž15 x 40 =
žWe need to break apart the 15 since it is not a multiple of 10.  It is easy to multiply by multiples of 10.
What 2 numbers can we break apart the 15 into?

 Call on a few students to explain how to break about the 15.

We can break apart the 15 in many ways.  Let’s break apart the 15 into 10 + 5.

(10 x 40) + (5 x 40)=

400 + 200=600

Underline the basic facts which is 1 x 4=4.

Next, count your zeros and add them behind the 4 which gives you 400.  For the next problem, the basic facts are 5 x 4= 20.  Add one zero behind the 20, which gives us 200.  Last, add 400 + 200=600.

Because I want the students to use area models, I show a quick video before the students go to their seats.   

 Possible Misconception(s):

1.  Not adding the zero when using the short cut to multiply by tens

In order to get students to understand that when they multiply by tens that there is always a zero in the ones place, I will use examples.  In the problem above, the students multiply 10 x 40.  I would explain to students that 1 x 4 = 4 but they are not multiplying by 4, they are multiplying by 40 - which is 4 - tens.  1 x 40 = 40 so 10 x 40 would be 40 ten times which equals 400. They can also draw a visual model to represent the problem.



Group or Partner Activity

20 minutes

To give the students practice with the skill and to allow them to work with their classmates, I will allow the students to work in pairs.  I let my students work in pairs because it is small enough for all of the stdents to be heard.  The activity the students will work on will require the  students to make a model of the distributive property (4.NBT.5 Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.)  The pair can choose a problem to solve from a list of 2 digit multiplication problems.  The activity is as follows:

1.  The students will work together to break apart a problem into 2 simpler problems. (MP2 -Mathematically proficient students make sense of quantities and their relationships in problem situations.)

2. Cut out an area model of each simpler problem with grid paper (MP4)

3.  Glue the model on the construction paper

4.  Find the product 

5. Explain how the model helped find the product.

 

Independent Activity

10 minutes

To let me see how well each student understood this skill, the students will complete an independent assignment.  The students will need paper and pencil to solve the problem.  Have the problem displayed on the Smart board.

Problem:

20 people gave money to a charity.  They each gave $25.  How much did they give in all?

 

Directions:

1.  Use the distributive property to solve.

2.  Explain how the distributive property helped you find your answer.

 

As the students work on the independent activity, I walk around to observe their work.  Any student that is having a difficult time finding the product is identified and will be put in a small group for further instruction.  

From my observation, I noticed several students struggling with this skill.  I am not surprised because multiplying a 2 digit number by 2 digit number has always started out difficult for a lot of the students.  Even though we have worked on the distributive property in other lessons, it was with multiplying a 1 digit by 1 digit.  The students seemed a bit confused by breaking apart the 2-digit number, multiplying, and then adding the two partial products.  We will continue to work on the skill.