Pre-Instructional Assessment
Lesson Part
Activity Description/Teacher Does
Pre-Assessment
(20 minutes)
“The pre-test for this chapter is going to look a little
different, I want you to try your best, and I need
you to use a model on every problem.”
If students turn it without attempting models, send
them back for a second look.
Students do
Give students 20 minutes to
take the examination, with
the opportunity for additional
10 during computer pod time
(if necessary).
Lesson Outline
Lesson Part
Title:
Lesson Length:
Materials:
Standard:
Central Focus:
Learning Target:
Academic
Language:
Instruction
Inquiry
Introduce
Posters
(2 minutes)
(Posted for duration
of unit)
Activity Description/Teacher Does
Students do
Lesson 1
60 minutes
Student whiteboards, blank paper, magnetic circle models (teacher set), “Shading
Fractions” worksheet (2 pages), poster paper (2 posters: One with 4 quadrants
and one for Questions), exit slip.
CCSS.MATH.CONTENT.5.NF.A.1
Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an
equivalent sum or difference of fractions with like denominators. For example, 2/3
+ 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
Students will add fractions with unlike denominators by using a variety of
strategies and models to produce equivalent fractions with like denominators.
Students will solidify and unify conceptual understanding of what a fraction is to
both represent fractions and add fractions with like denominators on one model.
Numerator, denominator, equal parts, part, whole, shade, overflow fraction, mixed
number, common denominator, model, number line, represents
“I am very impressed by what you all knew on
yesterday’s “Show What you Know” quiz. Today
we are going to build upon what you already know
about fractions, and we will be using models to
build, identify and add fractions with like
denominators.”
“We are going to learn a lot of new things about
fractions, and I want to have a place where we can
put everything we know, and add everything that
we learn”
Encourage students to get up and read and/or
contribute to these posters throughout the unit.
Get out a blank sheet of
paper and a pencil. Put your
name on it, but do nothing
else.
Tell students:
“I want you to add to these
two posters whenever you
learn something knew. As
long one of your classmates
or I are not talking, feel free
to stand up and add to the
poster during individual work
time. I also want you to read
Word Wall
(Same for all
lessons)
Household
Makeup
(5 minutes)
Create a large space for a “Word Wall” on the
whiteboard, where key vocabulary will appear for
student reference. Add words as they come up in
context, and discuss the words in detail. Have the
class echo chant the word, show a model (if
possible) and have at least one student repeat the
definition in his or her own words. When students
discuss concepts, be sure that they use this
academic vocabulary in context. If words are not
being used, reference the word wall by pointing
and ask “How can you say that like a
mathematician?” Hereafter such words will appear
in bold. These words should be discussed in the
same way and added to the word wall as they
come up in context.
Fractions in both notation (# form) and model form
represent real things, and have real value. For
example:
Sentence Frame:
“There are ____ people in my family. ____ of them
are girls. So, ____ of my family are girls”
what other people have said.
If you see your idea already
on the poster, put a check
mark next to it to show that
you agree.”
Students will use the word
wall for reference when
talking with elbow partners,
in small groups, or in largegroup discussion.
Word wall will be erased at
the end of every day.
Have students use this
sentence frame to complete
the sentence with their own
families. Encourage
discussion of how different
families have different sized
wholes.
Model your own household makeup for the class
using the sentence frame:
“There are 4 people in my family. 3 of
them are girls. ! of my family are girls”
What does the numerator represent?
The total number of what we are concerned with
(girls).
What does the denominator represent?
The total number in the whole unit (total people).
Guide students to the class consensus that the
numerator represents the parts out of a whole.
Show what you
know
(10 minutes)
What if the whole changes?
Q: “What if I’m going to get a little brother soon, do
I count them?”
A: “You may, but what happens to the size of your
whole family when that happens?”
Write the following statements on the whiteboard:
1. “I know/think a fraction is"”
2. “I know/think a fraction has"”
3. “I can represent the fraction with these
models"”
Students will write at least
three bullets per statement,
and should draw at least
three different
representations.
*A model is a picture representation of a fraction.
Give students 5 minutes to respond on a piece of
Encourage those who claim
blank paper.
After 5 minutes, have students share what they
wrote and drew with their elbow partners.
Direct Instruction
(5 minutes)
Circulate the room and take pictures of some
models to project via “AirServer”
“My favorite no”
(3 minutes)
Be sure to show examples of the following models:
array (area model), bar graph, number line, group.
(Whether or not you saw it when circulating the
room) draw a model with unequally partitioned
Mystery Pizza
(5 minutes)
“Shading
Fractions”
Activity
#1-4 only
(5 minutes)
pieces
.
Ask students:
“Which “third” do you want?” and “Does this
model represent thirds? Why or why not?”
Use magnetic circle models ($) on whiteboard.
Place 5 $’s on the board.
Ask students:
“If the pizza was cut into $’s, but there are 5 slices
left on the table, how many pizzas were there to
begin with? What is our whole? How can we write
a fraction in number form to show how much pizza
we have?”
Students may call the fraction improper, rename it
as an overflow fraction, or a mixed number.
Distribute materials (Students elect one
representative to gather a table-set). Have students
complete #1-4 independently, and then discuss
their answers with their elbow partner.
(After 3 minutes) Look at #4 together; see if they
can transfer the concept from “mystery pizza” to
this rectangle model. (Possible misconception: ! )
Elaborate on concept of the whole: “Wholes touch;
if the models do not touch (emphasize the gap
between the two models) it means there are two
separate wholes. On #4, each whole has 2 equal
parts; we have 3 shaded parts out of 2 total parts.
to finish early to explore
more models and
representations.
Ask students to listen to one
another and respond
respectfully.
Sentence frames:
“I know think a fraction
is/has _________”
“My model shows the
fraction ____ because ___
out of the ___ pieces are
shaded”
Have students explain
models using the frame: “My
model shows the fraction
____ because ___ out of the
___ pieces are shaded”
Students should identify that
models have to be split into
equal parts. (That model
shows one # and two $’s.)
Think-pair-share.
Use equity sticks to call on
students to share what the
pair discussed.
Sentence frame:
“Each whole has ___ pieces
in it. There are ___ pieces
left. The fraction must be
____”
Students draw a line below
#4 (visual stopping point for
those who race ahead).
Students will discuss with
their elbow partner to
compare what they wrote for
each model. Pairs should
discuss how they knew;
especially on #4.
Students should continue to
use the sentence frame:
“____ out of the ____ boxes
Our fraction is 3/2”
“Shading
Fractions”
Activity # 5-15
(10 minutes)
Informal
AssessmentWhiteboards
(10 minutes)
Some students have prior understanding of
equivalent fractions; tell those who finish early that
they may:
1. Write 3 equivalent fractions for each model.
First, project Keynote presentation onto board to
model adding fractions on one model.
Adding fractions with a like denominator on one
model.
Students may try to draw two models to represent
both fractions separately, and add the
denominators together. To avoid this, start by
reminding students of the “Household Makeup”
activity. “I represent one person in my family, and
my whole family has 4 people. So, I represent $ of
my family. [Draw a bar model of $]. If I were to
add my sister, she would represent another $ of
my family. [Draw a second bar model of $]. My
sister and I together represent 2/4 of our family,
because the whole (denominator) is still the same
size. I would not add all of these boxes together,
because my whole family is still 4 people.”
1 2
Direct model one problem on whiteboard ( + =),
4 4
and explicitly assign different shading for each
number (ie. $ = solid shading, and 2/4 = polka
dots.)
!
Formal
assessment:
(5 minutes)
Students work in pairs to create and solve addition
problems with like denominators using one model.
(Advanced students may work with fractions with
doubled/unlike denominators).
Administer the Exit Slip for Lesson 1
(Assessments, page 3).
Set timer for 5 minutes. Remind students “this is a
chance to show how you feel about today’s lesson
and show what you can do.”
were shaded, so the model
represents ______”
Students work
independently to complete
shading fractions activity.
Ask for student input in
terms of academic language
and procedure.
Get out whiteboards and
markers.
All students will copy/work
through the model of the first
equation together on
whiteboards.
Ask students to take turns in
pairs thinking of addition
problems (on one
whiteboard) and the partner
will solve on their own. (ie.
one partner writes
Ie: Student A writes
1 2
+
5 5
and Student B draws one
model split into 5 pieces,
and shades appropriately to
solve. The!students assess
the model (ie. equal parts,
different shading) and switch
roles.
Students have 5 minutes to
complete the exit slip.
Direct students to staple the
completed exit slip to the top
of all papers from today’s
lesson and turn the packet
into the “turn in box.”
Lesson Outline
Lesson Part
Title:
Lesson Length:
Materials:
Standard:
Central Focus:
Learning Target:
Academic
Language:
Instruction Inquiry
Word Wall
(2 minutes)
Speaking the
same Language
(10 minutes)
Activity Description/Teacher Does
Students do
Lesson 2
65 minutes
Fraction tiles (student sets), magnetic fraction bars (teacher set), student
whiteboards, “Growing Fractions” activity sheet, “Making Equivalent Fractions”
activity sheet, “Number Line” sheet, exit slip.
CCSS.MATH.CONTENT.5.NF.A.1
Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an
equivalent sum or difference of fractions with like denominators. For example, 2/3
+ 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
Students will add fractions with unlike denominators by using a variety of
strategies and models to produce equivalent fractions with like denominators.
Using prior knowledge of models and equivalent notation, represent equivalent
fractions and add fractions with doubled denominators on one model.
Equal partitioning, equivalent fractions, common denominator, equal sized
wholes, relationship, represent, value, convert, compare.
“Yesterday worked on building models to
represent fractions. Today we are going to use
those models to find equivalent fractions so that
we can add fractions with doubled denominators.”
Gather as many words as they remember from
yesterday.
Ask that students: “Raise your hand if you speak a
language other than English”
“There are so many different languages in this
classroom. What if we couldn’t all speak the same
language? Wouldn’t it be hard to get work done?
Fractions are the same way – sometimes their
denominators are not the same, and we need to
become translators so that they can work together.
Sometimes we need to combine them, sometimes
we need to”
Get out magnetic fraction bars. Put the whole bar
on top, and a # underneath, next to a $ bar
(making !).
Ask students:
“I want to add # and $, what do I have to do first?
Can I add “twourths” or “fwoos”?”
Get out whiteboards,
markers and student fraction
tiles.
Students must provide an
example, model (on
whiteboard), or brief
definition for the words that
they volunteer.
Compare languages in
classroom to fractions with
unlike denominators to
realize that they cannot be
combined without making
them “speak the same
language” or “walk on the
same line.”
Have students experiment
with fraction tiles to see how
many $’s are in #.
Trading in
(5 minutes)
I have to convert # so that it speaks the same
language as $, how can I do that? Which tiles fit?
*Make sure students “trade-in” the tiles
rather than add them to the existing !.
Explore fraction tiles to see which tiles can “speak
the same language” and name this action as
finding common denominators. “What does it
mean when I say Mrs. King and I have something
in common?”
Explore more fractions that
have the same value and
write the new tiles on the
whiteboards.
“Sometimes two things can be equivalent even
when they don’t look the same. Remember when
we worked with equivalent numbers in decimals?
102 is equivalent to 100?”
Whiteboard
Practice –
Strategic/Equal
partitioning
(10 minutes)
When we convert fractions, we make something
called an equivalent fraction. So, look at my
fraction bars. Two $’s fit right on top of one #
model. Could we say that they have the same
value? So, 2/4 = #.
Draw a number line on the board. Stress the
importance of labeling 0 and 1.
When we draw any models, it is important to make
sure that they have equal parts. To make this
happen, it is helpful to have a strategy when we
split them up. We call this strategic partitioning.
(Note: “Guessing” is not a strategy.)
Ask students:
“What do we know about the
parts of fractions?” (looking
for: “equal sized parts”).
“Who knows a strategy I could use to split this
model into $’s? How many lines do we draw to
make 4 parts? You may use your fraction tiles if
you need to.”
Students should partition
models into $’s using a
strategy. Call on one
student to see how they
portioned their model. Ask if
anyone had a different way.
Ask students to partition1/6’s and 1/8’s, following
the same guidelines.
Whiteboard
Practice – Adding
fractions with
doubled
Ask students to copy this
number line down on their
whiteboards.
There is another important piece when it comes to
modeling. What if I wanted to compare two
numbers?
Ask students to compare #
and ! using models and
“pop up” their whiteboards.
Select students who show equal sized wholes
and ask them to come to the front and share.
Ask: “Would you want to wash # of my car,
or # of a school bus? What is the
difference?”
Students solve # + $ *Check for both equal
partitioning and labeling all equivalent fractions.
Ask students to justify their
choice to make the same
size. How does that help us
to compare the fractions?
Ask students to draw a
number line to solve
#+$=
using one model (number
denominators
(5 minutes)
Write
3 1
2 1
= and + = on whiteboard, and
+
5 10
3 6
ask students to solve on their whiteboards and
“pop up” to check.
line only). Ask them to draw
the number line and label all
equivalent fractions.
! Tell students
! to “start by starting with the largest
Growing
Fractions
(15 minutes)
denominator first (ie 1/5’s), and then split it up into
more parts (ie. 1/10’s).
*Potential misunderstanding: Be sure to
mention that the largest denominator will
be the smallest number.
Work on #1 together on whiteboards.
Ask: “How can I shade this so that this
fraction (?/4) has the same value as #?
Introduce rows and columns. Have students label
the rows and columns, AND label each column
with the equivalent fraction as they grow.
Think-Pair-Share: “What do you notice
about the rows and columns?”
*Differentiated
tasks
Students who demonstrated understanding of
equivalent fractions on yesterday’s “Shading
Fractions” worksheet will go to back table
(removed) and work on:
Students who self-identify as unsure of equivalent
fractions, and all students who did not
demonstrate understanding on yesterday’s class
work/exit slip:
Give students “Making Equivalent
Fractions” worksheet
Whiteboard/Direct
Instruction –
Building an area
*Students use this in lieu of growing fractions #1-4.
Come back to seats and discuss the meaning of
equivalent fraction and value and how models
help to find it as a whole group.
*Tell students to only use 1/3 of the whiteboard per
large model
Ask students to draw and
label 1/2, then add two next
to it (“growing” the fraction).
Sentence frame:
“My partner and I noticed
that ________________”
Encourage students to
notice that although the
model is getting bigger, one
full row is always shaded.
Complete “Growing
Fractions” #1-4
Challenge Math: Using
problems on page 255
in the textbook, students
solve addition and
subtraction problems on
any model.
Circulate the posters in
the room: (“Play with
me,” fraction quadrant
and/or questions) – no
more than 2 students at
any poster.
Students work for 3 minutes
to “play” with worksheet,
partitioning fractions and
labeling them with
equivalent fractions.
3 minutes to discuss
observations with a partner.
Call on students using
equity sticks.
Get whiteboards and
markers out.
model
(5 minutes)
Students will use one large rectangle model to
partition the model to show $ and 1/3, thereby
using the model to find a common denominator.
Ask students to start with columns for “what we
have” – just to make it so we are all looking at the
same picture.
“Shading Two
Fractions on One
Model”
Worksheet
(10 minutes)
Formative
Assessment
(5 minutes)
Homework
Ask students to draw a third model. Students
should combine the two models on the third
model.
Circulate the room and prompt students
who struggle.
Use this sentence frame:
“I made ___ columns on the first model,
and ___ rows on the second model. To
show both on one model, I have to make
____ columns and ____ rows.
Tape a copy of the “Shading Two Fractions on
One Model” worksheet on the board Complete #1
together; model sentence frame as you shade.
Possible misconception: Shading rows instead of
columns. Address this misconception by having
students label the rows and columns.
Circulate room and ask students (at random) to
model their sentence frame aloud to say what they
are doing on the problem they are working on.
Exit Slip
Number line worksheet.
Ask students to draw one
large rectangle model.
Use the sentence frame:
“I need to make 4 ______ to
show the fraction $.”
Ask students to draw a
second large rectangle
model.
Ask – “What is important
when we draw this model?”
(equal sized whole)
Use the sentence frame:
“I need to make 3 ______ to
show the fraction 1/3.”
Complete worksheet.
Use Sentence Frame:
“I need to shade _____
rows/columns out of ____
rows/columns to show the
fraction _________”
Repeatedly expose students
to both procedure and
language in context.
5 minutes to complete exit
slip, staple it to the top of
their worksheets and turn in
to the turn in box.
Tell students:
“Each number line has a
certain amount of tick
marks. Your job is to write
down all of the equivalent
fractions. We will be using
this tomorrow in class, so be
sure to fill it in completely!”
Lesson Outline
Lesson Part
Title:
Lesson Length:
Materials:
Standard:
Central Focus:
Learning Target:
Academic
Language:
Instructional Inquiry
Picking the right
Number Line
(10 minutes)
Activity Description/Teacher Does
Students do
Lesson 3
45 minutes
Homework (“Number Lines” worksheet), practice equations on index cards,
Clock strategy worksheet, plastic sleeves (makeshift whiteboard), “Adding
Fractions with an Area Model II” worksheet (page 1 only), iPad with Keynote
presentation (teacher), student whiteboards and “Mathematical Mad Libs”
Homework.
CCSS.MATH.CONTENT.5.NF.A.1
Add and subtract fractions with unlike denominators (including mixed numbers)
by replacing given fractions with equivalent fractions in such a way as to
produce an equivalent sum or difference of fractions with like
denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b
+ c/d = (ad + bc)/bd.)
Students will add fractions with unlike denominators by using a variety of
strategies and models to produce equivalent fractions with like denominators.
Students will use a variety of models to find common denominators and write
equivalent fraction sentences to add fractions with unlike denominators.
Columns, rows, simplify, combine, value, equivalent fraction equation, area
model, overflow fraction, area model, strategic partitioning, shade, represent.
“Yesterday we worked on using models to find a
common denominator with doubled
denominators; today we are going to use the
same idea of growing fractions to build an area
model – the post-it models that you see all
around the room. These will help us to find a
common denominator and show our thinking
when we add fractions with unlike denominators.”
Get out Homework and check that number lines
are labeled with all equivalent fractions.
Distribute pocket protector plastic sleeves and
turn homework into whiteboards.
Use number line worksheet/whiteboard to:
1. Find the right number line
2. Show (and label) the addition to find the
right answer.
Work through example together (teacher draw
number line on whiteboard)
1 1
+
10 2
Pick the number line that can show both #’s and
1/10’s. Mark where you are starting (what you
have; #), with a dot. Jump however much you
!
Get out homework, and
whiteboard markers.
All students should work
through example 1 on their
whiteboards.
Students should then erase
the whiteboard.
Teacher: Strategically pass
out these four equations on
index cards so that the
difficulty matches the
student skill level.
2 3
=
+
5 10
2 1
+ =
3 6
Table groups work together
!
!
!
1 1
+ =
4 2
3 1
+ =
8 4
!
are adding (1/10) and label. Use the number line
with all equivalent fractions to see how many
jumps to do.
Note: when trying to visualize jumps with a
common denominator, start at 0 and see how far
to the second fraction.
Rewrite equivalent fraction equation and solve.
1 5
6
+ =
10 10 10
!
Revisiting the
Clock Strategy
(10 minutes)
Disperse “Clock Strategy” worksheets.
“We tried this strategy on the quiz, but I want to
try and solve it just like we solved the number
lines.” (I suggest splitting into the larger fraction
first).
to solve each problem.
The “leader” for each
problem (the student who
holds the index card)
should direct the discussion
for that particular problem.
Sentence frame:
“I start with ____ so we
mark that point on the
number line. Then we
need to find out how many
jumps to add. We need to
jump _____. The
equivalent fraction
equation is ___________.”
5 minutes - Students work
with elbow partner to solve.
Partners present their
strategy with the other set
of partners at the group
table.
Activity: strategically partition the clock, write
the equivalent fraction sentence and solve.
Can you simplify your answer? Ask class what
simplify means. How is it related to value and
equivalent fractions?
iPad Presentation
(Direct Instruction)
(10 minutes)
Anticipating resistance to area model:
Students may automatically go to the least
common denominator, rather than the
multiplicative denominator. Use this problem to
encourage those students to use this strategy.
Review addition with the same denominator and
doubled denominator with student input.
Assign a color for each fraction. Label the
columns and rows.
Ask students the following guiding questions to
prompt discussion. Select students at random
with equity sticks.
Q: “What do we have to do first?”
A: “Split the whole into ____ equal parts”
Q: “How can I show the fraction ___?” “How can
I add the second fraction to it?”
A: “Shade ___ in blue, and shade ____ in green”
Actively participate.
Students may write directly
on iPad to contribute, and
should be ready to answer
all questions and/or
contribute observations,
interpretations, and
alternate strategies/ideas.
Use sentence frame:
“I will shade ____
columns/rows out of ____
columns/rows to represent
the fraction _______”
Q: “Do I have to rewrite the equivalent fraction
sentence?”
Q: “Do I need to simplify?”
*Stress the example with an overflow fraction; it
will be important in their exit slip.
“Adding Fractions
with an Area Model
II” Worksheet (Page
1)
(10 minutes)
Leave last example (with work shown) on
projector for student reference.
Distribute “Adding Fractions with an Area Model
II” page 1.
Draw a line beneath #1 to
discourage students from
continuing on to #2.
Circulate and help guide students as necessary.
Closure/Assessment Independently solve #2 (may use #1 for
(5 minutes)
reference).
10 minutes - Solve #1 with
table partner. Do not do
complete #2.
(Partners who finish
early may poster-walk or
help other students).
Turn in this worksheet
when finished.
Note: Students may struggle because this will
produce a mixed number.
Homework
Provide specific feedback on this assessment
before tomorrow. Students will use feedback to
guide their work during the next lesson.
Mathematical Mad-Libs
“You will use the vocabulary list to fill in the
blanks, and will create their own (at least 2) MadLibs to share in class tomorrow.”
“Use mine as a reference,
but be creative when
making your own! See if
you can incorporate models
or notation into your MadLibs.”
Lesson Outline
Lesson Part
Title:
Lesson Length:
Materials:
Standard:
Central Focus:
Learning Target:
Academic
Language:
Instructional
Inquiry
Homework
Activity
(10 minutes)
Word Wall
(5 minutes)
Activity Description/Teacher Does
Students do
Lesson 4
60 minutes
Corrected Pre-Assessments, blank paper (1 sheet per group), “Adding Fractions
with an Area Model II” (pages 2-4), “Fraction Strikeout!”
CCSS.MATH.CONTENT.5.NF.A.1
Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an
equivalent sum or difference of fractions with like denominators. For example, 2/3
+ 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
Students will add fractions with unlike denominators by using a variety of
strategies and models to produce equivalent fractions with like denominators.
Students will use academic language in meaningful contexts and add fractions
with unlike denominators with a variety of models.
Students use knowledge of key words and concepts to create a definition of
numerator and denominator. Students use sentence frames, and notation to
describe their actions when adding fractions with unlike denominators.
“Yesterday we practiced with the area model, and
Get out homework, put
the number line; both can be very helpful tools for
everything else away.
finding a common denominator. Today we will be
practicing with both, but first we will focus on all of
the academic language that we’ve been working so
hard on.
Students will look over the work from a different
Get out homework and
table. Each student will read the created Mad-Libs collect into a pile. Rotate
aloud, and the table will select their favorite one.
work one table clockwise.
During share-out portion of this activity, discourage
groups from sharing Mad-Libs with the same
keyword; therefore table groups should initially
select 2 favorites.
5 minutes - Students take
turns reading the Mad-Libs
aloud, and then select 2
favorites.
Circulate as they share and work and prompt them
to facilitate meaningful discussion of why they
made their selection, and what criteria they used to
make their selection.
5 minutes – Call on each
table and have one
representative share their
selection (including author’s
name), and say why they
chose it.
Ask for contributions of words that we have been
using over the past three days. Prompt with
models and questions if necessary. Review each
word/concept briefly within context by drawing a
model, writing notation, and/or having a student
“We liked this one because it
showed _______”
Actively participate, accept
volunteers to contribute (but
only allow each student to
contribute once).
Academic
Language
(20 minutes)
volunteer describe the definition.
Students will use the knowledge that they have
gained to revise their original answer to #2 from the
pre-assessment (“What is a numerator? What is a
denominator? Explain and label”). Students will
work in groups to amend and combine their
response, and meaningfully incorporate academic
language in context. Students will then read and
amend/add to two groups answers.
Monitor during this time to facilitate discussion,
encourage quiet students to participate, and focus
attention on incorporating academic language.
Hand back quizzes with
feedback and give 2 minutes
to review their own quiz.
4 minutes - Tell students to
discuss their answers (with
feedback) at table groups;
read exact answer to group.
5 minutes - Give students
time to come up with their
groups’ best answer, given
all of the academic language
on the board, and write it on
a blank piece of paper.
Students should incorporate
as many of the words from
the word wall as possible.
Have students rotate their
papers one table
counterclockwise.
3 minutes – Read definitions
aloud, and amend it to
reflect more/better academic
language (if possible), and
give positive feedback.
Rotate papers one more
time, counterclockwise.
3 minutes – Repeat.
Return papers to original
tables/authors.
3 minutes – Read their own
aloud and discuss their
peer’s input and/or
amendments.
“Adding Fraction
with an Area
Model II”
(page 2)
(15 minutes)
Hand back page 1 with feedback and give them 2
minutes to review.
*Differentiated
tasks
Students who show proficiency on page 1 of the
“Adding Fractions with an Area Model II” worksheet
or those whose errors are easily correctable with
Distribute page 2 of “Adding Fractions with Area
Model II” worksheet
Complete page 2 of
“Adding Fractions with
feedback (ie. unequally sized models) will stay at
their desks and:
Because this model resulted in an overflow
fraction, many students may lose track of how
many squares to “add”
Bring one of the post-it posters up to the front of
the room with an addition problem that will result in
an overflow fraction that already has an area model
drawn. While above students work, these students
(and any who self-identify as unsure) will tell
teacher what to do. Using post-its to shade will
reveal the problem with putting two post-its in one
square. This will remediate misunderstanding.
All of these students will be given feedback to circle
what they are adding so that they can visualize
what to add.
“Fraction
Strikeout”
(15 minutes)
Game using number lines to add/subtract fractions.
There are two “levels of difficulty;” 1/3’s and 1/6’s.
Students will select their own partner, and number
line, and play until no numbers remain. These are
printed as a full page front/back (though they are
shown side by side in “Materials”).
Area Models II”
Complete challenge page
using any strategy
(models and/or algorithm)
Students provide feedback
on what to shade/do
Use sentence frame:
“I will shade ____ out
columns out of ____
columns to show the fraction
____”
“I am adding _____ to it, so I
must also shade ____ rows
out of ____ rows and
regroup the ____ squares
that overlap.”
Students will then complete
page 2 of “Adding Fractions
with Area Models II”
Each partnership needs 1
worksheet to play.
Students self-select a
partner, and play the game
until no numbers remain.
Directions:
First, label the number line with all equivalent
fractions.
Player 1 creates an equation with an answer that is
available on the number line and circles that
answer on the line (ie. 0+# = #). Player 2 then
crosses out the circled answer (#), and uses that
number to start his/her addition or subtraction
equation (# + 1 = 1 #). Players alternate until no
numbers remain.
Assessment
(5 minutes)
Homework:
Teacher reads directions aloud, and draws a
number line on the board ($’s). Call one student
up to help with demonstration, and model the first
two moves.
Exit slip
Finish “Adding Fractions with an Area Model II”
(page 2, if not finished, and pages 3-4).
Turn in “Fraction Strikeout”
worksheet with both student
names into the turn in
basket. Turn exit slip
directly into teacher.
Optional: Review pre-assessment for tomorrow’s
post-assessment.
Post-Instructional Assessment
Lesson Part
PostAssessment
(20 minutes)
Activity Description/Teacher Does
Students do
Special Instructions:
“Think of all of the words that we have discussed over the past week. What role
do they play in describing and adding fractions? What models did you use? Create
your own “Mathematician’s Word Wall” on #1 and use those words to help guide
the rest of your answers.”
Leson 1, Page 1/4
Fractions Poster Started w/class in first activity on Day 1
All 3 were accessible throughout the unit – students could contribute during free time.
Lesson 1, Page 2/4
Lesson 1, Page 3/4
Lesson 1, Page 4/4
Bravo, you may
use your
shortcut!
Name: _____________________________________
Check out MY Method!
“Hey Miss Stewart, I really know this stuff,
in fact I know a “shortcut” that is worth a million bucks.
It can solve any problem, in a fraction of the time
And I can show you HOW and WHY it works, isn’t that sublime?”
Topic:
Method Name:
I can GET THE RIGHT ANSWER:
I can SHOW MY WORK (show your SHORTCUT)
I can show HOW it works WITH A MODEL and/or THE LONG WAY.
I can EXPLAIN WHY it works with WORDS. *What is your shortcut REALLY doing?
Not quite, let’s
look at WHY it
works a little
more…
Lesson 2, Page 1/4
Lesson 2, Page 2/4
(Extra Support)
Directions: Split up the models to make equivalent fractions, and write the new fraction underneath.
Making Equivalent Fractions
Challenge: What happens to the fraction when you split the model into equal sized pieces?
.
Lesson 2, Page 3/4
Label the COLUMNS and ROWS. Think about how we can shade
the entire area model to show the each.
1
5. 4
1
1. 3
!
!
3
6. 4
2
2. 3
!
!
2
7. 3
1
3. 2
!
!
4.
1
8. 3
1
!
Lesson 2, Page 4/4
(Homework)
Name:
Number Lines
0
1
0
1
0
1
0
1
Lesson 3, Page 1/4
3-4 new posters (much
like these) were put
around the room on
days 2, 3 and 4 for
students to “play” with.
Limit 2 students per
poster at any given
time.
Lesson 2, Page 2/5
Lesson 3, Page 3/5
Sentence frame – Posted
Direct/Interactive Instruction
Direct/Interactive Instruction
Direct/Interactive Instruction
Direct/Interactive Instruction
Closure – Modeling Together
Lesson 3, Page 4/5
(Serves as both classwork and assessment)
Lesson 3, Page 5/5
(Homework)
Name:
Mathematical Mad-Libs
1. Using your vocabulary from the Mathematician’s Word Wall, complete
these sentences to describe how to add fractions with unlike
denominators.
The
Mathematician’s
Word Wall:
! Numerator
First, find a
so that the
! Denominator
! Part
fractions can “speak the same language”.
! Whole
Like
1
2
and
6
12
we must find an
fraction;
aka a fraction that has the same
! Equivalent
! Value
.
! Simplify
!
!
6
, which means we have
8
3
before we get our final answer; .
4
!
In the end, you may end up with a fraction like
to
! Equally
Partitioned
!
Overflow
!
Mixed #
!
Common
Denominator
Sometimes we draw models add fractions with unlike denominators. If I
were to draw an area model of
and 5
1 2
+
3 5
.
!
I would draw 3
!
! Equal
! Shade
! Columns
! Rows
! list.
2. Create your own Mad-Libs using at least FOUR words from vocabulary from the
1.
2.
!
Lesson 4, Page 1/5
Lesson 4, Page 2/5
Lesson 4, Page 3/5
Lesson 4, Page 4/5
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Names:
Lesson 4, Page 5/5
Printed and distributed whole page front/back.
Names:
Names:
Directions:
Player 1 creates an equation with an answer that is available on the number
line and circles that answer on the line (ie. 0+! = !). Player 2 then crosses
out the circled answer (1/2), and uses that number to start his/her equation
(! + 1 = 1 !). Players alternate until no numbers remain.
Don’t Forget!:
1. Label this number line. (Hint: Include ALL equivalent fractions)
2. Numbers may only be used once.
3. You must jump more than one place on each play.
4. You must use every number on the line (including 0)!
5. Write your full equation in the blank space below.
Working with –––‘s
Fraction Strike-out!
Names:
–––‘s
Fraction Strike-out!
Working with
Don’t Forget!:
1. Label this number line. (Hint: Include ALL equivalent fractions)
2. Numbers may only be used once.
3. You must jump more than one place on each play.
4. You must use every number on the line (including 0)!
5. Write your full equation in the blank space below.
Directions:
Player 1 creates an equation with an answer that is available on the number
line and circles that answer on the line (ie. 0+! = !). Player 2 then crosses
out the circled answer (1/2), and uses that number to start his/her equation
(! + 1 = 1 !). Players alternate until no numbers remain.