Common Core State Standards

Follow-Up Day 1Grade 6

Facilitators’ Training

PREPARING FOR SUCCESS IN ALGEBRADEMONSTRATION 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 stems2. Using mathematical and language lenses to select the types of questions to ask 3. Vocabulary and steps to use to teach words4. 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 24:1The ratio of 24:1 is represented in cameras as 24x

Language Objectives

Objectives should be written for all four modalities:

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)

Language Objectives

Task-Based Language Objectives

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.

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 Objectives

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 Students will _(verb phrase)_ using _(target language)_. 

① Students will use _(target language_) to _(verb phrase)_.

Examples of Verbs/Verb Phrases

Used in 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.

Sample Language Objectives

Target Language

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

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 focus1. 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

TEACHING WORDSIt’s not enough to hold students accountable for learning language. We need to support their learning of language.

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Teaching Words

Teaching & Learning Framework

Best Practice: Teaching Words

Vocabulary Teaching Technique1. Repeat word 3 or more times2. Show students a sentence using the

target word from their textbooks3. Talk about how it is used4. Make up new sentences using the word5. Have students practice using the word

with partners6. Remember that some students need

more practice than others to use language accurately

Selecting the Right Words to Teach is Key

Guiding QuestionsGuiding Questions

Is the word unknown?Is the word unknown?

Will it improve studentsWill it improve students’’ ability to understand ability to understand the texts students read for your class?the texts students read for your class?

Will students use the word in other Will students use the word in other assignments?assignments?

Will knowledge of the word lead to Will knowledge of the word lead to improvements in studentsimprovements in students’’ knowledge of knowledge of academic language?academic language?

What about academic words?

Averil Coxhead developed a list of 570 academic words that are used in a variety of academic disciplines.

What Words do Teachers Need to Teach?

Apply Assume ContainSelect MaintainAccess Determine Specify

Minimum Release Survive Identify Inevitably Coherent Persist

http://www.victoria.ac.nz/lals/resources/academicwordlist/

Example of Academic Words

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 in the Longman’s on-line dictionary, http://www.ldoceonline.com/.

To conclude something by reasoning, in other words, by thinking about it and 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 verbInference = a nounInferential = an adjectiveInferentially = 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 _________

• After the stock market crashed, the number of people ________ buying stocks would not be wise.

• After the ________ that the teacher hated her, she gave up trying to do well in class.

• 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

Teach it very carefully over days and weeks. Whenever possible, tables and charts to help students learn the meanings of new words.

Miles

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Hours

1 2 3 4 5

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.

Talking with Others

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

Conversations about Mathematics

CCSS Standards of Mathematical Practices

Source: Tools for the Common Core Standards

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

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.

Mathematically Speaking

Activity

Handout: Mathematically Speaking

A Challenge: There is a lot to teach in all classes, especially in Algebra!

EnglishLearners

1

23

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Academic Success

Helpful Necessary

• Include language objectives

• Provide language instruction

• Provide language exposure

• Provide sufficient practice

• Provide feedback

• Engage students

To Teach the Language of Algebra…

Lunch

Enjoy!