Objective
To provide practice organizing and displaying data
with a tally chart and determining the maximum, minimum, range,
and mode of a set of data.
1
materials
Teaching the Lesson
Key Activities
Students guess, estimate, and then count the number of objects in a container. They tally
the class results in a chart and find the minimum, maximum, range, and mode for the data.
Key Concepts and Skills
• Create a tally chart. [Data and Chance Goal 1]
• Find the maximum, minimum, range, mode, median, and mean for a set of data.
ⵧ Math Journal 1, p. 38
ⵧ Study Link 2 4
䉬
ⵧ small box of raisins (or 3-ounce cup of
raisin substitute) per student
ⵧ slate
See Advance Preparation
[Data and Chance Goal 2]
• Use data landmarks to make a prediction. [Data and Chance Goal 2]
• Use and describe a strategy for estimating volume; describe the difference between
an estimate and a guess. [Measurement and Reference Frames Goal 2]
Key Vocabulary
guess • estimate • tally chart • landmark • maximum • minimum • range • mode
Ongoing Assessment: Informing Instruction See page 108.
2
materials
Ongoing Learning & Practice
Students play Addition Top-It to practice addition facts.
Students practice and maintain skills through Math Boxes and Study Link activities.
Ongoing Assessment: Recognizing Student Achievement Use Math Masters,
page 506. [Operations and Computation Goal 1]
3
Students use tally marks to
record dice sums.
ENRICHMENT
Students make a prediction
based on a sample.
ⵧ Game Master (Math Masters, p. 506)
ⵧ per partnership: deck of number cards;
regular or polyhedral dice (optional)
materials
Differentiation Options
READINESS
ⵧ Math Journal 1, p. 39
ⵧ Student Reference Book, p. 263
ⵧ Study Link Master (Math Masters, p. 51)
EXTRA PRACTICE
Students find data
landmarks.
ⵧ Math Journal 1, p. 38
ⵧ Teaching Masters (Math Masters,
pp. 52 and 53)
ⵧ 5-Minute Math, pp. 34, 37, 38, and 40
ⵧ 1 large box of raisins (12 or 15
ounces); two 6-sided dice
Additional Information
1
Advance Preparation For Part 1, use 2-ounce boxes of raisins, one box for each student. Or
have at least 14 boxes for students to share to get a representative set of data.
1
Place an unopened 2-ounce box of raisins near the Math Message.
106
Unit 2 Using Numbers and Organizing Data
Technology
Assessment Management System
Math Masters, page 506
See the iTLG.
Getting Started
Mental Math and Reflexes
Math Message
Pose addition problems. Suggestions:
Guess how many raisins are in the box. Write your
guess in Problem 1a on page 38 in your journal.
10 10 20
12 10 22
15 10 25
30 13 43
40 56 96
24 61 85
175 426 601
238 546 784
693 168 861
Study Link 2 4 Follow-Up
䉬
Ask partners to read the numbers in Problem 1 to
each other. Remind students that the word and is
not used when reading whole numbers.
Encourage students to add interesting number facts
to the Numbers and Their Uses Museum.
1 Teaching the Lesson
SMALL-GROUP
ACTIVITY
Ask students to share their guesses in small groups. Emphasize
that guessing, estimating, and organizing are skills they use on a
daily basis. In this lesson students will gather, organize, and
summarize data on the number of raisins in a box.
䉴 Collecting, Organizing, and
PARTNER
ACTIVITY
RAISINS
Interpreting a Set of Data
GOOD FOR YOU!
䉴 Math Message Follow-Up
NET WT. 1/2 OZ.
(Math Journal 1, p. 38)
Pass out a box of raisins to each student. Then guide the class
through the following activity.
Student Page
Date
Time
LESSON
2 5
䉬
1. Use your
Counting Raisins
1
-ounce
2
box of raisins. Complete
each step when the teacher tells you. Stop
after you complete each step.
Collecting the Data
1. Ask students to open their box of raisins and, without
emptying it, count the number of raisins they see at the top
of the box. Tell them to use this count to estimate the total
number of raisins in the box. Ask them to record their
estimate in Problem 1b.
3. Discuss the difference between a guess and an estimate. An
estimate is a guess that employs a strategy. To support English
language learners, point out that the Math Message answer is
a guess because students did not have any information about
the raisins in the box. When students looked into the box, they
could use a strategy for making an estimate because they saw
the size of the raisins and how they were packed inside.
2. Make a tally chart of the
class data.
Answers vary.
a. Don’t open your box yet. Guess about
Number
of Raisins
Number
of Boxes
how many raisins are in the box.
About
raisins
b. Open the box. Count the number of
raisins in the top layer. Then estimate
the total number of raisins in the box.
About
raisins
c. Now count the raisins in the box.
How many?
2. Encourage students to describe their estimation strategies. For
example: “I saw 7 raisins on top and figured 5 rows. Five rows
of 7 is about 35 raisins.”
71–75
raisins
3. Find the following landmarks for the
class data.
Answers vary.
a. What is the maximum, or largest,
number of raisins found?
b. What is the minimum, or smallest,
number of raisins found?
c. What is the range? (Subtract the
minimum from the maximum.)
d. What is the mode, or most frequent
number of raisins found?
Try This
4. What is the median number of raisins found?
5. What is the mean number of raisins found?
Answers vary.
Answers vary.
38
Math Journal 1, p. 38
Lesson 2 5
䉬
107
Number
of Raisins
Number
of Boxes
29
/
30
//
31
32
///
33
34
35
///
36
////\
37
//
38
////
39
/
40
41
42
4. Have students empty the box and count the raisins. Suggest
that they count the raisins as many times as they need to,
until they get the same number more than once. Have them
record the total in Problem 1c.
5. Discuss counting techniques. Some students may have lost
track of the count when counting the raisins by 1s. Suggest
that a more accurate and efficient way might be to count by 2s
or to group the raisins by 5s or 10s.
Organizing the Data
Ask students to report the exact number of raisins in their boxes.
Record the numbers on the board in the order in which they are
reported. Partners then use the class data to complete the tally
chart in Problem 2 in their journals.
To help students get started, ask them to complete the first
column by writing the numbers in order, beginning with the
smallest number of raisins and ending with the largest number
of raisins. Students then make a tally mark on the appropriate
line in the second column for each number on the board.
43
Ongoing Assessment: Informing Instruction
44
/
45
46
Watch for students who do not use the fifth tally mark to cross the first four.
Point out that tally marks organize counts by 5s and show each number
between 5 and 10 as five plus one or more ones.
Tally Chart
Analyzing the Data
Use questions such as the following to elicit discussion:
NOTE If graphing software is available, this
would be a good time to familiarize students
with the features that allow them to analyze
data.
●
Does anyone know what a landmark is? An object or feature
that stands out
●
What are some examples of ways we use landmarks? Sample
answers: When giving directions, we might say, “Go straight
ahead, turn right at the second stoplight, then go until you see
the playground.” When describing a location, we might say
“The tallest building you see is right next to the city square.”
Following this discussion, students complete Problems 3–5 in their
journals on their own. Tell them that they will use landmarks to
describe their raisin data.
Have students look for the following. To support English language
learners, write the key terms on the board along with their
definitions and examples.
䉯 The largest number of raisins found—the maximum
䉯 The smallest number of raisins found—the minimum
䉯 The difference between the maximum and the minimum—
the range
䉯 The most frequent number of raisins found—the mode
108
Unit 2 Using Numbers and Organizing Data
Links to the Future
The median is reviewed in Lesson 2-6. The mean, introduced in Third Grade
Everyday Mathematics, is reviewed in Lesson 3-4. Calculating the mean of a
data set is a Grade 5 Goal.
Encourage students to talk about the distribution of the data in
their tally charts. Terms like clumps, bumps, holes, way-out
number, and all-alone number are fine for describing these data.
For example:
NOTE The word range is sometimes defined
as the interval between the smallest and the
largest number in a set of data—for example,
the interval from 29 to 45. Everyday
Mathematics defines range as “a number—
the difference between the minimum and the
maximum.” For example, if the minimum is
29 and the maximum is 45, the range is 16.
If one single number or value occurs most
often in a set of data, that number or value is
called the mode. Sometimes two or more
numbers occur most often. All of these
numbers or values are called modes.
䉯 “The most anybody got was 45. But 45 is way out by itself,
and the next biggest is 40.”
䉯 “The smallest is 29. There’s a little group near the bottom—
one 29 and two 30s.”
䉯 “There’s a big clump of tally marks between 35 and 39.”
䉯 “The table has some holes—at 31, 32, 34, and 39.”
Finally, ask students what they think is the typical number
of raisins in a box. Expect a variety of answers, such as the
number that occurs most often or a number where the counts
cluster most heavily.
Adjusting the Activity
Have students describe how the mean, median, and mode of the data
are similar and different. Ask them to explain which landmark they think provides
the best possible picture of the raisin data and why.
A U D I T O R Y
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉬
V I S U A L
2 Ongoing Learning & Practice
䉴 Playing Addition Top-It
PARTNER
ACTIVITY
(Student Reference Book, p. 263; Math Masters, p. 506)
Students play Addition Top-It to develop automaticity with
addition facts. See Lesson 1-2 for additional information.
Math Masters
Ongoing Assessment:
Page 506
Recognizing Student Achievement
夹
Use the number sentences on Math Masters, page 506 generated in the Addition
Top-It game to assess students’ automaticity with basic addition facts. Students
are making adequate progress if they are able to find the correct sum for each
number sentence. Some students may demonstrate proficiency with addition of
three addends or multidigit numbers.
[Operations and Computation Goal 1]
Lesson 2 5
䉬
109
Student Page
Date
䉴 Math Boxes 2 5
Time
LESSON
䉬
1. A number has
6
1
2
8
5
3
4
in
in
in
in
in
in
in
the
the
the
the
the
the
the
Sample answers:
34
68
2
Write the number.
1, 8 4 3, 6 2 5
4
3. Write , , or to make each
(7 ⴱ 7) (3 ⴱ 5)
100 66
62 2
52 9
d.
e.
and
H
I
K
J
148 149
94
b. 3 centimeters
c.
5
35
a. 5 7 6
8
b.
About
䉴 Study Link 2 5
6. Multiply mentally.
a.
6.5
K œJ œ
and
5. Measure these line segments to the
1
nearest centimeter.
2
About
Writing/Reasoning Have students write a response to the
following: Explain how you know that the pairs of sides
you chose in Problem 4 are parallel. Sample answer: No
matter how far the sides are extended, they will never meet or
cross.
149
parallelogram HIJK.
a. 14
c.
Mixed Practice Math Boxes in this lesson are linked with
Math Boxes in Lessons 2-7 and 2-9. The skill in Problem 6
previews Unit 3 content.
4. Name the two pairs of parallel sides in
number sentence true.
b.
(Math Journal 1, p. 39)
2. Write five names for 34.
hundreds place,
millions place,
tens place,
hundred-thousands place,
ones place,
thousands place, and
ten-thousands place.
26
3,003 3,300
12 12 24
200 50 100
30 30 50 10
INDEPENDENT
ACTIVITY
䉬
Math Boxes
2 5
d. 9 centimeters
e. 8 4 128
(Math Masters, p. 51)
7 56
5
INDEPENDENT
ACTIVITY
䉬
18
45
32
16
39
Math Journal 1, p. 39
Home Connection Students collect data about the sizes of
their families. Go over in class the definition of family as
described on the page. Students also answer questions
about data displayed in a tally chart.
NOTE A few teachers have reported that family size is a sensitive topic with
some students in their classrooms. If you anticipate this to be an issue, consider
replacing family size with the number of radios, televisions, pets, or smoke
detectors in the home. Adjust the activities in Lesson 2-6 accordingly.
Study Link Master
Name
STUDY LINK
25
䉬
1.
Date
Time
Collecting Data
Make a list of all the people in your family. Include all the people living at
home now. Also include any brothers or sisters who live somewhere else.
The people who live at home do not have to be related to you. Do not forget
to write your name in the list.
72 73
You will need this information to learn about the sizes of families in your class.
How many people are in your family?
people
The tally chart at the right shows the number
of books that some students read over the
summer. Use the information to answer the
questions below.
2.
How many students reported the
number of books they read?
3.
4.
Number of
Books
Reported
4
What is the maximum (the largest
5
number of books reported)?
6
8
////\ //
////\ /
//
////
7
What is the minimum (the smallest
number of books reported)?
///
////\
2
3
27
2
8
6
5.
What is the range?
6.
What is the mode (the most frequent
number of books reported)?
5
Practice
7.
9.
80
230 90 80 60
30 50 210
8.
10.
Unit 2 Using Numbers and Organizing Data
70 70 70
100 40 70 Math Masters, p. 51
110
Number of
Students
210
Teaching Master
Name
3 Differentiation Options
LESSON
25
䉬
Date
Time
Dice-Roll Tally Chart
Tally marks are vertical marks used to keep track of a count.
The fifth tally mark crosses the first four.
71
Examples:
READINESS
䉴 Recording Data with
PARTNER
ACTIVITY
one
/
two
three
///
////
////\
////\ /
////\ //
////\ ///
////\ ////
////\ ////\
six
//
seven
(Math Masters, p. 52)
nine
ten
1.
Roll a pair of dice and find the sum.
2.
Make a tally mark next to the sum in the chart below.
3.
Set a timer for 3 minutes. Roll the dice and make a tally mark for each sum
until the timer goes off.
Sum
4.
Tallies
To provide experience with tally marks, have students complete a
tally chart of dice rolls. When students have finished, discuss why
tallies are an easy way to keep track of data and how they make it
easier to compare results. Tallies are grouped in fives and make it
easier to count. It is easier to compare groups of five rather than a
lot of single marks.
Answer the questions below.
a.
2
4?
times
4
7?
times
5
11?
b.
6
Answers vary.
How many times did you roll a sum of
3
times
Which sum was rolled the most number of
times?
7
c.
8
Which sum was rolled the least number of
times?
9
10
d.
How many times did you roll the dice in all?
e.
On the back of this page, write two more things
that you notice about the data you collected.
times
11
12
䉴 Making a Prediction Based
eight
five
5–15 Min
Tally Marks
ENRICHMENT
four
PARTNER
ACTIVITY
Math Masters, p. 52
5–15 Min
on a Sample
(Math Journal 1, p. 38; Math Masters, p. 53)
To apply students’ understanding of data landmarks,
have them predict, based on the data collected from
the half-ounce raisin boxes, how many raisins are in a
12- or 15-ounce box. Ask students to describe how they made
their predictions.
䉴 5-Minute Math
SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience with data landmarks, see
5-Minute Math, pages 34, 37, 38, and 40.
Teaching Master
Name
LESSON
25
䉬
Date
Time
Making a Prediction Based on a Sample
Sometimes large numbers of people or things are impossible to count
or take too much time to count. A smaller sample of data is often used
to make predictions about a larger group or population.
You and your class collected, recorded, and analyzed data about
1
the number of raisins found in -ounce boxes of raisins.
2
Use the raisin data you collected on journal page 38 to answer the
following questions.
1.
NET WT. 1/2 OZ.
Without opening it, how many raisins do you think are in a large box
(12 or 15 ounces) of raisins?
About
2.
RAISINS
raisins are in a
-ounce box.
GOOD FOR YOU!
EXTRA PRACTICE
Answers vary.
Explain the strategy you used to make your prediction.
Sample answer: I took the median number
1
of raisins from a –
2 -ounce box and multiplied
by 24 (12-oz box) or 30 (15-oz box).
3.
1
Suppose you only knew the number of raisins in a single -ounce box of
2
raisins. Would that affect your prediction about the number of raisins in the
large box? Why or why not?
Sample answer: My prediction would not be
as reliable, but it would still be close. There
wasn’t a big difference between the minimum
and maximum in our class data.
Math Masters, p. 53
Lesson 2 5
䉬
111