Exam 5: Using Numbers in Sensible Ways

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Joe Blue was estimating 92 × 31. He said that rounding 31 to 30 then taking 92 × 30 (which is 2760) is a better estimate than rounding 92 to 90 and then taking 90 × 31 (which is 2790) because, in the first case, you lost only 1 by rounding 31 to 30, but, in the second case, you lost 2 by rounding 92 to 90. Explain how Joe's reasoning is INCORRECT. Your answer should show number sense.

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Question 1

Correct Answer:

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Estimating 92 × 31 via 92 × 30 will be "off" by 92. Estimating 92 × 31 via 90 × 31 will be "off" by only 2 × 31, or 62.

Show how you would mentally compute each calculation. A) 0.75 × 36 B) 34 × 12 + 34 × 8 C) 3458 - 1734 - 400 + 1734

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Question 2

Correct Answer:

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Possible explanations include:
A) 27, from 3/4 of 36
B) 680, from 34 × (12 + 8)
C) 3058, from 3458 - 400 (the other terms give 0)

Name two types of estimates you use in daily life.

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Question 3

Correct Answer:

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Could be length of time to drive to campus, amount of money to fill tank with gas, amount of money needed at cash register, cost of meals for a week, and so on

Estimate the indicated quantity and tell how you did it. A) 15% of $51.07 B) 25% of 1998 C) 125% of 47 D) 48% of 212 E) 4% of 201

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Question 4

Demonstrate number sense in estimating the following expressions and responding to the question about your answer. Write enough to make your thinking clear. 75.48% × 883.375 × 567/566 is about _. Is your estimate less than, equal to, greater than the exact answer? Why? (Don't figure the exact answer out!) _

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Question 5

Betty was asked to give her best estimate for 25% of 7991.8. She estimates by taking 1/4 of 8000, which is 2000, and taking 1/4 of 0.8, which is 0.2. Therefore, her estimate is 2000.2. Comment on Betty's reasoning.

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Question 6

Use benchmarks to estimate each calculation. Explain how you arrived at the estimate. A) 60% of $271 B) 87 × 52 C) 32% of $595.45

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Question 7

Show how you would estimate: A) 391 × 612. B) 0.74 × 798. C) 32% of 19. D) 196% of 25.

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Question 8

A person who is calculating the exact answer to 18 × 15 mentally starts by thinking about factors of 18. The person would finish the mental calculation by calculating:

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Question 9

A person can reasonably calculate the exact answer to 1563 - 198 mentally by:

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Question 10

For each of the following, mentally calculate the exact answer and write it in the blank. Use number sense. Then write enough to make your thought process clear. A) $3618 + 2472 - 2618 - 472 =$ $\underline{\quad\quad}$ B) $( 25 \times 29 ) + ( 25 \times 11 ) =$ $\underline{\quad\quad}$

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Question 11

Name an item that costs approximately $500,000.

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Question 12

0.3347876 × 629.847291143 is CLOSEST to:

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Question 13

Show how you would mentally compute the exact results of each calculation. A) 3000 - 2575 B) 0.75 × 24 C) 24 × 13 + 24 × 7

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Question 14

For each, describe two different strategies for performing the following computation mentally. A) 29 + 58 B) 74 - 28 C) 8 × 15

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Question 15

Estimate each calculation with a brief explanation. A) 65% of 37 B) 140% of 52 C) 18% of 971 D) 8/9% of 120 = _____ (decimal)

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Question 16

Describe how you would mentally compute the exact result in each calculation without using the standard algorithm. Your description should be concise and include the exact result. A) 234 - 119 B) 12% of 150 C) 25 × 2/5

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Question 17

Which calculation does NOT show how to mentally calculate 16 × 25?

(Multiple Choice)

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Question 18

Tell how one might mentally compute each calculation. A) 25 × 104 B) 25% of 104 C) 200% of 104

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Question 19

42,189 ÷ 511,264 is about how many percent?

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Question 20

Showing 1 - 20 of 38

Exam 5: Using Numbers in Sensible Ways

Show how you would mentally compute each calculation. A) 0.75 × 36 B) 34 × 12 + 34 × 8 C) 3458 - 1734 - 400 + 1734

Name two types of estimates you use in daily life.

Estimate the indicated quantity and tell how you did it. A) 15% of $51.07 B) 25% of 1998 C) 125% of 47 D) 48% of 212 E) 4% of 201

Betty was asked to give her best estimate for 25% of 7991.8. She estimates by taking 1/4 of 8000, which is 2000, and taking 1/4 of 0.8, which is 0.2. Therefore, her estimate is 2000.2. Comment on Betty's reasoning.

Use benchmarks to estimate each calculation. Explain how you arrived at the estimate. A) 60% of $271 B) 87 × 52 C) 32% of $595.45

Show how you would estimate: A) 391 × 612. B) 0.74 × 798. C) 32% of 19. D) 196% of 25.

A person who is calculating the exact answer to 18 × 15 mentally starts by thinking about factors of 18. The person would finish the mental calculation by calculating:

A person can reasonably calculate the exact answer to 1563 - 198 mentally by:

Name an item that costs approximately $500,000.

0.3347876 × 629.847291143 is CLOSEST to:

Show how you would mentally compute the exact results of each calculation. A) 3000 - 2575 B) 0.75 × 24 C) 24 × 13 + 24 × 7

For each, describe two different strategies for performing the following computation mentally. A) 29 + 58 B) 74 - 28 C) 8 × 15

Estimate each calculation with a brief explanation. A) 65% of 37 B) 140% of 52 C) 18% of 971 D) 8/9% of 120 = _____ (decimal)

Describe how you would mentally compute the exact result in each calculation without using the standard algorithm. Your description should be concise and include the exact result. A) 234 - 119 B) 12% of 150 C) 25 × 2/5

Which calculation does NOT show how to mentally calculate 16 × 25?

Tell how one might mentally compute each calculation. A) 25 × 104 B) 25% of 104 C) 200% of 104

42,189 ÷ 511,264 is about how many percent?

Reasoning About Quantities

Numeration Systems

Understanding Whole Number Operations

Some Conventional Ways of Computing

Meanings for Fractions

Computing With Fractions

Multiplicative Comparisons and Multiplicative Reasoning

Ratios, Rates, Proportions, and Percents

Integers and Other Number Systems

Number Theory

What Is Algebra

A Quantitative Approach to Algebra and Graphing

Understanding Change: Relationships Among Time, Distance, and Rate

Further Topics in Algebra and Change

Polygons

Polyhedra

Symmetry

Tessellations

Similarity

Curves, Constructions, and Curved Surfaces

Transformation Geometry

Measurement Basics

Area, Surface Area, and Volume

Counting Units Fast: Measurement Formulas

Special Topics in Measurement

Quantifying Uncertainty

Determining More Complicated Probabilities

Introduction to Statistics and Sampling

Representing and Interpreting Data With One Variable

Dealing With Multiple Data Sets or With Multiple Variables

Variability in Samples

Special Topics in Probability

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