Counting with Arrays

Math Lesson 3


NCTM Standards
Number and Operations: Students will understand the meaning of operations and how they relate to one another;
            (Grade 3): understand various meanings of multiplication and division; understand the effects of multiplying and dividing whole numbers.

Number and Operations: Compute fluently and make reasonable estimates;
            (Grade 3): develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results.

Representation: Students will create and use representations to organize, record, and communicate mathematical ideas.

NETS Standards
Students will discuss basic issues related to responsible use of technology and information and describe personal consequences of inappropriate use. (Performance Indicator 2)

Students will use telecommunications efficiently to access remote information, communicate with others in support of direct and independent learning, and pursue personal interests. (Performance Indicator 4)

Grade level: 2-3               

Duration: 1-2 days

Objectives: Students will learn to use a digital camera and count a large group of objects using the array method of multiplication.  Students will demonstrate problem-solving skills in making a "tidy" array.

Materials: Packages of familiar items (from bulleting board, see lesson 2), digital camera, gallon-sized Ziploc plastic bags.

Preparation: Clear a large area so that each child may have his/her own space to make a large array either on the floor or a large platform area using their packaged items.

Procedures: Start by asking students to recall the estimates they made about the packaged items on the Estimation Station bulletin board.  Ask, "what are some ways we could count these items?"   Accept all answers-- make sure conversation includes arrays and be sure to discuss all possibilities to show that creating an array may be the most efficient way (you won't lose count, it's neat and organized, etc.).  Build up students' desire to find out how many objects are in their package and suggest that they use an array.  Explain that when they create an array, they may run into some problems; ask "what problems might we run into."  Address each problem and suggest those that have not been given in order to cut down on difficulties that may arise during the activity.  Remind students of the book A Remainder of One by Elinor J. Pinczes.  Should they have any objects left over, they should rework their array to fit in any extras (this may be perhaps, the most difficult part of the exercise, but it is important for children to understand that an array cannot have any leftovers and that there is always more than one way to create an array).

Students should spread out so that each has a large area to work at.  Open each package and allow approximately one hour for each child to finish their array (depending on the number of objects in students' packages).  Assist the children should any problems arise.  As they finish their array, work with students individually with the digital camera.  Explain its use and model correct usage for each child.  Each student should take a digital photo of their array.  After digital camera work is completed, students should make a numerical representation of their array using multiplication.  Using a calculator, they should use this multiplication problem to figure out how many objects were in their package.  Each child should put their objects into a Ziploc bag and label the bag with the number of objects inside.

Conclude the lesson with a recap of the activity.  What were some difficulties?  Did you find a shortcut?  Do you think another way of counting would have been easier?  Were you surprised at how many objects were in your package?  Thank the students for their hard work.

Assessment of Objectives: An informal assessment will be performed during discussion.  Monitor the progress of each child's array development and correct usage of the digital camera.  Formal assessment will rest in the actual array and numerical representation.  Check for correctness and understanding.