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- The student will identify appropriate uses for estimation.
- The student will round purchase prices to estimate total purchases in a school store setting.
- The student will practice estimating by using rounding and mental computations to arrive at estimates.
Connection to Bloom’s Taxonomy
- Clear Jar ( or other container )
- Crayons or Colored Pencils
- Dictionary ( Printed and/or on the Web )
- Happy Cap Erasers ( or any other small sized school store item appropriate for estimating quantity )
- Index Cards
- Item Cards from the Geddes Kit List
- Worksheets for lesson plan 4 (see sidebar)
What is an estimate?
Ask several students to use a dictionary or on-line dictionary to define the word “estimate.” Record several of those definitions on the board. In general, an estimate is an approximate calculation. Use Word Origin by Hannie in the sidebar for additional clarification.
Ask students to think about times when they may use estimating outside of the classroom.
- Have you ever purchased something on sale?
- What does it mean to buy something on sale?
Have students brainstorm responses to the following two questions. Some possible responses may include:
- To determine how long it will take to drive somewhere unfamiliar
- To determine how long it will take to complete a homework assignment
- To determine how much time will be needed to complete a project at work or home
- To determine how much money to bring to the grocery store to purchase a week’s worth of food
- To determine what time to set the alarm clock based on how long it will take to get ready in the morning
- To determine how many suitcases to pack for a week-long family vacation
- To determine how much gasoline will be needed to fill the car gas tank
- To determine a weekly or monthly budget for household expenses
- To determine how much food to prepare for a party
Discuss why estimation is useful and explain to students the overall purpose of estimation. Students should understand that estimates provide approximations or reasonable answers to questions. Although the exact amount or number might not be known, an estimate helps to plan and prepare. Estimates actually help people to solve problems. The world around us is filled with unknowns. We do not and will not always know or have the exact answer to a question or problem. However, estimates provide people with a way of making reasonable, intelligent approximations when the exact answer is not easily or readily available.
Exploring and Learning
- Fill a jar with Happy Cap Erasers or any other small-sized school store item. Show a single item to students so that they have an idea as to the item’s shape and size. Then show the class the filled jar of erasers and ask them to estimate the number of erasers or items in the jar. Record student estimations on the board.
- As a class, look at the list of estimates and determine if there was a wide range of estimates or were the numbers fairly close to one another.
- Discuss how estimates are derived by asking students to share their approaches, thought processes, and methods for developing their estimates. Often estimates are developed based on prior knowledge, rough calculations, or simply an educated guess.
- Explain that estimating is very useful when making purchases. It is a helpful way to calculate quickly the total amount to be purchased and to ensure you have enough money for your purchases.
- Use the Estimating Store Purchases - Guided Practice (PDF) as a transparency to help guide students through the process of estimation. Explain to students that making estimates in a store may involve rounding, mental calculations, or using paper and pencil to do quick calculations. It is often better to estimate a little higher to ensure that you have enough money to afford the purchase.
- Present students with the following scenario:
RG and Hannie are purchasing for their Raymond Geddes Elementary School Store. Today in math class, they learned about estimation and want to practice what they have learned for the school store. RG and Hannie will help estimate the total price of two different purchases. With this information, the students will know whether or not they have enough money to buy what they want to sell at the school store. Sniffer will tabulate the exact total price using a calculator.
Can you help RG, Hannie, and Sniffer estimate the students’ purchases?
- To help complete the scenario, pair students together and provide them with a copy of Estimate Store Purchases Worksheet (PDF). Explain and list on the board or as a transparency the following instructions:
- Use rounding to generate an estimate for each item.
- Use a calculator to determine the actual total price.
- Does each student have enough money to make his/her purchases?
- As a class, review the results and determine if Natalie and Matt have enough money to make their purchases? Student estimations should determine that Natalie does not have enough money to purchase all the items that she wanted to buy. Review with students Natalie’s 2 alternatives found on the Estimate Store Purchases Worksheet Key (PDF).
- The scenario involving Matt provides a different look at estimation. Some students will overestimate Matt’s total purchase price when rounding upward. Estimating by rounding upward showed that Matt could not afford all his items. However the actual price for all of his items was less than the $75.00 he had to spend. Rounding each item’s price upward yielded an overestimate. Review the upward estimation on the Estimate Store Purchases Worksheet (PDF) with students. Explain that when you are making purchases, it is often better to overestimate than to underestimate the total purchase price.
- Provide students with additional practice at estimating purchase totals by creating item cards using index cards and the Geddes Kit List (PDF). You can create up to 20 item cards, each containing the item name and corresponding purchase price. For example, one card will state “Retro Pencil $8.64/Display”. Fold the cards in half and place them in a container.
- Call two students to the front of the classroom to lead the activity. One student will roll a die and the other will draw an item card from the container. Divide the remainder of the class into teams of 3-4 students. All students will participate by estimating (using mental computation only) a total purchase price within their assigned teams. Remind students that you do not want the actual total price, but an estimate. To estimate in this activity means to round the item price first and then to multiply that price by the quantity rolled on the die.
- Ask each team to jot down their estimate. Students will share their estimates aloud after each card is drawn and die rolled. Did everyone arrive at the same estimate? If not, discuss any differences in creating the estimate.
Extended Learning and Practice
- Open up your own school store using the Geddes School Store Kit and our School Stores: An Operating Manual. Operating a school store is an excellent opportunity for inquiry based/hands-on learning that is both fun and rewarding. Create an instant real life business in your classroom by using the merchandise in the Geddes Kit and following the school store operations manual. A school store will allow opportunity for raising money, provides a service to students, and creates an atmosphere of responsibility while building valuable team working skills. This lesson demonstrated how customers use estimation prior to making purchases. Identify several other ways estimation can be used within a school store. Some possibilities include: estimating and forecasting future sales based on prior actual sales data, estimating the amount of shelf space needed to display store items, or simply estimating how much help will be needed to operate the store.
- Challenge students by using two dice to perform mental computations for each item card created in step 10 of the Exploring and Learning component. Explain to students that estimation is very helpful when the quantities increase and you can begin to group by tens.
- Have students think about what it means to overestimate versus underestimate. Ask which do you think is better, and why. Provide one or two examples to support your answer.
- Visit http://www.ed.gov/pubs/parents/Math/grocerymath.html (U.S. Department of Education Archives) for additional estimation activities that can be completed at the grocery store.
- Visit Figure This! Math Challenges for Families. The Challenge Index contains estimation challenges. This website was developed by the National Council of Teachers of Mathematics.
The lesson objectives can be assessed by evaluating the Estimate Store Purchases Worksheet (PDF) with the Estimate Store Purchases Answer Key (PDF). Use the Assessment of Student Progress (PDF) to assess students’ overall abilities to meet the lessons learning objectives which include rounding purchase prices, estimating individual item totals, and estimating overall purchase amounts.
Provide each student with an index card and have them answer the following questions on one side of the index card:
- What are two new things that you have learned?
- What else would you like to learn about this topic?
On the back side of the index card, instruct the students to draw a picture of something they learned about during this lesson. The index cards can be hole punched and held together with a simple shower curtain ring.