##
* *Reflection: Developing a Conceptual Understanding
Monster Bash - Section 5: Guided Practice

When teaching this lesson, I thought about teaching students the property of zero (anything times zero is zero) and the multiplicative identity property (anything x 1 equals itself). However, I decided to address these properties later on. I wanted students to focus on conceptualizing multiplication instead of memorizing properties and definitions. Also, I didn't want to confuse students!

Another thought: After teaching this lesson, I realized I wanted to color coordinate my 11x17 poster posters accordingly:

- x 0 - Yellow
- x 1 - Blue
- x 2 - Turquoise
- x 3 - Pink
- x 4 - Turquoise
- x 5 - Red
- x 6 - Pink
- x 7 - Green
- x 8 - Turquoise
- x 9 - Pink
- x 10 - Red

I thought the colors would help facilitate pattern awareness later on when students could see Equation Posters x1-x5.JPG and Equation Posters x6-x10.JPG next to each other.

Turquoise: Multiples of two

Pink: Multiples of three

Red: Multiples of five

*Developing a Conceptual Understanding: Reflection*

# Monster Bash

Lesson 1 of 7

## Objective: SWBAT explain the concept of multiplication.

The goal of this seven-day Multiplication Kick-Off is to review multiplication facts and to build a deep understanding of why we multiply! These seven lessons provide a gradual learning progression that slowly increases with complexity. You could teach these lessons in the middle of a unit or at the beginning of a Multiplication Unit. I taught these lessons within my Measurement Unit at the beginning of the year. Here's why: I didn't want to wait until my multiplication unit to review multiplication facts and to teach students how to solve a simple algorithm. After teaching these lessons, I could then implement daily fact and algorithm homework practice (1-digit x multi-digits). Here’s the order in which I taught these lessons:

The goal of this activity was to help make multiplication understandable, fun, and memorable! I wanted to give students a context to discuss multiplication in the upcoming lessons. Not only that, but students loved creating monster paper plates so student engagement was high! For each of the following lessons, student had their monster paper plates on their desks as a reference and visual aid. This worked! Students continually went back to this monster problem to reason with multiplication.

Day 2: Multiplication: x0, x1, x2

1. I started by teaching x0, x1, and x2 as these are the easiest multiplication facts. Many of my students were still mixing up 5 x 0 and 5 x 1. They didn’t truly understand the meaning behind x0 and x1.

2. Students used both a number line on paper and unix cubes to show how to multiply by 0, 1, and 2. The goal was for students to make the connection between repeated addition (something students are very familiar with) and multiplication.

3. To further build number sense and a deeper understanding of multiplication, students analyzed patterns they noticed between counting by ones and counting by twos.

4. Finally, we applied new learning to a simple algorithm. Students grasped this concept quickly and were very successful.

1. Next, we moved onto x4 facts so that we could build upon previous learning of x2 facts. It’s easier for students to learn their x4 facts when they understand x2 facts. They quickly catch on that 4 x 6 is when you “just take two jumps of 6 and then double it.“

2. Students used both a number line on paper and unfix cubes to show how to multiply by 4. The goal was for students to make the connection between repeated addition (something students are very familiar with) and multiplication.

3. To further build number sense and a deeper understanding of multiplication, students analyzed patterns they noticed between counting by fours and counting by twos.

4. Finally, we applied new learning to a simple algorithm. Again, students grasped this concept quickly and were very successful.

1. I decided to teach x3 and x6 next as students can use the x3 facts to get to x6 facts. To solve 5 x 6, you can first take five jumps of three (5x3) and then double it to get 5 x 6. For this reason, it’s easier for students to learn x6 facts right alongside x3 facts.

2. Students used both a number line on paper and unix cubes to show how to multiply by 3 and how to multiply by 6. The goal was for students to make the connection between repeated addition (something students are very familiar with) and multiplication.

3. To further build number sense and a deeper understanding of multiplication, students analyzed patterns they noticed between counting by threes and counting by fours. Finally, we applied new learning to a simple algorithm.

4. Again, students grasped this concept quickly and were very successful.

Day 5: Multiplication: x10, x5, x9

1. We moved onto x10, x5, and x9. Students discover how to use 10 to better understand x5 and x9 facts. “Times five” is just “half of x 10.” For example, to find 7 x 5, you can “take seven jumps of ten and then split the product in half.” Students also learn that 6 x 9 is the same as “six jumps of ten – six.” For this reason, it’s easier for students to learn x9 and x5 facts alongside x10 facts.

2. Students used both a number line on paper and unix cubes to show how to multiply by 3 and how to multiply by 6. The goal was for students to make the connection between repeated addition (something students are very familiar with) and multiplication.

3. To further build number sense and a deeper understanding of multiplication, students analyzed patterns they noticed between counting by fives and counting by tens as well as counting by nines and counting by tens.

4. Finally, we applied new learning to a simple algorithm. Again, students grasped this concept quickly and were very successful.

1. Next, students focused on x8 facts. Students discover how to use x4 facts to better understand x8 facts. For example, to find 8 x 5, you can “take five jumps of four and double the prouct.” For this reason, it’s easier for students to learn x8 alongside previously covered x4 facts.

2. Students used both a number line on paper and unix cubes to show how to multiply by 8 and how to multiply by 4. The goal was for students to make the connection between repeated addition (something students are very familiar with) and multiplication.

3. To further build number sense and a deeper understanding of multiplication, students analyzed patterns they noticed between counting by eights and counting by fours.

4. Finally, we applied new learning to a simple algorithm. Again, students grasped this concept quickly and were very successful.

The final facts that we covered were x7 facts. This is because x7 is the most difficult to connect with other facts. For this reason, it’s easiest if taught last!

2. Students used both a number line on paper and unix cubes to show how to multiply by 7. The goal was for students to make the connection between repeated addition (something students are very familiar with) and multiplication.

3. To further build number sense and a deeper understanding of multiplication, students analyzed patterns they noticed when counting by sevens.

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#### Creating Monsters

*30 min*

I began by showing students an example of a monster created from a paper plate: Teacher Monster Example. Immediately, student's interests were peaked! I said: *Today, your group gets to make ten monsters! First, you'll want to cut out the eyes and mouths. Then, glue these down on the paper plates. You can then add some color and name your monsters using the labels. *I handed the following items out to each group of five students and asked students to begin creating their Ten Monsters! Students couldn't wait to begin.

- 10 Paper Plates
- Monster Eyes and Mouths
- 10 Labels for Names

Often, students would come up to me to show their monster or an idea their group came up with. Each time, I would hold up the group's monster and share it with the class. This increased student excitement and had a snowball effect. Soon, there was a line of students, ready to share! I loved watching students proudly transform their paper plates: Alfred, Toodles, and Rascal. Students began to take ownership of their monsters by naming them: Naming Monsters. I knew that this connection students had with their monsters would increase student engagement later on as well.

As students finished creating, I explained: *We will be giving cookies to your monsters today! I'll give each group one hundred cookies to cut out. You can keep track of your cookies in this zip lock bag. *I then handed out copies of One Hundred Cookies to each group and provided each group with a bag: Cookies.

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#### Opening Lesson

*10 min*

Once students were ready to move on, I showed them the Multiplication Vocabulary Poster and we acted the word out together. Teacher: *Multiplication! *Students: *Multiplication!* Altogether: *A fast way *(running motion with fists up, elbows bent, and arms moving back and forth)* to add the same number over... and... over *(Counting on fingers). We acted this out a few times and then I asked students to Turn & Talk: *What is multiplication? Can you give an example? *Students offered examples such as "It's when you have two groups of five pencils and you multiply 2 x 5 to get the number of pencils."

I explained our goal for the day: *I understand multiplication facts! *I continued: *When you multiply, it is important to understand the process of multiplication. Many of you know that six time six is thirty-six, but can you explain why? *

I then asked students to Turn & Talk: *Explain our goal today. *I ask students to Turn & Talk for many reasons. Sometimes it helps solidify concepts while other times, it provides students with another opportunity to hear the directions. Student discourse helps students successfully process information.

#### Resources

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#### Teacher Demonstration

*20 min*

At this point, I excitedly introduced students to a special monster I created named, Lucy. I told students: *Lucy has a problem and needs your help. *I explained Lucy's Problem: *Lucy is having a Monster Bash! She wants each guest to get ____ cookies. If she invites ____ friends, how many cookies will she need in all? *I then filled in the blanks in the word problem. Let's say that *Lucy is having a Monster Bash! She wants each guest to get 0 cookies. If she invites 0 friends, how many cookies will she need in all? *Turn & Talk! The property of zero (anything times zero is zero) is such a simple concept, but it's an important property to review and understand conceptually

*.*I could hear students explaining, "If Lucy gives away zero cookies and zero friends come to her party, they she would need ZERO cookies!" I then said:

*Please hold up zero paper plates*

*and give zero cookies away.*The students laughed and said, "That's impossible!"

We moved on... I changed the numbers in the problem to 0 cookies and 1 friend. *Okay, then what if Lucy has one guest come and she decides to give away 0 cookies per guest? Hold up one monster. Give that monster 0 cookies. How many cookies does Lucy need? *Turn & Talk! Again, students replied with, "That's not possible!" I kept at this all the way through 0 cookies per guest x 10 monsters.... I think my students got the point!

**Listing x0 Facts:** According Mathematical Practices MP4, students need to be able to write equations to describe situations. So, in order to add another layer of practice and understanding, we made a list of equations for zero, starting with 0 x 0, ending with 0 x 10. Students created this list in their journals: 0 Cookies Per Guest. Then we created a poster together as a class: Zero Cookies Per Monster Poster. I preprinted the labels before the lesson: Number of Cookies Labels, Number of Friends Labels, and Total Cookies Labels. We determined where the labels should go on the poster as a class.

**Modeling x0 Facts:** As students finished making a list of x0 facts, I wanted to provide students with another opportunity to model x0 equations. I asked them to draw a 0 x 0 on the dry erase grid on the backs of their white boards. Again, students said, "We can't!" I moved onto 0 x 1... then 0 x 2... then 0 x 3... Of course, they weren't able to draw any of them! After I felt that all student truly understood the zero property, we moved on to multiplying by one.

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#### Guided Practice

*40 min*

I went back to Lucy's problem. Let's say that *Lucy is having a Monster Bash! She wants each guest to get 1 cookie. If she invites 0 friends, how many cookies will she need in all? Can you hold up zero monsters and given them 1 cookie? *My kids responded: "No! We can't!"

Then we went on to 1 cookie x 1 monsters. Only this time, when I asked students to hold up one monster and give him/her one cookie, they were able to! I asked: *How many cookies will Lucy need if she gives away one cookie to each guest and one monster comes to her party? *One! Then I asked, *What if two monsters come? *We held up two monsters and gave each monster one cookie. I asked: *How many cookies will Lucy need? *Two! *What if three monsters come? *We held up three monsters and gave each monster one cookie. I asked: *How many cookies will Lucy need? *Three! We continue this all the way up to 1 cookies x 10 monster friends.

**Listing x 1 Facts:** To add another layer of practice, we created a list of equations for one, starting with 1 x 0, ending at 1 x 10. Students created this list in their journals: 1 Cookie Per Guest. Then we created a poster together as a class: One Cookie Per Monster Poster.

**Modeling x1 Facts: **Then students created a model for each equation on their white boards: Drawing x1 Arrays. I asked students to Turn & Talk: *Do you see a pattern? *According Mathematical Practices MP4, students should be able to analyze relationships mathematically to draw conclusions. When we discussed as a class, students said, "Each time, it goes up by one." *Why is that? *"Because you're counting by ones." *Wait a minute, we are multiplying here. *"But Mrs. Nelson, multiplication is a fast way of adding the same number over and over!"

Next, we went on to 2 cookies per monster! I went back to Lucy's problem. Let's say that *Lucy is having a Monster Bash! She wants each guest to get 2 cookies. If she invites 0 friends, how many cookies will she need in all? *I asked students to hold up 0 monsters. I asked:

*How many cookies will Lucy need if she gives away two cookies to each guest and zero monsters come to her party?*Zero! Then I asked,

*What if one monster came?*Students held up one monster and gave each monster one cookie. I asked:

*How many cookies will Lucy need?*One!

*What if two monsters come?*We held up two monsters and gave each monster two cookies. I asked:

*How many cookies will Lucy need?*Four! We continue this all the way up to 2 cookies x 10 monster friends.

**Listing and Modeling x2 Facts: **At this point, students knew what to do and were ready to continue on without me. I explained: *Please remember to make a list of x2 equations and then model your x2 facts on the grid. *Here, a student made her list, 2 Cookies Per Guest and here, you can see a student Drawing x2 Arrays. Then, we discussed patterns with x2: *What did you see? *"Each time, the array went up by two." *Why do you think that is? *"Because we're counting by twos!" *I thought we were multiplying! *"Multiplying is just a quick way of adding!" We also completed the Two Cookies Per Monster Poster as a class.

Note: Some students finished with their x2 facts quickly and were ready to move on independently to x4. They made a list of x4 equations: 4 Cookies Per Guest and created models for each equation: Drawing x4 Arrays.

**Progression of Learning**

We only modeled up to x2 facts today for a couple of reasons. First, we ran out of time to go beyond this point and second, the purpose of today's lesson was to build a foundation for following lessons. If students can model x2 facts, students can use this understanding to conceptualize more challenging facts, such as 8 x 9 later on.

**Common Core Connection**

Often times, students are expected to simply memorize multiplication facts without truly understanding the meaning behind the facts. This lesson engaged students in Math Practice 2: Reason abstractly and quantitatively. I wanted students to "make sense of quantities" using their monster plates in order to contextualize abstract equations.

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- UNIT 1: Measuring Mass and Weight
- UNIT 2: Measuring Capacity
- UNIT 3: Rounding Numbers
- UNIT 4: Place Value
- UNIT 5: Adding & Subtracting Large Numbers
- UNIT 6: Factors & Multiples
- UNIT 7: Multi-Digit Division
- UNIT 8: Geometry
- UNIT 9: Decimals
- UNIT 10: Fractions
- UNIT 11: Multiplication: Single-Digit x Multi-Digit
- UNIT 12: Multiplication: Double-Digit x Double-Digit
- UNIT 13: Multiplication Kick Off
- UNIT 14: Area & Perimeter