Grid Method for Division

Welcome Back!!
This week I will be discussing division. As we know, division is often an operation that can be frustrating to our students. After doing some research, to better help my students to divide, I came across this strategy to divide called the Grid Method for Long Division.

Standard: 
CCSS.MATH.CONTENT.4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

STEP-BY-STEP INSTRUCTIONS

Suppose that we want to solve the equation 324÷2.

STEP 1:
First we draw a grid. The number of sections in the grid depends on the number of digits in our dividend. For this equation, our grid will have 3 sections. We write the digits from 324 inside the grid, and we write our divisor (2) on the left side.

STEP 2:

Now we ask ourselves, “How many times can 2 go into 3?” The answer is 1, so we write a 1 on top of the grid. We now multiply 1×2 to make 2, and take that 2 away from the 3. This leaves us with 1.

STEP 3:

Now we bring that 1 over to the tens place of the next section on the grid. This gives us a 12 in the next section.

Now we ask ourselves, “How many times does 2 go into 12?” The answer is 6, so we write a 6 on top of the grid. Now we multiply 6×2 to make 12, and take that 12 away from 12. This leaves us with 0.

STEP 4:

We carry that 0 over to the tens place of the next section on the grid. This doesn’t affect that number, so we still have 4 in the next section.

Now we ask ourselves, “How many times does 2 go into 4?” It goes 2 times, so we write a 2 on top of our grid. Now we multiply 2×2 to make 4, and take that 4 away from the 4. We are left with 0, which means that we have no remainder.

To find the final quotient, we simply list the digits from the top of the grid: 1, 6, 2. So 324÷2=162.

Reflection:

What I like about this strategy is that it will give students who struggle with the standard algorithm for division, can use this. It is neater and spreads the divined out. I often find that students who struggle with the standard algorithm for long division. struggle with it because it becomes sloppy. I would use this extra strategy to assist my students who are having difficult with other strategies that the curriculum offers. It can be a strategy for my intervention group. 

QUIZ, QUIZ, TRADE

Welcome back!!

This weeks post will be about Mathematical Vocabulary.
When teaching mathematics, it is common to tell students that math has a vocabulary of its own. The common issue I see when students are discussing work in math is their ability to use the correct math vocabulary to make their point. 

Todays post aligns with the Math Practice 6 (MP.6)

MP.6: Attend to Precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

Here is a fun  activity that can be done in the classroom to assist with building students ability to understand how to use mathematical vocabulary:

QUIZ QUIZ TRADE!!

Quiz, Quiz Trade is a cooperative learning activity from Kagan Publishing and Professional Development

It is a activity that can be used all subject areas. Here is how it can be used for mathematics and mathematical vocabulary

Step 1: Create Questions

Provide each student with a flash cards about the current unit of study. One side of the card has a question or vocabulary term and the other side provides the answer or definition.

*Example:
Vocabulary Word                                         

Definition 

Step 2: Pair Up

Have students use stand up/ hands up and pair up method to find a partner

*Instructions for Stand Up, Hand Up, Pair Up

Partner A holds up the flash card with the Math Vocabulary word to show Partner B the question. Partner B answers. Partner A praises if correct or coaches if incorrect. They switch roles and Partner B asks Partner A the next question (another vocabulary word).

Step 3: Hands Up

After thanking each other and switching cards, Partner A and B raise their hands to find a new partner and repeat the process for an allotted amount of time.

Sample Template for Vocabulary Cards

Vocabulary Word:	Definition:
Vocabulary Word:	Definition:
Vocabulary Word:	Definition:
Vocabulary Word:	Definition:
Vocabulary Word:	Definition:

Video example of QUIZ, QUIZ, TRADE in action

Reflection:

What I learned from this cooperative learning activity is how to expand my classroom, beyond the normal vocabulary learning techniques. I see many opportunities for students to become engaged and learn while having fun. In order for students to be more effective communicators in mathematical discussion, vocabulary needs to be understood. Fun activities like this can be the catalyst for better discussion in math class. 

Place Value Relationships

Hello all my name is Maalik Wise, and welcome to my Blog. For my first post I decided to focus on Generalize Place Value Understanding, with a deeper focus on Place Value Relationships and one way to teach this topic to a 4th Grade mathematics class.

Curriculum Source: Envision Math 2.0 (Scott Foresman, Addison Wesley)

Content Standards: 

• 4.NBT.A.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
•  4.NBT.A.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form

Mathematical Practices Used: 

• MP.2: Reason abstractly and quantitatively
• MP.3: Construct viable arguments and critique the reasoning of others.
• MP.8: Look for and express regularity in repeated reasoning

Mini Lesson:

Explain to students that they have learned how to read and write numbers in different ways. 

Anchor Chart with the different ways to write numbers should be displayed for students

 Today they are going to learn how to explain the relationship between adjacent digits. (Review the word adjacent) 

 *Adjacent means next to or adjoining something else 

Write the following number on the board 88,676

·     Write the number on a place value chart then write the value of each digit. 

• Explain that the 8s are adjacent to each other so the value of the 8 in the ten thousand place is ten times greater than the 8 in the thousand place to check I can multiply 8,000 x 10 = 80, 000

•     Explain that the 6 in the hundreds place is 100 times greater than the 6 in the ones place because 6 x 100 = 600

Explain to students that in order for a digit to be ten times greater they have to be next to each other and the same digit

Practice:  students solve questions 1 and 3 on page 13

*The Highlighted Problems

Teacher check students work and  review solutions with students 

1.(Sample Answer): No; The 5s have to be next to each other for the value of one 5 to be ten times as great as the value of the other

3. 7,000; 700; The value of the first 7 is ten times as great as the value of the second 7.

Students complete Quick Check or Independent Problems: 6,12, and 20 for assessment and differentiation

6. 50,000;5,000

12. 6,000;60

20. B

After students complete the quick check, students are placed into groups based on their results.

0-1 points intervention (group I)

2 point On level group (o)

3 points (group A)

Group Istudents will work in small groups with teacher on Intervention lesson for 10 minutes then work independently to complete intervention work sheet

Group O and A  solve question 13-20

Group A Intervention Lesson:

·     Give each student an intervention sheet 1-2

·     Have each student write a 3 digit number on their place value chart with two digits that are next to each other the same

·     Have each student (one at a time)

1.    write their number on the board

2.    read the number aloud

3.    write the value of each digit 

4.    explain the relationship between the digits that are the same

·     Have students practice by completing the intervention sheet 

·     Students who understand move on to the second activity, review intervention sheet with remaining students.  

Teacher will check in with groups A and O to review questions and solutions.

Closing:

Ask students to turn to a partner to explain when are digits ten times the value of another digit

Reflection: My take away from this week post is that it is place value relationships are the core of all the other topics in the fourth grade. The goal would be for students to learn that in a  multi digit whole number, a digit in one place represents ten times what it would represent in the place immediately to its right. It is important for our students to have resources available to them, such as Place Value Charts, Vocabulary word walls and anchor charts to better assist and give a visual to their learning.