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Common Core State Standards
Follow-Up Day 1
Grade 6
Facilitators’ Training
PREPARING FOR SUCCESS IN ALGEBRA
DEMONSTRATION CENTER
A Collaboration among:
 Los Angeles USD
 University of California, San Diego
 San Diego State University
 University of California, Irvine
Teaching & Learning
Framework
LAUSD SDAIE Lesson
Template
Session Objectives
In this session, we will consider:
1.The pivotal role of language objectives in fostering
students’ conceptual and language development and
ways to write them using sentence stems
2. Using mathematical and language lenses to select
the types of questions to ask
3. Vocabulary and steps to use to teach words
4. An activity to have student practice using academic
and mathematics vocabulary
Language Objectives
Warm Up

There are 100 seats in a theater, with 30 in the balcony
and 70 on the main floor. 80 tickets were sold including
all the seats on the main floor. What is the ratio of
empty seats to occupied seats? What is the ratio of
empty seats to occupied seats in the balcony?
What is the meaning of 24x?
The camera has a zoom lens ranging from a wide angle of
25mm to a full telephoto of 600mm. (Both 35mm equivalents)
These two numbers produce a ratio of 1000:25 or the equivalent ratio of 24:1
The ratio of 24:1 is represented in cameras as 24x
Language Objectives
Objectives should be written for all four modalities:
Language Objectives
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Identify what students should know about English
and do with it in a particular task.
Support the students‘ development of English.
Language objectives help students learn language
that supports their learning in math classes as well
as in other contexts.
Language objectives include a verb (or verb phrase)
Handout: (Developing Effective Language Objectives)
Task-Based Language Objectives
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Task-based language objectives specify the
language students need to learn to complete tasks in
mathematics classes.
Language objectives emphasize the development of
expressive and receptive language skills.
Language objectives are obtainable.
Language objectives are measurable.
Language objectives support the Common Core
Standards.
Sample Language Objectives


Students will explain the solution to a ratio problem
using past tense verbs: like determined, concluded,
found, …
Students will defend a position about ratios using
present tense verbs (like maintain, contend, argue).
Sample Language Objective

Students will revise a paragraph in which they
describe a proportion using correct present tense
verbs.
 Note
that language objectives are most effectively
communicated using verb phrases:
 Students will point out similarities and differences
between two solutions using the words similar to and
different from.
Sentence Frames
①
①
Students will _(verb phrase)_ using _(target
language)_.
Students will use _(target language_) to _(verb
phrase)_.
Examples of Verbs/Verb Phrases
Used in Language Objectives
Sample Language Objectives
Read pages 3 -5 of the
handout.
Put a check next to two
objectives in reading, writing,
and listening & speaking that
you might use when teaching
quadratic equations.
Compare your choices with a
partner.
Target Language
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The specific language students are supposed to
learn.
What language teachers want their students to
know to understand math instruction and to
participate effectively in math lessons.
The target language could be vocabulary words or
grammatical structures.
It could be a specific sentence structure (e.g.,
learned through a sentence frame).
The language has to be listed.
Key Points

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Language objectives are communicated to students
clearly, both in speech and writing.
They can be posted in the classroom.
They can be referred to before, during, and after a
task.
Writing Language Objectives
Review the handout.
 Work with a partner and referring to the
example on page 7, write your own objectives.

Teaching & Learning
Framework
Algebra: Questioning Strategies
Quality and Purpose of Questions
•Teacher questioning has been identified as a critical and challenging
part of teachers’ work.
•The act of asking a good question is cognitively demanding; requires
considerable pedagogical content knowledge (Shulman, 1987).
•A number of research studies have shown that teachers rarely ask
‘higher order’ questions, even though these have been identified as
important tools in developing student understanding (Hiebert &
Wearne, 1993; Klinzing, Klinzing-Eurich, & Tisher, 1985; Nystrand,
Gamoran, Kachur, & Prendergast, 1997).
Quality and Purpose of Questions
•Based on 800 minutes of observations of seven teachers, Jo Boaler
(2004) and her research team developed nine categories of teacher
questions that were derived from an analysis of practice.
•They did not invent the categories a priori, rather they studied
different examples of the teaching in their sample and attempted to
describe and name the different types of questions they recorded.
•Their data show that when teachers ask more conceptual questions,
students start to ask conceptual questions themselves.
Jo Boaler Questions Types
The question types have a mathematical focus
1. Fact
6. Applying
2. Terminology
7. Extending
3. Concept
8. Focusing
4. Probing
9. Context
5. Discussion
Handout: (Table 1. Teacher Questions)
Questions: Tips for Promoting ALD
These tips have a language focus
1. Calling On
8.
2. Partner Time
9.
3. Wait Time
10.
4. Probing
11.
5. Model Structures
12.
6. Question Frames
13.
7. Small Group Questions
14.
Handout: Questioning: Tips to Promote Academic Language
26
Teaching Words
TEACHING WORDS
It’s not enough to hold students accountable for learning
language. We need to support their learning of language.
Teaching & Learning
Framework
Best Practice: Teaching Words
Vocabulary Teaching Technique
1. Repeat word 3 or more times
2. Show students a sentence using the target word
from their textbooks
3. Talk about how it is used
4. Make up new sentences using the word
5. Have students practice using the word with
partners
6. Remember that some students need more
practice than others to use language accurately
Selecting the Right Words to
Teach is Key
Guiding Questions
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Is the word unknown?
Will it improve students’ ability to understand the
texts students read for your class?
Will students use the word in other assignments?
Will knowledge of the word lead to improvements in
students’ knowledge of academic language?
What Words do Teachers
Need to Teach?
What about academic words?
Averil Coxhead developed a list of
570 academic words that are used in
a variety of academic disciplines.
Example of Academic Words
Apply
Assume
Contain
Select
Maintain
Access
Determine
Specify
Minimum
Release
Survive
Identify
Inevitably
Coherent
Persist
http://www.victoria.ac.nz/lals/resources/academicwordlist/
Basic Steps to
Teaching Vocabulary
Step One: Getting the students ready and
engaging their interest.
Step Two: Teaching the word explicitly.
Step Three: Providing independent practice.
Step Four: Providing formative assessment.
Handout: Basic Steps to Teaching Vocabulary
Step One: Getting the students
ready and engaging their interest.
Signal that vocabulary instruction will
take place and explain why.
Today we are learning new vocabulary. I
will ask you to use this vocabulary when
you do your peer work and make your
oral presentations in front of the class.
You will also find the word useful in your
writing assignment. The first word you
learn is an important one. You will use it
in most your classes.
Specify what the students will do.
You will listen, repeat the word and use
the word orally and in writing.
Prepare the students to take notes.
You will take notes as I explain the word.
Step Two: Teaching the Vocabulary
Explicitly
Introduce the new word.
The new word is the word
infer.
Pronounce the new word
clearly a few times.
Listen to me pronounce the
word. INFER
Ask your students to
pronounce the word after
you. Break up polysyllabic
words.
Please repeat the word after
me.
Step Two: Teaching the Vocabulary
Explicitly
Write the word on the board or
overhead and point to it. Tell students
to read and write it
infer
Teach the meaning of the word by
giving the students a student-friendly
definition.
To form an opinion that something is
probably true because of information
that you have.
You can sometimes find useful definitions To conclude something by reasoning, in
other words, by thinking about it and
in the Longman’s on-line dictionary,
http://www.ldoceonline.com/.
being able to give reasons for it
Step Two: Teaching the Vocabulary
Explicitly
Provide student-friendly examples and
lots of example sentences. Tell students
to write them.
If I get an A on my science test, I might
infer that I studied enough and now
know the material.
--infer something from something --
A lot can be inferred from these
statistics/the evidence.
-- infer that -From the evidence, we can infer that the
victim knew the thief.
Step Two: Teaching the Vocabulary
Explicitly
Give students additional information
about the word so that they can use it.
You could explain its related word forms,
the words it is used with, and/or the
particular way it is used.
Infer = a verb
Inference = a noun
Inferential = an adjective
Inferentially = an adverb
Guide the students in reading a sentence
containing the word two or three times.
If everyone in the sample of 200 students
likes Ana, I might infer that Ana is popular.
Since there was a large crowd waiting
outside the hotel, we may reasonably infer
that someone important was inside.
Step Three: Provide Independent
Practice
In this step, you need to use a familiar
instructional strategy to engage students
in an activity.
Pair Work
•Find a partner.
•Interact for three minutes.
•Use sentence frames that I give you to
practice using the word infer in complete
sentences
Sentence Frames
Infer conclusions from the _______.
Yes, people may correctly infer that they
are sister because they __________ .
Step Three: Provide Independent
Practice
Take turns completing these sentences with the
words inference, infer or inferred.
1. The incorrect results were based on an _________
2. After the stock market crashed, the number of people
________ buying stocks would not be wise.
3. After the ________ that the teacher hated her, she gave
up trying to do well in class.
4. After the success of Twilight, I can _____ that Breaking
Dawn will be equally successful.
Step Three: Provide Independent
Practice
Sentence Completion
1. If everyone refused to complete a questionnaire, I might
infer that …
2. If a sample is not a random one, I might infer that …
3. If only 30% of the 50 students interviewed gave the
correct response, I might infer that…
4. If a sample provides a good match for a population, I
might infer that …
Step Four: Provide Formative
Assessment
Hold each student accountable for using
the word. Provide feedback, as
appropriate. For example, ask each
student to use the word to complete a
task in which they write a complete
sentence using the word.
Task: Write two complete sentences using
the word infer.
What to do about Content Vocabulary
Proportional
Miles
45
Hours
1
2
3
4
5
Teach it very carefully over days and weeks.
Whenever possible, tables and charts to help
students learn the meanings of new words.
Talking with Others
Talking with others about ideas and work is
fundamental to learning. All students, particularly
second language learners, need opportunities to
develop their cognitive academic language
proficiency.
Cummins, J. (1996). Negotiating identities: Education
for empowerment in a diverse society. Ontario, CA.:
California Association for Bilingual Education.
Conversations about Mathematics
Classroom instruction should support bilingual students engagement in
conversations about mathematics that go beyond the translation of
vocabulary and involve students in communicating about mathematical
concepts. One of the goals of mathematics instruction for bilingual students
should be to support all students, regardless of their proficiency in English, in
participating in discussions about mathematical ideas. Teachers can move
toward this goal by providing opportunities for bilingual students to
participate in mathematical discussions and by learning to recognize the
resources that bilingual students use to express mathematical ideas.
Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual
mathematics learners. Mathematical Thinking and Learning, 4(2&3), 189–
212
CCSS Standards of
Mathematical Practices
Source: Tools for the Common Core Standards
Mathematically Speaking Activity
Teacher Instructions:
 All
students complete both mathematical tasks or problems.
 Student pairs are formed.
 Target vocabulary words are written on the MS chart. For
lower grades, the teacher can fill in the words.
 The two students write their names across the top. One
student explains half of the completed task or a given
problem to the other student as he or she tallies on the chart
each time a target word is used in the explanation. Students
keep talking until all target words have been used.
 The other student then takes a turn doing the same.
Mathematically Speaking Activity
Example
Comparing Two Ratios – Grade 6 -- McDougal Littell Chapter 6 Section 1
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CA – Grade 6 NS1.2 Interpret and use ratios in different contexts (e.g., batting
averages, miles per hour) to show the relative sizes of two quantities, using appropriate
notations (a/b, a to b, a:b ).
CaCCSS – Grade 6RP – Understand ratio concepts and use ratio reasoning to solve
problems.

1. Understand the concept of a ratio and use ratio language to describe a ratio relationship
between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo
was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received,
candidate C received nearly three votes.”

3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by
reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or
equations.
Handout: Mathematically Speaking
A Challenge: There is a lot to teach in all classes,
especially in Algebra!
English
Learners
1
2
3
4
5
Academic Success
To Teach the Language of Algebra…
Helpful
Necessary
• Include language objectives
• Provide language instruction
• Provide language exposure
• Provide sufficient
practice
• Provide feedback
• Engage students
Lunch
Enjoy!