Fun With
Fractions
2nd Grade Unit Plan
CCSS 2.G.3.
Kathy Reck
EDI 685
November 5, 2013
Table of Contents
Page
Unit Overview
2
Lesson 1 – Roomy Rectangles
4
Lesson 2 – A Party with Pattern Blocks
10
Lesson 3 – Estimation Station
14
Lesson 4 – Friendly Fractions
19
Lesson 5 – Dare to Compare
23
Lesson 6 – Groovy Groups
39
Lesson 7 – Fraction Flags
46
Assessment of Student Learning
50
Bibliography
51
1
Unit overview
By CCSS’s, in first grade students learned how to partition circles and squares into two
and four parts. Students have also had exposure to hexagons, pentagons, trapezoids,
squares, rectangles, triangles, and circles. In this second grade unit lesson about
fractions, students will explore fractions of geometric shapes, leading them to
proficiency of the following Common Core State Standard:
CCSS.Math.Content.2.G.3. Partition circles and rectangles into two, three, or
four equal shares, describe the shares using the words halves, thirds, half of,
a third of, etc., and describe the whole as two halves, three thirds, four
fourths. Recognize that equal shares of identical wholes need not have the
same shape.
In lesson one, students will do a hands-on folding activity in order to help them
describe and compare fractional parts. This lesson helps students understand how to
partition circles and rectangles into two, three, or four equal shares, and describe the
whole as two halves, three thirds, four fourths. Literature, art, and technology are
incorporated into this lesson.
Lesson two contains hands-on activities with pattern blocks to help solidify the lesson
from yesterday. Students learning objectives will be to understand how to partition
circles and rectangles into two, three, or four equal shares, and describe the whole as
two halves, three thirds, four fourths. Technology is incorporated into this lesson.
In lesson three, students will learn to estimate fractional parts in a variety of hands-on
activities in order to describe the shares using the words halves, thirds, half of, a third
of, and to describe the whole as two halves, three thirds, four fourths. Literature and
student movement around the room is incorporated into this lesson.
Lesson four has students comparing fractional parts. In this lesson students will
partition circles and rectangles into fractional parts and describe the parts using
fractional terms. This lesson is rich in technology.
In lesson five, students compare fractional parts of shapes. Students will partition
circles and rectangles into fractional parts and describe the parts using fractional terms.
This lesson has a literature component along with activities requiring technology.
Lesson six teaches students how to describe shares or parts of groups as halves, thirds,
and fourths. This lesson is rich in movement and hands on activities. This lesson
incorporates some movement around the room is part of this lesson.
Lesson seven is the culminating lesson which integrates social studies with math.
Students will explore flags from around the world and analyze their fractional patterns.
2
Students will replicate a flag to hang on our Fraction Flags bulletin board. This lesson is
rich in literature, the arts, and also incorporates some use of technology.
All lessons in this unit begin and end with reviewing learning objectives with the
students. In addition, each lesson is rich with cooperative learning in pairs, small
groups, and whole class discussions.
3
Unit Lesson – Fantastically Fun Fractions
Lesson 1: Roomy Rectangles
Grade Level
2nd
Time Needed
60 minutes
Materials Needed
90 rectangles –
approx. 4x6 inches
each
Book: Full House An
Invitation to
Fractions by Dayle
Ann Dodds
3 hershey bars to
demonstrate sharing
(and optional bag of
mini’s to share with
class)
Access to Youtube
denominator video:
http://www.youtube.
com/watch?v=x8VX
W1GakB8
Introduction: In today’s lesson we build on students’ prior
knowledge in a hands-on activity which has students folding
rectangles into 2, 4, and 8 equal parts. Students describe fractions
and compare the various rectangles to one another.
Background: By CCSS, in 1st grade, students learned basic
concepts of half and fourths (quarters) as equal parts of a whole.
Today we introduce eighths and the concept of numerator and
denominator. Although these are not part of the CCSS, the concepts
are included in the lesson since they are tested as part of the
Everyday Math curriculum used by the school district.
GLCE(s):
CCSS.Math.Content.2.G.3. Partition circles and rectangles into two,
three, or four equal shares, describe the shares using the words
halves, thirds, half of, a third of, etc., and describe the whole as two
halves, three thirds, four fourths. Recognize that equal shares of
identical wholes need not have the same shape.
Engagement:
Read aloud: Full House: An Invitation to Fractions by Dayle Ann
Dodds
Ask students:
Does anyone remember a time when you used a fraction? Turn and
talk with a partner.
Have a group discussion about personal connections to fractions,
asking students to describe their partner’s connection.
Possible answers: Students may recall their work with fractions from
kindergarten and first grade where they were introduced to
4
identifying fractions of regions. They may or may not be able to identify ½ as used in
sharing “half” of something.
Exploration:
Tell students that their learning objectives for today are:
“I can partition circles and rectangles into two, three, or four equal shares”
“I can describe the whole as two halves, three thirds, four fourths.”
Hand out three rectangles to each student. Invite students to fold their rectangle into
two equal parts, without giving further instructions. Students might make the error of
folding two times. This is okay. It is part of the learning. The purpose is to see how
many ways students can find to fold their rectangle in half. There will be two ways:
diagonal and horizontal/vertical. Have students compare their squares. Draw answers
on board.
Ask students:
What is the word we use for one of these two equal parts of a whole? (Half, halves)
What are the different ways we can write/represent one of these two equal parts?
(possible answers: 1/2, half, halves, half-of, one out of two, two out of two) Label
these parts on the drawings.
How many ways did we find to make two halves? (two (or more, if students determine
that the horizontal fold is different than the vertical fold, etc.)).
Next, invite students to take their 2nd rectangle and fold it into four equal parts.
Students might make the error of folding four times. This is okay. It is part of the
learning. Time permitting, this would be a good extension conversation to have with
the group. Ask students to compare this newly folded rectangle with the students in
their group.
Ask for student volunteers to model their different rectangles. Draw answers on board
to show comparisons. There will be three (or more possible ways to fold the square
into four equal parts, depending on the orientation of the paper).
Ask students:
What is the word we use for one of these four equal parts of a whole? (fourths,
quarters)
5
What are the different ways we can write/represent one of these four equal parts?
(possible answers: 1/4, fourth, quarter, one-fourth-of, one-quarter-of, one-out-of-four)
Label these parts on the drawings.
How many ways did we find to make four equal parts? (three (or more, depending if
students determine that the horizontal fold is different than the vertical fold).
Watch for the error of folding the rectangle diagonally. Folding diagonally can create
two equal parts, but not four equal parts.
Invite students to fold their 3rd rectangle into eight equal parts. This will require three
folds, but again, students might make the error of folding eight times. This is okay. It
is part of the learning. Time permitting, this would be a good extension conversation to
have with the group.
Ask for student volunteers to model their different folded rectangles. There will be 3
(or more ways to show the folds, depending on student perspective of orientation of
the paper).
If students have not arrived at all the ways to fold the paper, have them brainstorm
together in groups of four.
Ask students:
What is the word we use for one of these eight equal parts of a whole? (eighths)
What are the different ways we can write/represent one of these eight equal parts?
(possible answers: 1/8, eighth, one-eighth-of, one-out-of-eight)
How many ways did we find to make eight equal parts? (three (or more, depending if
students determine that the horizontal fold is different than the vertical fold)).
Explanation:
As students are doing this part of the activity, teacher should be showing the work on
the Smartboard.
For rectangle number one, we determined that the parts of the whole were called
halves. Have students write ½ on each half of the rectangle.
Ask: “How many halves make up this whole rectangle?” (two). Count out loud as a
class “one-half, two halves.” “When we add the two halves together, we have the
6
whole.” Write ½ + ½ = 2/2 and 2/2 = 1, on the board. Explain that ½ is called a
fraction.
Ask students: Must the parts be equal to be half? (Yes) Hopefully a few students will
say no. Write the tally of yes and no answers on the board to be addressed later in a
sharing demonstration. Don’t give away answer yet.
Ask students to color ½ of their rectangle yellow.
Repeat this with rectangle two (the one folded into quarters). Recall the information
written on the board about this rectangle. Have students write ¼ in each section of the
rectangle.
Ask students: Must the parts be equal to be fourths? (Yes) Hopefully a few students
will say no. Write the tally of yes and no answers on the board to be addressed later in
a sharing demonstration. Don’t give away answer yet.
Ask: “How many fourths make up the whole rectangle?” (four) Count out loud as a
class “one-fourth, two-fourths, three-fourths, four-fourths.” When we add all of these
together, we have one whole.” Write ¼ + ¼ + ¼ + ¼ = 4/4 and 4/4 = 1, on the
board. Remind students that we are writing fractions.
Ask students to color in ¼ of the rectangle with red. Then color another ¼ of the
rectangle with blue. Finally color the remaining part of the rectangle with green. (It is
important that all students use the same colors.)
Ask students: “How much of the rectangle is colored red?” ( ¼ ) “Blue?” ( ¼ )
“Green?” (2/4 or ½ ) Write 2/4 and/or ½ on the board.
“How do you know that the green section is two-fourths?” (Count one-fourth, twofourths)
“Can anyone tell me what the bottom number represents?” (The total number of parts
of the whole)
“Can anyone tell me what the top number represents?” (the number of parts of the
whole that we colored)
“Compare the red and blue sections together to the green section. What do you
notice?” (they are the same size)
“How much of the rectangle is purple?” (0/4)
“How do we write this?” (zero over four)
“How much of the rectangle is colored in any color?” (4/4)
“How do we write this?” (four over four)
7
“How much of the rectangle is not red?” (3/4)
“How do we write this? (three over four)
“Compare this rectangle to the “halves” rectangle. What do you notice?” (the green
section is the same size as the yellow section).
“How much of the “halves” rectangle is black? (0/2)
Repeat this process with the eighths rectangle and make similar comparisons.
Revisit the question asked earlier: Do the parts need to be equal? Ask students if
anyone wants to change his/her answer. If anyone is still in doubt, do the following
sharing demonstration:
Ask a student to help demonstrate sharing. Offer that student part of your candy bar.
Break the candy bar into 2 unequal parts.
Ask the student which part he/she would prefer (whisper that he should pick the larger
part).
Ask: “Why would you want the larger part of the candy bar?”
Possible answer: “Because it is bigger than the other part.”
Ask: “Do is it half of the candy bar?”
Draw the candy bar on the board with a dashed line where the break occurred so the
whole class can see.
Extension:
Write one of the fractions on the board. Recall that students said the top number
represents the number of colored parts and that the bottom number represents the
total number of parts. Introduce the terms Numerator and Denominator.
The numerator is the number on the top. The Denominator is the number on the
bottom. We will watch a short video clip about this:
http://www.youtube.com/watch?v=x8VXW1GakB8
Take quiz that goes along with this video. Teacher will need to pause the video after
each question is presented. Have students “think-pair-share” for answers. Have
students go to the A, B,C, D corners of their choice. Repeat for each question. Pause
after each answer to clarify any questions.
For struggling students, have them log onto Sheppard Software website for fraction
work. www.sheppardsoftware.com
8
Evaluation:
Have students chorus read the learning objectives with teacher. Ask students to rate
their own knowledge of our learning objectives on a scale of 1-4. Students should keep
their eyes closed as they hold up 1, 2, 3, or 4 fingers.
Tell students that they are making a drawing of a rectangular summer vegetable
garden. On a clean sheet of paper, with name and student number on the top,
students should include the following:
 rectangular garden
 Color 1/4 red for tomatoes
 Color ¼ green for green peppers
 Color 2/4 yellow for corn
9
Unit Lesson – Fantastically Fun Fractions
Unit Lesson 2: A Party with Pattern Blocks
Grade Level
2nd
Time Needed
60 minutes
Materials Needed
Pattern Blocks for the
whole class: hexagons,
trapezoids, rhombuses,
triangles
Internet access to
http://www.youtu
be.com/watch?v=
DnFrOetuUKg
27 copies of Fraction
message sheet
(attached)
Introduction:
In this lesson students will identify parts of
whole shapes as fractional parts of those geometric shapes.
Background:
In the previous lesson, students learned to
partition a rectangle into two, four, and eight parts. They were also
introduced to the concept of numerator and denominator. Today we
will work on thirds and sixths, in addition to halves, and fourths.
GLCE(s):
CCSS.Math.Content.2.G.3. Partition circles and rectangles into two,
three, or four equal shares, describe the shares using the words
halves, thirds, half of, a third of, etc., and describe the whole as two
halves, three thirds, four fourths. Recognize that equal shares of
identical wholes need not have the same shape.
Engagement:
Play Mr. R’s Fractions, Fractions song
http://www.youtube.com/watch?v=DnFrOetuUKg
Invite students to turn and talk to a partner about connections they
made with the video. Give students 1 minute to discuss. Talk as a
group about a few of their connections.
Possible answers: four quarters makes one whole, denominator
down, numerator on top, one-fourth, equal pieces (an important
concept to tease out), parts of a whole (an important concept to
tease out).
10
Exploration:
Tell students that their learning objectives for today are:
“I can partition circles and rectangles into two, three, or four equal shares”
“I can describe the whole as two halves, three thirds, four fourths.”
Distribute pattern blocks to each student. In pairs, students should determine the
answer to the following teacher lead questions, recording answers and illustrate
pictures of their work.
1. How many green triangles fit onto the blue rhombus? (2)
2. If the blue rhombus is one whole, what fraction of does one green triangle
represent? (1/2)
3. How many green triangles fit onto the red trapezoid? (3)
4. If the red trapezoid is one whole, what fraction of one is the green triangle?
(1/3)
5. How many red trapezoids fit onto the yellow hexagon? (2)
6. If the yellow hexagon is one whole, what fraction of one is the red trapezoid?
(1/2 )
7. How many green triangles fit onto the yellow hexagon? (6)
8. If the yellow hexagon is one whole, what fraction of one is the green
triangle?(1/6)
9. How many blue rhombuses fit onto the yellow hexagon? (3)
10. If the yellow hexagon is one whole, what fraction of one is the blue rhombus?
(1/3)
11. How many blue rhombuses fit onto the red trapezoid? (1 and a half, or one
plus a green triangle)
12. If the red trapezoid is one whole, what fraction of one is the green triangle?
(1/3)

More challenging questions:




If
If
If
If
the
the
the
the
red trapezoid is one whole, how much is the yellow hexagon? (2)
blue rhombus is one whole, how much is the yellow hexagon? (3)
green triangle is one whole, how much is the blue rhombus? (2)
green triangle is one whole, how much is the red trapezoid? (3)
Teacher should attend to questions and make sure students have the right idea.
11
Explanation:
Let’s look at the yellow hexagon.
How many red trapezoids covered it?
How many blue rhombuses covered it?
How many green triangles covered it?
What do you notice?
Extension:
Tell students they will be creating their own geometric pattern.
Model the putting four squares together to make a large square. Illustrate this shape
by outlining the square and partitioning it into the four smaller squares. Label each
square ¼.
Students: Make a geometric pattern using 3 to 8 of the same pattern blocks. Illustrate
your geometric shape. What fraction of the shape is each of your pattern blocks?
If you take one pattern block away from your creation, what fraction of blocks is left?
Have students repeat this activity using a different pattern block.
Evaluation:
Have students chorus read the learning objectives with teacher. Ask students to rate
their own knowledge of our learning objectives on a scale of 1-4. Students should keep
their eyes closed as they hold up 1, 2, 3, or 4 fingers.
Hand out the Fraction Message sheet for students to complete. Clarify any questions
about terminology with students: first, last, middle, second, third, fourth, fifth, sixth
(meanings of the capitalized words are not needed). Model numbers one, two, and 15
with the students. This is an independent activity.
12
13
Unit Lesson – Fantastically Fun Fractions
Unit Lesson 3: Estimation Station
Grade Level
2nd
Time Needed
60 minutes
Materials Needed
Book: Give Me Half
by Stuart J. Murphy
28 copies of each
activity (attached):
 Halfness
 What’s Left?
Activity materials:
 Four thick books,
different
thicknesses
 4 clear cups
 4 cups of dried
beans in a big
container
 12 coins
 Four pieces of
string approx. 36
inches. Tied each
piece closed so
that it makes a
loop.
 16 Measuring
tapes
 16 yardsticks
 16 rulers
Introduction: In this lesson, students will sharpen their
estimation skills through a variety of hands-on activities.
Background: Teacher will need to set up 7 stations for the
Exploration part of this lesson. Key words to identify with students:
estimation, irregular shape, and verify.
GLCE(s):
CCSS.Math.Content.2.G.3. Partition circles and rectangles into two,
three, or four equal shares, describe the shares using the words
halves, thirds, half of, a third of, etc., and describe the whole as two
halves, three thirds, four fourths. Recognize that equal shares of
identical wholes need not have the same shape.
Engagement:
Read aloud: Give Me Half by Stuart J. Murphy
Who can tell me what “half” means? (two EQUAL parts) – if
students do not remember the word equal, tease this out by asking
questions such as,
“So if I want so share half of my granola bar with you, I can do this?”
- illustrate an uneven amount for “half” on the board.”
1 piece of paper with
a line at ¼. Color in
the ¼ with red.
14
Exploration:
Tell students that their learning objectives for today are:
“I can describe the shares using the words halves, thirds, half of, a third of”
“I can describe the whole as two halves, three thirds, four fourths.”
“I can recognize that equal shares of identical wholes need not have the same shape.”
Prior to this activity, set up 7 stations, with a ruler, yardstick, and measuring tape at
each:
1. Four thick books
2. 4 clear cups, one large container of beans
3. 12 coins
4. Several extra measuring tapes, yardsticks, and rulers
5. Several extra measuring tapes, yardsticks, and rulers
6. 4 loops of string
7. Several extra measuring tapes, yardsticks, and rulers
Teacher:
“Today we will be using our senses to “estimate” half of something. Turn and talk with
a partner about the word estimate.’“(means to guess or judge)
Invite partners to share their opinions with the class:
Possible answers: guess, judge
Halfness Activity. Hand out the activity page. Teacher explains to students that they
will work in small groups of four. Show students each of the seven stations and model
what they will do at each, while reading the directions from the activity page.
“There are seven estimation stations for the students to rotate through. For some of
the stations, students may want to do the activity individually, while other activities
require partner work. Each group will begin at a different station. Do each activity 3
times, recording answers on your paper. You will need to come up with a way to check
your estimation in order to check your guess.”
Teacher should circulate around room to answer questions and make sure students are
on track.
When all groups have had a chance to visit the seven stations, reconvene as a class.
Explanation:
Ask students if their estimations got better each of the 3 guesses? Visual assessment:
ask the students for a thumbs-up, sideways, or down.
15
At which stations did your estimates get better with each try? (they each likely got
better, but for the distance activities, the students may use the information from their
first guess to make their second guess perfect.)
Explain why your estimates got better.
Ask students how they checked their visual estimates.
Possible answers: measured with a ruler, measured by comparing both parts
Which visual estimations were the hardest?
Which visual estimations were the easiest?
Extension:
Distribute the What’s Left? Activity to each student.
This will be a whole class activity. Tell students that, together, we will be estimating
how much food is showing in each problem. These 4 problems get progressively
harder, so don’t rush the last two questions. Give students time to explain their
reasoning.
Homework for tonight: Find something at home to estimate. Ideas: estimate how
much water is in a cup, estimate the half-way point across your room?, estimate 1/3 of
a pile of pennies, estimate ¾ of your pile of stuffed animals. Find a way to verify your
guess. Illustrate your estimate on paper and write a sentence about how close your
estimate was to your guess.
Evaluation:
Formative Assessments:
Have students chorus read the learning objectives with teacher. Ask students to rate
their own knowledge of our learning objectives on a scale of 1-4. Students should keep
their eyes closed as they hold up 1, 2, 3, or 4 fingers.
Hold up a piece of paper with a line at ¼. (Color ¼ of paper red) Ask students to
estimate how much of the paper is colored red and write a sentence about their
estimation.
16
17
18
Unit Lesson – Fantastically Fun Fractions
Unit Lesson 4: Friendly Fractions
Grade Level
2nd
Time Needed
60 minutes
Introduction: In this lesson, students will learn how to identify
equivalent fractions (friendly fractions).
Background: Prior to this lesson, students have learned halves,

28 copies of
thirds, fourths, fifths, sixths, and eighths. In this lesson students will
learn to identify equivalent fractions. Equivalent will be a new term,
which the video introduces very well.

activity sheet
(attached)
C.O.W
GLCE(s):
Materials Needed
Fraction Strips
Internet access to:
YouTube video:
http://www.youtube.
com/watch?v=wL4hI
CyMLKU
Promethean Planet:
http://www.prometh
eanplanet.com/en/Re
sources/Item/76426/
comparing-fractionsand-equivalentfractions#.UnVD2vkq
hng
Sheppard Software:
http://www.sheppard
software.com/mathg
ames/fractions/equiv
alent_fractions_shoot
.htm
CCSS.Math.Content.2.G.3. Partition circles and rectangles into two,
three, or four equal shares, describe the shares using the words
halves, thirds, half of, a third of, etc., and describe the whole as two
halves, three thirds, four fourths. Recognize that equal shares of
identical wholes need not have the same shape.
Engagement:
Watch Equivalent Fractions video:
http://www.youtube.com/watch?v=wL4hICyMLKU
Pause video at each visual in order to talk through meanings with
students. The middle of this video has a cute animated cartoon that
illustrates equivalent bars of gold.
After the video, ask students to turn and talk with a partner about
the meaning of equivalent.
Ask students to share their answers. Possible answers: the same as,
two fractions that are different but mean the same, equal to.
Fraction Pizza:
http://math.rice.edu/
~lanius/fractions/frac
4.html
19
Exploration:
Tell students that their learning objectives for today are:
“I can describe the shares using the words halves, thirds, half of, a third of”
“I can describe the whole as two halves, three thirds, four fourths.”
Load the following Smartboard interactive flipchart about equivalent fractions. Begin
this presentation on slide 7.
http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractionsand-equivalent-fractions#.UnVD2vkqhng
Hand out Fraction Strips sheet to all students:
Students will work in pairs to complete this sheet. Model the first 3 lines of the sheet:
First bar: 1/2
2nd bar: 1/3, 1/3
3rd bar: invite students to help with this: 1/4, 1/4, 1/4
Invite students to complete the sheet, excluding the bottom three rows. Students who
find this easy may want to experiment with the bottom three rows. Model coloring
each bar a different color (all halves will be one color, all fourths will be one color, etc.).
Students cut out each bar and fractions. Explain that it will be important for them to cut
on the lines so that the fractions are the right size.
Explore what fractions are equivalent to each other. Model: ½ = two ¼’s. Have
students write down their findings in their journal, using illustrations. We will have a
discussion about findings shortly. Teacher should circulate around room to answer
questions and make sure students have the right idea.
Explanation:
Have students display their findings to the class. After each presentation, say to the
class, “If you also discovered that ___ = ____, give me a thumbs up/wink/pat yourself
on the shoulder.”
Possible answers:
½ = ¼, ¼ = 2/4 = 1/8, 1/8, 1/8, 1/8 = 4/8
1/3 = 1/6, 1/6
2/3 = 1/6, 1/6, 1/6, 1/6
¼ = 1/8, 1/8
2/4 = 1/8, 1/8, 1/8, 1/8
¾ = 1/8, 1/8, 1/8, 1/8, 1/8, 1/8 = 6/8
20
Watch for and clear up misconceptions about equivalent fractions. Say “I’m so glad you
brought this up Johnny. We should talk about this because I am sure some of your
classmates got this answer, too.”
Possible problem areas: students did not cut on the lines. Some fractions look like
they might be equivalent, but they are not.
Extension:
Get computers from Computer Cart on Wheels. Have students log-on to one of two
programs, both of which allow students to practice equivalent fractions.
Sheppard Software activity: Instruct students to begin on Level 1 of Game 1. Students
should email me their results at [email protected]
http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_shoot.ht
m
or
Fraction pizza only the Intro and Part 2 (the other parts can be completed by the more
advanced students)
http://math.rice.edu/~lanius/fractions/frac4.html
Evaluation:
Exit slip: students should write down three sets of equivalent fractions they can
identify. It is okay to use the strips of paper we used in the Exploration activity.
21
22
Unit Lesson – Fantastically Fun Fractions
Unit Lesson 5: Dare to Compare
Grade Level
2nd
Time Needed
60 minutes
Materials Needed
Book Gator Pie by
Louise Mathews
Introduction: In this lesson, students learn to compare the
sizes of fractions.
Background: Students have already learned about halves,
thirds, and fourths. Now they will learn how to compare the sizes as
greater than, less than, or equal to. Remind students that the
greater than sign opens toward the larger number/fraction and
points to the small fraction.
Pie pictures
(attached)
GLCE(s):
28 copies of
Compare Activity
Packet (attached)
CCSS.Math.Content.2.G.3. Partition circles and rectangles into two,
three, or four equal shares, describe the shares using the words
halves, thirds, half of, a third of, etc., and describe the whole as two
halves, three thirds, four fourths. Recognize that equal shares of
identical wholes need not have the same shape.
C.O.W.
Internet access to:
Promethean Planet
flipchart for
Smartboard:
http://www.prometh
eanplanet.com/en/Re
sources/Item/76426/
comparing-fractionsand-equivalentfractions#.UnVQ3Pkq
hni
Engagement:
Have students predict which series of fractions is smallest to largest:
½, 1/3, ¼, 1/6, 1/8
1/8, 1/6, ¼, 1/3, ½
Ask students to hold up one finger if they think it is the first series of
fractions; hold up two fingers if they think it is the second series of
fractions.
Read aloud Gator Pie by Louise Mathews
Fraction Monkeys
interactive activity:
While reading the book, show pie pictures cut into halves, thirds,
fourths, eights, hundredths.
http://www.fraction
monkeys.co.uk/activi
ty/
Ask students: What happened at the end of the story?
23
Exploration:
Tell students that their learning objectives for today are:
“I can describe the shares using the words halves, thirds, half of, a third of”
“I can describe the whole as two halves, three thirds, four fourths.”
We are going to figure out how fractions compare in size to each other.
Ask for volunteers to hold pie pictures (shown during story) so students can put the
pies into order from largest to smallest fractions.
Students will be standing in order ½, 1/3, ¼, 1/8, 1/100th
What do we notice about the denominator? Ask for clarification about which number is
the denominator.
Students should notice that the denominator gets bigger as the fractions get bigger
from left to right.
Teacher: “Who can tell me what happens to the slices of pie, going from left to right)?”
(the pie slices get smaller)
Teacher: “So you are telling me that as the denominator gets bigger, the pieces of pie
get smaller?” (Yes!!)
Teacher: “Then what happens to the pieces of pie as the denominator gets smaller
(going from right to left)?” (They get bigger.)
Teacher: “Now let’s say this is your very favorite kind of pie. Which share would you
like to have, and why?”
Possible answers: ½ because it is biggest, 1/8 because I could share it with some
friends, 1/4 because ½ would be too much at one time.
Thank students for volunteering with the pies. They can be seated
Today we will explore this notion of comparing the sizes of fractions.
Show Promethean Planet Flip chart slides 1-6, which explain comparisons of fractions a
little bit differently:
http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractionsand-equivalent-fractions#.UnVQ3Pkqhni
24
The activity sheet I am going to give you has a lot of “pies” on it. We are going to
color our pies according to the fractions shown. On the second page, we move to color
coding number lines. We will decide which fraction is greater than, less than, or equal
to the other. Remind students that the greater than sign opens toward the larger
number/fraction and points to the small fraction.
Work sheets and answer sheets attached and available at:
http://www.visualfractions.com/worksheets/compare/compareworksheets.pdf
Explanation:
Ask students why the fractions get smaller as the denominator gets bigger.
Possible answers: the whole must be divided into more pieces.
What happens if we have the same denominator and different numerators? How can
we tell if one fraction is bigger than the other? Give the example of 2/4 and ¾. Which
fraction is larger?
Extension:
Have students each get a computer from the C.O.W. Have students log onto Fraction
Monkeys interactive program:
http://www.fractionmonkeys.co.uk/activity/
Point out that in this activity, students are working on a number line from zero to one.
They will determine the arrangement of fractions on that number line. This requires
some knowledge of equivalent fractions learned in the prior lesson.
Evaluation:
Formative assessments:
Have students chorus read the learning objectives with teacher. Ask students to rate
their own knowledge of our learning objectives on a scale of 1-4. Students should keep
their eyes closed as they hold up 1, 2, 3, or 4 fingers.
Give students a similar question to the one they did at the beginning of the lesson.
Have them put the following fractions in order from biggest to smallest.
1/3, 1/100, ½, 1/8, ¼
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26
27
28
29
30
31
32
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34
35
36
37
38
Unit Lesson – Fantastically Fun Fractions
Unit Lesson 6: Groovy Groups
Grade Level
2nd
Time Needed
60 minutes
Materials Needed
Introduction: In today’s lesson, we will explore how fractions
can show equal parts of a group of objects.
Background:
By the end of today’s lessons students can
identify fractional parts (halves, thirds, fourths).
52 pretzel rods
GLCE(s):
Pictures:
 1 square showing
halves
 1 square showing
2 unequal parts
 1 circle showing
pie wedges in
thirds
 1 circle showing 3
unequal sections
horizontally
 1 rectangle
showing fourths
 1 rectangle
showing 4
unequal parts
CCSS.Math.Content.2.G.3. Partition circles and rectangles into two,
three, or four equal shares, describe the shares using the words
halves, thirds, half of, a third of, etc., and describe the whole as two
halves, three thirds, four fourths. Recognize that equal shares of
identical wholes need not have the same shape.
Manipulatives such
as colored counters –
25 per student
9 stacks of activity
questions (attached)
– cut and group
ahead of time
Individual questions
for formative
assessment-attached
Engagement:
Show the students a bowl of 52 pretzel rods. Ask the students how
these pretzels could be related to our math lesson for today.
Possible answers: we are going to measure them, we will eat them,
we will group them, count them.
Tell students that by the end of the lesson, they will find out how the
pretzels relate to our learning objective for the day.
Tell students that in today’s lesson, we will learn how fractions can
represent parts of a group of objects.
Exploration:
Tell students that their learning objectives for today are:
“I can describe the shares using the words halves, thirds, half of, a
third of”
“I can describe the whole as two halves, three thirds, four fourths.”
“I can recognize that equal shares of identical wholes need not have
the same shape.”
39
Review with students the idea of halves, thirds, and fourths of a whole. Hold up two
pictures of a square, one divided in half and the other in 2 unequal parts.

Teacher: “Do both of these squares show halves? “Turn and talk with a partner
about your thoughts.”

Some students may think both pictures show half, while others do not.

Teacher: “Those who think both pictures show halves of a pie, tell me why.”

Possible response: because they each have two parts. Accept any answer.

Teacher: “Those who do not think that both pictures show halves, tell me why.”

Possible response: because the one square has unequal parts.

Teacher: “So what you are telling me is that the parts have to be equal to be
halves?”
Teacher to the group who thought both pictures showed halves: “what do you
think of their reasoning?”


Possible responses: students do not agree, students now see
Clarify any misconceptions about halves. They MUST be equal.
Show students a set of pictures of a rectangle divided into three parts. One picture has
thirds and the other picture has unequal parts of 3.
Go through the same questioning (bulleted dialogue) as with the previous pictures.
Repeat for the set of circles. The set of circles might be trickier since one picture is not
cut into pie wedges.
Clarify any misconceptions about a circle divided in this manner. It would be possible
for a circle to be divided into thirds this way, but it would take a lot of multiplication
and division to do it accurately.
Now move onto the new topic of fractions representing groups of objects.
Teacher: “We know that we can divide an object into equal parts, I wonder if we can
divide groups of objects into equal parts?”
Have eight students volunteer to be part of a group at the front of the room.
40
Tell the students that you would like to divide this group in half. “How many parts do
we need to create? Use your fingers to show me.”
Model counting off: person 1 stand on the left, person 2 stand on the right, next
person on the left, etc.
Teacher: “How do we know we have two-halves?”
Possible response: The groups have an equal number of people.
Teacher: “Now I want to divide this group into fourths. How should I do that?”
Possible responses: count by fours, guess and then rearrange, count off 1, 2, 3, 4, 1,
2, 3, 4… Accept all responses and write them on the board.
Model counting off and grouping: 1, 2, 3, 4, 1, 2, 3, 4
Teacher: “How many groups do we have? (4)
Teacher: “How many people in each group?” (2)
Teacher: “How do we know that we successfully divided this group into fourths?” (the
groups are equal)
Tell students that you now want to divide the class into thirds (deliberately make the
groups unequal, but don’t students this). Note, if students are absent, divide the class
into groups that will eventually be evenly divided - ex: if 25 students are present, make
5 unequal groups.
After the class is grouped by “thirds,” ask them:
“Would you please make sure that our group is divided into thirds?” Some students will
say yes it is, while others may disagree. Ask students for reasoning for their answers.
The intent of this activity is for students to determine that their class or “group” can be
divided into thirds - 3 equal parts.
Have students rearrange themselves so that they are in 3 equal groups.
Teacher: “Yes! You just used fractions to show parts of our whole group!”
Thank the students and invite them to be seated.
Explanation:
We just saw that we can use fractions to divide groups of objects or people into parts.
41
What one thing is very important when using fractions to show parts of a group?
Tease out the word “equal” parts.
Ask students if it would be “equal parts” if the numbers in each group were different.
How do you think this concept of using fractions to show parts of a group of objects
could apply to things that happen in our everyday lives?
Possible responses: when we bring a treat and want to share it, when we want to split
up a pile of rubber bands between friends, when we have candy to share with a friend.
Extension:
Tell students that in this next activity, we will be working in groups of three to answer
some the questions on a stack of activity cards. Students will use manipulatives such
as counters, to help find the answers to these questions. It is important that each
student is engaged in helping to find the answers to these questions.
Ask for 3 students to come to the front to model this activity. On the document
camera, display 12 counters. Place the activity cards near them, face down. Have one
student draw the top card and read it to the group. Students should work together to
find a solution to the question. One person records the answer on the card.
Assign groups and hand out counters and activity cards. Circulate around room
answering questions and checking for understanding (asking groups how they got their
answers).
Students done early should make up their own story problem similar to the questions
they just had. Exchange questions with members of their group.
After groups have finished the activity, go over answers with the class. Visually assess
student success with questions by asking for a thumbs-up or down after each question.
Evaluation:
Ask students if they figured out what the pretzel rods had to do with today’s math
lesson. (They are to share) How will we figure out how to divide this set of pretzels
evenly? (Pass them out one at a time).
How many pretzels did you each get? (2) Did anyone get more? (no) Did anyone get
less? (no) So do each of you have a fraction of the whole group of pretzels? There
were 52 pretzels in the group. What is the fraction of pretzels that you have? (2/52)
42
Formative assessments:
Have students chorus read the learning objectives with teacher. Ask students to rate
their own knowledge of our learning objectives on a scale of 1-4. Students should keep
their eyes closed as they hold up 1, 2, 3, or 4 fingers.
Time permitting, give students the individual practice sheet.
Otherwise, ask students for to hold up fingers (1-4) to represent their level of
understanding for today’s objective which was to demonstrate how fractions can show
equal parts of a group.
43
44
45
Unit Lesson – Fantastically Fun Fractions
Unit Lesson 7: Fraction Flags
Grade Level
2nd
Time Needed
45-60 minutes
Materials Needed
Internet access to:
Which is Your Flag?
Introduction: Students will examine and analyze state and
world flags to look for fractional patterns.
Background: Students have learned how to identify objects
divided into halves, thirds, and fourths. They will use this knowledge
to explore, identify, and make state and country flags with colors
that display these patterns.
http://www.youtube.com
/watch?v=L9SPiZ_54rc
GLCE(s):
Flags of all Countries of
the World:
CCSS.Math.Content.2.G.3. Partition circles and rectangles into two,
three, or four equal shares, describe the shares using the words
halves, thirds, half of, a third of, etc., and describe the whole as two
halves, three thirds, four fourths. Recognize that equal shares of
identical wholes need not have the same shape.
http://www.youtube.com
/watch?v=PwGc35XoKNc
World Flags:
http://www.youtube.com
/watch?v=QPBQC7jAJt4
C.O.W.
30 half sheets of paper
27 summative
assessments
Books:
Flags of the World by
Sylvie Bednar
Engagement:
Inform students that we will watch a short video which shows many
country flags from around the world. They should be using their
prior knowledge about halves, thirds, and fourths, to identify flags
with colors that display these attributes.
Watch flags video: Which is Your Flag?
http://www.youtube.com/watch?v=L9SPiZ_54rc
Complete Flags of the
World by DK
Exploration:
Flags by Jason Cooper
Tell students that their learning objectives for today are:
“I can partition rectangles into two, three, or four shares using the
words halves, thirds, half of, a third of, a fourth of”
“I can describe the whole as two halves, three thirds, four fourths.”
Flags of the Fifty States
by Randy Howe
The World Encyclopedia
of Flags by Alfred
Znamierowski
46
Last week’s newsletter informed parents that we would be exploring state and country
flag colors that display patterns of halves, thirds, and fourths. In order to engage
students more fully, it would help for them to have a personal connection to the flag
they choose to illustrate. Some students may come from other states or countries,
have relatives from other countries, or they may be interested in finding out more
information about a particular state or country.
Tell students that we will be making a Fraction Flag bulletin board. They will be
illustrating one flag to put on this board. There are many resources around the room
with state and world flags. Students will work as partners and should look through
these items to:

Identify 3 flags with patterns of half, thirds, fourths, or some other fractional
pattern

Identify 3 flags without a fractional pattern
Each student should record these flags and state or country names in their journal,
showing a pencil illustration of that flag. Students should identify if the flag pattern is
halves, thirds, fourths, or another fractional pattern (they must be able to identify the
fraction). Optional: computers to investigate state and country flags.
During this time, videos will be displayed for students to look at during their
investigation:
http://www.youtube.com/watch?v=QPBQC7jAJt4
http://www.youtube.com/watch?v=PwGc35XoKNc
As students finish early, they can help other students identify flags that meet the
requirements.
Explanation:
Students share their findings.
Teacher: “Let’s share flags with patterns of half.” Ask for volunteers to tell which state
or country and what the pattern looked like. How do we know that this flag has a
pattern of half? (Two EQUAL parts) Ask if anyone else recorded that country.
Continue to ask for volunteer until all half patterns have been spoken for. In a
quadruple-T-chart (halves, thirds, fourths, other), keep track of countries on the board.
Record student name next to the country name.
Teacher: “Now we will share flags with patterns of thirds.” Ask for volunteers to tell
which state or country and what the pattern looked like. How do we know that this flag
has a pattern of thirds? (Three EQUAL parts) Ask if anyone else recorded that country.
47
Continue to ask for volunteer until all half patterns have been spoken for. Record
findings on board.
Teacher: “Next we will share flags with patterns of fourths.” Ask for volunteers to tell
which state or country and what the pattern looked like. How do we know that this flag
has a pattern of fourths? (Four EQUAL parts) Ask if anyone else recorded that country.
Continue to ask for volunteer until all half patterns have been spoken for. Record
findings on board.
Teacher: “Did anyone find a different fractional pattern?” Ask for volunteers to tell
which state or country and what the pattern looked like. How do we know that this flag
has a fractional pattern? (EQUAL parts) Ask if anyone else recorded that country.
Continue to ask for volunteer until all half patterns have been spoken for. Record
findings on board.
Review all the t-chart with the class. Assign students to a particular flag to replicate on
a half piece of paper.
Extension:
Hand out half sheets of paper. Invite students to make their assigned country flags.
Drawings should reflect halves, thirds, fourths, and other fractions appropriately. Ask
students if they remember the very important detail about fractions: Equal parts.
If they finish early, they can get a computer out to research information about their
chosen country. They should write this information on the back of their flag.
Evaluation:
Have students chorus read the learning objectives with teacher. Ask students to rate
their own knowledge of our learning objectives on a scale of 1-4. Students should keep
their eyes closed as they hold up 1, 2, 3, or 4 fingers.
Give students the following summative assessment that addresses all CCSS standards.
48
49
K-12 Student Performance Assessment: Unit Level 2
All Initial Endorsement Candidates are required to gather evidence on how well their K-12 students performed during a
Candidate-created unit. The data from the assessment will be shared with the university field coordinator. The data will be used
primarily to assist the College of Education in assessing its program and will not be used as a means of assigning the
Candidates’ semester grades.
Candidate’s Name_____________________________________________________________________
Grade Level _______________________ Number of Students Enrolled ______________________
ELEMENT or
INDICATORS
(0)
UNSATISFACTORY
(1)
PROGRESSING
(2) PROFICIENT
(3) DISTINGUISHED
Knowledge of Content
The student does not have
a basic knowledge of the
content.
The student displays a
basic knowledge of the
content.
The student displays solid
content knowledge.
The student displays
extensive content knowledge
and continues to pursue
further knowledge.
Student Interaction
Student interactions are
characterized by conflict,
sarcasm, or put-downs.
Students do not
demonstrate negative
behavior toward one
another.
Student interactions are
generally polite and
respectful.
Students demonstrate
genuine caring for one
another as individuals and as
students.
Student Pride in Work
Students demonstrate little
or no pride in their work.
They rush through to get
the “task” completed and
do not focus on high
quality work.
Students complete
most of the “tasks,” but
invest little of their
energy in the quality of
the work.
Students complete the
“tasks” and demonstrate
pride in their completed
work.
Students take obvious pride in
their work and initiate
improvements in it (i.e. by
revising drafts on their own
initiative, helping peers, and
ensuring that high-quality
work is displayed).
Student Participation
Limited engagement in the
activity.
Somewhat engaged in
the activity.
Actively engaged during
the activity.
Highly engaged and
enthusiastic during the
activity.
Totals
Be sure that each row’s total is equal to the number of students you have in your class.
(e. g. if there are 25 students enrolled then each row should total 25)
Types of evidence used to assess student learning
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________
Candidate’s response to lesson experience and student learning
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
____________________________________________________________________________________________________
(McCrea & Patterson, 2004)
McCrea Revised 2008
50
Bibliography
Lesson 1:
Alder, D. A. (1996). Fraction fun. New York, NY: Holiday House.
Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,
C.G., Pitvorec, K.,& Saecker. P. (2012). Everyday mathematics teacher lesson
guide (Common Core State Standard ed., Vol. 2, pp. 592-643). Chicago, IL:
McGraw-Hill Companies, Inc.
Dodds, D.A. (2007) Full house an invitation to fractions. Sommerville, MA: Candlewick
Press
Miller, M., & Lee, M. (2002). Mega-fun fractions. In Common Core Georgia State
Standards. Retrieved November 1, 2013, from http://ccgpsmathematicsk5.wikispaces.com/file/view/Mega-Fun%2BFractions.pdf
Understanding fractions (2012, April 10). In Pearson Education, Inc.. Retrieved
November 2, 2013. Retrieved from
http://www.youtube.com/watch?v=x8VXW1GakB8
Lesson 2:
Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,
C.G., Pitvorec, K.,& Saecker. P. (2012). Everyday mathematics teacher lesson
guide (Common Core State Standard ed., Vol. 2, pp. 592-643). Chicago, IL:
McGraw-Hill Companies, Inc.
Miller, M., & Lee, M. (2002). Mega-fun fractions. In Common Core Georgia State
Standards. Retrieved November 1, 2013, from http://ccgpsmathematicsk5.wikispaces.com/file/view/Mega-Fun%2BFractions.pdf
Mr. R's fractions-fractions song (n.d.). In Mr. R's World of Math and Science. Retrieved
November 1, 2013, from http://www.youtube.com/watch?v=DnFrOetuUKg
51
Lesson 3:
Murphy, Stuart J. Give me half! New York: HarperCollins, 1996. Print.
Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,
C.G., Pitvorec, K.,& Saecker. P. (2012). Everyday mathematics teacher lesson
guide (Common Core State Standard ed., Vol. 2, pp. 592-643). Chicago, IL:
McGraw-Hill Companies, Inc.
Miller, M., & Lee, M. (2002). Mega-fun fractions. In Common Core Georgia State
Standards. Retrieved November 1, 2013, from http://ccgpsmathematicsk5.wikispaces.com/file/view/Mega-Fun%2BFractions.pdf
Lesson 4:
Allen-Stokes, T. (2011, March 29). Equivalent fractions. In You Tube. Retrieved October
25, 2013, from http://www.youtube.com/watch?v=wL4hICyMLKU
Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,
C.G., Pitvorec, K.,& Saecker. P. (2012). Everyday mathematics teacher lesson
guide (Common Core State Standard ed., Vol. 2, pp. 592-643). Chicago, IL:
McGraw-Hill Companies, Inc.
Comparing fractions and equivalent fractions (2011, February 21). In Promethean
Planet. Retrieved November 2, 2013, from
http://www.prometheanplanet.com/en/Resources/Item/76426/comparingfractions-and-equivalent-fractions#.UnVQ3Pkqhni
Equivalent fractions shoot (n.d.). In Shepphard Software. Retrieved October 2, 2013,
from
http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_sh
oot.htm
Lanius, C. (2008). Who wants pizza?. In Rice University Department of Mathematics.
Retrieved November 2, 2013, from
http://math.rice.edu/~lanius/fractions/index.html
Miller, M., & Lee, M. (2002). Mega-fun fractions. In Common Core Georgia State
Standards. Retrieved November 1, 2013, from http://ccgpsmathematicsk5.wikispaces.com/file/view/Mega-Fun%2BFractions.pdf
52
Lesson 5:
Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,
C.G., Pitvorec, K.,& Saecker. P. (2012). Everyday mathematics teacher lesson
guide (Common Core State Standard ed., Vol. 2, pp. 592-643). Chicago, IL:
McGraw-Hill Companies, Inc.
Comparing fractions and equivalent fractions (2011, February 21). In Promethean
Planet. Retrieved November 2, 2013, from
http://www.prometheanplanet.com/en/Resources/Item/76426/comparingfractions-and-equivalent-fractions#.UnVQ3Pkqhni
Fraction monkeys (n.d.). In SUMS Online. Retrieved November 2, 2013, from
http://www.fractionmonkeys.co.uk/activity/
Hester, S. (n.d.). Making a cake. In Georgia Department of Education. Retrieved
November 2, 2013, from
http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathCake
Visual fractions worksheets: Compare (n.d.). In Visual Fractions. Retrieved November 2,
2013, from
http://www.visualfractions.com/worksheets/compare/compareworksheets.pdf
Lesson 6:
Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,
C.G., Pitvorec, K.,& Saecker. P. (2012). Everyday mathematics teacher lesson
guide (Common Core State Standard ed., Vol. 2, pp. 592-643). Chicago, IL:
McGraw-Hill Companies, Inc.
Feaman, M. (2008). 2nd grade number sense lesson plan: Fractions - #2. In Juab
School District. Retrieved October 26, 2013, from
https://www.juab.k12.ut.us/index.php?option=com_content&view=article&id=11
68:2nd-grade-math-lesson-plan-fractions&catid=66:grammar&Itemid=58
53
Lesson 7:
Bednar, S. (2009). Flags of the world. New York, NY: Abrams.
Complete flags of the world. (2008). New York, NY: DK Publishing.
Cooper, J. (1997). Flags. Vero Beach, FL: Rourke Publishing.
Hosein, A. (2010). Flags of all countries of the world. In You Tube. Retrieved November
3, 2013, from http://www.youtube.com/watch?v=PwGc35XoKNc
Howe, R. (2009). Flags of the Fifty States (2nd ed.). Guilford, CT: Lyons Press.
Kids. (2012). World flags: Learning flags of countries. In You Tube. Retrieved
November 3, 2013, from http://www.youtube.com/watch?v=QPBQC7jAJt4
Miller, M., & Lee, M. (2002). Mega-fun fractions. In Common Core Georgia State
Standards. Retrieved November 1, 2013, from http://ccgpsmathematicsk5.wikispaces.com/file/view/Mega-Fun%2BFractions.pdf
Znamierowski, A. (2013). The World Encyclopedia of Flags. Wigston, Leicestershire,
England: Lorenz Books.
54