Maria L. Bajorek - MITTEN - Introduction to Estimation and Making Arrays

Number and Operations: Students will understand meanings of operations and how they relate to one another;
(Grade 2): understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.
(Grade 3): understand various meanings of multiplication and division.

Measurement: Students will apply appropriate techniques, tools, and formulas to determine measurements;
(Grade 2): use repetition of a single unit to measure something larger than the unit, develop common referents for measures to make comparisons and estimates.
(Grade 3): develop strategies for estimating the perimeters, areas, and volumes of irregular shapes.

NETS Standards

Students will use a variety of media and technology resources for directed and independent learning activities (performance indicators 1 and 3).

Grade level: 2-3

Duration: 1-2 days

Objectives: Students will be exposed to the concept of estimating and organizing a group of objects into an array to count the exact number of items. They will create their own arrays and practice elements of estimation.

Materials: Computer, digital video projector, PowerPoint software and copy of Math is All Around presentation, 40 plastic chips and one copy of one-inch grid per child, Kidspiration software (with one computer for each child), one copy of One Hundred Hungry Ants and A Remainder of One both written by Elinor J. Pinczes.

Preparation: Connect personal computer to digital video projector and place in a spot where all students can see the PowerPoint presentation.

Procedures: Begin by showing students a group of 40 plastic chips and ask them to discuss, with a seat partner, how many chips they think is are in the group? Regroup and discuss children's "guesses" and talk about why they might be good (or rash) decisions. Set the group of chips aside and prepare to show Math is All Around, the PowerPoint presentation.

Discuss each slide while the presentation is running. Ask the children to answer the questions on the screen and explain why estimation is important. Go over estimation strategies that are presented in the slideshow, as well as any strategies the students use themselves. Be sure to stress the convenience of making arrays when counting these objects by setting up similar situations such as, "You have a box crackers that you brought to class for snack. How will you know how many to give each student or how many crackers are in the box?" Making an array is an easy solution! It's just like making groups, but much neater. You can count with a quick glance when objects are organized this way. Encourage students to formulate their own estimates for groups and photos shown on the slideshow. Relate the concept of an array to multiplication by counting rows x columns and saying the equation. ("Two rows of five chips is ten chips total. 2 x 5 = 10")

When the slideshow has been completed, focus on the group of chips that were previously discussed. Explain to the students that they will all receive a group of chips of the same number that this group has. Using their one-inch grid paper, they are to count how many chips are actually in the group. Remind them what an array is and how they can use it to count the chips with their grid paper. When this activity has been completed, ask the class how many chips they found and how they discovered this. Read One Hundred Hungry Ants by Elinor J. Pinczes to the students. Remind the class that there are many ways to make an array with one group of objects. Ask the class to give their seat partner a sentence describing their array (such as "4 rows of 10 chips equals 40 chips) and to experiment with the chips to find a different array for the same group of items. Allow students to make any additional arrays of their own and challenge their partner to make some estimates.

(Time permitting, you may do the following activity on the same day, or save it for the next day.) Begin the day's instruction with a review of the previous activity and read A Remainder of One by Elinor J. Pinczes to the students. Ask the class to define an array and throughout the story, point out any arrays pictured and described. Discuss why an array is "tidy" and how you can make sure to create a tidy array.

Students will work independently to create an array using the super-grouper function with clipart on the Kidspiration software in the computer lab. Remind students to use the strategies they have discussed and encourage the use of problem-solving skills. Second graders will create arrays of 6, 10, or 12. Third graders will create arrays of 18, 24, 30, or 40. Encourage students to include a multiplication representation in their printout. Hang the finished products around the room. Close lesson by reviewing arrays, estimation, and any new strategies brought out by the computer lab experience.

Assessment of Objectives: An informal assessment will be made during class discussion; are students contributing thoughtful ideas that are relevant to new concepts? Are they making reasonable estimates and/or using the highlighted strategies from discussion? Do they understand the notion of different arrays for one set of objects? How are they showing this with the chips in class and the computer activity? Formal assessment will be performed on printouts made of Kidspiration arrays. How many ways have they come up with to make an array of their number? Are the labels correct? Have they included a multiplication problem? (Expectations will be different for 2nd and third grades. The goal for second grade is to understand the concepts, while the goal for 3rd grade is to have them mastered.)