The Estimation Station

Math Lesson 2


NCTM Standards
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.

Data Analysis and Probability: Students will formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them;
            (Grade 3): collect data using observations, surveys, and experiments; represent data using tables and graphs such as line plots, bar graphs, and line graphs;

Data Analysis and Probability: Students will select and use appropriate statistical methods to analyze data;
        (Grade 3): describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed;

NETS Standards
Students will practice responsible use of technology systems and software. (Performance Indicator 2)

Use general purpose productivity tools and peripherals to support personal productivity, remediate skill deficits, and facilitate learning throughout the curriculum.
 (Performance Indicator 3)

Grade level: 2-3               

Duration: 1-2 days

Objectives: Students will challenge "common knowledge" against newly learned estimation strategies and put those strategies into use.  Students will consider variables in estimating different groups of objects and practice skills of representing numbers. They will count estimation data and graph it on the computer.

Materials: Access to a bulletin board, string and clothespins (optional), eight clear (or not entirely printed on) packages of familiar items, such as jelly beans, or cotton balls, post-it notes, computers, and ClarisWorks for Kids software.

Preparation: Staple packages (leave one to the side) to Estimation Station bulletin board with enough room for each student to stick a post-it note around each package.

Procedures: Begin by showing one package of familiar items to the students (not posted on the bulleting board).  Discuss all that has been presented about estimation and strategies for making estimates.  Ask students to discuss with a partner how many objects are in the given package.  Urge students to make their own estimate and then share with a partner, stressing that it's okay to have a different estimate than their partner.  At this point, walk around the room with the package so that each child may have a close-up view of the items inside.  Explain to the students how you would prepare to make an estimate, modeling strategies discussed earlier. 

Direct students' attention to the bulletin board.  Note that there are many familiar packages on the board and describe what they are.  Tell the students that they will be estimating the number of items in each bag, using what they know about estimation.  Remind them to consider the size of the package, the amount of air inside the packaging, and the size of the items inside the package, when making an estimate.  Direct students to make their estimate and write it on a Post-It note, along with their reasoning (why did they make that guess, what considerations did they make, and/or a number sentence that describes the estimation process).  Each student will make an estimation for each package, completing one Post-It Note per package.  Upon completion of giving their estimate, they will stick the note under the corresponding package.  When all students have finished, discuss how they might find out how many objects are actually in each package.

(The next activity may take place the following day.) Review the elements of a bar graph with third grade (i.e. title(s), columns, rows, labels, bars, etc.).  Discuss reasons why we might graph something and give instances where they might see a graph (such as the current Sunrise/Sunset chart they are working on in class).  Ask what they might be able to graph from the bulletin board.  Guide discussion to the estimate values students posted on the board.  Allow students to look at and talk about the variety of estimate values stuck on the board.  Briefly address a simplified issue of averages (a number that most of the answers seem to be around)  and why each package will have a different average estimate.  "The pretzels may have a smaller average than the M&Ms because the pretzels are bigger..."

Assign one package per student from the bulletin board.  Each child will collect all the Post-It Notes for his/her package and organize them into groups of estimates; 0-50, 51-100, 101-200, 201-300, 301 +. Guide the students to the computer and through the first steps of opening ClarisWorks for Kids, graphing to 10 option.  Allow students to graph the number of estimates for each group for their specific package. Remind them to include a title and talk about what labels would go where (provided there were a space for labels).  Students will work in partners on the computer to oversee the work of their peer.  This will be printed upon completion of a graph for each child.  Compare and explain the differences between graphs and talk about why there are differences.  Discussion should include elements of variation in packages and how it relates to estimate values, range of estimates, and the difference in grouping the estimates, if any.

Assessment of Objectives: An informal assessment will be performed on the process of estimating with the packages on the bulletin board. Did the students make a reasonable estimate, does their explanation make sense, and have they used featured strategies?  A formal assessment will be taken of the graph printouts and responses on reflective worksheet.