Multiplication Array: Part I Measuring It Out

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Students will be able to solve the problem of setting up a multiplication array by precisely measuring, in inches, to create 36 boxes, 6 inches by 6 inches square .

Big Idea

Measurement is the lowest scoring concept on national and state tests - fit it in everywhere!

Introduction and Engaging Students with Inclusion

5 minutes

In my classroom, every math lesson starts with an inclusion question or activity.  The purpose of this activity is to activate prior knowledge and help the students feel included.  When I was setting up putting centimeter cubes into separate table bin, I was thinking about how I can tie perimeter to something the kids have experience with - using just one question.  My decision is to ask my students to share with their groups any time they had to measure around a flat surface. 

I asked for volunteers to share, I need to make sure I made the question clear enough.  One student shares they had to help their uncle measure the perimeter of a room so they could buy decorative tile to go around the edges.  Another student shares they helped their father build a fence around a horse corral.  A third student talks about measuring around the outside of a quilt to buy fabric to make a boarder.  After hearing these three students, I believe the question was clear, and that after the examples are given, the remaining students would understand the topic they are to discuss.

During this couple of minutes of discussion I walk around straightening/organizing things in the room.  I want to hear my students' discussions, so I could assess where their understanding of perimeter is as well as to find more great examples to share with the class.  At this point I do not interrupt their conversations, unless there is a disagreement and then I hover around to see if the students can solve the issue on their own.  I believe that if I step in immediately I haven't given them the chance to solve problems or use the strategies I have taught them. 

Sometimes a student will catch my eye during a disagreement and I will nod to them if they are working towards solving the problem .... or when they make eye contact they will start to use some of the strategies we have practiced in class.    One of the things I love about using Tribes strategies in my classroom is they are built into my everyday teaching - at the heart is teaching students to be able to resolve conflict no matter how minor it is and teaching students to become leaders.  You will see this in the video when students are working together. 

I start every lesson with Inclusion. It is my way to hook students and get them ready to learn. Today, I ask questions such as:

Have you every used a multiplication table?  When and How?

What is an array?

I allow for enough time for each student in the group to answer the question and then pose the next question. 

Designing A Grid to Gather Fact Families

45 minutes

I start this lesson by showing the students a large piece of butcher paper and telling them I need to divide the paper into 6 rows and 6 columns totaling 36 boxes. I give them a little time to think to themselves on how to do this - suggesting they use their Math Journals to draw a picture if needed. I know that it generally takes an entire class period to complete the chart. 

I then ask the students to discuss this problem at their tables and see if they can come up with a solution the table group agrees with.

I typically have a student ask what size is the paper, and I answer with, "It is 36 inches across". Then I ask them if they think the paper is shorter or longer than it is wide.  They will agree it is longer. 

After a few minutes of discussion I stop, and ask for attention.  I ask if anyone figured out a solution to creating 36 equal boxes on the paper. 

A strategy I use to keep discussions on track is a card that has "working" on one side and "finished" on the other.  I take an index card and fold it in half along the length and have  the students write the labels. Students know to flip the card from "working" to "finished." This way I can tell if students have had adequate time to discuss the problem. I have found this helps to really keep the students on task with their discussions, because they know they may have time to talk about other things if they are done with their work. 

Once students have discovered the solution, we create boxes that are six inches in length and width. I then model how to measure the paper.  Because I want students working with different partners, I pair students by drawing their names on craft sticks. In my classroom, another goal of partnering is to grow social skills.  By having students work with a different partner they are getting to know each other and are more accepting of each other.  If they get a partner that they struggle to work with they will try harder because they know they are only partners for a short period of time. 

After my students know who their partner is they get their materials - meter/yard stick, pencil, paper and black marker - and spread out throughout the room to create their array charts. In my reflection I share how I support students in this work by not "doing their work" for them, and why I think this is an important practice.

Student Reflection

5 minutes

I always close my lessons with reflection - whether it is reflection as whole class, in groups, pairs or written.  Because we are still at the beginning of the year I am focusing as much on bechavior and collaborative skills so I need to have reflection include social skills and personal behavior skills as well as reflection on content. 

 Today's focus for reflection is on their behavior. Problem solving is more accessible and effective in a group setting, but the group will not be successful if they don't collaborate. In tomorrow's lesson the groups of students will need to be finding factor families of the numbers from 1 - 36. 

I've created an activity I call Reflection 1, 2, 3 based on the fourth step in the Tribes Five Step Lesson Plan. It requires students to reflect in content/thinking skills, social skills and personally.  

 Reflection 1, 2, 3

1.  What did you learn about creating a 6 x 6 chart today

2.  What went well with your group?  What didn't work well?

This question gives students an opportunity to talk about what was good and then next is to air differences to help the group work better the next day. 

3.  How did you support your group?  If something did not go well what can you personally do to ensure it does tomorrow?

Students in my multiage classroom are a range of 9 - 12 years old.  Kids and adults of all ages need opportunities to reflect on their own behavior and to recognize positive collaboration in groups. 

These questions are extremely important to reinforce the content that was covered in today's lesson - measurement.

Standards Alignment

I've described below how the activities/assessment meets the Common Core Math Standards (Some of the interpretation and language is derived from 5th Grade Mathematics Unpacked Content, Instructional Support Tools For Achieving New Standards, created by North Carolina Department of Public Instruction.)

Assessment of MP1 Students seek the meaning of a problem and look for efficient ways to represent and solve it - creating the multiplication array chart. 

MP2 Fifth graders should recognize that a number represents a specific quantity.  In this activity they had to understand that the squares were measured in 6 inch side lengths.

MP3 In fifth grade, students may construct arguments using concrete referents, such as objects, pictures and drawings.  They explain calculations based upon models and properties of operations and rules that generate patters.  They refine their mathematical communication skills as they participate in the in mathematical discussion involving questions like "How did you get that?" and "Why is that true?" They explained their thinking to others in their group and other groups. 

MP4 Students experiment with representing problem situations in multiple ways including numbers, mathematics. They also evaluate the utility of models to determine which models are most useful and efficient to solve problems. 

MP5 Fifth graders consider the available tools (including estimation of the size of the squares) when solving a mathematical problem and decide when certain tools might be helpful (using the inch measurements on a meter stick).

MP6 Students refined their mathematical communication skills by using clear and precise language in their discussion with others and in their own reasoning.  They needed to use the words inches, columns, rows, square, diagram, model.