Thinking with Whole Numbers: Number Sense, Estimation, and Mental Computation

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Consider Investigation 7.1 (page 7-2) and then read on.

Investigation 7.1Uses of Mental Arithmetic

 ◆ Underscore the value of estimation and mental computation in everyday life ◆ 4–8 ◆ Groups of four + class discussion

The aim of this investigation is to help students reflect on the following questions: With the widespread use of calculators and computers, is estimation skill more or less important today than in the pre-electronic age? Is mental calculation still an important skill? Complete Part I on your own and then discuss your answers with your group or class. It may be a good idea to do Part II with your group.

Part IMath Uses

Take a minute or two to list the ways you use mathematics in everyday life.

Share your ideas with your group or class. List the suggestions on a piece of paper or chalkboard using the following categories: written math, mental math, or calculator math. Obviously, there will be disagreements. Many people keep track of their spending for groceries, for instance, by mentally estimating a running total. Many others bring a calculator to the grocery store. Some individuals bring a pad and a pencil to keep track. (Really.) Resolve disagreements by taking a vote—the majority wins. Analyze the distribution of examples among the three categories, (a) What does this Math-Uses activity reveal about the everyday uses of mathematics? (b) What are the instructional implications of your results?

Part IIMiscalculating Calculators

As the use of calculators and computers grows, so does the need for estimation to check the reasonableness of answer. After all, if such electronic devices are given incorrect data or instructions, they simply do as they are told. In brief, garbage in, garbage out.

In each of the following cases, a person has used a calculator to determine the answer. Estimate whether each answer is plausible. If an answer is implausible, determine how the miscalculation occurred. Consider how you can “zero in” on the error.

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Item cost for a remodeling project were $1,027.99, $396.00, $2,333.67, $27.95 for a total of $6,552.66.

A business account included expenditures for $100.97, $30.50, $1,230.85, $26.12 and $3,597.19 for a total of $4,962.122.

Checks written during a week for $70.27, $125.66, $199.99, $30.52, and $82.50 for a total of $308.95.

Receipts for $50.50, $136.95, $88.20, $145.75, and $156.90 for a total of $478.30.

A tally of a card game scores of 20, 50, 30, 90, 100 points produced a total of 380 points.

A check of grocery charges of $5.25, $1.18, $1.99, $2.05, $9.65, $9.65 resulted in a total of $59.54.

Total of 175 yards for a football running back who gained 12 yards, 8 yards, 15 yards, and 5 yards on four runs.