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http://graphingstories.com/

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EL Glossaries for MAth, science, ELa and Social studies Elementary-Middle and High

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EL Glossaries for MAth, science, ELa and Social studies Elementary-Middle and High

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These glossaries are to provide permitted testing accommodations of ELL/MLL students. They should also be used for instruction during the school year.

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Lists of mathematical language for grades Prek-8

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Lists of mathematical language for grades Prek-8

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**Perfect for teaching the language of Math!!

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The page you requested is currently not unavailable. Please try again later.

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This site has a list of glossaries that LLs can use for standardized testing. They are listed by core subject then by language. Ideally, students would use these throughout the school year in class so they will be comfortable with it during testing.

http://www.doe.mass.edu/mcas/testadmin/lep-bilingual-dictionary.pdf

Below links to picture dictionaries.

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A collection of side-by-side images by mathematical concept, used to generate a discussion about how the two images are the same but different.

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Same But Different is a powerful routine for use in math classrooms. The images can be used for teaching a way of thinking: grayscale thinking, categorical thinking; helping students to build a network of ideas and an approach for learning and thinking about mathematics.

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Math.Practice.MP1

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

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Math.Practice.MP3

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

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Math.2.NBT.B.5

Common core State Standards

Math: Math

2: Grade 2

NBT: Number & Operations in Base Ten

B: Use place value understanding and properties of operations to add and subtract

5:
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. What tools does Ms. LaCour use to support her ELL students?

2. What are the benefits of having students lead the number talk?

3. How do number talks encourage students to try new math strategies?

School Details

Acorn Woodland Elementary School
1025 81st Avenue
Oakland CA 94621

Data Provided By:

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Engaging in Productive Struggle: Number Talks

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Students in Monique LaCour's second grade class explore subtraction strategies through student-led number talks. Class begins with a review of number talk roles and sentence frames. Then, students break off into small groups for the number talk, where they share and try new strategies to solve a subtraction problem.

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common core resources /mathematical practice standards /

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My dad gave me one dollar bill
'Cause I'm his smartest son,
And I swapped it for two shiny quarters
'Cause two is more than one!

- Excerpt from "Smart," by Shel Silverstein

As a student, I struggled with math. I didn't understand why it came so naturally to some students, but not to me. Looking back, however, I realize that I had an advantage that I wasn't even aware of - I understood the language in which the problems were written, even if I didn't understand how to solve them! Although it is easy to assume that many English language learners (ELLs) will excel in math because math is a "universal language" and students may have had prior educational experience that included mathematical instruction, that assumption can lead educators astray.

As I spoke with teachers and did research for this article, it became very clear that making sure that students understand math vocabulary and have ample opportunities to use it are very important. Solving word problems, following instructions, understanding and using mathematical vocabulary correctly - all of these skills require a language proficiency that sometimes exceeds our expectations. We tend to think of mathematics as a subject that does not require a strong command of language. In reality, however, mathematical reasoning and problem solving are closely linked to language and rely upon a firm understanding of basic math vocabulary (Dale & Cuevas, 1992; Jarret, 1999).

For many educators, the challenge of bringing language and math instruction together is a relatively new one. ELL teachers who hadn't taught content areas previously are now being asked to lead or support instruction in the math classroom, and many math teachers who don't see themselves as language instructors are now responsible for providing effective math instruction to ELLs.

High school math teacher Hillary Hansen learned just how big a role language plays in math instruction when she taught her first Basic Math course for ELLs last year. She wanted so much to provide the students with the good foundation they needed, but she felt unable to reach the students or engage them in her lessons, and by the end of the year she was exhausted and frustrated.

That summer she had an opportunity to join a district Sheltered Instruction Observation Protocol (SIOP) cohort to receive professional development and support to meet the needs of ELLs in content classes. She learned about the importance of language acquisition, building background knowledge, increasing student language production, and explicitly teaching academic language. She began this school year with a new set of tools and a deeper understanding of the instructional scaffolding ELLs need in order to learn the content while also learning English. I am happy to report that while Hillary still feels challenged and is working very hard, this year has been much more successful for her and her students.

As a result of more effective instruction, her students:

understand the content better and are working together to find creative ways to learn

discuss math more and know how to use the instructional supports their teacher has in place

are comfortable with math and asking questions to get the help they need.

Hillary feels that she is providing them with the foundation they need not only to understand the mathematical concepts, but also to successfully interact within a math classroom in order to continue learning more advanced concepts.

Following are some strategies that Hillary and some of the other teachers I spoke with found helpful this year, and that they recommend as best practices when teaching math to ELLs.

The importance of teaching academic vocabulary

Vocabulary instruction is essential to effective math instruction. Not only does it include teaching math-specific terms such as "percent" or "decimal," but it also includes understanding the difference between the mathematical definition of a word and other definitions of that word.

The following example, used in a presentation by Dr. Judit Moschkovich of the University of California at Santa Cruz, underscores why vocabulary must be introduced within the context of the content (Moschkovich, 2008):

In this problem, the student is instructed to "find x." The student obviously knew the meaning of the word "find" because he/she "found" it on the page and circled it. The student even put a note on the page to help the teacher in locating the lost "x". The student understood the meaning of "find" in one context, but not in the appropriate mathematical context.

I recently helped a math teacher create a Sheltered Lesson, and I was surprised to find that there were some vocabulary words that I didn't understand. My lack of familiarity with the words hindered my ability to do the math problem and gave me a deeper empathy for ELLs who struggle in the same way with vocabulary and comprehending math assignments. Following is a list of tips for explicitly teaching mathematical academic vocabulary:

Demonstrate that vocabulary can have multiple meanings. Help students understand the different meanings of words such as "table" and "quarter," as well as how to use them correctly in a mathematical context.

Encourage students to offer bilingual support to each other. Students will understand material better if they explain it to another student, and the new student will benefit from hearing the explanation in their first language. (Check the hotlinks for a list of bilingual translations of math vocabulary in multiple languages).

Provide visual cues, graphic representations, gestures, realia, and pictures. Offer students the chance to work with objects and images in order to master vocabulary. If there aren't enough items for each student, use manipulatives on the overhead or posted throughout the classroom, and demonstrate the vocabulary in front of the students. For example, Hillary created a Math Word Wall that has three parts: key vocabulary, "in your own words" definitions, and a variety of ways to portray a function. For example, multiplication is portrayed by the following symbols: x, *, and ( ).

Identify key phrases or new vocabulary to pre-teach. This strategy will help students decide which math function they should apply. Example: "more than" means "add." (See hotlinks for more references about math vocabulary.)

The importance of reading and understanding written math problems

Written word problems present a unique challenge to ELL students and teachers alike. In Reading and Understanding Written Math Problems, Brenda Krick-Morales writes, "Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation - ELLs who have had formal education in their home countries generally do not have mathematical difficulties; hence, their struggles begin when they encounter word problems in a second language that they have not yet mastered" (Bernardo, 2005).

Teacher Xiao-lin Yin-Croft has encountered this pattern in her classroom of bilingual Chinese students in San Francisco. She has developed a very creative way to use her students' background knowledge of math as a stepping stone for other language learning. She does this by accelerating math instruction at the beginning of the school year and then building on what students have learned in math in reading and other content areas. In Building Bridges for the Future, a Colorín Colorado "From the Heart" article, Xiao-lin explains her strategy:

First, we read math word problems; I demonstrate the logical thinking process while translating words into pictures and, finally, into number sentences. Soon, they start to explain their own thinking after reading complicated word problems that involve several steps. They correct each other, and argue about which number sentences they should use to arrive at the correct final results. As they sharpen their math skills, I capitalize on their enthusiasm to teach them how to extract the most important information from texts, and move them toward the oral and reading fluency they need to understand and discuss more challenging texts.

Even if you aren't accelerating math instruction, however, there are a number of ways to help students master word problems. Krick-Morales offers suggestions in the previously mentioned article, such as explicit instruction of key vocabulary, daily practice of problem solving, repeated readings of the word problem together as a class, and hands-on activities such as movement, experiments, or drawing to help students comprehend the problem. As students become more familiar with math vocabulary, they will be able to solve problems more easily.

The importance of building background knowledge

As the opening quote from the Shel Silverstein poem reminds us, background knowledge plays a critical role in math class! My colleague Hillary found that sometimes her students would get "lost" in a problem simply because they didn't understand the context. Following are some tips to help in building background knowledge of students.

Modify the linguistic complexity of language and rephrase math problems. Students will understand the problem better if it is stated in shorter sentences and in language they understand.

Guide students to cross out the unnecessary vocabulary in word problems. Doing so allows students to focus on the math function required. For example, one problem Hillary's students came across referred to a "school assembly." Even though the meaning of that phrase wasn't important in the solving of the math problem, students didn't know it wasn't important, and the lack of understanding contributed to their confusion.

Build knowledge from real world examples. Try to reinforce concepts with examples that students can picture and talk students through the situation. For example, if you need to paint a room, you need to know how much area will be covered so that you know how much paint to buy. Look for familiar ideas or props that can be used to engage students such as recipes, news stories about the economy, or discussion of personal spending habits.

Use manipulatives purposefully. This is important at all grade levels. Hillary has found math cubes to be very useful in having students represent the numbers in the problems and then manipulate the cubes to get the answer. She used the cubes and the terms "hot" and "cold" numbers when teaching with the concept of negative numbers. Students would use the red cubes as "hot" or positive numbers and the blue cubes as "cold" or negative numbers. As students laid out the number of hot cubes and cold cubes represented, they could easily see if the answer would be a positive or negative number by which color had the most cubes. A problem such as -2 + 1 = -1 would look like this:

The student then removed pairs of cubes - one red, one blue - until they could no longer remove any blocks. The remaining blocks represent the answer.

The importance of increasing student language production in the content area

As I've worked with content area teachers in my district to develop Sheltered Instruction lessons and activities to enhance ELL learning, I've told them, "If a student doesn't say it in your class, they're never going to say it." This is a bit dramatic, but it's true to some extent. When students learn new vocabulary, the opportunity to use it must be presented in class, because students are unlikely to try it out on their own - especially academic words like "parallelogram" or "function"!

Here are some tips to increase student-to-student interaction with academic language in the math classroom:

Have students translate symbols into words, and write the sentence out. Hillary used this strategy to check students' comprehension of problems before they solved them. For example, 3x + 4 = 16 would be written out, "Three times X plus four equals sixteen." This helps students process the operations involved in the question and gives them an opportunity to think through how to solve it. It also gives students a chance to familiarize themselves with important vocabulary words.

Create a "sentence frame" and post it on the board. Write the format of the sentence you would like students to use in discussion and then hold them accountable for using it. For example, "The answer is _______ degrees because it is a _________ triangle.

Have students share problem-solving strategies. This involves asking a simple question such as, "Did anyone else get the answer in a different way?" Then allow enough wait time so students can think through how their problem-solving process was similar or different to the one offered.

Allow students to discuss how they are thinking about math. This is a way of redirecting the lesson from teacher-to-student to student-to-student. For example a student might ask a question, "How do you know what kind of triangle it is?" Instead of the teacher answering and going to the board and pointing out the names and different triangles, the teacher can simply ask, "Does someone have an answer? Or "Would someone like to offer help to Mario?" Allow students to share how they think about the math concept and any tips they have for remembering the information.

Incorporate writing activities like math journals. This is an excellent way for students to process what they've learned and what questions they still have. The journal could start with simple prompts such as, "One thing I learned today..." "One thing I still don't understand..." "One way I can get the help I need..." "The answer to this problem is..." Writing out the answer to a problem is a very important skill to develop because many state math tests require a constructed response to questions.

Challenge students to create their own math problems. This can be a fun activity if students create a problem similar to the ones you have used in class and they exchange problems with a partner. By creating the problem and checking the answer they are reinforcing their own learning.

Using technology

Technology can also be a powerful tool in math instruction for ELLs. Here are some ideas ways you can play with technology in a math lesson:

Look for educational resources that accompany your school's technology tools and programs. There may be online or software programs available for teachers. For teachers who have an electronic whiteboard in the classroom, there are many resources available on links that can be easily accessed and brought into the classroom.

Look for interactive games that offer students a chance to practice their mathematical skills. Nintendo DS has an educational game called Brain Age, which is not language specific. The game provides excellent mathematical training for numbers and tracks results, showing student improvement over time.

Find out what's available online. Vital NY (Video Teaching and Learning for NYS Educators) on Teachers' Domain offers an online library of free media resources from the best in public television. Teachers' Domain resources include video and audio segments, Flash interactives, images, documents, lesson plans for teachers, and student-oriented activities. (Free registration required.)

If students are using a graphing calculator, ensure that they learn how to use it. Based on background and prior educational experience, students might not be familiar with how to use a calculator nor some of the more sophisticated models, such as the graphing calculator. Give students a chance to practice solving problems with their calculators once you have reviewed different functions. Texas Instruments offers numerous activities and product tutorials in their educational materials.

Even if it doesn't come easily at first, there are ways to get ELLs excited about math. By keeping their language skills and needs in mind when planning mathematical instruction (and by helping your colleagues do the same), you will be taking important steps in helping students master mathematical concepts and skills - and who knows? Your students may be the next generation of economists, rocket scientists, and math teachers just waiting for the tools they need!

Note: I'd like to thank my Minnesota colleagues, Hillary Hansen at Burnsville Senior High School and Kim Olson at Hidden Valley Elementary, as well as Xiao-lin Yin-Croft from San Francisco, for providing many of the helpful math teaching tips in this article. It is inspiring to know that there are talented, creative teachers who are always finding better ways to teach and are willing to share the knowledge.
Common Core Math and ELLs: Blog Posts
These posts from our Common Core blog highlight resources that can be used in Common Core math instruction for ELLs.
EngageNY: Common Core and Math
The EngageNY website provides materials focused on curricular examples, standards for mathematical practice, and other materials for professional development.
Discovery Education: Puzzlemaker
Puzzlemaker is a free puzzle generation tool for teachers, students and parents where users can create and print customized word search, criss-cross, math puzzles, and more using their own word lists.
Catherine Snow: Word Generation
Catherine Snow's new website provides information and resources for educators who would like to learn more about Word Generation and how it is implemented. Includes links to comprehensive academic word list that students need to master to comprehend academic content.
Dave's Math Tables: English/Spanish Dictionary
List of English math vocabulary words with the Spanish equivalent.
PBS Teachers: Math Lessons
PBS Teachers offers a database of multimedia math lessons and activities that can be searched by grade or topic.
SMART Notebook Lesson Activities
Browse lesson activities and materials for classrooms using SMART notebook software. Choose the country or region, and search by curriculum standards, subject and grade level.
Colorín Colorado Webcast: English Language Learners in Middle and High School
This webcast features Dr. Deborah Short and discusses effective instructional strategies for teaching English language learner students in middle and high school, such as the SIOP model.
Translating Word Problems
This is a great site for teachers in the elementary levels, as it provides a list of keywords you can teach your ELLs to look for as they read word problems. Also included are useful ideas and tricks to better prepare students to understand written math problems.

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Math Instruction for English Language Learners

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My dad gave me one dollar bill'Cause I'm his smartest son,And I swapped it for two shiny quarters'Cause two is more than one! - Excerpt from "Smart," by Shel Silverstein As a student, I struggled with math. I didn't understand why it came so naturally to some students, but not to me.

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Graphs
manipulativess
place value blocks
visuals (representations and models)
use of white boards and markers
graphs
graphic organizers
modeling the problem
computer programs

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-poster cues
-sentence frames
-student presentations
-number talks
-direct instruction of vocabulary
-small group instruction
-feedback
-opportunity to share student work
-accountable talk moves
-partner work
-group work
-student work analysis
-choral repeat
-word bank/word wall
-allow L1
-rephrasing w/content language
-cognates
-peer review
-Gallery Walk
-Error Analysis
-Stations with assigned roles
-Language Body
-Consistent usages of posted basic sentence stems
-Train students in S-S Collaboration

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-example on page
-manipulatives (unifix cubes, straws, 10 frames)
-wait time for determining structure
- strategic grouping
- place value charts
-Anchor charts
- math models
-think aloud
-word bank (sentence starters/frames)
- discussion protocol or process
-native language

# data[].attributes.body
-sentence starters, frames, and stems
-pre-teach vocabulary in native language (video articles)
-word walls with pictures and organized by unit
-word bank in English/native language
-Math language dictionaries
-reduce number of tasks
-number/concept charts
-strategic partnering
-modeling expectations

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1. Make sense of problems and persevere in solving them

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1. Make sense of problems and persevere in solving them

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-Non-verbal demonstration (e.g. acting out)
-Illustrations/visual models and videos
-Vocabulary instruction (word walls, sentence frames, consistent use of vocabulary, 7 steps)

-Cognates, translate into L1, bilingual dictionary

-Reusable structures for activities (e.g. routines for small group talks, assigned roles [facilitator, scribe, reporter, etc.])
-Graphic organizers
-Anchor Charts
-Slow release of responsibility
-Intentional small groups
-Partner talk
-Time to process alone
-Whole class discussion
-Introduction of multiple problem-solving strategies

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manipulatives:
calculators
number charts/number lines
place value base-ten blocks
pattern blocks
cuisenaire rods
connecting cubes
counter and ten frames
visuals:
videos
grphs
graph paper
tables
reference sheets
word bans
word walls
anchor charts
part/part/whole models
translating technology
white-boards
Realia:
measuring tape
rulers
real money
clocks
stop watches
3-D objects
building blocks
refection on strategies

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- Sentence Starters/Frames
- Teaching multiple strategies
- Group Work/Peer Support
- Discussions
- Graphic organizers
- Questions provided that students can ask

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I was told not to put other languages for key vocabulary on my worksheets because “it’s a waste of time.”

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I was told not to put other languages for key vocabulary on my worksheets because “it’s a waste of time.”

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This interactive middle school science testlet on forces and motion contains 5 multi-part tasks.

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This interactive elementary mathematics testlet on pre-algebra operations and reasoning contains 5 multi-part tasks.

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Amazon.com: Be Amazing! Toys Energy Stick: Toys & Games

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Discussion and Supporting Materials

Thought starters

1. What are academic conversations?

2. Why is it important to value oral language?

3. How can you engage students in academic conversations?

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Academic Conversations with ELLs: Series Overview

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Discover how to engage ELLs in academic conversations. Maria Santos and Jeff Zwiers provide an introduction to a video series on academic conversations. Jeff describes the importance of oral language while Maria introduces how OUSD has been focusing on academic conversations.

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Math Word Wall

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Doing and talking Math and Science

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"Everyone tells us we need to teach this way, but no one has shown us how. This shows us how!"

~ teacher at NSTA conference in 2014

"For the first time in over 20 years of teaching, I'm confident that my students understand this. They don't need to memorize formulas or math jingles. They really understand the math."

~ a seventh grade Algebra teacher

"When I do my walk-arounds, I see 100% engagement in high-level math discussion. That's never happened before, and it's exciting."

~ principal in a participating school

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"Everyone tells us we need to teach this way, but no one has shown us how. This shows us how!" ~ teacher at NSTA conference in 2014 "For the first time in over 20 years of teaching, I'm confident that my students understand this. They don't need to memorize formulas or math jingles.

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Mathematics Implementation Resources - Science, Technology Engineering, and Mathematics (STEM)

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In Massachusetts, mathematics education builds students' understanding and skills through active engagement in meaningful mathematics. The content and practice standards included in the Massachusetts Mathematics Curriculum Framework focus on developing students in the following areas: