Lesson: Properties lesson 4

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Lesson Objective

What is an array?

Lesson Plan

See plan for charts

 

I.                   Curriculum Standards

 

ü Count by 3 to 30 and 4 to 40, starting at any multiple of 3 or 4.   [M.1.2.a]

ü Define multiplication as repeated addition. [M.11.2.a]

ü Explain the connection between multiplication and skip counting. [M.11.2.b]

ü Create arrays as models of repeated addition.  [M.11.2.c]

 

 

 

 

 

II.                    The Point

 

What is an array?

 

 

 

 

 III.                Materials Needed

 

      Copies of 2.10.4 Problem Solving Task

      Optional: Enlarged Problem Solving Task

      Math Journals/ Glue Sticks

      12 counters per student

      Slates and markers

      Examples of real-life arrays: egg carton, box of pencils, sheet of stickers, Sudafed blister pack, etc.

 

 

 

 

IV.                 Lesson Outline

 

     Time:  60 Minutes

 

                          5 min. – Understanding the point and the problem-solving task

                          5 min. – Independent problem-solving

                        30 min. – Whole-Class Discussion/Practice/ Summary

     10 min. – Slate Math

     10 min. – Mental Math

 

 

 

 

  V.             Learning Activities

 

1.   Understanding “the point” and the problem-solving task (5 min.)

 

       Distribute a Problem Solving Task slip and 12 counters to each                        student.  

 

Students try to read and understand the task independently.  Provide support as needed as students retell the task to partners, the class, or themselves.

 

 

       2.  Independent problem-solving (5 min.)

 

            Students use counters to solve the problem on their slates.    

 

 

3.  Whole-Class Discussion/Practice/Summary (30 min.)

 

 

PART I – Whole-Class Discussion

                       

The Big Ideas:

 

ü An array is a rectangular arrangement of objects in rows and                           columns.

 

ü An array shows equal groups of objects.

 

ü Each row has the same number of objects and each column                                          has the same number of objects.

 

ü  Mathematicians describe arrays by saying how many rows there are and how many items there are in each row.  (Model the language of  ____ by ____arrays.)

 

ü  We can show arrays with dots, squares, objects, etc.

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                       

 
   

 

 

 

                          2 by 6 arrays: 2 rows, 6 per row

 

                          2 x 6

 

                          6 + 6

 

 

ü  The total number of objects in an array can be found using repeated addition, skip counting, or multiplication.

 

 

 

Possible Discussion:

 

Students share and discuss their responses to the problem.

 

 

ü  You might place counters on the overhead or a magnetic surface so that they can be manipulated during the discussion to show the possible arrays.

 

 

ü  As students suggest ways that the 12 desks could be arranged, ask students to find the total items in each array.

 

                                    How many rows?

                                    How many columns?

                                    What would the addition sentence describes the array?

                                    What would the multiplication sentence describes the array?

 

 

ü  Students will most likely encounter the fact that each array can be shown two ways (2 x 6; 6 x 2).  (Multiplication is commutative.)  The number of rows and the number of desks in each row can be reversed.

 

                        Are these different arrangements?

 

                         [They will look different in a classroom, but it is important for                 students to realize that t they are the same arrangement turned                     sideways.  You might demonstrate rotating an array 90º to help              students see this.  Since multiplication is commutative, the                             total amount in the array will not change if the number of rows                and the number in each row are reversed.]

 

 

 

                  

 

 

 

 

 

 

 

The Point:

 What is an array?

 

 

                                                                                                                           

                                           
   

Ms. Price has 12 desks in her classroom.

 

How many different ways can she arrange the desks so that each row has the same amount of desks?

 

 

 
 
   
 
     
     

1 row, 12 in each row  (1 x 12)

12 + 0 = 12

 

 

12 rows, 1 in each row (12 x 1)

1+1+1+1+1+1+1+1+1+1+1+1 = 12

 

 
     
 
 
 
     
 
   

2 rows, 6 in each row (2 x 6)

6 + 6 = 12

 

 

6 rows, 2 in each row (6 x 2)

2+2+2+2+2+2 = 12

 

 

 
     
     
 
 
 
     
 
   
 
   

SOLUTION:   There are 6 ways that Ms. Price can arrange the desks.

 

SUMMARY:  An array is a rectangular arrangement of objects in rows and                                    columns.  Each row has the same number of objects and each column                        has the same number of objects.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PART II – Whole Class Practice

 

Students practice:

a.    describing arrays

b.    arranging counters into arrays

c.    drawing arrays

d.    finding the total number of items in an array

 

 

 

a.    Describing arrays

 

         Hold up a real-life example of an array:

 

                                   

 

 

 

 

 

 

 

 

      

 

       Create an array on the board or the overhead:

 

                       

   
   
 
   
 
   

 

 

 

 

 

 

 

                       

 

 

 

 

 

 

 

 

 

 

 

 

b.    Arranging Counters in Arrays

 

                        Place your counters in an array that has:

                        5 rows

                        3 counters in each row

 

                        How many counters in all?

                                                Write the multiplication number sentence.

                       

 

 

c.    Drawing Arrays

 

                        Draw an array that has:

                        4 rows

                        5 counters in each row

 

                        How many counters in all?

                        Write the multiplication number sentence.

 

 

                         Draw an array that has 8 dots.

                        How many rows?

                        How many dots in each row?

                        How many dots in all?

                        Write the multiplication number sentence.

 

 

 

PART III Summary

 

ü  Stop and have students look back at the question that is The Point of today’s lesson. 

 

ü  Students work together with teacher to compose a statement that answers The Point’s question.  Students record the statement into their journal as a summary of their learning from the lesson.   

 

                                Example:

 

                 An array is a rectangular arrangement of objects in rows and                 columns. 

 

                 Each row has the same number of objects and each column                              has the same number of objects.

 

 

 

ü  Special Lifework:  Ask each student to bring in a real-life example of an array over the next 2-3 days in order to create an Array Museum in your classroom.  (You can tell students that if they cannot find an array, they can make one.)

 

 

 

 

 

4.    Slate Math (10 min.)

 

                        Plan slate math/ counting practice according to students’                                                      instructional         needs.

 

 

 

 

5.    Mental Math (10 min.)

 

  Students participate in a Mental Math practice session. 

 

                       

 

 

 

Lesson Resources

2.10.4.doc  
40
2.10.4 Enlarged Task.doc  
48
2.10.4 Problem Solving Task.doc  
51

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