Step By Step!

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Objective

Students will explore the relationship among numbers and be able to explain the basic steps of division in a variety of ways.

Big Idea

Students love to run up and down steps; however, they never stop to think about the repeated process, through steps students will better understand the relationship among numbers using a variety of basic operations to be able to explain the methods of divi

Warm Up!

20 minutes

To make the connection, I ask students what happens if they run up and down steps for about ten minutes.  ( tired, I give up, I stop) I say exactly! So, what happens when you guys are trying to explain the steps to division.  ( I stop, I forget, I can't remember) What if we can learn a simple method to help us remember and explain the steps of division better? Who is ready to give it a try?

In this lesson I want my students to explore the use of the four basic operation(algorithms) to understand the relationship between numbers, so that they can better explain the methods of dividing four digit dividends by one and two-digit numbers with and without remainders. To give students a better understanding of remainders, I will use base tens to represent the quotient with a remainder. This will allow students to make connections of how remainders are determined. (MP7) Look for and make use of structure.

To get started I review the parts of a division problem to make sure students understand how to use correct mathematical terms when explaining their answers.

Model1.docx

After that , I model what I want them to be able to do throughout the lesson.  First, I make mention of all of the operation I will use as I demonstrate how to divide a two-digit dividend by a one-digit divisor.

Demonstration:

Sometimes you guys will encounter a division problem set up sentence form, how would I set this problem up to solve?

 42 ÷ 7

Response:

Place the divisor (7) before the division bracket and place the dividend (42) under it.    

7)42

Ok! Now that the problem is set up we should examine the first digit of the dividend (4). It is smaller than 7.

Can we divide now?

Response:

 No, because the dividend 4 is smaller than the divisor 7. Therefore, it cannot produce a whole number.

I ask students to take a guess about what I need to do next.

Response:

 Next take the first two digits of the dividend (42) and determine how many 7's it contains. In this case 42 holds six sevens (6*7=42). Place the 6 above the division bracket. 

   6

7)42

After we have divided, I make mention of the next step here.  I tell students now it is time for us to multiply. Can you tell me which numbers I need to use to do this?

Response:

Multiply the 6 by 7 and place the result (42) below the 42 of the dividend.

   6

7)42

  42

I tell students we are almost finished here. Can anyone think of the next step?

Response:

Draw a line under the 42 and subtract it from 42 (42-42=0). Since the result is 0 the division is finished and 6 is the answer.To give students a better understanding of remainders, I will use base tens to represent the quotient with a remainder. This will allow students to make connections of how remainders are determined.

I repeat this strategy and increase the dividend by one digit to demonstrate dividing three and four digit dividends by one and two-digit divisors. However, I ask a student volunteer for a sheet of notebook paper, I show them how to turn the paper horizontal to form columns in which to place the digits according to the value when dividing numbers. Throughout the next two demonstration I will ask students to justify each step. It is my hope that during demonstration and active conversation students will better understand relationships among numbers, how to use the four basic operations, compute better, and make reasonable estimates to help them become more fluent. (MP8) Look for and express regularity in repeated reasoning.

I may repeat the division process to make sure students understand, before I move them deeper into the lesson.

 

Applying the Method!

10 minutes

Alright guys you are moving up the steps now! Everything we do has steps. In this portion of the lesson we will be using the steps to making dice to create our own dice. We are going to use them in a fun activity to help us better understand division. 

Before the lesson starts, I have students work in their assigned groups to make their diceMaking Dice

I want to give students some additional practice before they are paired in groups. I explain, I know a fun way for you guys to explore division. Who is ready to get  a little active?  Everyone raise their hand! To make sure all students gain a better understanding of remainders, I ask a student volunteer to create a model using base tens to represent the quotient with a remainder. I write a division problem on the board. 24 divided by 5. I carefully work my way through the problem explaining each step along the way. I get students involved by asking them to tell me what to do next.  Students notice that have 4 left over. As the student volunteer begin to represent the quotient with the remainder, I ask him to explain how he will represent the remainder, and why? This will allow students to make connections of how remainders are determined.

MP1-Make sense of problem and persevering in solving them.

Directions:

Divide students into groups of two or three. Provide each group with a hundreds board.pdf, dice, and highlighters. Have one student in each group to choose a number and lightly color it with the highlighter.  Roll the dice and divide the number highlighted on the hundreds board by the number displayed on the dice.  Continue until time is up. 

As students are working their way through this concept I will circle through each group asking students to explain the process. I hope to see that they can visually see the repeated pattern used when dividing.  (Divide, Multiply, Subtract, Bring down, Repeat) For instance, I may ask students who are subtracting what step comes next.  

Working it Out!

20 minutes

I start by saying let's use those steps STEPPERS..

In this section of the lesson, I want students to practice (pair work.docx) working on dividing two- and three-digit dividends divided by one- and two-digit divisors. Students will work with a partner to work their way through the given problems.  

I have students turn their lined notebook paper horizontal to form columns in which to place the digits when dividing numbers.  I ask students to justify their answers by explaining the use of the four basic operations. To give students a better understanding of remainders, I ask them to represent the problem using base tens. This will allow students to make connections of how remainders are determined. When they have constructed their explanation, I ask students to check their answer with a calculator, and turn to their neighbor and ask them to check and explain their work.

Questions:

what happens if the divisor is larger than the first number in the dividend?

Response:

Bring on another number until your dividend is larger than your divisor.

After you divide, what do you need to do next?

Response:

multiply the number on top by the divisor.

what operation do you perform after you multiply?

Response:

You will need to subtract.

After you have subtract, what do you need to do next?

Response:

Check to see if you have a number to bring down, if you do bring down, and start-over at divide.

MP8-Look for and express regularity in repeated reasoning.

When their time is up, have students pairs to share what they noticed with other pairs. As students are engaged in conversation I will circle the room to check or understanding. 

Students Sharing their thinking.jpg

Exit Ticket!

10 minutes

Material: note taking paper.pdf

Motivate 

I start this portion of the lesson by inviting students to join my team of STEP WRITERS.  They are eager to know what this is! 

Math Journal Entry

I explain....... I want you guys to demonstrate what you have learned by constructing your own division problem. After you all have construct your problem, I want you to solve the problem and explain your answer by writing a brief description of how you solved your problem. As students are working, I circle the room to reinforce the purpose of this lesson. For instance, I ask some students to explain the steps of division.  While it is crucial that students’ work, abilities and progress be tracked and assessed throughout the entire learning process, it is also important that I have proof of what students have learned during that process. This journal entry tells me and the student what areas are clear to the student, and which will require more work.

 When students are finished working on their exit ticket. I will invite student volunteers to share their work. I will use their work to assess students knowledge, and to see if I need to re-teach this lesson in a smaller setting.

students express their work.jpg