Standard Algorithm Book

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Objective

SWBAT multiply a 2-digit number by a 2-digit number using the standard algorithm method.

Big Idea

Students will create a book to model the steps of the standard algorithm.

Teacher Demonstration

60 minutes

In order to have the time necessary to complete this lesson, we skipped our regular Number Talk routine. 

Standard Algorithm

The Common Core Standards at the 4th grade level specifically state that students should be able to multiply by multi-digit numbers using strategies "based on place value and the properties of operations." The goal is to make sure students are conceptualizing the multiplication process using equations, rectangular arrays, and/or area models instead of just memorizing a set of procedures using the standard algorithm. Even though the standards don't specifically address the multiplication standard algorithm at the 4th grade level, I choose to teach this strategy as alternative method for students to use when verifying their work. I almost always require students to show their work using an equation, array, or area model as well. 

Goal & Introduction

To begin, I introduced today's goal: I can multiply a 2-digit number by a 2-digit number using the standard algorithm method. I then explained: All of you already know how to use the standard algorithm to solve a multiplication problem where there is a single digit number times a multi-digit number, such as 3 x 498. Today, we are going to learn how to use the standard algorithm to solve a double-digit x double-digit number, such as 67 x 43.

Lesson Design

For today's lesson, I wanted students to take the time to break down and analyze the standard algorithm steps. So I designed an activity where students would create a little book showing each algorithm step on a new page. Throughout this activity, students will also color-coordinate each step to help them better understand the standard algorithm process. 

Getting Ready

I passed out two 8 1/2 x 11 sheets of white paper to each student. I modeled the following steps:

  1. Fold the papers in half (hamburger style).
  2. Open the papers back up. Cut along the fold of each paper. This results in four half sheets. 
  3. Stack half sheets together. 
  4. Fold in half again (hamburger style).
  5. Staple along center fold. 

Cover Page

Once students were ready, we began by designing the book cover. I showed students how to create 8 sections by drawing a line in the center (without a ruler) and then halving each "half" until there were 8 sections. Then, I modeled how to write, "How to Multiply 2-digit by 2-digit numbers using the standard algorithm." Here's the Teacher Model of Cover and a student's Book Cover

Vocabulary

Next, we reviewed key vocabulary, including multiplication, multiplicand, product, and partial products. I wanted to make sure students were using mathematical words to explain their thinking (Math Practice 3). Here's the Teacher Model of Vocabulary and a student's Vocabulary page. 

Steps

On the six pages, I modeled each step to take in order to solve 67 x 43. For example, for the first step, we modeled (using a single color) how to multiply 3 x 7 to get 21. I explained: When you get a product that is ten or more, you always carry the number of tens. In this case, we have two tens so we "carry the 2." We wrote the step in word form as well, "Multiply the digits in the ones place."

Step 3: Put a Zero in the Ones Place

When we got to Step 3, I handed out 8 Smiley Face Stickers. to each student. I thought that placing a smiley face sticker in place of writing a zero would be more engaging and memorable.

Student Examples

Here are student examples of each step: 

Practice Problems 

When we finished recording the steps of the standard algorithm, we moved on to creating practice pages. On these pages, we solved the following problems altogether as a group:

  • 13 x 26
  • 38 x 14
  • 56 x 40
  • 99 x 99

During this time, I made sure to begin with easier problems and build up to more complex 2-digit x 2-digit problems. I also slowly released more and more responsibility to students by allowing students time to work ahead of me. Here are student examples of these practice problems: Practice A and Practice B

Independent Practice

In order for students to go on to the next task, I wanted to make sure they understood how to use the standard algorithm to solve 2-digit x 2-digit problems; so I provided two more practice problems for students to solve independently: Practice C. This also gave me the opportunity to provide further one-on-one support to some students. 

Student Practice

40 minutes

Partners

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. Some students finished the two practice problems sooner than their partners. These partners began working on the student-practice page at different times. Some adjusted later on by having their partners skip problems in order to catch up. Others just kept checking answers with each other, even if they were on different problems.  

Student Practice Page

For student practice today, I wanted students to continue solving 2-digit x 2-digit multiplication problems. I passed out a practice page found at Commoncoresheets.com.

Monitoring Student Understanding

While students were working, I conferenced with every group. At times, I would provide students further instruction. Other times, my conferencing goal was to support students by asking guiding questions (listed below). 

  1. Can you explain this step to me? 
  2. What is the first step to the standard algorithm? 
  3. What can you cover up while you multiply the ones? (The digit in the tens place.)
  4. What are some common mistakes that students might make?
  5. Why do you write down a 0 in the ones place of the second partial product?
  6. Why is important to line up the digits? 

Here's an example of student work: Proficient. I apologize for not capturing any video during this time!