Skills:
Solving problems using
fractions, percents, and angle
measures
Teaching Gracie’s Day
Students analyze a table and circle graph that
show how a dog spends 24 hours.
Tasks
Tier 1
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Below Level
Tier 2
On Level
Tier 3
Above Level
Gather data from a table and circle graph.
X
X
X
Compare and contrast data in tables and circle graphs.
X
X
X
Compute fractions of a number.
X
X
X
Apply percentage concepts.
X
X
X
Relate fractions and percents.
Understand central angles.
X
X
Complete a circle graph.
X
X
Find the percent of a number.
X
X
Getting Started
See the tips below for introducing the lesson. Make copies of the student data sheet (page 54) and the
appropriate leveled activity sheet for each group of learners (pages 55–57).
Access prior knowledge by reviewing the properties of circles, the uses of circle graphs and fractional
equivalents of benchmark percents commonly used, such as 50% and 25%.
Tier 1
• Use the Data: Clarify that the
table and circle graph show
the same data in different
ways. A circle graph relates
parts to a whole (the full
circle is the whole, or 100%).
Read the sections of the
circle graph as fractions or
percentages of the dog’s day.
• Write About It: Help students
verbalize what they see and
how it conveys information
before they write their
responses.
• Complete a Graph: Guide
students to understand that
the sum of all the fractions in
the table is 1, which matches
the graph. For item 8, help
students find each fraction of
24 for the number of votes for
the two dogs. Also discuss
the number of votes each
other name received.
Tier 2
• Use the Data: Discuss how a
circle graph shows parts related to
a whole (100%) and the relationship
between the two displays and the
advantages of each. Talk about
other kinds of data for which a
circle graph is useful.
• Complete a Graph: Remind
students that there are 360 degrees
in a circle. Explain that the central
angles that form the parts of this
circle represent each percent of
allowance and that the greater the
central angle, the greater the part
of the allowance shown. Students
can use a protractor to check angle
measures as they label the sectors
of the circle graph. Have volunteers
explain how they use visual
reasoning for the labels.
• Plan a Budget: Remind students to
find each percent of $800 to answer
the question.
Tier 3
• Use the Data: Discuss
item 1 together. Review the
relationships among central
angles, circles, and data.
Point out that 360 is divisible
by the denominators of the
fractions shown. Ask: If a
circle has 360 degrees, how
big is the central angle for 1/3
of it? How much is it for 2 /5?
Ask a volunteer to explain the
answer to item 7.
• Make a Table: Point out that
students must convert hours
of activities to fractions of a
day.
• Write About It: Discuss why
graphs are better displays
for certain data, while tables
more effectively show other
kinds. Have partners discuss
their ideas before writing.
53
Name
Skills:
Date
Gracie’s Day:
Solving problems using
fractions, percents, and angle
measures
Data Sheet
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
My dog Gracie has a great life. Each day includes only her
favorite activities. Look at the table and graph to see what I
mean.
Both show how Gracie spends a typical 24-hour day.*
Compare the table and the circle graph.
*Note that neither display shows eating times. That’s because
Gracie wolfs down her meals in no time at all!
A Day in the Life of a Dog
Activity
Fraction
of Day
Sniffing
1/12
Sleeping
1/2
Playing with a ball
1/8
Staring out a window
1/6
Chewing something valuable
1/8
Chewing
something
valuable
Sniffing
Staring out
a window
Sleeping
Playing
with a ball
The next time you hear sayings like “treated like a dog” or “works like a dog,” think twice about it!
54
Name
Gracie’s Day:
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Use the Data
Date
Activity Sheet
Complete each sentence.
1.
There are
2.
Gracie spends more of a day
3.
She spends the least amount of time a day
4.
She spends the same amount of a day
as she does
.
5.
Gracie spends 4 hours of her day
.
6.
Twenty-four hours is
7.
Gracie spends
hours in one day.
than on anything else.
.
% of a day.
% of a day sleeping.
Write About It
How can you tell by looking at the graph that Gracie spends half her day sleeping? Explain.
How does the graph show that the dog spends one-fourth of a day chewing something or playing
with a ball? Explain.
Complete a Graph
Best Dog Names
Mr. Metzger’s class took a survey on dog
names. The table shows the results. The
circle graph shows the same data. Use the
data in the table to add percentages to the
graph.
Name
Fraction of Votes
Bailey
1/12
Chewy
1/6
Gracie
1/3
Mugsy
3/12
8.
There were 24 students who voted
in the survey. How many votes did
Bailey get?
Pebbles
1/6
9.
How many votes did Chewy get?
Bailey
Pebbles
Chewy
Mugsy
Gracie
55
Name
Gracie’s Day:
Use the Data
1.
Date
Activity Sheet
Answer each question based on the Data Sheet.
What is Gracie’s favorite activity?
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
What percent of her day does she spend doing it?
2.
What is Gracie’s least time-consuming activity?
What percent of her day does she spend doing it?
3.
On which two activities does Gracie spend the same number of hours?
How many hours does she spend on each?
4.
Why is a circle graph useful for showing the data listed in the table?
5.
How does the size of each part of the circle graph relate to the time Gracie spends on the
activities?
Gracie’s Spending
Complete a Graph
The table to the right shows how Gracie would spend
her allowance (if she had one). Use the data to label the
percentages of the circle graph below it.
Plan a Budget
What if Gracie had $800 to spend? Use the percentages
given in the table to find out how much she would spend
on each of the six items listed.
Steak
Bones
Dog biscuits
Slippers
Squeaky toys
Doggy magazines
Item
Part of Allowance
Steak
45%
Dog biscuits
20%
Squeaky toys
15%
Bones
5%
Slippers
10%
Doggy magazines
5%
Doggy magazines
Slippers
Bones
Squeaky toys
Dog biscits
56
Steak
Name
Gracie’s Day:
Date
Activity Sheet
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Use the Data
1.
How can you figure out the number of hours a day Gracie spends on each activity?
2.
What fraction of a day does Gracie spend staring out the window?
How many hours is that?
3.
How many hours does Gracie spend chewing?
4.
On which activity does Gracie spend half the time she spends staring out the window?
Angles created around the center of a circle are called central angles.
The sum of the measures of the central angles of any circle is 360 degrees.
5.
One part of the graph is formed by a central angle of 180°.
Which activity does it represent? Explain.
6.
One part of the graph is formed by a central angle of 30°.
Which activity does it represent? Explain.
7.
What if one day Gracie slept for only 11 hours but chased her tail for an hour?
What fraction of the circle graph would show the tail-chasing time?
How big would the central angle be for that section?
How Tiger Spends His Day
Make a Table
The circle graph shows how
Roy’s cat Tiger spends its day.
Use the circle graph to fill in
the table.
Write About It
On the back of this page,
summarize what your graph
and table show. Then compare
and contrast Tiger’s day with
Gracie’s day. List your ideas.
Kicking
litter on
floor
Chasing his tail
Activity
Fraction of Day
Hiding
under bed
Scratching
furniture
Sleeping
Purring
57
Answer Key
Gracie’s Day
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Tier 1, page 55: Use the Data: 1 . 24
2 . sleeping 3 . sniffing 4 . playing with ball,
chewing 5 . staring out window 6 . 100
7 . 50; Write About It: The sleeping section
of the circle takes up 1 ⁄ 2 the space. When you
look at both sections together, they take up
1 ⁄ 2 the circle; Complete a Graph: see graph
at right; 8 .2; 9 .4
Pebbles
60
Bailey
30
Chewy
60
Mugsy
90
Gracie
120
Tier 2, page 56: Use the Data: 1 . sleeping;
Doggy magazines
50% 2 . sniffing; 8 .333% 3 . playing with
a ball, chewing something valuable;
18
3 hours 4 . It gives a quick visual snapshot
Slippers
36
Bones
for comparing data and shows related
18
parts of a whole . 5 . The bigger the part
Squeaky toys
of the circle graph, the more time Gracie
54
spends on the activity . Complete a Graph:
Dog biscits
see graph at right; Plan a Budget:
72
Steak $360
Bones $40
Dog biscuits $160
Slippers $80
Squeaky toys $120 Doggy magazines $40
Steak
162
Tier 3, page 57: Use the Data:
1 . You find that fraction of 24
2 . 1 ⁄6 of a day; 4 3 . 3 4 . sniffing 5 . sleeping; She sleeps half the
day since 180 is 1 ⁄ 2 of 360 . 6 . sniffing; She sniffs for 1 ⁄12 day
since 30 is 1 ⁄12 of 360 . 7 . 1 ⁄ 24; 15°; Make a Table:
How Tiger Spends His Day
Activity
Fraction of Day
Chasing his tail
1/16
Sleeping
7/16
Purring
1/8
Scratching furniture
3/16
Hiding under bed
1/8
Kicking litter on floor
1/16
Write About It: Check student summaries and comparisons.
80