Detecting the Pattern

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Objective

4.NBT.5 SWBAT multiply one, two, and three digit numbers using a variety of skills.

Big Idea

Students Love to investigate, using a variety of skills students will detect the pattern for solving multiplication problems.

Warming Up!

20 minutes

 

To warm students up before they start their new jobs as detectives, I give them some investigating tools (manipulatives), and review the big idea of this warm up activity.  This video explains how students are responding to the beginning of this lesson.

 

 

 

Introduction to Lesson:

In this section of the lesson students used manipulatives to explore the relationship of addition and multiplication.  They are only going to work with numbers 1-9, because I want them to understand that even if they were to multiply two digit numbers they would still carry out the problem one digit at a time according to place value.   We will build our way up to multiplying two, three, and four digit numbers by the end of this lesson.  

MP4-Modeling with mathematics. This allows students to use models/representations to help them translate the solution to mathematical explanations.

MP8-Look for and express regularity in repeated reasoning. Helps students to reason better mathematically.

Students are given 10 minutes to create and solve one digit multiplication problems using manipulatives.

Questions:

What do you notice about the array you are building?

If you have 2 x 5= 10 , and wanted to multiply 2 x 6= what amount would you add to your array?

How do you know it is right?  Can you use addition to check it? If so, How?

Do you think there is a relationship between addition and subtraction? if so can you demonstrate another model to show me?

Adjustments for this section is not necessary because we are working with both concrete and abstract skills.  However, I will assist students as needed. 

Applying the strategy

20 minutes

In this section I write 55 x 32 on the board or overhead. I know we started off multiplying one digit numbers. I want to see if students can carry those problem solving skills over into multiplying two digit numbers.

 I ask students how they would begin to solve it. Several students knew how to explain the process.  Then I complete the problem as students indicate. I as student volunteers to explain why this method works.  Even though some students were able to explain how to solve the given problem, many students had a hard time understand the concept of place value.

For students who appear to be having a hard time, I give them some graph paper.  I tell them that the graph paper will help them to remember the importance of place value as they solve the problem.  

Step-by Step Procedure: 

  I tell them that the objective is for them to be able to multiply two-digit numbers together.  I ask them to use the arrays to represent what I write. This can help them see the process of solving problem, and serve as retained skills for them to use when solving problems later.

Making the Connection:

I begin this process by asking students what each digit  in our introductory problem represent.  For example, "5" represents 5  tens, and  ones. "3" is 3 tens, and "2" is 2 tens.  This helps students to understand the order of multiplying two digit numbers. I ask, could you try this with different numbers?,. How would you describe the problem in your own words?,. Can you explain?

Students can identify the place of each number and the value. Some students are able to make the connection between place value and multiplying.

MP1-Making sense of problem and persevering in solving them. 

  I may not always allow students to be at the center of the conversation because I want them to grasp how to use mathematical language correctly when explaining how to solve.  However, I will continue to guide students as needed.

 For clarity, I ask students to check this answer using a calculator.  

We do one additional example using 27 x 18 together.  We repeat this pattern using three and four digit numbers.  During this problem, I ask student volunteers to answer and record the four different parts of the problem: I tell students they can use this as a guide during the independent part of this lesson. I give students index cards to write down their sample problem. Index_Cards_Template.pdf

   27

 x 18

 = 56 (7 x 8 = 56)

 =160 (20 x 8 = 160)

 = 70 (7 x 10 = 70)

 =200 (20 x 10 = 200)

Exit Ticket!

20 minutes

 

Students are given the choice to create their own problems, or choose from the examples listed on the board.exit ticket.docx  I tell them they can do it in any order; because some student may not want to try the harder problems first.  I want to give them some flexibility. As student are busy working with their problems I circle the room to assess what they are thinking.  Several student grasped the concept pretty quickly, and are working their way through the problems without using the arrays  or given steps as assistance. 

Some students are working with ease, however, they are continuing to make minor mistakes.  Some are forgetting to carry, some are having difficulty with placing the numbers in the correct space, and checking for  minor mistakes along the way.  

Depending on the severity of misconceptions, I plan to reteach this lesson to a smaller group of students soon.

 

Extension:

Student volunteers can share out what they have learned.  In this video my student explained how to solve a two digit multiplication problem step by step. I notice that he had some difficulty explaining his steps using mathematical terms. However, he did understand the process. I chimed in a time or two to check for understanding.  I plan to reteach this lesson in a smaller group because I want to model how to explain the problem solving process using mathematical language.  

 

 

Student Work Sample