Fractions
Teaching Tips: First Grade
Using Best Instructional Practices with Educational Media to Enhance Learning
Boston University
School of Education
July 6, 2015
Contents
Unit Overview
page 3
Teaching Routines
page 4
Lesson 1
page 6
Lesson 2
page 16
Lesson 3
page 25
Alignment to CCSS: Mathematics
page 35
Alignment to CCSS: English Language Arts
page 36
Alignment to ISTE Technology Standards: Students
page 37
Alignment to ISTE Technology Standards: Teachers
page 38
Credits
page 39
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Contents
Unit Overview
CCSS: Mathematics
Key Vocabulary
Watch Together
half, halves, fourth,
quarter, precise
Peg's Pizza Parlor
Lesson 1
•Attend to precision.
•Partition circles and rectangles into two and four
equal shares, describe the shares using the words
halves, fourths, and quarters, and use the phrases
half of, fourth of, and quarter of. Describe the whole
as two of, or four of the shares. Understand for these
examples that decomposing into more equal shares
creates smaller shares.
fraction, thirds,
sixths, cranky, fair,
share, flavor
Lesson 2
•Construct viable arguments and critique the reasoning
of others.
•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.
denominator,
numerator,
recyclables, bin,
container
Lesson 3
•Make sense of problems and persevere in solving
them.
•Construct viable arguments and critique the reasoning
of others.
•Attend to precision.
•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.
SMART Notebook™
file: Vocab–Fraction
Words
Play Together
Peg’s Pizza Place
Cut It in Half
Hungry Pirates
Explore with
a Friend
Peg’s Pizza Place
Share at Home
Parent Letter
SMART Notebook™
file: Sorting–
Fractions
Make the Cake
Make the Cake
Parent Letter
Fractions Splat
SMART Notebook™
file: Pattern Blocks
Classroom Chart:
Fraction Words
Peg and Cat
Estimate
SMART Notebook™
file: Vocab–
SMART Notebook™ Fraction Notation
file: Sorting–Unit
Fractions
Bubble Bath
Bubble Bath
Parent Letter
SMART Notebook™
file: Sorting–Unit
Fractions
3
Contents
Teaching Routines
Maintain Brisk Pacing
Research demonstrates that “brisk” pacing is related to greater content coverage, increased motivation and engagement, and, in
turn, higher levels of student achievement.
• Note the time allocated to each component of the lesson. Monitor the length of your teaching and children’s turns so that all
activities are completed within the allocated time.
• Establish a predetermined system for calling on children to work at the whiteboard. For example, write each child’s name on a
Popsicle stick and place the sticks in a jar. To call a child to the board, draw a stick from the jar. When a child’s name is selected,
set that stick aside, leaving only the sticks of children not yet chosen.
• Invite all selected children to the whiteboard at the same time when more than one child will be playing.
• Limit time spent in Turn and Talk to 10–15 seconds to maintain attention and focus.
Engage All Children
When children are highly focused and engaged, they attain higher levels of achievement.
• Position children so they do not block the screen when they stand at the whiteboard, so that everybody can see the videos,
games, images, and activities.
• Involve all children in thinking about the correct answers even if it is not their turn at the whiteboard.
• Use strategies such as Turn and Talk. For example, ask all children to tell a partner the answer they would choose, or if they
agree/disagree with a stated choice.
• When the child at the whiteboard gives an answer, invite all the others to show “thumbs up” if they agree with the answer or
“thumbs down” if they disagree.
• Observe children’s understanding of key concepts. When most children demonstrate understanding by rapidly choosing correct
responses, wrap up the lesson.
• When partners share a tablet, position the device between them so that it is easily accessible to both.
Support Independent Learning
When teachers notice and name the learning strategies children use, children are more likely to become strategic and independent
learners.
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Contents
Teaching Routines
Use Key Vocabulary Frequently
When children have many opportunities to hear and use new vocabulary words, they are more likely to acquire and use the words
on their own.
• Repeat key words as often as possible during the lesson, as well as during other parts of the school day when use of these words
is appropriate.
• Ask children to use key words while playing the games.
• When children are at the whiteboard, encourage them to use key words to describe their actions. For example, “There are six
olives on cow’s half of the pizza.”
• When children are invited to turn and talk, encourage them to use key words. For example, “We can fairly share the toppings
by moving one topping at a time onto each piece of cake.”
Mediate Game Play
When well-developed educational media programs are effectively joined with a sound classroom curriculum, children demonstrate
high levels of motivation and engagement as well as notable increases in early literacy and mathematics skills and knowledge.
• Load the game on the computer and minimize it before you begin the lesson. This allows you to optimize instructional time by
beginning game play as soon as you and the children are ready.
• Preview the screen to explain what children will do. Point out game features such as selecting objects, moving objects, and
repeating the game instructions.
• Quickly mute/unmute the sound by using the mute button on the top row of the computer keyboard. You can also use the volume
down/up buttons on the keyboard, or the volume controls on the interactive whiteboard, to adjust the sound.
• If the touch function doesn’t work, use your computer to click on the item the child touches. • Establish a routine for quick distribution of individual tablets or whiteboards. For example, choose one child in each row of
children to pass items. • Prepare for the worst! Have a dry erase board or manipulatives available to carry out activities intended for the interactive
whiteboard (such as using pattern blocks to demonstrate fractions).
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Contents
Lesson 1: Preview
Video: Peg’s Pizza Parlor (1:58)
Preview the video:
pbskids.org/peg/videos/pegs-pizza-parlor
Video: Cut It in Half (1:59)
Preview the video:
pbskids.org/peg/videos/cut-it-in-half
Game: Peg’s Pizza Place
Preview the game:
pbskids.org/peg/games/pizza-place
Peg and Cat have another BIG problem!
One of the teens at Peg’s Pizza Place has
ordered half a pizza, but Peg and Cat don’t
know what a “half” means.
Peg, Cat, Ramone, and the chef lead
everyone at the pizza parlor in a song as
they cut pizza and all kinds of other things in
half: dispensers for spices, hand-held
devices, apples and pears, tables or chairs,
even a saxophone.
Peg needs help putting the correct number of
toppings on each customer’s pizza. After
Peg reads the order, players move the
topping pieces onto the pizza. Peg counts
the toppings before saying the next order.
Ramone and the chef demonstrate cutting a
whole pizza in half to create two parts of
equal size. As they sing about cutting the
pizza, they encourage Peg and Cat to
remember that “there are two halves in
every whole.”
Ramone and the chef sing the final line of
the song, “There are two halves in every
whole.”
The number of customers and topping pieces
increase as children play. When two
customers share a pizza, different toppings
go on each half. When four customers share,
different toppings go on each fourth.
Although the game focuses on cardinality,
this lesson uses the game to teach the
concepts of halves, fourths, and quarters.
6
Contents
Lesson 1: Big Idea
Big Idea
Develop Understanding
1. Develop understanding of
dividing items in equal-size
pieces and the fraction word
half by watching two brief
videos.
2. Extend understanding of
dividing items into equal
sizes and using precise
fraction words to describe
the pieces (including half
and fourth/quarter) by
doing an interactive
whiteboard activity.
Shapes can be
partitioned into two and
four equal shares, and
these shares are
described as halves,
fourths, and quarters.
Key Vocabulary
half
fourth
precise
halves
quarter
Apply Understanding
1. Apply understanding by
using precise fraction
vocabulary while playing a
game with teacher guidance.
2. Refine understanding of
fractions and fraction
vocabulary by playing a
game, doing an interactive
whiteboard activity, or
reading and responding to
books with a friend.
Make sure to:
• Emphasize that a whole cut into halves is made up of two same-size pieces, and a whole cut into fourths/quarters
is made up of four same-size pieces.
• Describe the whole as two of, or four of, the shares.
7
Contents
Lesson 1: Objectives
Watch Together
Introduce or review math concepts
and hear new vocabulary in
context.
In this lesson, children will:
• attend to precision (mathematical practice)
Build Background
Activate and build children’s
background knowledge.
Get Ready to Play
Preview the game.
Play Together
Play a teacher-led game.
Explore with a Friend
Practice with one or more partners
at a learning center.
Review, Connect, Reflect
Review big idea, connect to home,
and evaluate student learning.
• partition circles and rectangles into two and four equal shares
• describe shares using the words half, halves, fourth, and quarter
and the phrases half of, fourth of, and quarter of
• understand that a whole cut into halves is made up of two samesize pieces, and a whole cut into fourths is made up of four samesize pieces
• describe the whole as two of, or four of, the shares
• acquire and use new vocabulary, such as precise
• read and respond to books about fractions
• use technology to learn, working individually and in groups
8
Lesson 1: Watch Together, Part 1
Contents
Time: 5 minutes
Teacher Prep
1. Launch the video Peg’s Pizza Parlor,
then press the pause button to stop it from
playing.
pbskids.org/peg/videos/pegs-pizza-parlor
2. Launch the video Cut It in Half. Press
pause and minimize the video to place it
on the dock for easy access.
pbskids.org/peg/videos/cut-it-in-half
To introduce children to the concept that items can be partitioned into two equal shares,
display the video Peg’s Pizza Parlor. Before watching, explain that in this video Peg and
Cat are taking pizza pie orders from customers—the teens—at Peg’s Pizza Place. When
one of the teens places her order, Peg and Cat don’t know one of the words the teen
uses, so they aren’t sure how to fill her order.
To set a purpose, tell children that after watching this video you will ask them what Peg
and Cat learned about the word half that helped them fill the teen’s order. Play the
video.
3. Open two SMART Notebook™ files:
Vocab–Fraction Words and Sorting–
Fractions. Minimize the files.
To deepen children's understanding of half, after watching:
4. Open the game Peg’s Pizza Place and
minimize it to place it on the dock.
pbskids.org/peg/games/pizza-place
• Emphasize that the two halves in a whole are precisely the same size. Say: Half a
pizza means one of two same-size pieces in a whole pizza.
5. If you plan to use tablets for Explore
with a Friend, set them up with the game
Peg’s Pizza Place.
• Ask: What is half a pizza? (Do not accept “one of two pieces in a whole pizza” as an
accurate response.)
Close the video.
NOTE: Before the lesson, create a login at
pbskids.org and play the game a few
times. Log in again before playing the
game with the class so that it advances
more quickly to pizzas divided into halves
and quarters.
9
Lesson 1: Watch Together, Part 2
Contents
Time: 5 minutes
To develop the understanding that items can be partitioned into two equal shares,
display the video Cut It in Half. Explain that in this video children will learn about cutting,
or dividing, items in half.
To set a purpose, tell children that after they watch, you will ask them to recall items the
characters cut in half. Play the video.
To deepen understanding of partitioning items in half, after watching, ask:
• What are some of the items Peg and her friends cut in half? (spices, hand-held
devices, hat, apples, pears, tables, chairs, saxophone)
• What does it mean to cut an object in half? (to divide it into two same-size pieces)
• How many halves are there in every whole? (two halves in every whole)
Close the video.
10
Contents
Lesson 1: Build Background
Time: 5 minutes
To continue building children’s understanding of partitioning shapes
into equal shares, display the SMART Notebook™ file called Vocab–
Fraction Words.
Vocab–Fraction Words
To review half/halves:
• Point to the first circle and say: This is a whole circle. Tap this circle
to display the word “whole.”
• In the next circle, point to the shaded half and ask children to turn
and talk with their partners to answer the question: What is this
part of the whole called? Invite a few children to share the answer,
then tap the shaded half to reveal the word half.
To introduce fourths/quarters:
• Point to the last circle and explain that the whole has four parts
that are each precisely the same size. Tell children that when a
shape is divided into four equal parts, each part is called a fourth
of or a quarter of the whole shape.
• Tap the circle to display the words fourth and quarter and have
children repeat each word with you.
Close the Vocab–Fraction Words file. (NOTE: To reset this file at any
time, select the blank second page, then select the previous page
with the circles.)
11
Contents
Lesson 1: Get Ready to Play
Time: 5 minutes
To develop understanding and use of fraction words, display the game Peg’s Pizza
Place.
Connect the game to previous lesson segments.
• Explain that, as they saw in the videos and in the Fraction Words activity, in the game
Peg’s Pizza Place pizza is divided into halves (two same-size pieces) and fourths or
quarters (four same-size pieces).
Describe the purpose of the game.
• Press the play button and have children listen to Peg as she introduces the game and
provides instructions for the first round of play. Then mute the sound.
• Tell children that as they play, they must count and place pizza toppings on a whole
pizza, half of a pizza, and a fourth or quarter of a pizza.
Explain the technology features of the game.
• Point to the notepad and call children’s attention to the illustration of the character, the
topping, and the number showing how many pieces of that topping the customer
wants. Demonstrate how to move each topping onto the pizza.
• Tell children that after they move the correct number of toppings onto the pizza, they
need to press the purple “done” button. Then Peg will count the toppings.
• Unmute the sound and press the “done” button to complete the round and get the
next pizza order.
12
Contents
Lesson 1: Play Together
Time: 10 minutes
To encourage children to use precise fraction vocabulary:
When only one character orders a pizza:
• Call on one or two children (depending on the number of toppings ordered) to put toppings on the pizza.
• Before a child selects “done,” mute the sound.
• Ask: If the customer wants to share a whole pizza with a friend so that they would each get equal amounts of pizza, what would s/he
do? (Cut the pizza in half, which means cutting the pizza into two same-size pieces.)
• Unmute the sound and have the child select “done” to complete the round and get the next pizza order.
When two or four characters share a pizza:
• Ask: How much pizza does each character want? (half of, quarter of, or fourth of a pizza)
• Call on one child to put toppings on the first part of the pizza.
• Before a child selects “done,” mute the sound and ask the child to use precise math vocabulary to describe how s/he shared the
toppings. For example: “There are six olives on cow’s half of the pizza.”
• Unmute the sound and have the child select “done.”
Repeat this process with the other parts of the pizza, each time prompting children to describe the pizza using precise fractional
vocabulary.
When most children are using the vocabulary correctly, stop playing and ask:
• How many halves in a whole? (two halves in a whole)
• How many fourths or quarters in a whole? (four fourths or quarters in a whole)
13
Lesson 1: Explore with a Friend
Contents
Learning Center Time: 10 minutes
Option 1: To provide additional practice using fraction words, set up a learning center at
the computer or on tablets with the game Peg’s Pizza Place.
Tell children to take turns placing the toppings. Prompt them to use precise math
vocabulary by asking:
• How many same-size pieces is the pizza divided into? (two or four)
• What is the size of each piece of pizza? (half, fourth/quarter)
• How much of the pizza will each character get? (a half of, a fourth of, or a quarter of
the pizza)
Option 2: To provide additional practice understanding that halves and fourths/quarters
need to be same-size pieces of a whole, set up a learning center at the interactive
whiteboard with the SMART Notebook™ file called Sorting–Fractions.
As you observe children sort, prompt them to notice and name the parts of each whole
by asking: How do you know where this shape goes? Answers might include: “These two
same-size pieces make up the whole, so they are halves.” “These four pieces are not
precisely the same size so they aren’t fourths.”
Option 3: To reinforce ideas related to dividing items into equal-size pieces and using
precise fraction words to describe the pieces, create a learning center where children
can read and discuss children’s books. Suggestions include:
• Full House: An Invitation to Fractions, by Dayle Ann Dodds
• Give Me Half!, by Stuart J. Murphy
• If You Were a Fraction, by Trisha Speed Shaskan
Differentiated Learning
Use Option 1 for children who need
additional practice using fraction
words. Most children will be able to
play the game successfully on their
own. Use Option 2 to provide additional
challenge. Consider which children will
be able to complete the task on their
own and which will need teacher
guidance, then group them accordingly.
Use Option 3 to provide all children
with opportunities to learn more about
fractions and fraction vocabulary
through reading. As you assign
children to this learning center, remind
them to connect what they have
learned about fractions and fraction
words as they read and respond to
the books.
14
Lesson 1: Review, Connect, Reflect
Contents
Time: 5 minutes
To support children’s independent learning, review the lesson’s key concepts. Ask:
• If two friends want to share a pizza equally, what can they do? (divide it into two
halves)
• If four friends want to share a pizza equally, what can they do? (divide it into four
fourths or quarters)
To connect to home:
• Tell children: When you are sharing foods such as pizza, cake, or fruit, divide the
items into equal pieces and practice using precise words such as half, fourth, or
quarter with your parents, siblings, or friends to describe each person’s share.
• Help parents support children's use of these ideas and strategies by sending the parent
letter home with children.
Teacher Reflection
• Did most children use fractional
vocabulary (half, fourth,
quarter)? If not, review the words
briefly and use them repeatedly
when you play this game and do
other activities. Prompt children to
use the words on their own.
• Were most children able to use
technology to play the game
successfully at a learning center?
If not, preview game screens to
explain what children will do.
Point out features such as
selecting objects, moving objects,
and repeating game instructions.
• Did you stay within the
recommended time limits? If not,
review brisk pacing routines to
see if these might help (page 4).
15
Contents
Contents
Lesson 2: Preview
Helpful Background
The lesson focuses on the fractional units of
one-half, one-third, and one-fourth. In some
rounds of the game Make the Cake,
children divide the cake into sixths.
Video: Hungry Pirates (2:44)
Preview the video: pbskids.org/peg/videos/
hungry-pirates
When the pirates start fighting over a pile of
peaches, Peg asks Ramone to help divide
them up fairly so that everyone gets the
same number. Ramone explains that it’s like
dealing cards, giving one to each player at
a time so that everyone ends up with the
same number of cards.
Peg collects all 16 peaches from the four
pirates and distributes them one at a time to
each pirate until they all have four peaches.
In the end, the pirates are happy that
“nobody got less, nobody got more,”
everybody got their fair share.
Game: Make the Cake
Preview the game:
pbskids.org/peg/games/make-the-cake
Players help Cat make birthday cakes. First,
they choose the cake: ice cream, chocolate,
or honey. Then they cut the cake into two,
three, four, or six same-size pieces. After the
cake is cut, Cat tells players that each piece
is one-half, one-third, one-quarter, or onesixth of the cake.
Next, players place an equal number of
toppings and candles on each piece to
practice fair sharing. They click on the
finished cake for the birthday guest to blow
out the candles. Then the pieces are
distributed to everyone at the party.
Create this classroom chart to help children
gain familiarity with fractional units.
Display it near the learning center for use
during Explore with a Friend.
Fraction Words
halves
thirds
fourths
quarters
16
Contents
Lesson 2: Big Idea
Big Idea
Develop Understanding
1. Develop understanding of
fair sharing by watching a
video.
2. Extend understanding of
fractions and the fraction
word thirds by interacting
with virtual and real pattern
blocks.
Objects can be
partitioned into two,
three, or four equal
shares and these shares
can be described using
the words halves, thirds,
fourths, half of, third of,
quarter or fourth of.
Key Vocabulary
fraction
thirds
sixths
cranky
fair
share
flavor
Apply Understanding
1. Apply understanding of fair
sharing and precise fraction
vocabulary by playing a
game with teacher guidance.
2. Deepen understanding of fair
sharing and fractions by
playing a game, doing an
interactive whiteboard
activity, or reading and
responding to books with a
friend.
Make sure to:
• Encourage children to share their reasoning about fractions by asking: How do you know?
• Emphasize that a whole cut into halves is made up of two same-size pieces, a whole cut into fourths/quarters is
made up of four same-size pieces, and a whole cut into thirds is made up of three same-size pieces.
17
Contents
Lesson 2: Objectives
Watch Together
Introduce or review math concepts
and hear new vocabulary in
context.
Build Background
Activate and build children’s
background knowledge.
Get Ready to Play
Preview the game.
Play Together
Play a teacher-led game.
Explore with a Friend
Practice with one or more partners
at a learning center.
Review, Connect, Reflect
Review big idea, connect to home,
and evaluate student learning.
In this lesson, children will:
• construct viable arguments and critique the reasoning of others
(mathematical practice)
• partition circles into two, three, four, or six equal shares
• describe shares using the words fraction, halves, half of, thirds, a
third of, fourths, a fourth of, sixths, a sixth of
• describe the whole as two halves, three thirds, four fourths/
quarters, or six sixths
• acquire and use new vocabulary and concepts, such as cranky,
fair, share, and flavor
• read and respond to books about fractions
• use technology to learn, working individually and in groups
18
Contents
Lesson 2: Watch Together
Time: 5 minutes
Teacher Prep
1. Open the Hungry Pirates video.
pbskids.org/peg/videos/hungry-pirates
2. Gather a set of pattern blocks for each
pair of children, including 1 hexagon, 2
trapezoids, 3 blue rhombi, and 3 triangles.
3. Open the SMART Notebook™ file called
Pattern Blocks. Minimize the file to place it
on the dock for easy access.
4. Open the game Make the Cake and
minimize the file.
pbskids.org/peg/games/make-the-cake
5. If you plan to use tablets, set them up
with the game Make the Cake. Mute the
sound for use in Play Together.
6. Create the Fraction Words classroom
chart (see page 16).
To introduce the idea of fair sharing, display the Hungry Pirates video. Before watching,
tell children that in the video:
• The pirates are very hungry and this makes them very cranky—that means grumpy or
angry.
• They are fighting over who gets the peaches that fell from a tree.
• Ramone tells them they must share fairly—each person must get an equal number of
peaches—and shows them how to divide the peaches equally.
To set a purpose, tell children that after they watch, you will ask them to tell you what
Ramone taught the pirates to do to fairly share. Play the video.
To deepen understanding, after watching the video, ask:
• What did Ramone teach the pirates to do so that everyone got a fair share? (They
divided up the peaches equally by giving each person one at a time until all the
peaches were gone.)
• Why do you think it’s called fair sharing? (Because everyone gets the same number or
amount.)
Close the video.
7. At a learning center, set up the game
Make the Cake or Fractions Splat:
www.sheppardsoftware.com/mathgames/
earlymath/fractions_shoot.swf
19
Contents
Lesson 2: Build Background
Time: 10 minutes
To deepen understanding of fractions and introduce thirds, display the SMART Notebook™ file called Pattern Blocks. Explain that
sometimes, to fairly share, one whole object needs to be divided into smaller, equal parts.
To demonstrate with halves:
• Drag a hexagon into the center of the whiteboard. Then drag two trapezoids onto the screen.
• As you fit each trapezoid onto half of the hexagon (rotating as needed), tell children that when we divide a whole object into two
equal-size parts, each part, or fraction, is called a half. Ask:
—How many trapezoids make up one whole hexagon? (two)
—How many halves make up a whole? (two)
—What fraction of the hexagon is one trapezoid? (one-half)
To provide guided practice with thirds:
• Pass out a set of pattern blocks (1 hexagon, 2 trapezoids, 3 blue rhombi, and 3 triangles) to each pair of children, and explain that
they will figure out how to divide the hexagon into three same-size parts, or thirds.
• Tell children to work with their partners to find the shape that is a third of the hexagon and to test their choice by placing three on top
of the hexagon. Remind them that three of the correct shape will cover the whole hexagon.
• Invite a pair to the whiteboard to place three rhombi on top of a hexagon (they will need to rotate rhombi they drag from the bottom
of the screen).
• Ask: What shape is a third of the hexagon? (rhombus) How do you know? (Three rhombi cover up the whole hexagon.)
Explain that when we divide a whole into even smaller same-size pieces, we use other fraction words to describe each. For example,
when a whole is divided into four same-size pieces, each is one fourth or one quarter; if we make six same-size pieces, each is one
sixth.
Close the Pattern Blocks file.
20
Contents
Lesson 2: Get Ready to Play
Time: 5 minutes
To develop understanding of fair sharing, display the game Make the Cake.
Describe the purpose of the game.
• Press play and listen to Cat’s introduction.
• Remind children that they will be making birthday cakes for Peg and her friends.
Connect the game to prior lesson segments.
• Explain that the children will use what they learned about dividing wholes into equalsize pieces to fairly share a cake and toppings.
Explain the technology features of the game.
• Point to each cake and name the three flavors: ice cream (the pink one), chocolate
(brown), and honey (yellow).
• Invite one child to the whiteboard to choose a cake, and ask the child to name the
flavor before touching the screen to make the selection.
• Next, point to and name the fruit toppings (raspberries, blueberries, strawberries).
Invite another child to choose (and name) a topping.
• Mute the sound and tell children that as they play the game, they must listen carefully
to Cat’s instructions. Cat will tell them how many guests at the party will share the
cake, how to cut the cake, and how to fairly share the fruit toppings and candles.
Tablet Option: As some children play the game at the whiteboard, pairs can play along
on a tablet. Before distributing the tablets, mute the sound (to avoid competing sounds).
Instruct children to make the same choices that children at the board make.
21
Contents
Lesson 2: Play Together
Time: 10 minutes
Relaunch the game to start it from the beginning. Listen to Cat’s introduction, then invite four children to the whiteboard.
• Have one child choose the cake flavor, another choose the topping, and a third cut the cake (then these three children can return to
their seats).
• Mute the sound after listening to Cat’s instructions for placing the toppings, and ask:
— What size pieces did we cut the cake into? (halves, thirds, fourths/quarters, or sixths)
— How do you know? (e.g., two same-size pieces are halves)
— How much cake will each guest get? (one-half, one-third, one-fourth/quarter, or one-sixth)
To support children’s understanding of fair sharing and emphasize reasoning:
• Have children tell their partners what they will do to fairly share the fruit toppings. After about ten seconds, ask a child to share the
strategy (move one topping at a time onto each piece of cake until there are no more left) .
• Unmute the sound and have the child at the board fairly share the toppings and the candles on the cake. Before the child presses the
checkmark, mute the sound and ask:
— How many [blueberries] were there in all? (e.g., four)
— When you fairly shared, how many [blueberries] did you put on each [half]? (e.g., two)
• Model using fraction words to describe parts of a whole (e.g., two is one-half of four).
To play again, unmute the sound. Have the child press the check mark and touch the cake to blow out the candles. Select the purple
button (with the round arrow) and invite different children to the board for each round.
When most children are fairly sharing, end the game and review key concepts. Ask:
• What is fair sharing? (giving each person an equal number of objects or equal parts of a whole)
• If we divide an object into [two, three, four, six] same-size pieces, what is the size of one of those pieces? (a half, third, fourth or
quarter, sixth)
22
Lesson 2: Explore with a Friend
Contents
Learning Center Time: 10 minutes
Option 1: To provide practice with fair sharing, set up a learning center at the interactive whiteboard,
computer, or tablet where a pair or small group of children can play the game Make the Cake. Tell
children to take turns following each of Cat’s instructions. Remind them (and prompt as necessary) to
use fraction words (half, third, fourth, quarter, sixth) to describe each same-size piece.
Option 2: To provide practice associating fraction words with the number of parts in a whole, set up the
game Fractions Splat at the whiteboard or computer: www.sheppardsoftware.com/mathgames/
earlymath/fractions_shoot.swf
• Explain to children that to play this game they need to take turns selecting a picture that matches
each fraction word; they can use the Fraction Words chart (see page 16) to help remember what
each word means.
• Set up the game by choosing HALVES, THIRDS, AND FOURTHS, then select Relaxed mode/SLOW.
Play one round of the game to demonstrate how to play.
• Show children how to start a new round (select PLAY AGAIN, then choose the second game and
Relaxed mode/SLOW).
• As children play, ask them which fraction they’re looking for and how they know which picture to
choose.
Option 3: To reinforce ideas related to dividing items into equal-size pieces and using precise fraction
words to describe the pieces, create a learning center where children can read and discuss children’s
books. Suggestions include:
• Apple Fractions, by Jerry Pallotta
• Fractions, by Sara Pistoia
• Jump, Kangaroo, Jump!, by Stuart J. Murphy
Differentiated Learning
Use Option 1 for children who
need additional practice
understanding the concept of
fair sharing. Most children will
be able to play the game
successfully on their own.
Use Option 2 to provide
children with practice
associating fraction words with
the number of parts of a
whole. Consider which children
will be able to complete the
task on their own and which
will need teacher guidance,
then group them accordingly.
Use Option 3 to provide all
children with opportunities to
learn more about fractions and
fraction vocabulary through
reading. As you assign children
to this learning center, remind
them to connect what they
have learned about fractions
and fraction words as they
read and respond to the books.
23
Lesson 2: Review, Connect, Reflect
Contents
Time: 5 minutes
To support children’s independent learning, review the lesson’s key concepts. Remind
children that knowing how to divide objects into same-size pieces helps to fairly share.
To connect to home:
• Tell children: When you share a group of objects, use the strategy of distributing one
at a time to make sure it’s fair and everyone gets the same number. When you need
to share a whole object, divide the whole into same-size pieces to fairly share.
• Help parents support children's use of these ideas and strategies by sending the parent
letter home with children.
Teacher Reflection
• Did most children fairly share? If
not, watch Hungry Pirates again,
emphasizing and discussing the
strategy for fair sharing (page
19). Alternatively, play the game
Make the Cake again, together
or at a learning center.
• Did most children use new
vocabulary correctly (cranky, fair,
share, thirds, sixths, flavor) during
and after this lesson? If not,
review the words briefly and use
them repeatedly in this lesson and
other activities. Prompt children to
use the words on their own.
• Did most children remain
engaged throughout the lesson? If
not, review routines to engage all
children to see if these might help
(page 4).
24
Lesson 3: Preview
Contents
Helpful Background
This lesson focuses on unit fractions. Unit
fractions always have a numerator of 1
(e.g., 1/2, 1/3, 1/4, 1/6). Children will
work with unit fractions in several ways:
• They will be introduced to fraction
notation in a sorting activity.
Video: Peg and Cat Estimate (2:08)
Preview the video: pbskids.org/peg/videos/
peg-and-cat-estimate
Game: Bubble Bath
Preview the game:
pbskids.org/peg/games/bubble-bath
Peg and Cat need more bins for the piles of
metal, plastic, and paper that need to go to
the recycling center. They don’t know how
many more bins they need, but counting
every bottle, can, and carton will take too
long. Ramone tells Peg she can estimate by
making a careful guess. She compares the
size of each pile to the size of the bin.
Peg is having a bubble party and needs help
filling the tub. Players choose a container—
such as a cup, bowl, jar, pail, or pitcher—to
pour water into the tub. One container of
water is poured into the tub to show how
much of the tub it fills.
.
Peg estimates that the metal pile is about the
same size as the bin, the plastic pile is about
as big as two bins, and the paper pile is
about the same size as three bins. Ramone
delivers the bins; thanks to Peg’s good
estimates, it all fits.
• They will learn to identify the numerator
as the number of shaded parts in a
whole and the denominator as the
number of same-size parts in the whole.
• After watching Peg and Cat Estimate,
children will use unit fractions to
describe what fraction of the recyclables
fit in each bin. As they play Bubble
Bath, children will use unit fractions to
describe what fraction of the whole tub
each container fills.
Players then estimate how many of those
containers they need to fill the tub, selecting
one of three choices. After they pour each
container, a dotted line shows how much of
the tub it filled. If players choose too few,
more containers are added. If they choose
too many, the tub overflows. Players may get
a bath toy after estimating correctly.
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Contents
Lesson 3: Big Idea
Big Idea
Develop Understanding
1. Develop understanding of
the vocabulary numerator
and denominator and
demonstrate their meaning
by doing an interactive
whiteboard activity.
2. Develop understanding of
the use of unit fractions to
describe parts of the whole
by watching a video.
Objects can be
partitioned into two,
three, or four equal
shares and these shares
can be described using
the words halves, thirds,
fourths, half of, third of,
quarter or fourth of.
Key Vocabulary
denominator bin
numerator
container
recyclables
Apply Understanding
1. Use unit fractions to describe
a fraction of a whole by
playing a game with teacher
guidance.
2. Use unit fractions to describe
a fraction of a whole by
playing a game, doing an
interactive whiteboard
activity, or reading and
responding to books with a
friend.
Make sure to:
• Encourage children to describe what the numerator and denominator represent when using fraction notation.
• Help children connect fraction notation with fraction vocabulary (e.g., one-half, one-third, one-fourth).
26
Contents
Lesson 3: Objectives
Build Background
Activate and build children’s
background knowledge.
Watch Together
Introduce or review math concepts
and hear new vocabulary in
context.
Get Ready to Play
In this lesson, children will:
• make sense of problems and persevere in solving them
(mathematical practice)
• construct viable arguments and critique the reasoning of others
(mathematical practice)
Preview the game.
• recognize and use fraction notation (e.g., ⅓)
Play Together
• describe fractions using precise language such as one-half, onethird, one-fourth, denominator, and numerator
Play a teacher-led game.
Explore with a Friend
• practice estimating
Practice with one or more partners
at a learning center.
• acquire and use new vocabulary and concepts, such as
recyclables, bin, and container
Review, Connect, Reflect
• read and respond to books about fractions
Review big idea, connect to home,
and evaluate student learning.
• use technology to learn, working individually and in groups
27
Lesson 3: Build Background, Part 1
Contents
Time: 10 minutes
Teacher Prep
1. Open two SMART Notebook™ files, Sorting–
Unit Fractions and Vocab–Fraction Notation.
Minimize the second file to place it on the dock.
2. Open the video Peg and Cat Estimate. Pause
the video and minimize it, to place it on the dock.
pbskids.org/peg/videos/peg-and-cat-estimate
3. Gather individual whiteboards and markers for
pairs of children to use while playing the game.
To review the words half/halves, display the Sorting–Unit Fractions file.
• Point to the circles in the three boxes and remind children that when
whole objects are divided into equal-size parts, we call each part a
fraction.
• Point to the circle divided into halves. Ask: How many halves are in
one whole? (two)
• Point to the shaded half and ask: How much of the whole does this
part represent? (one-half)
To demonstrate connecting fraction notation with fraction vocabulary:
4. Open the game Bubble Bath and minimize the
file. pbskids.org/peg/games/bubble-bath
• Point to the “½” and tell children that this is how to write the fraction
“one-half” with numbers. Explain that the bottom number is the
denominator, which tells how many parts make up the whole; in this
example, there are 2 halves in a whole so the denominator is 2.
5. Set up the Bubble Bath game and/or the online
game Fractions Splat at a learning center.
www.sheppardsoftware.com/mathgames/
earlymath/fractions_shoot.swf
• Explain that the top number is the numerator, which tells the number
of parts of the whole that you have or are working with. Point out that
in this example the numerator represents the parts that are shaded
and so this numerator is 1.
6. If you plan to use tablets in Explore with a
Friend, set them up with the Bubble Bath game.
28
Lesson 3: Build Background, Part 2
Contents
Time: 10 minutes
To provide guided practice:
Sorting–Unit Fractions
• Point to the notation “⅓” and tell children that this fraction means one-third. Then ask:
—What does the numeral 3, the denominator, represent in this fraction?
(the number of same-size parts that the whole is divided into)
—What does the numeral 1, the numerator, represent?
(the number of shaded parts)
• Repeat these steps for “¼,” explaining that this fraction means one-fourth or quarter.
• Call children’s attention to the shapes along the bottom. Explain that they will sort the
shapes by figuring out what part of the whole each represents. Point out that some
pieces do not represent one-half, one-third, or one-fourth (or quarter) and that those
shapes should be sorted into the box titled “other.”
• Point to one of the shapes and tell children to turn and tell their partners the name of
the shaded part using the correct fraction word.
—Next, invite a child to come to the whiteboard to move the shape to the
appropriate box.
—Ask: How did you know where to put the shape? (e.g, “I put it in the one-third
section because it is divided into three equal parts and one part is shaded in.”)
• Repeat these steps until all pieces are sorted, inviting different children to name the
shaded part using the correct fraction word and to move the shape to the appropriate
box.
Close the Sorting–Unit Fractions file.
29
Contents
Lesson 3: Watch Together
Time: 10 minutes
To create a context for the use of unit fractions, display the video Peg and Cat
Estimate. Explain that Peg and Cat are packing up recyclables—used items such as
metal, plastic, and paper that can be used again or turned into something else. Peg
and Cat must estimate how many recycle bins—or containers—they need to pack up
each kind of recyclable. Remind children that an estimate is a careful guess.
To set a purpose, tell children that after they watch, you will ask them to tell you
how many more bins Cat needed for each pile of recyclables. Play the video.
After viewing, ask: How many bins did Peg and Cat need for each type of
recyclable? (1 for metal, 2 for plastic, 3 for paper) Close the video.
To support children’s use of unit fractions, display the Vocab–Fraction Notation file.
• Point to the image of the two bins of plastic recyclables and say: Peg filled two
whole bins with plastic recyclables. What fraction does one of these bins
represent? (½)
Vocab–Fraction Notation
• Invite a child to write ½ in the space below each bin of plastics. Point out the
denominator and the numerator and ask children to turn and tell their partners
what each means.
• Call on a child to share the answer. (The denominator means that 2 bins equals
the whole pile of plastics; the numerator means that 1 bin equals one half the pile
of plastics.)
• Repeat these steps for the pile of paper recyclables.
Close the Vocab–Fraction Notation file.
30
Contents
Lesson 3: Get Ready to Play
Time: 5 minutes
To support children’s use of unit fractions, display the game Bubble Bath. Tell children
they will estimate how many containers they need to fill the whole tub with water; then
they will identify the fraction that shows how much of the tub one container filled.
Describe the purpose of the game.
• Press play and listen to the instructions from Peg’s mom.
• Remind children that Peg is having a bubble party and wants help filling the tub with
water using different kinds of containers, such as cups, bowls, and buckets.
Connect the game to previous lesson segments.
• Explain that as they did after watching the Peg and Cat Estimate video, they will use
fractions to describe how much of the tub is filled by one container.
Review the technology features of the game.
• Invite a child to the whiteboard to choose a container to fill the tub. Then, have the
child touch the container to pour water into the tub.
• After the numbers for estimating how many containers are displayed, mute the sound.
• Point to the dashed line on the tub and say: When we play this game, we will use a
fraction to describe how much of the tub the container will fill.
Distribute individual whiteboards with markers and tell children they will use these to
write the fraction.
31
Contents
Lesson 3: Play Together
Time: 10 minutes
Reload the game to start a new round. Invite two children to the whiteboard. Have one child select a container.
To support children in estimating and explaining their reasoning:
• Have children turn and tell their partners how many [name of container] they estimate are needed to fill the tub and why they think
that’s a good guess. After a few seconds, call on a child to share the estimate and reasoning.
• Ask the class to show thumbs up if they agree or thumbs down if they don’t.
To encourage children to use unit fractions to estimate amounts:
• Have the second child tap the suggested number. When the containers are displayed along the bottom of the screen, ask: If the answer
is correct and it takes [three pitchers] to fill the tub, what fraction of the tub will one [pitcher] fill?
• Have children write this fraction on their individual whiteboards. Then have the two children at the whiteboard take turns tapping each
container to fill the tub.
To support children in checking their estimates:
• If the answer is correct, ask: How many [pitchers] filled the tub? Then say, for example: Three—so one [pitcher] equals one-third of the
whole.
• If the estimate is too low, have the children continue to select containers until the tub is full. Then say: We needed four [pitchers], not
three. So, one [pitcher] represents one-fourth or one-quarter. Have a child write the correct fraction.
• If the estimate is too high, the tub will clear and you will need to provide the correct information. For example, say: We needed only
two [pitchers] to fill the tub. So, what fraction of the whole tub does one [pitcher] represent? Have a child write the correct fraction.
Continue playing until most children are estimating correctly and using the correct fraction, inviting different children to the whiteboard for
each round. Remind children that they can describe same-size pieces of a whole using fraction words (such as half or halves) or by writing
a fraction (such as ½).
32
Lesson 3: Explore with a Friend
Contents
Time: 10 minutes
Differentiated Learning
Option 1: To provide practice with estimating and using fractions to describe part of a whole, set up a
learning center with the interactive whiteboard, computer, or tablets where a pair or small group of
children can play Bubble Bath. Tell children to take turns following the instructions from Peg’s mom.
• As children play, remind them (and prompt as necessary) to estimate how many containers are
needed to fill the tub and ask how they know.
• Ask: What fraction of the tub does that container fill? How do you know?
Option 2: To provide practice associating fraction words with the number of parts in a whole, set up the
game Fractions Splat at the whiteboard or computer.
• Explain to children that to play this game they need to take turns selecting a picture that matches
each fraction word; they can use the Fraction Words chart (see page 16) to help remember what
each word means.
• Set up the game by choosing HALVES, THIRDS, AND FOURTHS, then select Relaxed mode/SLOW.
Play one round of the game to demonstrate how to play.
• Show children how to start a new round (select PLAY AGAIN, then choose the second game and
Relaxed mode/SLOW).
• As children play, ask which fraction they’re looking for and how they know which picture to choose.
Option 3: To reinforce ideas related to associating fraction words with the number of parts in a whole,
create a learning center where children can read and discuss children’s books such as:
• A Fraction’s Goal—Parts of a Whole, by Brian P. Cleary
• Fractions, by Sara Pistoia
• Fraction Fun, by David A. Adler
Use Option 1 for children who
need additional practice
estimating and using fractions
to describe a part of a whole.
Most children will be able to
play the game successfully on
their own.
Use Option 2 to provide
children practice associating
fraction words with number of
parts of a whole. Consider
which children will be able to
complete the task on their own
and which will need teacher
guidance, then group them
accordingly.
Use Option 3 to provide all
children opportunities to learn
more about fractions and
fraction vocabulary through
reading. As you assign children
to this learning center, remind
them to connect what they
have learned about fractions
and fraction words as they
read and respond to the books.
33
Lesson 3: Review, Connect, Reflect
Contents
Time: 10 minutes
To support children’s independent learning, review the lesson’s key concepts.
Remind children that they can describe same-size pieces of a whole using fraction words
(such as half or halves) or by writing a fraction (such as ½). Ask:
• When we write numbers with fractions, what does the numerator—the number on the
top—tell us? (how many parts of the whole)
• What does the denominator tell us? (the total number of equal-size parts in the whole)
To connect to home:
• Tell children: Fractions are often used in cooking recipes. When you help your family
cook, you can use what you know about fractions to gather the right amount of an
ingredient.
• Help parents support children's use of these ideas and strategies by sending the parent
letter home with children.
Teacher Reflection
• Did most children make a careful
estimate of how many containers
were needed? If not, watch the
video Peg and Cat Estimate again
and emphasize strategies for
estimating.
• Did most children express “how
much?” with fractions? If not, use
the Sort–Unit Fractions file to
review fractions. Prompt children
to use fraction words (e.g., onehalf, one-third) and notation (e.g.,
½, ⅓) to express and write how
much one part of a whole is.
• Did most children use new
vocabulary throughout the lesson?
If not, review the Teaching
Routines for using key vocabulary
frequently (page 5) to see if these
strategies help.
34
Alignment to CCSS: Mathematics
Contents
Lesson 1
Lesson 2
Lesson 3
•
•
Geometry
1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using
the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.
Describe the whole as two of, or four of the shares. Understand for these examples that
decomposing into more equal shares creates smaller shares.
•
2.G.A.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.
Mathematical Practice
•
MP1 Make sense of problems and persevere in solving them.
•
MP3 Construct viable arguments and critique the reasoning of others.
MP6 Attend to precision.
•
•
•
35
Alignment to CCSS: English Language Arts
Contents
Lesson 1
Lesson 2
Lesson 3
L.1.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based
on grade 1 reading and content, choosing flexibly from an array of strategies.
•
•
•
L.1.5 With guidance and support from adults, demonstrate understanding of word relationships and
nuances in word meanings.
•
•
•
L.1.6 Use words and phrases acquired through conversations, reading and being read to, and
responding to texts, including using frequently occurring conjunctions to signal simple relationships
(e.g., because).
•
•
•
Vocabulary Acquisition and Use
36
Alignment to ISTE Technology Standards: Students
Contents
Lesson 1
Lesson 2
Lesson 3
a. Interact, collaborate, and publish with peers, experts, or others employing a variety of digital
environments and media.
•
•
•
d. Contribute to project teams to produce original works or solve problems.
•
•
•
•
•
•
a. Advocate and practice safe, legal, and responsible use of information and technology.
•
•
•
b. Exhibit a positive attitude toward using technology that supports collaboration, learning, and
productivity.
•
•
•
a. Understand and use technology systems.
•
•
•
b. Select and use applications effectively and productively.
•
•
•
2. Communication and Collaboration
4. Critical Thinking, Problem Solving, and Decision Making
b. Plan and manage activities to develop a solution or complete a project.
5. Digital Citizenship
6. Technology Operations and Concepts
37
Alignment to ISTE Technology Standards: Teachers
Contents
Lesson 1
Lesson 2
Lesson 3
c. Promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and
thinking, planning, and creative processes.
•
•
•
•
•
•
d. Model collaborative knowledge construction by engaging in learning with students, colleagues, and others in faceto-face and virtual environments.
•
•
•
a. Design or adapt relevant learning experiences that incorporate digital tools and resources to promote student
learning and creativity.
•
•
•
b. Develop technology-enriched learning environments that enable all students to pursue their individual curiosities
and become active participants in setting their own educational goals, managing their own learning, and assessing
their own progress.
•
•
•
a. Demonstrate fluency in technology systems and the transfer of current knowledge to new technologies and
situations.
•
•
•
b. Collaborate with students, peers, parents, and community members using digital tools and resources to support
student success and innovation.
•
•
•
c. Communicate relevant information and ideas effectively to students, parents, and peers using a variety of digitalage media and formats.
•
•
•
•
•
•
1. Facilitate and Inspire Student Learning and Creativity
a. Promote, support, and model creative and innovative thinking and inventiveness.
2. Design and Develop Digital-Age Learning Experiences and Assessments
3. Model Digital-Age Work and Learning
4. Promote and Model Digital Citizenship and Responsibility
c. Promote and model digital etiquette and responsible social interactions related to the use of technology and
information.
38
Credits
Contents
These lessons were developed by PBS in partnership with the Boston University School of Education.
Boston University
Dr. Jeanne R. Paratore, Professor of Education and Program Director
Reading/Literacy and Language Education
Dr. Alejandra Salinas, Assistant Professor, Math Education
Dr. Lisa M. O’Brien, Post-Doctoral Fellow, Language and Literacy
Chu Ly, Doctoral Candidate, Literacy and Language Education
Consulting Producer and Editor
Beth Kirsch
Peg + Cat @ 2015, Feline Features LLC
SMART Notebook is a trademark of SMART Technologies.
The contents of these Teaching Tips were developed under a grant from the U.S. Department of
Education. However, the contents do not necessarily represent the policy of the U.S. Department
of Education, and you should not assume endorsement by the Federal Government.
[PR/Award No. U295A100025, CFDA No. 84.295A]
© 2015 Public Broadcasting Service (PBS). All rights reserved.
39