Strategies for English Language Learners
using EdGems Math
Table of Contents
ELL Levels – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 2
Target Trackers and Self-Assessment Rubrics – – – – – 3
Unit Assessments – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 5
Performance Tasks – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 6
Unit-Based
Strategies
Rich Tasks – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 8
Tic-Tac-Toe Activities – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 9
Vocabulary Journals – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –11
The Multi-Lingual Glossary – – – – – – – – – – – – – – – – – – – – –– – – 14
Student Lessons – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 15
Explore! Activities – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 18
Leveled Practice Activities – – – – – – – – – – – – – – – – – – – – – – – 20
Lesson-Based
Strategies
Teacher Gem Activities – – – – – – – – – – – – – – – – – – – – – – – – – – – 21
Student Gem Activities – – – – – – – – – – – – – – – – – – – – – – – – – – – 22
Online Practice and Gem Challenges
––––––––––––––
23
Exit Cards – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 24
The eBook – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 25
EdGems Core ~ ELL Strategies
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Copyright ©2018 All Rights Reserved
English Language Learner (ELL) Levels
Different states use different language proficiency assessments, but most of the proficiency levels are similar. For
the purpose of this resource, we are using Proficiency Level Descriptors used by many states that include three
levels of language proficiency:
Emerging (includes newcomers):
*Newcomers are ELL students who have been in the country 12 months or less.
• English learners at this level have minimally to somewhat developed oral and written English skills.
• Emerging learners mostly speak at a basic level with one word or short phrases.
• At this stage, students will require a lot of language support in order to communicate.
• Some suggestions to support emerging and newcomer ELLs:
Labeling of illustrations or images
Use of various types of visuals
Connecting words using cognates
Translating words to primary language
Use of sentence frames to communicate
Expanding:
•
•
•
•
English learners at this level have moderately developed oral and written skills.
With proper language support, such as sentence frames and word banks, they can communicate on various
topics.
Students at this level have social language fluency, but require some support in academic language.
Some suggestions to support expanding ELLs:
Use of sentence frames
Opportunities for oral language practice
Word banks
Visuals
Cognates
Students at this level are encouraged to speak in English as much as possible. Use of primary language is always
acceptable, but the use of English language is highly recommended.
Bridging:
•
•
•
•
English learners at this level have well developed oral and written skills.
They are able to communicate in different ways that are appropriate to different tasks, purposes, and audiences.
Students at this level may still need occasional support in academic English.
Some suggestions to support bridging ELLs:
Use of close reading strategy
Communicate with the use of sentence frames
Creating note-making journals
Work in structured collaborative or partner scenarios
ELLs at all levels of English language proficiency fully participate in grade-level tasks in all content areas with
varying degrees of scaffolding in order to develop both content knowledge and English.
EdGems Core ~ ELL Strategies
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Unit-Based Strategies for
Target Trackers and Self-Assessment Rubrics
The Target Tracker, found on every Teacher Unit Page, provides students with a self-assessment tool that helps
them visualize and track their progress on the unit’s learning goals. Students also have a place to record what
components of a learning target needs additional work. Teachers may choose to print this document for students
to include or paste in an interactive math journal.
•
•
The Target Tracker is most beneficial for ELLs when used in tandem with one-on-one, informal conferencing.
•
The Target Tracker provides learning goals in an organized, visual format for each lesson in the unit.
Depending on the students’ level, you can select specific goals for them to focus on (as opposed to the
overwhelming task of them trying to master them all).
•
The conferencing time also provides an opportunity to directly address what certain students might need more
assistance with. Time during the teaching day is tight, but these quick one-on-one sessions can provide a world
of difference for ELLs.
•
Conferencing times can be planned to occur at the same time that a small group is being pulled for front
loading or re-teaching, or while students are working independently, etc. Find a time that works best for you to
ensure that it happens.
These quick mini-conferences are used to meet and set goals for each unit, to help students track their
progress, and to meet again throughout the unit for one-to-one assistance in their areas of need.
Conferences should be planned at least three times per unit, especially for lower level ELLs who greatly benefit
from the direct support. ELLs will feel confident when tracking their own progress, but also from having their
accomplishments reinforced through a quick one-on-one conversation. Since the Target Tracker provides a place
for students to record what they need more assistance in the Skills to Improve section, teachers are able to see the
areas that they can provide one-on-one support with, rather than trying to guess. For many ELLs, they will feel
much more comfortable writing areas of weakness down as they come across them as opposed to directly asking
for help. Target Trackers can also be added to Math Journals or kept in a separate log together for easy access.
Sample Target Tracker Conferencing Format:
Conference 1
On the first day of the unit, set aside time for a quick 1-2 minute conference to meet with each ELL and
give them their Target Tracker for that unit. Go over the learning goals, and select which goals they will
focus on (if you are narrowing their scope of goals to fewer than the number provided). It is important
to model how to use the Target Tracker to record their progress and to note what they need help with.
Conference 2
Using the Target Tracker as a talking point, check in with each student after the first lesson to make
sure they are on the right track (and to make sure they understand how to use the Target Tracker).
Check to see if their goal for the lesson was met, and whether they noted anything in the Skills to
Improve section. When first introducing the Target Tracker, the second conference may include
modeling how to use the Target Tracker again by walking through a problem together, noting what
they did not understand in the Skills to Improve section, and checking off their level of progress.
Conference 3
After another lesson, have a quick conference with each student to check progress again and provide
any one-on-one assistance, re-teaching, etc. Be sure to note the progress that students are making on
meeting their lesson goals.
*Depending on student levels, mini-conferences may be needed as a quick check in for each lesson.
Conference 4
After the unit is completed, meet with the student to review their Target Tracker and note the progress
they made on their goals. Re-teach any concepts they are still missing, if needed. The one-on-one
praise, attention to areas of need and reinforcement of concepts is key.
EdGems Core ~ ELL Strategies
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Student self assessment is another great way to gather information about a student’s understanding of a concept.
Student self assessment is when you give students opportunities to stop, think and determine if they fully
understood a concept after a lesson, project, or cooperative learning experience. It can be extremely helpful
for ELLs, as it gives them time to slow down and process what they are learning. Self assessment also improves
metacognitive skills, increases self awareness, and encourages critical thinking. Allow students to stop, think, and
self assess using a tool such as the Math Self Assessment Rubric below. Rubrics can be adjusted and customized
based on the concept being taught.
Math Self Assessment Rubric
4
2
3
Advanced
Proficient
Somewhat
Proficient
I am starting to
understand the math
concept but still need
some help.
1
Emerging
I fully understand the
math concept and
could teach it to a
classmate.
I have a strong
understanding of
the math concept
even though I may
sometimes make a
mistake.
I correctly used 4
new math terms in
my project.
I correctly used 3
new math terms in
my project.
I correctly used at
I did not incorporate
least 1 new math term any new math terms
in my project.
in my project.
Mathematical
Strategies
I used the
appropriate math
strategy and my math
computation was
correct on the first
try.
I use the appropriate
math strategy and my
math computation
was correct after 2
tries.
I am still learning
how to use the
appropriate math
strategy but
am starting to
understand it.
I did not use the
correct math
strategy and my
math computation is
incorrect.
Oral
Presentation
I can explain the
math concept
correctly using
academic language.
I can explain the
math concept
correctly using some
academic language.
I can explain the
math concept
correctly using
everyday language.
I cannot explain the
math concept.
Content
Vocabulary
I do not understand
the math concept yet
and I need a lot of
help.
Customize
based on project
(teachers can
customize this
row based on
activity)
EdGems Core ~ ELL Strategies
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Unit-Based Strategies for
Unit Assessments
Unit Assessments include Selected Response and Constructed Response components. Teachers have the option to
select questions in order to make a targeted assessment by using the Word documents. Because multiple versions
of the assessments are provided, teachers can use the assessment as diagnostic, formative or summative feedback.
Unit Assessments can be differentiated to meet the various types of learners in your classroom.
•
Teachers have the option of creating targeted assessments. They are able choose the type and number of
questions to include in the test. Being able to choose the questions allows the teacher to assess the students’
strengths and weaknesses in the unit.
•
There are two types of Unit Assessment:
Version AT and BT are the tiered assessments. These are standards-based assessments that use simpler vocabulary and numbers. They have fewer problems and more space for students to do their calculations.
These versions are ideal for English Language Learners and students with learning disabilities or challenges.
Versions A and B are also standards-based assessments, but are more challenging. These assessments use more academic vocabulary and have more complex problems. These versions are appropriate for students who may need the extra challenge.
•
When designing your own assessment using the items provided, you may choose to structure a test so it
starts with easier questions and become more challenging as the test progresses. This enables students to gain
confidence as they start the test.
•
For Constructed Response items, students may be provided sentence frames to better support them in
providing their answers. Below are some ideas for response frames:
- I conclude that…because…
- My findings show that…
- Based on my work, I determined that…
- My calculations show that...
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Unit-Based Strategies for
Performance Tasks
The Performance Tasks provide applications of the standards addressed in the unit. These tasks contain Depth of
Knowledge Level 3 and 4 strategic and extended thinking questions where students apply multiple standards in a
non-routine manner to solve problems. These tasks ask students to explain their own thought processes or critique
the reasoning of others, and they typically take capable and persevering students ten to twenty minutes to solve per
task. Each task has a corresponding rubric.
For Newcomers and Emerging:
•
•
•
•
Create visuals to support student’s understanding of the task.
Front load and pre-teach key vocabulary words. Specifically, teach mathematics vocabulary and connect them
to their math symbols when appropriate.
Break up the task into smaller chunks. It may be appropriate to assign only one part of a task for some
students, or work on the same task over multiple days.
Co-create a pictorial input chart with students: Input charts are visual representations of the concepts you are
teaching.
Select the most important information to aid in understanding of the performance task. Create a large visual of the information. Timelines are helpful when dissecting word problems or performance tasks
that are presented in chronological order. Use a document camera to trace or draw the visual if necessary.
In addition to the sketch, include bulleted notes of all important information.
Decide beforehand how the information should be chunked and color coded. Color-code to distinguish one thought or concept from another.
Write/sketch as you talk to students. Stop to provide frequent opportunities for ‘heads together’ processing of the information. Give specific prompts about what has just been sketched/written.
The next day, add real pictures (usually printed from the computer) during the review of the chart.
For Bridging or Higher:
Use the same strategies as suggested for Newcomers and Emerging students, but with some differentiation.
• Use graphic organizers to help students organize information in the task
Table Graphs- Table graphs can help students organize new information in a chart format. Teachers can model how to create the table graph in front of students.
2 cups = 1 pint
1 cup of cherry juice = .5 pint
cherry juice+lemonade+lemon lime soda=cherry fizzy lemonade
Cherry Juice (pints)
.5
1
1.5
Lemonade (pints)
2
4
6
Lemon-Lime Soda (pints)
3
6
9
Cherry Fizzy Lemonade (pints)
5.5
11
16.5
2
8
12
22
*This chart should be done in front of the students. Model and discuss the conversions and equation. Black numbers
are done together; red can be done with partners or individually.
*This is a great time to bring realia--measuring cup and a pint glass. Demonstrate the relationship between the two
using water or juice.
EdGems Core ~ ELL Strategies
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•
Use a Word Problem Graphic Organizer (see page 17 for template) - these graphic organizers can help students
frame and organize information given in the performance task.
Prepare: What do I know about the problem?
Plan: What do I need to find out?
Solve: What mathematical strategy should I use to
solve this problem?
Review: Which answers make the most sense? Why?
Reflect: Questions I still have...
•
Explicitly teach mathematics vocabulary and have students keep a running learning log of new mathematical
terms. Students should define the word, give an example, and/or include a pictorial representation of the
concept.
Tips for Grouping Students:
• Reading and comprehending math text can be especially hard for English Language Learners. ELLs may need
more time to process and compute complex math texts. Cooperative learning groups can help reduce anxiety
for ELLs in math class.
• For newcomers and emerging students: Group or partner students with someone who speaks their primary
language but has a better command of English. This will help with translation. It is appropriate for students to
speak in their primary language.
• For bridging students and/or higher: You can be more flexible in grouping students.
• Group or partner students who are at the same math proficiency level.
• Group or partner students based on behavior and how well they work cooperatively.
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Unit-Based Strategies for
Rich Tasks
Rich tasks provide an opportunity for open-ended exploration of a topic. These tasks allow access for most levels
of learners and help facilitate rich mathematical discourse in the classroom. These tasks often have more than one
solution and can be solved in a variety of ways. Unlike EdGems Performance Tasks, which are content-specific and
designed to show student proficiency, Rich Tasks are designed to engage learners at their specific level.
Supporting ELLs with Rich Tasks:
• Frontload vocabulary terms
• Provide extra time to complete a task
• Utilize collaborative groupings to:
Provide students with ample opportunities for oral language practice
Allow them to work on problems together
Foster discussions using academic language for their proficiency level
• Discuss, clarify and model the task beforehand - add a guided practice step if needed
• Add visuals whenever possible
• Encourage use of manipulatives
• Use sentence stems
Additional Information on Sentence Stems:
Brainstorm some sentence stems that students can use throughout the year for discussion during Rich Task
activities.
• Make sure they remain visible and accessible for students to refer back to (on an anchor chart or table tent).
• Students can also keep these sentence frames in their Math journals to make them more portable and
accessible (encourage them to refer back to them regularly).
• Have some frames for tasks such as stating information, affirming a statement, and disagreeing with a
statement.
•
For example:
In order to…
I agree with your statement/idea/answer that…
I disagree with your statement/idea/answer because…
TIPS:
Always refer to the task when asking students to share ideas in whole group instruction.
Don’t be afraid to make changes in student groupings throughout the year.
Remember, your students’ language proficiencies are also improving, so the sentence frames may become more
complex as the school year progresses.
• Circulate around the room while students are working on the rich tasks. Make sure that they are using
academic language.
• For newcomers and emerging students, it is appropriate to use their primary language. However, encourage
students to use some of the academic vocabulary in either their native language or in English.
•
•
•
EdGems Core ~ ELL Strategies
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Unit-Based Strategies for
Tic-Tac-Toe Activities
Each unit has a corresponding Tic-Tac-Toe Board. Each Tic-Tac-Toe Board includes nine activities that extend
or look at the content of the unit in different ways. The Tic-Tac-Toe Boards include activities that make use of a
variety of multiple intelligences. Examples of activities range from writing (i.e., writing a story where the characters
are fractions and decimals), to calculating Body Mass Index, to making a brochure illustrating how to use number
lines to perform integer operations. The activities described on the Tic-Tac-Toe Boards can be found below each
unit’s Tic-Tac-Toe board, accessible on every Teacher Unit Page.
Tic-Tac-Toe activities can greatly support ELLs. These tasks provide authentic, and often kinesthetic, ways to
interpret math concepts. These activities also allow for real-life simulation of various mathematical tasks. The use
of models, organizers, movement and cooperative groups incorporated into the Tic-Tac-Toe activities provide
embedded support strategies for students.
Teachers can support ELLs by:
•
•
•
•
•
•
•
Using sentence stems and/or sentence frames when working though Tic-Tac-Toe activities.
Posting frames around the classroom and refer to them often as students are working in small groups.
Encouraging students to write or paste math phrases in a math journal.
Giving students plenty of opportunities to orally discuss math strategies, concepts and processes.
Providing models, diagrams, or graphic organizers when appropriate.
Allowing students to complete the tasks in collaborative groups.
Showing pictures, graphics, or realia that allow students to “see” what is being asked of the task.
Students may also benefit from self assessment once a Tic-Tac-Toe task is completed. Self assessment allows for
students to develop metacognitive skills, increase self-awareness, and help to take control of their learning. Self
reflection is a lifelong skill that students will carry with them into their professional careers. Allowing time for
student reflection is also a great way to incorporate critical thinking into the classroom. See example below.
Sample Self Assessment Rubric
**Adjust based on activity and needs of students
4
Advanced
Content
Vocabulary
3
Proficient
2
Somewhat
Proficient
1
Emerging
I do not understand
the math concept yet
and I need a lot of
help.
I fully understand the
math concept and
could teach it to a
classmate.
I have a strong
understanding of
the math concept
even though I may
sometimes make a
mistake.
I am starting to
understand the math
concept but still need
some help.
I correctly used 4
new math terms in
my project.
I correctly used 3
new math terms in
my project.
I correctly used at
I did not incorporate
least 1 new math term any new math terms
in my project.
in my project.
(continued on next page)
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Mathematical
Strategies
I used the
appropriate math
strategy and my math
computation was
correct on the first
try.
I use the appropriate
math strategy and my
math computation
was correct after 2
tries.
I am still learning
how to use the
appropriate math
strategy but
am starting to
understand it.
I did not use the
correct math
strategy and my
math computation is
incorrect.
Oral
Presentation
I can explain the
math concept
correctly using
academic language.
I can explain the
math concept
correctly using some
academic language.
I can explain the
math concept
correctly using
everyday language.
I cannot explain the
math concept.
Customize
based on project
(teachers can
customize this
row based on
activity)
ELLs may also benefit from using a Math Word Problem Graphic Organizer (see page 17 for template) like the one
below. Graphic organizers can help facilitate student thinking and support students in breaking down a task before
they attempt to solve a problem. This gives them critical think time and allows them to make a plan on how to
solve the task at hand. ELLs may also benefit from completing this graphic organizer in collaborative groups.
Word Problem Graphic Organizer
Use this graphic organizer to help students organize information from word problems.
Prepare: What do I know about the problem?
Plan: What do I need to find out?
Solve: What mathematical strategy should I use to
solve this problem?
Review: Which answers make the most sense? Why?
Reflect: Questions I still have...
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Unit-Based Strategies for
Vocabulary Journals
A special vocabulary journal, or a process for adding vocabulary to a general math journal, can provide excellent
practice and a reference for students to look back to when they come across a difficult word.
Newcomers and Emerging:
•
•
•
•
•
Write translations of the vocabulary word in the journal.
Adding visuals and examples they are working with from the text helps make the connection to the math term
more concrete.
Once this process becomes routine, ELLs will know what to expect and understand how this procedure can
benefit them.
Refer to the journal often so students get used to using it while working.
Another ELL strategy that works with vocabulary journals is to highlight any terms that are cognates. This
helps solidify the meaning for ELLs. *Cognates are words in two languages that share a similar meaning,
spelling and pronunciation.
For example, the word symmetry in Spanish is “la simetría.” The two words are very similar in spelling and
pronunciation, and they also have the same meaning.
Research has shown that 30-40% of all words in English have a related word in Spanish. That means that Spanish
speakers already have access to a huge amount of math vocabulary! As teachers, we need to help them make these
connections and capitalize on this vast amount of vocabulary that likely already exists within our Spanish speaking
ELLs.
Examples of Cognates in Math
English
angle
absolute value
acute triangle
algebraic expression
area
circumference
common denominator
line of symmetry
simplify
solution
standard form
sum
EdGems Core ~ ELL Strategies
Spanish
el ángulo
el valor absoluto
el triángulo agudo
la expresión algebraica
el área
la circunferencia
el denominador común
la línea de simetría
simplificar
la solución
la forma estándar
la suma
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Vocabulary Journal Sample Format
Word(and possible root
word)
Example 1 (Including
image and pg. #)
Word in Spanish (or
other home language)
identify cognate if
applicable
Example 2 (Including
image and pg. #)
Definition
Example 3 (Including
image and pg. #)
Image
Example 4 (Including
image and pg. #)
Sentence frame:
Sentence frame:
Sentence frame:
*Sentence frames should help students explain their reasoning (their answer, how they got it, etc.), and should include
some of the important unit vocabulary.
Bridging:
•
•
•
Create a vocabulary graphic organizer that supports their understanding of a vocabulary word.
Adding cognates and translations are good but not necessary for this level of ELLs.
Below is an example of the graphic organizer.
Notes
Definition
Vocabulary Word
Example
Non-Example
If you are choosing to add vocabulary to a general math journal being used in your classroom, set aside time to
plan and organize the journal in a way that will be useful to them.
• At the start of a unit, add a few pages dedicated to vocabulary in students’ journals.
• Leave a good amount of space, as they will be adding vocabulary and examples as the unit progresses.
• Leave room for visuals, definitions and examples (with page numbers from the lessons that the examples come
from).
• Have students tab the vocabulary section of each unit so that it is easy to find and refer back to.
Another useful strategy for taking notes by all ELLs is called Note Making. Note making allows for students to
pause to respond and reflect to the notes as they go. It encourages students to go beyond simply recording the
information.
Many students are accustomed to taking notes and listing the main points of a lesson, but they do not always
absorb the information or go back and use their notes. By adding their own reflections and perceptions, their own
ideas are validated and it becomes more meaningful; connections are then more likely to be made.
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Directions:
To set up Note Making, use a premade graphic organizer, or guide students in setting up notes in a format similar
to this:
Notes
Response
•
•
Students take their notes in the first column.
Rather than simply copying what the teacher is telling them, students will stop at various points to reflect on
what they are writing.
Does it make sense to them?
Does it remind them of something else?
Can they think of an example from their own lives?
This makes notes more meaningful for students, and allows them to have a connection to the concepts. It also
requires them to pause and think about what they are writing, and gives the opportunity to note if something is
confusing to them.
TIPS:
You can also use the note making as a formative assessment by noticing in the response section if computations
during the student’s reflection are incorrect. This allows teachers to quickly check for student understanding and
see student thought process.
ALL ELLs:
A Math Word Wall is also helpful in teaching students mathematical vocabulary. Although rarely used in the
secondary setting, a math word wall that a teacher consistently updates and refers to can assist students in
developing academic language.
• A Math Word Wall can be divided by unit. Each unit will include specifically chosen words that a teacher will
add as they appear in the unit.
• When introducing a new word, say and show the word, allow students to say the word, show the phonetic
spelling, give a definition, share examples and create a visual or symbol (if possible) that supports in student
understanding.
• Add the word (you may also choose to add the definition, a phonetic spelling and/or symbol) to the wall in
front of students.
TIPS:
Point to the word on the wall often. Be careful not to allow the word wall to become wallpaper - the more you use
it, the more valuable it will be for students.
• Word walls can be individualized to each classroom, depending upon the needs of your students.
• Word walls can be enhanced by adding clear visuals for students.
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Unit-Based Strategies for
The Multi-Lingual Glossary
This tool can be found as a footer, accessible on every student page in the Student Materials. In the multi-lingual
glossary, students have access to an extensive middle school math glossary, specifically for grades 6-9.
• The Multi-Lingual Glossary is featured in the following languages: Arabic, Chinese, French, Haitian-Creole,
Portuguese, Russian, Spanish, Tagalog, and Vietnamese.
• These glossaries can be an extremely valuable tool for students learning English. Students can use these to help
update their Math Vocabulary Journals, clarify cognates, or during peer discussions.
• Teachers should model for students how to use this tool and how to navigate the various pages.
• Students should print their glossary and keep them in their Math Vocabulary Journal as a go-to tool. The
glossary can also be a great resource when teaching math-specific vocabulary to students.
• Once students click on the Glossary link (see arrow below), they are taken to a page with links to the glossaries
in the languages listed.
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Lesson-Based Strategies for
Student Lessons
The student lessons are designed so that concepts can also be practiced at home, and so that students and parents
can learn a concept together through the examples provided. The detailed examples with step-by-step solutions
provide a springboard for learning the concept through mathematical representation before tackling problems
on their own. The examples also provide a variety of abstract and concrete representations of the concept being
addressed.
NOTE: All Student Lessons are also available online in Spanish.
Student Lesson Tips:
•
Spanish Language Option: All Student Lessons are provided online in Spanish, which is a great way to
increase parent involvement and understanding in guiding their students through the student lessons at home.
•
Use of the Target Tracker: Each lesson starts with a “target” (an objective) that matches those on the Target
Tracker on each Teacher Lesson page. Start by reading the target out loud to reinforce the most important
concept to focus on in the lesson. Refer back to it at the end of the lesson to see if the Target was met, using the
Target Tracker to record success and identify areas of need.
•
Vocabulary: Since these lessons contain informational text, vocabulary should be addressed first. Key
vocabulary is provided in the student lessons, and should be added to the student’s vocabulary journal (or
vocabulary section in their math journal). If the term is already in their journal, they can add an example from
the lesson (with page number) to that section of their vocabulary journal space to solidify their practice with
the word/concept.
•
Selection of Specific Problems: For ELLs, narrowing down the number of problems can be used in the
student lessons. Students should read all instructions, vocabulary, the introductory text, etc., but the number
or problems completed on their own can be narrowed down based on the Depth of Knowledge Level (1-3)
that they are arranged in. For example, some lower level ELLs (especially newcomers) may only be asked and
expected to complete the first level of practice problems. The expectations for different levels of ELLs can and
should vary, and it is appropriate to pair down the number and level of tasks expected for certain levels to
complete.
•
Manipulatives: These are a great tool to have readily available for ELLs. They should also be able to take them
home in order to use them with the Student Lessons. For example, if the problem calls for determining the
number of certain colors of jelly beans, colored counters should be provided to assist students in solving the
problem.
•
Review Problems: At the end of the Student Lessons, there are Review Problems that also serve as Warmup problems for the next lesson. This is an excellent opportunity for frontloading for ELLs. Based on what
is appropriate for your classroom, the Review Problems could either be used to check for understanding, or
to prepare your ELLs for what is coming next. Attaching a few upcoming vocabulary terms to this section
would help frontload for your ELLs as well. This section could also be used as something that you do in class,
as opposed to at home (for instance, if you wanted to meet with them in person to clarify concepts, check for
understanding or pre-teach specific parts of the upcoming lesson).
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The informational text nature of the lessons can also call for a Close Reading Protocol, explained in detail below.
Close Reading Protocol:
•
•
•
When addressing informational text, a Close Reading protocol can be applied to deepen understanding.
•
Close Reading can be used as students read the introductory text, as well as the example problems, so that they
are prepared by the time they get to the practice problems.
•
Depending on the text, the problem, etc., steps may be adjusted and/or eliminated.
Close Reading involves reading the same text multiple times, but with a different purpose each time.
The purpose of each read can be changed depending on the problem type or what works for your classroom,
but practicing a basic Close Reading protocol with your ELLs that they can replicate on their own provides
support with text heavy problems.
ELLs may benefit from using a Math Word Problem Graphic Organizer like the one below. Graphic organizers
can help facilitate student thinking and support students in breaking down a task before they attempt to solve a
problem. This gives them critical think time and allows them to make a plan on how to solve the task at hand.
ELLs may also benefit from completing this graphic organizer in collaborative groups. The Word Problem Graphic
Organizer on the next page can be used to assist students with steps 2 and 4 above.
Close Reading Sample Steps:
1. First read: The student reads the text for general understanding (gist), OR, an adult (parent,
teacher, etc.) can read it to the student so they can practice simply listening for overall point
of the lesson, an important skill to utilize as well. The student will then try to describe the
question in their own words. Prompt the students by asking, “Using your own words, what is
this question asking you to do, find or solve?”
2. Second read: The student reads for detail this time. They will identify and highlight or
underline information that will be useful to solving the problem. Are there words used that
they can add a symbol to? (such as writing a + if the word addition is used, a - if the word
subtract is used, etc.) Are there any important words to underline? Are there any parts of
the text that do not make sense to them? Have them write a ? next to those sections. Practice
having students ask, “What information do I need to understand the parts I do not know? How
can I find that information?” By engaging in this process, they may realize they understand the
problem better than they think they do! If they are unable to identify the unknown parts, they
may seek help from a partner, adult, etc. if available.
*Students are also eliminating the parts of the problem they actually DO understand, and narrowing it
down to what they don’t, rather than being overwhelmed by a large piece of text and giving up before
they even start.
3. Third read: Illustrate the problem. How could this problem be represented without numbers?
Not only are illustrations helpful for ELLs in providing visual reinforcement, but also are a way
to provide another means of expressing themselves. It can also take some potential intimidation
of working with numbers out of the way.
4. Fourth read: After completing a problem, does the answer make sense? Does it answer what the
text in the word problem is asking me?
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Word Problem Graphic Organizer
Prepare: What do I know about the problem?
Plan: What do I need to find out?
Solve: What mathematical strategy should I use to
solve this problem?
Review: Which answers make the most sense? Why?
Reflect: Questions I still have...
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Lesson-Based Strategies for
Explore! Activities
Each lesson has an Explore! activity to provide students with an opportunity to discover, apply or practice the
standards in a variety of methods, with a focus on the eight Mathematical Practices. The activities have questions
built in that enable students to reflect individually, as well as share with their partner, group, or in a full class.
Suggestions for implementing Explore! activities in the classroom can be found in the lesson by lesson Teacher’s
Guide.
For Newcomers and Emerging:
Use a piece of paper or cardstock to cover the text. Introduce problems one at a time. This will help prevent
students from feeling overwhelmed by the amount of work and/or text.
•
Close Reading - 1st Read:
Read the problem aloud to students (It helps them to hear what good fluency sounds like.)
Highlight key vocabulary.
Allow students to use Google translate to translate vocabulary to their primary language, or have students use the EdGems Multilingual Glossary located in the footer of the online program.
Draw or diagram to explain if possible. (Draw and Tell)
•
Close Reading - 2nd Read:
Echo read the text. Guide students in annotating the text. Use prompts to guide them. Try to use prompts that require one word or yes or no answers. Students may also use gestures or pointing to communicate their ideas and thoughts. You can provide them the prompts beforehand so they can translate it into their primary language. Don’t hesitate to mark-up the text.
Example prompts:
- What is the __________?
- Underline the __________.
- Is this the __________?
•
Close Read - 3rd Read:
Have students partner read the problem one last time.
Guide students in setting up the math problem (equations, etc.)
Model how to solve the problem. Slow down the steps. (Go back to images or diagrams you previously created. Use gestures to support what you are saying.)
Check for understanding. Solicit questions and need for clarification.
Provide students opportunity to talk with an elbow partner or group to share what they do and do not understand. (Let students teach each other. Use of primary language is appropriate.)
Repeat first and second read steps of close reading for all the word problems.
Allow students to work collaboratively in solving the problems.
Check in with each group as a formative assessment.
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For Bridging or Higher:
•
Use the same strategies as the ones suggested for Newcomers and Emerging students, but with some
differentiation.
•
Instead of translating vocabulary words to their primary language, provide students with a simplified
definition of the word. Use images and illustrations to support your explanation. *Alternative: You can ask
students to find the definition in an online resource before explaining it to them.
•
During the second read, support students with annotating by providing them with highlighters. Provide them
with prompts as you annotate as a class.
Examples of Prompts:
-What important information do we know?
-What is the question?
-What is the problem asking us to do?
Model solving the problem.
Partner students to work collaboratively in solving the rest of the problems.
•
•
Tips for Grouping Students:
For newcomers and emerging students: Group or partner students with someone who speaks their primary
language but has a better command of English. This will help with translation. It is appropriate for students to
speak in their primary language.
• For bridging students and/or higher: You can be more flexible in grouping students.
• Group or partner students who are at the same math proficiency level.
• Group or partner students based on behavior and how well they work cooperatively.
•
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Lesson-Based Strategies for
Leveled Practice Activities
The Leveled Practice assignments are available for each lesson to provide differentiation options. There are three
options for the Practice activities, ranging in skill level. The concepts covered at each level are all the same, but
with different expectations and levels of support. This provides an ideal scaffold for ELLs, who may benefit from
a more customized approach to the exercises through the Tiered level, while giving students that are exceeding
expectations an extra challenge. The Practice levels include:
•
Tiered Practice: This level of practice is for students who need more structured practice (ideal for language
learners). Tiered Practice sheets Lexile at approximately a second grade reading level. This level provides
scaffolded supports with more space and “friendlier” numbers.
•
Proficient Practice: This level of practice is for students who are at grade level and understand the material
without much need for scaffolding.
•
Challenge Practice: This level of practice is for students who have shown proficiency in the current concept
and are ready for opportunities to go beyond the requirements of the standards. The Challenge Practice may
include additional content/concepts from future topics that are not featured on the Proficient and Tiered levels
The Tiered Practice has features that make it more friendly and digestible for language learners. These features
include: 1) less-complex numbers; 2) shorter sentences; 3) more easily understood language; 4) more images and
visuals; and 5) more white space between the questions for work room.
All ELLs:
•
•
Highlight or underline keywords and concepts.
•
•
•
Use their notes to refer back to sample problems.
Remind students to use their vocabulary journals alongside their Worksheet Practice to help with words they
may have difficulty with,
Students may also benefit from using the Multilingual Glossary as an additional support.
If worksheet practice is done in the classroom, try partner work to allow ELLs to have discussions with peers
about the concepts.
Newcomers and Emerging:
•
Newcomers and emerging ELLs may need fewer problems than what is provided on the Tiered Practice. Gauge
your expectations of your students fairly and appropriately.
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Lesson-Based Strategies for
Teacher Gem Activities
The Teacher Gems are made up of eleven different collaborative and engaging activities that teachers can use in
each lesson. There are approximately three Teacher Gem activities per lesson. Each activity includes a “how to”
video, a written step-by-step explanation of directions, and a list of materials needed.
Strategies to support all ELLS:
• Model using the video
• Step-by-step directions
• Visuals
• collaborative discussions, etc.
Use of a discussion card (see example below) during the Teacher Gems activities. Discussion cards include sentence frames that help students in their collaborative discussions.
Categories such as affirmation, asking questions, etc. can each have a list of frames that students can choose from.
TIPS:
It is important to model how to use the frames before every activity to remind students how to use them
during discussions.
• A few reminders when grouping students for academic discussions:
Give specific time limits and instructions.
Make sure students are clear on the topic they are to discuss.
• ELL students may benefit from pre-writing and think time before engaging in the discussion.
• Limit groups to 2-3 students. Anything larger may cause some students to not participate.
• Allow time for students to share out and report on their discussions. This time can also be used to field
questions from their teacher or their peers.
• When possible, integrate student responses into future lessons or discussions so ELLs can make connections to
concepts.
Academic Language Discussion Forms
Ask for information
Share your thoughts
Agree
• Tell me about...
• I concluded that...because...
• My idea/finding is the same as
___
• Explain to me your idea about... • My findings show that...
• What is your perspective on ...? • Based on my work, I deter• I agree with ___’s idea/finding
• What is your response to...?
mined that...
that...
• To add to ___’s idea, I also conclude that...
Disagree
Ask for clarification
Paraphrase
• I understand what your are
• Would you please explain how/ • It is my understanding that...
saying, but I see it as...
why...?
• In other words...
• I disagree with your idea/find- • What do you mean when you
• What you are saying is...
ing because...
said...?
• My idea is different from yours • Would you please explain...a
because I found that...
different way?
•
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Lesson-Based Strategies for
Student Gem Activities
The Student Gems are digital open education resources (OERs) aligned to a Common Core State Standard that
address aspects of the lesson’s targeted concepts. Each resource window features information about the activity as
well as answer keys.
Each activity varies in format and depth of knowledge (DOK). Some are in the form of instructional videos
and interactive task slides, while others are teacher led activities. The final activity is typically a print-based
performance task meant for students to complete on their own. The activities progress from less difficult to more
difficult; so, it is very important that students do them sequentially to avoid feeling overwhelmed or discouraged.
•
•
•
•
•
Resource windows 1, and sometimes 2, often walk students through standards-related concepts. These can be
an ideal introduction to unit/lesson vocabulary and a “big picture” look at what is coming up within the lesson.
Resource windows 3 and 4 are extensions that are suitable for students who have a basic understanding of the
concept being taught. The type of resources vary from paper-based, online activities, etc. These resources can
be done individually or with partners.
Resource window 5 is typically an interactive quiz (i.e., Khan Academy quiz) that should be attempted once
students have a good grasp of the standard. With the Khan Academy quiz, students are able to ask for help in
a step-by-step format by clicking the green text under the question that says “Need Help?” (the steps appear
under the video).
Resource window 6 is a performance task meant for students to complete on their own.
The following are ideas to support all ELLs:
Close reading of the activity directions or problems
Review vocabulary
Read and discuss texts in chunks
Use of highlighters
Mark key vocabulary, data, and question
Provide students with scratch paper
Allow the use of Google Translate or other similar program or device
TIPS:
It is important that you partner your students strategically. You may partner your students based on their abilities
to help them engage in productive talk. For ELLs, your first consideration is to partner your lower level ELL
with a higher level ELL or native English speaker to provide language support. If you feel that your ELL is able
to handle the language with limited support, you may consider their abilities when partnering. It is important to
avoid a higher level student from taking over or doing all the work in the partnership. We want students to work
collaboratively and engage in productive talk.
NOTE: There are answers that students can access for many of the print-based resources. The answer keys are, by
default, “on”. To access the keys, students click the small key icon on the lower right of the window.
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Lesson-Based Strategies for
Online Practice and Gem Challenges
The student Online Practice items are modeled after online standards-based benchmark assessments given in
many states. Each lesson has an online practice set of 10 questions. The problems get progressively more complex
throughout the practice. The student version displays the questions one at a time. There are a variety of styles of
practice items, such as selected response, constructed response, drop down, drag and drop and matrix-style items.
Gem Challenges are four-item, standards-based online quizzes. Each Gem Challenge comes with full, handwritten solutions for both teachers and students. Students can see the solutions after taking Gem Challenge 2.
These challenges are only included in a lesson once a standard has been fully cover.
Teachers can support ELLs by:
•
•
•
•
Read and deconstruct each question together as a class. Use highlighters to identify the question in the
problem.
Use vocabulary journal during the online practice experience.
Vocabulary journals may include definitions, cognates*, word parts, and/or visuals to support understanding.
Have students work with targeted partners.
Avoid creating a partnership where one student dominates the other.
In the case of ELLs, find a partner that will support them in translating the key vocabulary in the questions. Be very clear that partners are not to PROVIDE the answers. Instead, they will work with their
partner to come up with an answer.
Allow the use of technology to support language and vocabulary. For example, use of Google Translate on an
iPad or Chromebook. Also, in the EdGems footer, a Multilingual Glossary allows students to call up common
middle school math terms in 10 different languages.
*Cognates are words in two languages that share a similar meaning, spelling and pronunciation. For example, the
word symmetry in Spanish is “la simetría.” The two words are very similar in spelling and pronunciation, and they
have the same meaning. Research has shown that 30-40% of all words in English have a related word in Spanish.
That means that Spanish speakers already have access to a huge amount of math vocabulary! Teachers should help
students make these connections and capitalize on this vast amount of vocabulary that likely already exists for English
Language Learners.
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Lesson-Based Strategies for
Exit Cards
Exit cards provide a quick and easy informal assessment to check for student understanding. Teachers can gauge
whether students have mastered the lesson concepts and decide the best course of action for next steps. For
example, teachers may need to reteach or follow up with certain students, or as a whole class depending on the
need.
Exit cards are great to use with English Language Learners for a variety of reasons:
•
•
•
Exit Cards are customizable to meet the variety of student levels or needs in their classrooms.
Teachers can assign fewer or shortened tasks to ELLs.
The smaller, more concise format of the Exit Cards may be helpful in easing anxiety for some students, as it
appears less formal and/or daunting than a full sheet.
Teachers can further support ELLs by:
•
Allowing students to tackle exit cards together. Collaborative groups could work well for assessing groups of
students. Groups allow ELLs to get support in completing the assessment and give them an opportunity to talk
and think before attempting the problem.
•
Adding visuals when appropriate. Graphics can lower the affective filter for students and help to make the task
more manageable.
•
Discussing any vocabulary that may be new/unfamiliar to students. Allow students to refer to their Vocabulary
Journal when discussing the prompt.
•
Modeling a think aloud for group of ELLs. Teachers can share their thinking on how they would set up a
similar problem, then allow students to complete the Exit Card on their own.
•
Providing models or diagrams to support thinking.
Exit cards are included in three places:
•
•
•
On the PowerPoint for each lesson (which enables the editing of the Card)
On each Lesson Page as a stand alone resource
In each lesson in the Teacher Guide text (as a highlighted resource), and in the online program.
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Lesson-Based Strategies for
The eBook
The eBook is an online version of the student textbook, with additional features that students can use such as
narration and highlighting that may be particularly useful for ELLs.
Narration Option Benefits:
•
•
The students can have the text read to them.
•
Pairing the reading of the text with a human voice is an extra boost that may help students grasp the concept
being taught.
•
•
Narration gives students access to teacher modeling and language from virtually anywhere.
•
•
Students can also jump around to select parts of the lesson that they may need repeated.
For many ELLs, the option of having something read to them is more digestible than trying to read it
themselves.
Students can point and click on any part of the lesson, and can pause and replay entire lessons or individual
words or sentences as needed.
An actual math teacher walks the students through the entire lesson (as opposed to an unnatural,
computerized voice). *This is particularly beneficial for ELLs, as terminology will be properly pronounced and
equations will be read correctly - hearing the exact phrasing and pronunciation of the terminology (especially with
more complex formulas that have subtle nuances) is vital for English Learners.
Highlighting Option Benefits:
It can be used to emphasize vocabulary terms.
•
Using the keyword search, students can type a word they want to focus on and have it highlighted throughout
the lesson.
•
If there is a term they are required to use in their response, or a key piece to a specific concept they are
struggling to understand, having this highlighted throughout the lesson as a reminder can be a powerful tool.
*An important note: For schools that do not offer one-to-one laptops, the comments or notes that one student makes in
an eBook will remain on the computer used to access the eBook and will not transfer to another computer. In the event
that a student does not use the same computer each day, that student’s comments may become changed or lost with
any additional student use on that device.
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