# Using Data

# Using Data; Addition and Subtraction of Fractions

The authors of Everyday Mathematics believe that students
should do serious and

substantial work with data. Unit 6 provides many activities designed to present
and

teach relevant data skills and concepts, allowing your child ample opportunities

to practice organizing and analyzing the data he or she collects.

The data that your child initially collects will usually consist of an
unorganized

collection of numbers. After organizing the data using a variety of methods , he
or

she will study the** landmarks** of the data. The following terms are called
landmarks

because they show the important features of the data:

The **maximum** is the largest data value
observed.

The **minimum** is the smallest data value
observed.

The **range** is the difference between
the maximum and the

minimum.

The **mode** is the “most popular” data
value—the value observed

most often.

The **median** is the middle data value
observed.

The **mean**, commonly known as the
“average,” is a central value

for a set of data.

At the end of the unit, students will have an opportunity to

demonstrate their skills in this area by conducting a survey of their

peers; gathering and organizing the data; analyzing their results; and

writing a summary report .

Your child will continue his or her work with the American Tour by

studying a variety of Native American measurements for length and

distance based on parts of the body. Students will convert these

body measures to personal measures by measuring their fingers,

hands, and arms in both metric and U.S. customary units. In

addition, your child will learn how to read a variety of contour-type

maps, such as climate, precipitation, and growing-seasons maps.

Finally, students will explore addition and subtraction of fractions by

using paper slide rules, the familiar clock face, and fraction sticks.

They will learn to find common denominators and apply this skill in

adding and subtracting fractions with unlike denominators.

**Please keep this Family Letter for reference as your
child
works through Unit 6.**

**Vocabulary
**

Important terms in Unit 6:

angle of separation A measureof how far fingers can be spread apart. The figure shows the angle of separation between a person’s thumb and first finger. |
Angle of separation |

** common denominator ** Any number except zero

that is a multiple of the denominators of two or more

fractions. For example, the fractions 1/2 and 2/3 have

common denominators 6, 12, 18, and so on.

**contour line** A curve on a map through places where a

certain measurement (such as temperature or elevation) is

the same. Often, contour lines separate regions that have

been colored differently to show a range of conditions.

**cubit** An ancient unit of length, measured from the

point of the elbow to the end of the middle finger.

A cubit is about 18 inches.

**decennial** Occurring or being done every 10 years.

**fair game** A game in which each player has the same

chance of winning. If any player has an advantage or

disadvantage (for example, by playing first), then the

game is not fair.

**fathom** A unit used by people who work with boats

and ships to measure depths under water and lengths

of cables. A fathom is now defined as 6 feet.

great span The distancefrom the tip of the thumb to the tip of the little finger (pinkie), when the hand is stretched as far as possible |

**landmark** A notable feature of a data set. Landmarks

include the median, mode, maximum, minimum, and

range.

** line plot **A sketch of data in which check marks, Xs,

or other marks above a number line show the

frequency of each value.

**map legend (map key)** A diagram that explains the

symbols, markings, and colors on a map.

**maximum** The largest amount; the greatest number in

a set of data.

**mean** The sum of a set of numbers divided by the

number of numbers in the set. The mean is often

referred to simply as the **average.
**

**median**The middle value in a set of data when the

data are listed in order from smallest to largest. If there

is an even number of data points, the median is the

mean of the two middle values.

**minimum**The smallest amount; the smallest number

in a set of data.

**mode**The value or values that occur most often in a

set of data.

normal span The distancefrom the tip of the thumb to the tip of the first (index) finger of an outstretched hand. Also called span. |

**population** In data collection, the collection of

people or objects that is the focus of the study.

**range** The difference between the maximum and

minimum in a set of data.

**sample** A part of a group chosen to represent the

whole group .

**simplest form** A fraction less than 1 is in simplest

form if there is no number other than 1 that divides its

numerator and denominator evenly. A mixed number is

in simplest form if its fractional part is in simplest form.

stem-and-leaf plotA display of data in which digits with larger place values are “stems” and digits with smaller place values are “leaves.” |
image id 5MhU05.L13.0003.T |

**survey** A study that collects data.

**Do-Anytime Activities
**

To work with your child on the concepts taught in this unit and in previous units,

try these interesting and rewarding activities:

Have your child design and conduct an informal survey. Help him or her collect

and organize the data, and then describe the data using data landmarks.

Challenge your child to create different ways in which the organized data can

be presented.

Encourage your child to develop his or her own set of personal measures for

both metric and U.S. customary units.

Building Skills through GamesIn this unit, your child will work on his or her understanding of angles and the addition and subtraction of fractions by playing the following games. For detailed instructions, see the Student Reference Book. Frac-Tac-Toe See Student Reference Book, pages 274–276This is a game for two players. Game materials include 4 each of the number cards 0–10, pennies or counters of two colors, a calculator , and a gameboard. The gameboard is a 5-by-5 number grid that resembles a bingo card. Several versions of the gameboard are shown in the Student Reference Book. Frac-Tac-Toe helps students practice converting fractions to decimals and percents . Angle Tangle See Student Reference Book, page 258This is a game for two players and requires a protactor, a straightedge, and paper. The game provides practice with measuring angles and estimating angle measures. |

**As You Help Your Child with Homework**

As your child brings assignments home, you may want to go over the instructions
together, clarifying

them as necessary. The answers listed below will guide you through this unit’s
Study Links.

**Study Link 6.1
**

3.

a. 59 b. 24 c. 33

d. 36 e. 39.5

Study Link 6.2

Study Link 6.2

1. a.–c. Answers vary.

2.

a. cm; ft | b. ounces; gal; liters |

c. m; miles | d. cm; ft; mm |

e. kg; lb; grams |

**Study Link 6.3
**

1. 73

2. 19

3. 53

4. Sample answer: Cross off the highest and lowest

values—31 and 73. Continue by crossing off the

highest and lowest values remaining. Finally, only

the number 53 remains. So 53 is the median.

**Study Link 6.4
**

1. tapes and CDs

2. books and magazines

3. movie tickets

**Study Link 6.5**

Sample answers given for Problems 1–3.

1. 5, 7, 7, 8, 8, 9, 10, 13, 14, 15, 15, 15, 20

2.

3. The number of minutes it takes to get ready

for bed

**Study Link 6.6**

1. Sample answer: The ages of the oldest people we

know

Title: The Oldest People Our Class Knows

Unit: Years

2. a. 77 b. 94 c. 85 d. 85

3. Sample answer: Scores on a science test

Title: Science Test Scores

Unit: % Correct

4. a. 32 b. 99 c. 66 d. 78.5

**Study Link 6.7
**

1. Florida; Arizona

2. Oregon; Washington

3. Answers vary.

4. Utah; Wyoming

**Study Link 6.8**

**Study Link 6.9**

**Study Link 6.10**

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