the mean and the median - mcgraw hill education · math journal 2, p. 255 ... the mean and the...

www.everydaymathonline.com

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

Lesson 10�6 835

Advance Preparation

Teacher’s Reference Manual, Grades 1– 3 pp. 124–126

Key Concepts and Skills• Order whole numbers.

[Number and Numeration Goal 6]

• Use data to complete a bar graph. [Data and Chance Goal 1]

• Find the median and mean of data sets. [Data and Chance Goal 2]

• Use graphs to ask and answer questions. [Data and Chance Goal 2]

Key ActivitiesChildren make bar graphs for given sets of data. They model the bar graphs with pennies and then rearrange the pennies to determine the mean (average) for each data set. They compare the mean and median of data sets.

Ongoing Assessment: Recognizing Student Achievement Use journal page 254. [Data and Chance Goal 1]

Ongoing Assessment: Informing Instruction See page 838.

Key Vocabularymean � average � median

MaterialsMath Journal 2, pp. 253 and 254Student Reference Book, pp. 80 and 83–85Home Link 10 �5 ruler or straightedge � tool-kit pennies or counters (30 per child) � stick-on notes (optional) � slate

Interpreting a Pictograph and Creating a Bar GraphMath Journal 2, pp. 255A and 255BStudent Reference Book, pp. 86–89Children use data from a pictograph to answer questions. Then they create a bar graph to show the same data.

Math Boxes 10�6Math Journal 2, p. 255Children practice and maintain skillsthrough Math Box problems.

Home Link 10�6Math Masters, p. 340Children practice and maintain skillsthrough Home Link activities.

READINESS

Graphing Dice RollsMath Masters, p. 339per partnership: 2 diceChildren make a bar graph to record dice-roll results.

ENRICHMENTMaking a Data SetMath Masters, pp. 341 and 342per partnership: countersChildren determine a set of data based on given landmarks and graph the data.

ELL SUPPORT Building a Math Word BankDifferentiation Handbook, p. 132Children add the term mean to their Math Word Banks.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

The Mean and the MedianObjectives To introduce the mean of a set of data; and to review the median of a set of data.t

�

835_EMCS_T_TLG_G3_U10_L06_576892.indd 835 10/5/11 10:49 AM

836 Unit 10 Measurement and Data

A Mean, or Average, Number of ChildrenLESSON

10 �6

Date Time

Activity 1 Make a bar graph of the data in the table.

The mean, or average, number of children in the six families in the table is 3 .

8

7

6

5

4

3

2

1

0

Num

ber o

f Chi

ldre

n

Kugel Abuka Lauer Miller Ellis BosnakFamilies

Activity 2(to be done later)

Use the table above. List the number of children in order.

112257

The median number of children in the six families in the table is

2 .

Family Sizes

Family Number of Children

Kugel 5

Abuka 1

Lauer 2

Miller 7

Ellis 1

Bosnak 2

240-266_EMCS_S_MJ2_G3_U10_576418.indd 253 2/28/11 2:33 PM

Math Journal 2, p. 253

Student Page

Getting Started

Math Message Make a bar graph of the data in the table on journal page 253.

Home Link 10�5 Follow-Up Have partners share answers.

6 × 9 = 54 7 × 8 = 56 9 × 4 = 36 3 × 90 = 270 70 × 7 = 490 80 × 6 = 480

60 × 70 = 4,200 80 × 80 = 6,400 40 × 90 = 3,600

Mental Math and ReflexesPose fact and fact extension problems like the following. Have children record the facts on slates and share their strategies for solving the fact extensions.

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 2, p. 253)

Check that children have completed the bar graph. Ask: What does the height of each bar represent? The number of children in that family

� Finding the Mean WHOLE-CLASS ACTIVITY

Number of Children(Math Journal 2, p. 253; Student Reference Book, pp. 83–85)

Ask whether anyone can remember how the class found an average class shoe length in an earlier unit. (In Lesson 3-1, 16 children lined up along a paper tape, each placing one foot heel-to-toe on the tape. After cutting off the leftover piece of tape, children folded the tape into 16 equal parts. Each part represented an average class shoe length.) Explain to the class that they are going to find the average number of children per family shown in the table using another method. Lead them in the following routine:

1. Cover each shaded cell in the bar graph with a penny (or other counter). What does each penny represent? A child

2. Level off the pennies; that is, rearrange the pennies so each column in the graph has the same number of pennies.

3. With a straightedge, draw a horizontal line just above the top row of pennies.

4. Remove the pennies.

PROBLEMEEEMMBLEBLEBLBLELLELLLLBLEBLEBLEBLEBLEBLEBLEBLEMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEEEEEEEEEEEPROBLEMSOLVING

LELELELLEMMMMMMMML MMMMMMMMMMMMMEEEEEEEEEEEGGGGGGGGGLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVVINVINVINVINVVINVV GGGGGGGGGGNNVINVINVINVINVINVINVINVINVINVINVIVINGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNGGGGGGGGGGGGGGGGGGGGGGGGSOLVING

ELL

NOTE Everyday Mathematics does not draw a distinction between bar graphs and histograms. For a discussion on how some people contrast them, see section 12.2.3, Organizing and Displaying Data in the Teacher’s Reference Manual.

Mathematical PracticesSMP1, SMP2, SMP4, SMP5, SMP6Content Standards3.OA.7, 3.NF.3b, 3.MD.3

836-839_EMCS_T_TLG_G3_U10_L06_576892.indd 836 3/12/12 11:54 AM

A Mean, or Average, Number of EggsLESSON

10 �6

Date Time

Activity 2(to be done later)

List the number of eggs in the clutches in order.

2468

10The median is 6 eggs per clutch.

10

9

8

7

6

5

4

3

2

1

0

Num

ber o

f Egg

s

a b c d eOstrich Clutches

Activity 1 Make a bar graph of the data in the table.

The mean, or average, number of eggs in thefive clutches is .6

�Ostrich Clutches

Clutch Number of Eggs

a 6

b 10

c 4

d 2

e 8

240-266_EMCS_S_MJ2_G3_U10_576418.indd 254 2/28/11 2:33 PM


Student Page

Lesson 10�6 837

NOTE Although the mean for this set of data is a whole number, the mean for other data sets will likely be between two whole numbers. A more efficient way to find the mean will be introduced in Lesson 10-7.

Links to the Future

The horizontal line represents the mean, or average, of this set of data. In this example, the mean number of children per family is 3. To support English language learners, discuss the social and mathematical meanings of the words mean and average. Emphasize that in this mathematical context, mean and average describe the same thing.

Ask children to count the number of shaded cells above the line and the number of unshaded cells below the line.

● Are the number of cells the same? Yes. Each time a penny was moved, a shaded cell was matched with an unshaded cell.

● How could you find the place to draw the horizontal line without using pennies? By trial and error, draw a horizontal line so that the number of shaded squares above the line is the same as the number of unshaded squares below the line.

Another method of finding the mean is to model each family by drawing a medium-size circle for each family and putting in the required number of pennies or counters to represent the number of children. The counters are then redistributed among the families (without adding or subtracting any) so each family has the same number.

Have children read the essay on The Mean (Average) on pages 83–85 in the Student Reference Book.

� Finding the Mean of INDEPENDENTACTIVITY

Ostrich Egg Clutches(Math Journal 2, p. 254)

Children make bar graphs of the data set about ostrich egg clutches. They use one of the methods from the previous activity to find the mean number of eggs.

Ongoing Assessment: Journal Page 254 �

Recognizing Student AchievementUse journal page 254 to assess children’s ability to complete a bar graph. Children are making adequate progress if they successfully complete the bar graph. Some children may be able to find the mean number of eggs. [Data and Chance Goal 1]

The activities in this lesson are an early exposure to finding the mean of a set of data. Finding the mean of a data set is a Grade 5 Goal.

PROBLEMBBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEMMMBLEBLLELBLLLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMMOOOOOOOOOOBBBBBBBBLBLBLBLBBLBLBLLLLLPROPROPROPROPROPROPROPROPROPROPRPRPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPRORORORROROROOOPPPPPPP MMMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEELELELEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBLELEELEMMMMMMMMMOOOOOOOOOBLBLBLBLBLBLBBLBBLBLOOOOROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINVINVINNNNVINVINNVINVINVINVINV GGGGGGGGGGGOOOLOLOOLOOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGOOOLOLOLOLOLOLOOO VVVVLLLLLLLLLLVVVVVVVVVOOSOSOOSOSOSOSOSOSOSOOSOSOSOSOOOSOOOSOSOSOSOSOSOSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING

Date Time

Interpreting a PictographLESSON

10 �6Big Bend National Park is located in southwestern Texas. It contains 801,163 acres of protected wilderness. About 350,000 people visit the park each year.

The pictograph below shows attendance at Big Bend National Park for one week in August. Use the data to answer the questions below.

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

KEY: = 50 people

Visitors to Big Bend National Park

1. How many people visited the park on Day 4? 500 people



4. How many more people came to Big Bend National Park on Day 7 than Day 6?

175 more people

5. How many fewer people came on Day 1 than Day 3?

125 fewer people

240-266_EMCS_S_MJ2_G3_U10_576418.indd 255A 4/11/11 4:00 PM

Math Journal 2, p. 255A

Student Page

836-839_EMCS_T_TLG_G3_U10_L06_576892.indd 837 4/11/11 8:31 PM

838 Unit 10 Measurement and Data

Date Time

LESSON

10 �6 Making a Bar Graph from a Pictograph

255B

Use the information shown in the pictograph to make a bar graph. Remember to add labels and a title to your graph.

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

KEY: = 50 people



Sample answer: Days of Visits1 765432

050

100150200250300350400450500550

Sam

ple

answ

er: N

umbe

r of V

isito

rs

240-266_EMCS_S_MJ2_G3_U10_576418.indd 255B 4/11/11 4:00 PM

Math Journal 2, p. 255B

Student Page

Date Time

Math BoxesLESSON

10 �6

3. James built a rectangular prism out of base-10 blocks. He used 30 cm cubes to make the base. He put 4 more layers of cubes on top of that. What is the volume of the prism he built?

150 cubic centimeters

2. There are 5 blocks in a bag. 2 blocks are red, 2 blocks are blue, and 1 block is green. What are the chances of pulling out a red block?

2 out of 5 chances

4. Complete.

1 gallon = 4 quarts

3 gallons = 12 quarts

1 pint = 2 cups

7 pints = 14 cups

1 liter = milliliters

5 liters = 5,000 milliliters

6. Color the circle so that it matches the description.

1 _ 2 blue

1 _ 3 green

1 _ 6 yellow

Which color would you expect the spinner to land on most often? blue

1. Measure each side of the triangle to the nearest centimeter.

cm4cm4

cm4

Perimeter = 12 cm 137–139

157–159

94

160 161

24 93

yellowblue

green

5. Molly is playing with 5 toy cars. This is only 1 _

3 of her set of cars. How many cars are in her complete set? Fill in the circlenext to the best answer.

A 5 _ 3 cars C 10 cars

B 5 cars D 15 cars

1,000

240-266_EMCS_S_MJ2_G3_U10_576418.indd 255 2/25/11 10:05 AM


Student Page

� Finding the Median INDEPENDENTACTIVITY

of Sets of Data(Math Journal 2, pp. 253 and 254; Student Reference Book, p. 80)

Have children complete Activity 2 on journal pages 253 and 254. Children find the median number of children per family and the median number of eggs per clutch. If necessary, have them read page 80 in the Student Reference Book to review how to find the median, or middle value, of a set of data.

Ongoing Assessment: Informing InstructionWatch for children who have difficulty finding the median. They can write the number of eggs in each nest on a small slip of paper or a stick-on note. Have them put the numbers in order and then find the middle number(s).

2 Ongoing Learning & Practice

� Interpreting a Pictograph and PARTNER ACTIVITY

Creating a Bar Graph(Math Journal 2, pp. 255A and 255B; Student Reference Book, pp. 86–89)

Have children examine the pictograph on journal page 255A. Ask them to explain what each smiley face means. 50 people Next ask them to explain what one-half of a smiley face means. 25 people Have children work independently or with a partner to complete journal page 255A. When they have finished, children create a bar graph on journal page 255B to show the same data. Discuss the scale for the bar graph. Since the pictograph key shows that each smiley face represents 50 people, the scale for the bar graph could be in increments of 50.

� Math Boxes 10�6 INDEPENDENTACTIVITY

(Math Journal 2, p. 255)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 10-8. The skill in Problem 6 previews Unit 11 content.

Writing/Reasoning Have children write an answer to the following: Choose one of the units of capacity in Problem 4. Describe the unit of capacity by using one of the personal

references for units of capacity from Lesson 10-5. For example, describe an object that has about the same measure as a liter (or the unit of capacity you chose). Sample answer: I have a water bottle that holds 1 liter of water.

PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMEMBLEBLLBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBLBBLBLBLLBLLLLPROPROPROPROPROPROPROPROPROPROPROPRPPROPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROOROROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELLELEEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOOBBBBLBLBLBLBLBBROOOROROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGLLLLLLLLLLLLLVINVINVINVINVINNNNVINVINNVVINVINVINVINV GGGGGGGGGGGOOOOLOLOLOOLOO VINVINVLLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGOLOOLOLOLOLOLOLOOO VVVVLLLLLLLLLLVVVVVVVVVVOOSOSOSOSOSOSOSOSOSOSOSOSOOOOOOSOSOSOSOSOSOSOSOSOSSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLVVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIISOLVING


� Home Link 10�6 INDEPENDENTACTIVITY

(Math Masters, p. 340)

Home Connection Children find the mean of a data set.

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Graphing Dice Rolls 5–15 Min

(Math Masters, p. 339)

To provide experience with making a bar graph, have children predict how many times they think they will roll a 1 and then make a graph to record their results. When

children have completed their graphs, have them discuss their predictions and results.

ENRICHMENT PARTNER ACTIVITY

� Making a Data Set 15–30 Min

(Math Masters, pp. 341 and 342)

To apply children’s understanding of landmarks (maximum, minimum, range, mode, and median), have them use the given median, range, and mode to display a

possible data set when 5 children share 15 cookies. Children record their work on Math Masters, page 342 and make a bar graph of their data set on Math Masters, page 341.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 132)

To provide language support for landmarks, have children use the Math Word Bank template found on Differentiation Handbook, page 132. Ask children to write the term mean, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information.

PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMEMBLEBLLBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBLBLBLBLBLBLLLLLLPROPROPROPROPROPROPROPROPROPROPROPRPPROPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROOROROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEELELELEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOOBBBBLBLBLBLBLBBROOOROROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGLLLLLLLLLLLLLVINVINVINVINVINNNNVINVINNVVINVINVINVINV GGGGGGGGGGGOOOOLOLOLOOLOO VINVINVINVLLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGOLOOLOLOLOLOLOLOOO VVVVLLLLLLLLLLVVVVVVVVVVOOSOSOSOSOSOSOSOSOSOSOSOSOSOOOOOSOSOSOSOSOSOSOSOSOSSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLVVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIISOLVING

LESSON

10�6

Name Date Time

Making a Data Set

Alto

geth

er, 5

chi

ldre

n ha

ve 1

5 co

okie

s in

thei

r lun

ch b

ags.

� T

he m

edia

n nu

mbe

r of c

ooki

es is

2.

� T

he ra

nge

of th

e nu

mbe

r of c

ooki

es is

5.

� T

he m

ode

of th

e nu

mbe

r of c

ooki

es is

2.

How

man

y co

okie

s co

uld

each

chi

ld h

ave?

Use

cou

nter

s an

d th

e dr

awin

gs o

f lun

ch b

ags

belo

w to

org

aniz

e yo

ur d

ata.

Dra

w c

ooki

es in

the

lunc

h ba

gs to

mat

ch th

e de

scrip

tion

abov

e.

Gra

ph y

our r

esul

ts o

n M

ath

Mas

ters

, pag

e 34

1. R

emem

ber t

o in

clud

e la

bels

an

d a

title

.

Sam

ple

answ

er:

Lunc

h ba

g A

Lunc

h ba

g B

Lunc

h ba

g C

Lunc

h ba

g D

Lunc

h ba

g E

79– 81

319-359_EMCS_B_MM_G3_U10_576957.indd 342 2/28/11 2:17 PM

Math Masters, p. 342

Teaching Master

Lesson 10�6 839

Name Number of Goldfish

Reba 3

Bill 1

Lucy 7

Meg 0

Nate 5

Pat 2

Name Date Time

Mean, or Average, Number of FishHOME LINK

10�6

Many of us learned that to find the mean (average) of a set of numbers, we add all the numbers and then divide the total by how many numbers we added. In today’s lesson, the class tried a different method of finding the mean. After your child has completed the page, ask him or her to explain how this method works. In the next lesson, we will introduce finding the mean by adding the numbers and dividing to find the answer.

Please return this Home Link to school tomorrow.

Family Note

83–85

Reba Bill Lucy Meg Nate Pat0

1

2

3

4

5

6

7

Num

ber o

f Gol

dfis

h

Names

The table below listshow many goldfisheach child won atthe school fun fair.

1. Put a pennyover each shaded squarein the bar graph.

2. Move the penniesso that eachcolumn has the same number of pennies.

3. Draw a horizontal line across your graph to show the height of the pennies when all of the columns are the same height.

4. The mean (average) number of goldfish won by children at the fun fair is .3

319-359_EMCS_B_MM_G3_U10_576957.indd 340 2/28/11 2:17 PM

Math Masters, p. 340

Home Link Master


the mean and the median - mcgraw hill education · math journal 2, p. 255 ... the mean and the...

Documents