Multiply Using the Basics

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Objective

4.NBT.B.5 Students will be able to multiply whole numbers using arrays.

Big Idea

Students will be able to use arrays to solve multiplication problems.

To Begin

10 minutes

In this lesson I want students to solve and then create a visual representation of the problem for this warm up.  As students and I work together solving and creating, I invite them to explain how and why this works.  Having students explain and illustrate their answers allows me to check prior knowledge.

I displayed the following chart on the board and invite students to explain how it can be used to solve multiplication problems.

Then I briefly go over the strategy and talk through how to do the problem. I chose to explain because it allows my students to hear the correct way to use arrays and relate math terms.

  I have recently noticed in some of their daily journals some students are using very vague words when explaining about how to solve problems.   The more my students are exposed to using mathematical terms the better they will become in explaining their reasoning mathematically. 

MP2-Reason abstractly and quantitatively.

 For struggling students I may invite them to build an arrays to represent one-digit multiplication problems just to make sure they gain a deeper understanding of why and how arrays are used to help solve multiplication problems. Eventually, I build them up to multiplying two and three-digit numbers.

Collaborate

20 minutes

We have been working on building arrays for about a week now! But, I want my students to examine different ways multiplication can be solved. Grouping students allows them to share their strategies.

Before we start, I want to make sure my students fully understand the purpose of using arrays. I tell them arrays can be useful models for multiplication which can be utilized in a variety of ways. Arrays are formed by arranging a set of objects into rows and columns.  Keep in mind that the rows and columns must have the same set of numbers.

For instance, the following array  consist of 3 rows and 4 columns:

xxxx

xxxx

xxxx 

 it represents the number sentence 3 x 4= 12. Let's count them together.  

Now I know we are working on two and three-digit multiplication problems, but this concept can still be used if we group numbers according to their place value.  

I invite students to the carpet to participate in an fun  interactive video.

While engaged in the activity, the students will do the following:

I asked them to take out a sheet of note-paper to jot down problem solving techniques. I walk around to see how students are drawing the problems and whether they can identify the problem solving steps being used. How does this relate to multiplication? Can you give another example?

MP7-Look for and make use of structure.

After the interactive video, I clarified any questions students has about multiplying.  I explained that when multiplying, the order of the numbers does NOT matter.   5 × 7 = 35   or   7 × 5 = 35

Any number multiplied by zero is zero.  4,567 × 0 = 0

Any number multiplied by one is equal to the number.  4,567 × 1 = 4,567

 Checking for Understanding:

 I gave the students a quick check to see if they understood what was being taught. Multiplication.pdf I created a space for each problem for students to explain their answer using arrays, or problem-solving steps.  As they worked on the given set of problems, I circled the room to check for understanding.  However, I only chimed in when I was needed. I pretty much worked as a facilitator .  

 

Because I find it very powerful for students to share and  talk about their work, I invite two or three student volunteers to share with the class.

  (click here to see a detailed explanation)

Student Work Sample

Wrapping it Up

10 minutes

 

To end this lesson I invite student volunteers to share a couple of examples of how they solved their problems.  I want students to experience different ways to solve problems. Hopefully, they can see  and explain the relationship between the arrays they made and the corresponding multiplication sentence.  If not, I encourage them to use mathematical language in their explanations.  Then I ask them to use arrays to model their explanations.

 How does this skill relate to multiplication?  Can you explain? Can you give another example. 

The first person up shared and explained their work, and then called on someone else to share and explain their work.  This process repeated itself until all volunteers shared their work. After that, I explained that this lesson will flow over to another lesson coming up on dividing.  

Student Sample