##
* *Reflection: Connection to Prior Knowledge
Big Multiplication and Long Division - Section 1: Do Now

As we were discussing the Do Now problems, one of my students mentioned a multiplication trick that she was taught in elementary school. This opened the discussion up for sharing tricks. I realized that even students who were comfortable with their multiplication tables were using some of these tricks to verify their answers.

Here are some of the tricks they shared:

3 - When you multiply a number by 3, the digits should add up to 3, 6, or 9.

*I asked my students what this trick reminds them of and they were able to recall the divisibility rules from an earlier lesson. See Divisibility Rules)

9 - When you multiply a number (single digit) by 9, the digits should add up to 9.

Students also had some tricks where they used their fingers, not to count, but to represent numbers.

I shared a trick for multiplying a 2 digit number by 11 that students were really excited about.

Add the digits of the number that is being multiplied by 11 and place them in between the tens and ones place of the number. For example, 23 times 11 would be 253.

This discussion was a great energizer for students because it gave them an opportunity to share their knowledge/"tricks" with their classmates.

*Multiplication Tricks*

*Connection to Prior Knowledge: Multiplication Tricks*

# Big Multiplication and Long Division

Lesson 3 of 10

## Objective: SWBAT review their long division algorithm.

*55 minutes*

#### Do Now

*10 min*

In preparation for this lesson on long division, the Do Now problems focus on multiplication. Some of my students continue to make mistakes with two digit multiplication in the process of performing long division. Today's Do Now gives students the opportunity to practice their multidigit multiplication skills.

**Do Now**

**1) 297 x 84 =**

**2) 4,375 x 26 = **

**3) 806,119 x 137 =**

As students work independently, I will circulate throughout the class looking for students who use their fingers to multiply or use paper to multiply single digit numbers. For these students I will assign multiplication homework as well as division homework. After 10 minutes, I will have students share their answers with their group. If they disagree on an answer, I will encourage them to review their work together.

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#### Division Algorithm

*20 min*

I will share with students that over time teachers and students have developed different ways of remembering the algorithm for division. I have developed my own method based on the animated tv family, the Simpsons, that I will share. Most students know of the Simpsons family, so I will begin by questioning students on their knowledge.

*Who is Homer Simpson? Who is Marge Simpson? Who is Lisa Simpson? Who Is Bart Simpson? Do they have a dog? *

The questions will garner some excitement for the upcoming lesson. Also, the questioning will ensure that all students are at least familiar with the characters of the show. Students know the dog's name is not Rover, but I will explain that we'll use an easier name to remember.

I will model an example with the Simpsons family directing us on what to do. I will display the directions on the board. (see Simpsons Division)

Example 1: 9632 / 4

*Dad, Homer, is telling us to*

**divide**first. How many times can 4 be divided into 9?*Mom, Marge, is telling us to multiply next. What is the product of 4 times 2?*

*The sister, Lisa, tells us to subtract the numbers. What is the difference between 9 and 8?*

*Bart, the brother, tells us to bring down the next number in the dividend.*

*Rover tells us to repeat the process. If there aren't any more numbers in the dividend, then Rover tells us we have our remainder.*

I will complete the problem with the class.

*What are different ways that we can check the quotient, our answer?*

It is important to mention that even students who are comfortable with their multiplication tables make mistakes because their long division work is unorganized. I will encourage students to organize their work by using columns to separate the place values.

#### Resources

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#### Group Work

*20 min*

Students are seated in groups of 3 or 4. They will be given a multiplication problem and division problem to complete. Students should work on the problems independently but compare their work and answers with their group. They will not be told that their answers match another groups' problem until the groups have completed the work.

1) 7,021/17 = 413 x 17 = 2) 9,396/29 = 324 x 29 = 3) 3,528/14 = 252 x 14 = |

4) 8,556/23 = 372 x 23 =

After about 10 minutes, I will give each group chart paper and a marker to show their problems and work. When groups have completed their work, I will inform them that if they did the math correctly, then another group has the matching multiplication problem to their division problem and vice versa. I will post the chart papers on the board and tell students to find the matching problems.

If students aren't successful in finding the matching problem, then we will go over the math as a class.

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#### Lesson Review

*5 min*

In elementary school, many students have been taught different tricks for remembering the multiplication tables. I will ask students to share with the class, tricks they may know.

*How do you remember your multiplication tables? Do you have any tricks?*

**Possible Answers**

- Students may use the trick for the 9 times tables where you use your hands. You put down the finger that you are multiplying by and count the rest of the fingers.

- Students may have a song that they were taught.

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- UNIT 1: First Week of School
- UNIT 2: Properties of Math
- UNIT 3: Divisibility Rules
- UNIT 4: Factors and Multiples
- UNIT 5: Introduction to Fractions
- UNIT 6: Adding and Subtracting Fractions
- UNIT 7: Multiplying and Dividing Fractions
- UNIT 8: Algorithms and Decimal Operations
- UNIT 9: Multi-Unit Summative Assessments
- UNIT 10: Rational Numbers
- UNIT 11: Equivalent Ratios
- UNIT 12: Unit Rate
- UNIT 13: Fractions, Decimals, and Percents
- UNIT 14: Algebra
- UNIT 15: Geometry

- LESSON 1: Adding and Subtracting Decimals with Card Sort Activity
- LESSON 2: Adding and Subtracting Decimals Algorithm
- LESSON 3: Big Multiplication and Long Division
- LESSON 4: Multiplying Decimals Card Sort
- LESSON 5: Multiplying Decimals Algorithm
- LESSON 6: Partial Product Strategy for Multiplying Decimals
- LESSON 7: Dividing Decimals
- LESSON 8: Dividing Decimals with Remainders
- LESSON 9: Operations with Decimals Jeopardy Review
- LESSON 10: Decimals Unit Exam