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this document.
Our Agenda
 Looking at a lesson
 A few quick ways to scaffold INSTRUCTION
 Questions?
 Visit http://goo.gl/Ua0fcf to access the electronic
version of this document.
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Let’s look at part of a
lesson.
 What do you notice that might be problematic for
English learners?
 What might you do to modify this lesson?
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Grade 6, Module 5, Lesson 11:
Volume with Fractional Edge Lengths and Unit Cubes
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How many 1 in x 1 in x 1 in cubes will fit in the following
prism?
Have students discuss their solution with a partner.
How many 1 in x 1 in x 1 in cubes would fit across the
bottom of the rectangular prism?
How did you determine this number?
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 How many layers of 1 in by 1 in by 1 in cubes would fit
inside the prism?
 If each cube represents dice that need to be
shipped, how many 1 in x 1 in x 1 in dice will fit in the
box?
 How did you determine this number?
 How is the number of cubes or dice related to the
volume?
 What other ways can you determine the volume of a
rectangular prism?
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Example 1 (5 minutes)
1. The same package in the opening exercise will be
used to ship miniature dice whose side lengths
have been cut in half. The dice are ½ in x ½ in x ½ in
cubes. How many dice of this size can fit in the box?
How many cubes could we fit across the length?
The width? The height?
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Now let’s look at how to
improve it…
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How many 1 in x 1 in x 1 in cubes will fit in the following
prism?
Have students discuss their solution with a partner.
How many 1 in x 1 in x 1 in cubes would fit across the
bottom of the rectangular prism?
How did you determine this number?
abright@pdx.edu
 How many layers of 1 in x 1 in x 1 in cubes would fit
inside the prism?
 If each cube represents dice that need to be
shipped, how many 1 in x 1 in x 1 in dice will fit in the
box?
 How did you determine this number?
 How is the number of cubes or dice related to the
volume?
 What other ways can you determine the volume of a
rectangular prism?
abright@pdx.edu
Example 1 (5 minutes)
1. The same package in the opening exercise will be
used to ship miniature dice whose side lengths
have been cut in half. The dice are ½ in x ½ in x ½ in
cubes. How many dice of this size can fit in the box?
How many cubes could we fit across the length? The
width? The height?
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Let’s look at another
example.
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3. A toy company is packaging its toys to be shipped.
Some of the very small toys are placed inside a cube
shaped box with side lengths of ½ in. These smaller
boxes are then packed into a shipping box with
dimensions of 12 in x 4 ½ in x 3 ½ in.
a. How many small toys can be packed into the
larger box for shipping?
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Here’s a re-wording:
Original
A toy company is packaging
its toys to be shipped. Some
of the very small toys are
placed inside a cube shaped
box with side lengths of ½ in.
These smaller boxes are then
packed into a shipping box
with dimensions of 12 in x 4 ½
in x 3 ½ in.
How many small toys can be
packed into the larger box for
shipping?
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Scaffolded
A toy company puts small toys
into boxes. The boxes are
cubes with side length of ½ in.
These small boxes are put
inside a bigger box with
dimensions of 12 in. x 4 ½ in. x 3
½ in.
How many toys can be put into
the larger box?
Another note on this
lesson
 Words are used interchangeably:
 Long/ length
 High/ height (and sometimes deep/ depth)
 Width/ wide
 Some words are have multiple meanings (like volume).
These relationships between these words need
to be taught!
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abright@pdx.edu
Amplify key language
 Text is written in present tense and may
be redundant for clarity.
 Sentences are short with no or few
clauses. (These may read awkwardly to
fluent speakers of English.)
 New sentences begin on a new line.
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 Contexts are familiar to students in
school.
 Names chosen for examples should
not be similar to content (including
names like Ray and Mark).
 Pictures/ visuals/ illustrations are used
to make content clearer.
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 Words with multiple meanings that might be
confusing are not used (ie, a garden plot and
the request to plot points on a coordinate
plane).
 Language is internally consistent (if practice
problems ask students to solve, the
assessments should use the same term). If
language is not internally consistent, then
different terms are highlighted and taught
(add, plus, sum, combine, all mean the same
thing).
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A Standard Example
(Lesson 8.1, p. 12)
Suppose a colony of bacteria
doubles in size every 8 hours
for a few days under tight
laboratory conditions. If the
initial size is 𝐵, what is the
size of the colony after 2
days?
Scaffolded Example
A group of objects doubles
every 8 hours.
Today there are B objects in
the group.
How many objects are in the
group after 2 days?
(There are 24 hours in one
day.)
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A Standard Example
(Lesson 8.1, p. 12)
A rectangular area of land is being
sold off in smaller pieces. The total
area of the land is 𝟐𝟏𝟓 square miles.
The pieces being sold are 𝟖𝟑 square
miles in size. How many smaller
pieces of land can be sold at the
stated size? Compute the actual
number of pieces.
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Scaffolded Example
Kim has a farm in the shape of
a rectangle.
The area of Kim’s farm is 𝟐𝟏𝟓
square miles.
Kim divides her farm into
pieces that are each 𝟖𝟑 square
miles in size.
How many pieces does Kim
make?
Provide side-by-side texts.
 Look at how useful this is! (Google translate
will even provide a read-aloud.)
 (Note: This is best for students who are
already highly LITERATE in their first
language. Do not assume this is the case with
all students.)
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Provide step-by-step instructions in
student-friendly language & use visuals.
 From a lesson on translating one-step word problems
to algebraic equations.
Directions:
a) Define a variable for each problem.
b) Write an equation to represent the information.
c) Be sure the equation requires the use of one inverse
operation to find the solution!
d) Show a check for each solution.
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2. Provide graphic organizers.
 Non-verbal displays of relationships
 A way to visually organize thinking
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Similarities and differences
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Graphic organizer
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Frayer model
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Foldables
 These don’t have to be from a template. Anything can
work!
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Have students identify
similarities and differences.
 Venn diagrams
 T-charts
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Similarities and Differences
Concept: Conic Sections
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parabola
ellipse
circle
hyperbola
Similarities and Differences
Concept: ____________
y 
x
4
1
y  6  (x  1)
2
x  5
2
(x  10)  y
5
y 7
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Similarities and Differences
Concept: Which does not
belong?
acute
right
obtuse
parallel
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(Can you think of another
term that would fit?)
3. Provide support for
speaking and writing
 Each day needs structured opportunities for
students to speak and write in English.
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Give concrete guidelines for speaking,
reading, writing or listening.
“Turn to your neighbor and explain…”
Write the day’s objective on the board and have students
read it along with you. Point to each word as you read
aloud.
Provide sentence frames for anyone who may benefit.
(“I know the area of parallelogram B is larger/ smaller ______ than the area of parallelogram A because
_____.”)
(More advanced students might be ready for some transition language like this:
http://writing2.richmond.edu/writing/wweb/trans1.html)
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Sentence frames (perhaps with word banks)
can support student explanations.
 Visit this link for some elementary examples from
Justin Johnson.
 See also page 24 of this fabulous document from
Kate Kinsella.
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 “The volume of my prism is ___units cubed. I found
this by ______.
 “My idea is similar to _____’s because ____.”
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 “I know the answer is a fraction because_____”
Word bank:
Added
Less than one
Combined
Whole number
Equal
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Have students chorally repeat
key vocabulary or phrases.
 Have students chorally repeat the key term in creative
ways.
 (“The word is pronounced hypotenuse. Again, hypotenuse.
Repeat after me: hypotenuse. Whisper it: hypotenuse. This
side of the room only: hypotenuse. Everyone wearing jeans,
hypotenuse.” )
 Why? It lowers the affective filter since there are multiple
voices speaking at once. It promotes fluency. It provides
and accurate auditory imprint.
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Be direct about language.
 EXAMPLE
OBJECTIVE FOR
A LESSON:
 Identify perfect
squares;
determine
square roots.
 Discuss the word square. Ask students to
describe what a square is: a shape with 4 equal
sides and 4 right angles. Have students point out
objects in the room that are squares.
 Introduce expressions with the word square that
students will use in this lesson – square number,
perfect square, squared, square root.
 Explain to students that the word square can be a
noun or a verb. In the expression “the square of a
number…”, square is a noun. In the expression
“if we square the number…”, square is a verb.
 Tell students that we will be using the word root in
the mathematical expression square root. Ask
students if they know any other uses of the word
root (roots of trees or plants, family roots). Point
out to students that in these cases, the word root
relates to the beginning or foundation for
something.
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Use online resources for key
vocabulary.
 How about a cool dictionary?
 Or what about Google translate?
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Provide word banks.
 These can provide appropriate
and relevant vocabulary to use
in speaking or writing about the
content.
Adjacent
Complementary
Congruent
Equal
Supplementary
Vertical
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Other rich ideas
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Use manipulatives!
 The more concrete and visual these ideas can be, the
better!
 Remember this thing? Use something from the
classroom instead!
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Connect to the real lives of students. Use
concrete examples whenever possible.
 Example: The same shape can have multiple names.
 This is a picture of Dalia. She is:








A sister
A student
A cousin
A daughter
An accountant
A friend
A driver
A winner
 All at the same time!
 In the same way, this slide can be seen as a closed figure, a
parallelogram, a rectangle, a polygon…
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Show finished examples and
provide a rubric for selfevaluation.
___ x 3 = ___
What factor can you use in this equation to
make a product that is even and between 10
and 40? Show all possible solutions. Explain
your strategy.
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Name and notice
•
•
Look at this mathematical
writing
Identify what qualities
make this mathematical
writing strong.
The Necessity of Language Instruction in Mathematics;
Angela Alcantar, Sunshine Price, and Michelle Stroup
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English Language Acquisition Specialists, Salem-Keizer
Public Schools. 2013.
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Use quick, formative
assessment to establish
background knowledge
 Teaching students how to find the mean and
median? What do they need to know?
 They must FIRST know how to:




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Count
Put numbers in order from smallest to largest
Add
Divide
Incorporate interactive
games.
 These can explicitly include scripted speech.
“When I substitute 8 for the variable c, my equation is
equal to 3.
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Replace obscure words or
contexts with things from a
high-frequency word list.
 Students learn English beginning with HIGH
FREQUENCY words. Here’s one example of a
list.
 Try to choose SCHOOL contexts.
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Allow students to show
what they know in different
ways.
 This includes allowing for students to share their
thinking in their first languages.
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CCSS.Math.Practice.MP4 Model with mathematics
In each of the 16 houses in
the neighborhood, there
were 2 dogs.
Say it with pictures.
Say it with numbers.
Say it with words.
How many dogs total lived in
the neighborhood?
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Say it with pictures.
@
@
@
@
@
@
@
@
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@
@
@
@
@
@
@
@
@
@
@
@
@
@
@
@
@
@
@
@
@
@
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Say it with numbers.
how many dogs
how many houses
2 x 16 = 32
Total number of dogs
Say it with words.
There were two dogs at
each house and 16
houses so I counted by
2’s sixteen times. I used
my fingers to help me
keep track.
The Necessity of Language Instruction in Mathematics; Angela Alcantar,
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Sunshine Price, and Michelle Stroup English Language Acquisition
Specialists, Salem-Keizer Public Schools. 2013.
Final things to keep in
mind
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Mathematics is not a
universal language
 MUCH of what we share with students is embedded
in language that is specific.
 Example: Think of the similarities and differences
between the words OF and OFF.
 Example: Hypotenuse is the longest side of a right
triangle. EVERYONE learns the word hypotenuse; ELs
need to learn the word LONGEST.
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Fractions may be
especially challenging
 The METRIC SYSTEM is used in pretty much
the entire rest of the world.
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We can’t assume literacy in L1.
 Not all students have had access to
ongoing formal education.
 Students may have yet-undiagnosed
learning differences.
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Students learn casual language
before academic language.
 This means they may sound comfortable
and fluent, but may need additional support
in their writing and speaking in an academic
register.
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Communicating in a new
language can be very stressful.
 Above everything else, we need to prioritize the
health and well-being of our students by ensuring
our classrooms are safe and welcoming.
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