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Welcome
California Mathematics and Science
Partnership (CaMSP)
Year 2, Follow Up 3
January 22, 2011
Slide 1
www.wordle.net
Slide 2
Agenda: Making the Invisible
Visible
•
We will identify the language of patterns and
ways to teach this language effectively.
•
We will reflect on recent research related to
the language of patterns and teaching this
language effectively.
Slide 3
Essential Questions
•
•
How can we identify the language that we
need to teach our students so that they can
discuss patterns?
What are effective instructional strategies
that help students learn this language?
Slide 4
Identifying Language Features
to Teach
Step 1: Analyzing language
use to identify the many
features.
Step 2: Limiting the features to
a manageable number.
Slide 5
Identifying the language features
to teach entails language analysis
of texts—oral and written
Written – written explanations, e.g.,
from the students’ textbooks and
teacher resources
 Oral – transcribed language use –
usually of teachers and students

Slide 6
Handout
Let’s analyze how we talk about
patterns.
Student talk = output
Our talk to students = input
Slide 7
We will be doing a task shortly that
requires you to use two handouts.
Handout 1: Patterns
Handout 2: The Language Needed to
Explain Patterns
Slide 8
You need a handout that looks like
this one:
Grade 6
Slide 9
You also need
this handout.
Stand up! Hand up! Pair up!
Slide 11
Steps
Read the handout on the language of
patterns. Circle the language you
might use to explain Pattern A.
 Stand up when you are done.
 Put your hand up, smile and establish
eye contact with someone else who
has finished reading the handout.

Slide 12
Steps
Find a partner. Do a high five.
 Partners interact for three minutes.
 They discuss the answers to several
questions.

Slide 13
Task—Answer these questions:
What language enables you to explain
patterns?
 Would you use any of the language in
the handout?
 What additional language would you
use?

Slide 14
Would you use any additional
vocabulary?
Slide 15
Vocabulary
TO GO UP
• to increase by a
number
Add:
a number plus 2
a number added to 2
TO GO DOWN
• to decrease by a
number
Subtract:
a number minus 2
a number less 2
Slide 16
Vocabulary
•
•
•
Downward
Upward
Sideways
Slide 17
Vocabulary
•
Pattern: A design or an arrangement of
numbers that models a general rule.
•
Term: Each design or number in the
pattern
Slide 18
What additional expressions
would you use?
Equivalent to
• Different from
• Similar to
•
What about prepositions?
On the top of the square
The figure in the middle
On the right
Slide 20
Would anyone use the word
functions?
Would anyone say:
• Functions are rules that describe the
relationship between two variables. They
are commonly expressed as equations.
• Functions are often expressed as
equations that include two variables, as in
x+3=y.
Slide 21
What about function table?
Did anyone say:
• Function tables represent pairs of numbers
that follow a certain rule, or function.
Slide 22
Function Table (cont.)
Did anyone say?
 A function table for x+3=y would
include a column of corresponding
numbers for "x" and a column for "y" to
reveal a numerical pattern.
Slide 23
Would anyone give an example
of a function table?
y = 2x + 6
X
y
1
8
2
10
3
12
4
14
Slide 24
Column
a line of numbers or words written
under each other that goes down a
page
Slide 25
Row
a line of things or people next to each
other
Slide 26
In a row
One after another, consecutively
Slide 27
Would anyone use unknown
numbers or the word let?
Did anyone say:
 When you are looking for unknown
numbers, let a variable represent that
numbers?
Slide 28
Timed Pair Share
1. Partners find a place to sit down. They decide who is
Partner 1 and who is Partner 2.
2. Teacher describes the task. Partners will take turns
explaining the patterns (B and C).
3. In pairs, Partner 1 explains Pattern B as Partner 2 listens
and completes the graphic organizer.
4. Teacher calls “time”.
5. Partners switch roles. Partner 2 explains Pattern C as
Partner 1 listens and completes the graphic organizer.
TASK: What language enables you
to explain patterns?
First Partner: Draws a table to explain the
pattern to his/her partner.
 Second Partner: The partner completes the
graphic organizer, writing down the language
his/her partner has used.
 Both Partners: Discuss the language.

Slide 30
Take a minute to prepare a
table.
Slide 31
Partners should draw a table
and explain it.
Slide 32
Example
Figure
1
2
3
4
Number of
Squares
?
Pattern B
Slide 34
Pattern C
Slide 35
What language did you or your partner use to
explain patterns?
Reminder: Complete the graphic organizer.
Slide 36
Identifying Language Features to
Teach

STEP TWO: Narrowing the language
features to those that students need to
learn.
Slide 37
Step 2: Narrowing the List of Features:
Using the guiding questions below, determine what
manageable list of features you would choose to teach.
Guiding Questions
• Is the language feature unknown?
• Will it improve students’ ability to explain patterns?
• Will it increase students’ understanding of math?
• Will students use the feature in other math assignments?
• Will knowledge of the feature help to improve students’
knowledge of academic language and/or the language of
math?
Key Language Features
Task: Write 6 key
features of language you
would want to teach
students before asking
them to explain patterns
in partner activities.
Slide 39
Slide 40
Perfect Practice in Conversation
Each time a teacher gets a student to practice
a language feature correctly, it helps the student learn the feature!
That’s right!
Adapted from David Howe 2006
Slide 41
How Much Practice is Needed?
Number of correct repetitions in a row of a new
word needed to “automatize” the word - NICHD
Type of Learner
Number of
Repetitions
Most Able
1 or 2
Average
4-14
Least Able
20+ (?)
(R. Lyon, 1997)
Slide 42
What techniques can we use to
teach students specific
language features?
Here are just a few (see handout
for other ideas):
Reading Aloud: Tables, equations, algebraic
expressions
Mathematically Speaking
Discussions and Analyses – e.g., of student
notes, textbook explanations, teacher
summaries …especially with word banks and/or
sentence stems!
Deliberate modeling and repetition – individual,
group and choral
Choral Repetition
Algebraic
Expression
Word Phrase
Operation
w+4
A number plus 4.
Addition
w–4
A number minus
4.
Subtraction
4 x w or 4w
4 times a number
Multiplication
w
4 divided by a
number
Division
4 or w/4
Choral Repetition
Algebraic
Expression
w+4
w–4
4 x w or 4w
w
4 or w/4
Word Phrase
Operation
Tips for Preparing Choral
Response Activities
Make sure to elicit at least four-six
sentences, phrases or words
 Try to make sure all sentences,
phrases or words are parallel in form

Slide 47
Choral Repetition for
Answering Questions
Listen -- Listen to the directions or prompt
Think--Think how you would respond.
Wait--Keep from blurting out the answer. Give everyone time to think.
Respond--When given the signal say or write your response.
Question
Why do we need to use choral repetition
in our classes?
Slide 49
What the Research Says
Slide 50
Summary
•
•
How can we identify the language students
need to know to discuss patterns?
What are effective instructional strategies we
can use to help students use this language?
Slide 51
Take a Break
Slide 52