Multiplication: x0, x1, x2

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Objective

SWBAT multiply a multi-digit number by 0, 1, and 2.

Big Idea

After modeling multiplication facts for 0, 1, and 2 using unifix cubes and a number line, students will multiply multi-digit numbers by 0, 1, and 2.

Explanation of Lesson Sequence

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:

 

Day 1: Monster Bash

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.

 

Day 3: Multiplication: x4

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.

  

Day 4: Multiplication: x3, x6

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.

 

Day 6: Multiplication: x8

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.

 

Day 7: Multiplication: x7

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.

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

Opening Activity

5 minutes

I began by reviewing the Multiplication Vocabulary Poster by making the same hand motions as yesterday. 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). Then I asked students to Turn & Talk: What is multiplication?

Lucy's ProblemLucy is having a Monster Bash! She wants each guest to get ____ cookies. If she invites ____ friends, how many cookies will she need in all? Relating multiplication to a scenario helps students develop a deeper understanding.

I asked students to spread out their Monsters on their desks. Turn & Talk: Explain Lucy's problem to a partner. 

 

Teacher & Student Demonstration

30 minutes

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, hundreds lines, unifix cubes in order to contextualize abstract equations.  

Number Line Model

I passed out a page protector and copy of the Hundred Number Line to each student. A number line is one of the best ways to relate multiplication to counting and build number sense. I asked students to get out their white board markers (thin works best) and erasers. I projected the Hundred Number Line so I could very explicitly provide directions.

Taking 1 jumps of 0

I started off by asking: How many cookies would Lucy need if she is giving one cookie away, but no monsters come to the party? "Zero!" Then I demonstrated how to take 1 jump of 0 cookies on the number line and how to mark the landing point (how many cookies needed)... 0. 

So if we Lucy gives away one cookie to each guest and 0 guest come to her party, how many cookies will she need? "Zero!"

By using a problem solving setting, multiplication facts become more meaningful. 

Taking Jumps of 1

We then moved on to taking jumps of 1: How many cookies would Lucy need if she is giving one cookie away and 1 monster comes to the party? "One!" Then I demonstrated how to take 1 jump of 1 on the number line and how to mark the landing point (how many cookies needed)... 1.

We continued this same process all the way to 1 jump of 10, going faster each time. At first, I could tell that many students didn't have experience taking jumps on a number line. They caught on quickly, though! 

At this point, I asked students to use the Unifix Cubes to model 1 x 0... 1 x 1... 1 x 2... 1 x 3... all the way up to 1 x 10. Students love using these cubes! Also, they helped provide another modeling method for those in need of more hands-on learning. 

I loved watching students build connections between the number line, Unix cubes, and Lucy's problem. Here, a student is Counting by one Four Times and is able to use the cubes to explain how many cookies Lucy would need if four monsters come to her party.

In order to further encourage students to build a solid connection between addition and multiplication, I asked: What if twenty monsters come to the party? Can you show me how many cookies Lucy would need? Again, this may seem simple, but the overall goal was for students to conceptualize multiplication and apply their understanding to new situations. Here's a student Counting by Ones

Taking Jumps of 2

We moved on to 2 cookies x _____ Monster friends. We followed the same process: taking jumps of two on the Hundred Number Line and modeling equations with the unix cubes. 

These students explain how many cookies Lucy would need if eight monsters were coming to the party: Distributing Cookies 8 x 2 = 16

I challenged students to model counting by ones up to 20 and counting by two up to 20. I wanted to see if they could begin seeing patterns. In this video, Finding Patterns, one student explains the pattern: "It's faster to count by twos than by ones." The other student shows that 1 x 16 = 2 x 8 (When you count by twos, you're counting two ones/two cookies).

We began a Patterns Chart to document students' observations. 

Guided Practice

30 minutes

At this point, I began teaching students students the multiplication algorithm. I like to teach the algorithm right alongside multiplication fact review. However, I start off very simple. 

Using the grid side of student white boards (to help line up digits), students followed along. Here's the string of problems that we completed together. At first I modeled, then students completed them with me, and then students solved problems independently. After modeling first few problems, most students caught on quite quickly.

  • 2 x 12
  • 2 x 222
  • 2 x 135
  • 2 x 602
  • 2 x 657
  • 2 x 981

 

Modeling the Algorithm

Explicitly teaching the alogrithm followed by a gradual release of responsibility helps students understand and apply the algorithm successfully. When modeling the algorithm, I used the same words over and over. 

For 2 x 135, I would say:

2 x 5 is 10, write down the zero, carry the one

2 x 3 is 6, plus the one is 7, write down the seven

2 x 1 is 2, write down the 2

Comma Placement

If the product resulted in more than three digits, I would then encourage correct comma placement by underlining the first three digits while saying: One, two, three, comma!

Release of Responsibility

As students gradually become more and more independent, I left out words and expected them to fill in the blanks: 

I would say:

2 x ____ is _____, write down the _____, carry the _____

2 x _____ is _____, plus the _____ is _____, write down the _____

2 x _____ is _____, write down the _____

One__________ (underlining the first three digits), _____!

Independent Practice

35 minutes

I passed out Algorithm x2 to each student. 

During this time, I rotated around the room and asked students to explain their thinking. This student did a beautiful job explaining the steps: Student Explaining Steps. During this time, I noticed that most students were able to successfully apply the algorithm. Others needed a little support. To scaffold this activity for these students, I would use the same prompts as above: 

 

2 x ____ is _____, write down the _____, carry the _____

2 x _____ is _____, plus the _____ is _____, write down the _____

2 x _____ is _____, write down the _____


Some students were done within five minutes. Early finishers checked their answers, Student's Completed Work,and then created multiplication rhyme posters using Multiplication Rhymes. I created a poster for Multiplication Rhyme 9 x 4 as an example: Teacher Example of Multiplication Rhyme Poster.