This session will present strategies to help teachers teach mathematics to English language learners including hands-on differentiation activities for teachers to do in the session.

1. Diana Cagle
ELL Symposium 2014

2. Choose a card from the front desk and
without talking find your partners
Once you have found your group, take a few
minutes to get to know them
We will share out afterwards

3. Academic Purpose Relationship Purpose
•Ability Grouping
(same level or peer
tutoring)
•Pick Their Own Group
(Good for feeling of
comfort but bad for social
or behavior)
•Gender Grouping
(female/female and
male/male)
•Fun Grouping
(pick cards, favorite foods,
animal with sounds, etc)
•Behavior Grouping
(some students just cannot
learn together)
•Quiet With Loud
(get those quiet students to
build relationship with the
loud ones)
WHAT KIND OF GROUPING DO YOU THINK THE ELLs WOULD LIKE AND WHY?

4. Positive teacher-student, student-student, and teacher-
family relationships are associated with:
• Increasing student feeling of safety at school
• Increasing academic test scores
• Increasing student understanding and meaningfulness of what is being
taught
• Reducing absenteeism
• Decreasing student dropout
• Decreasing student-student conflict
• Improving school climate
• Improving transition to school
• Decreasing risk-taking behavior
• Developing language skills
• Improving self-esteem
• Decreasing incidences of depression
WHY WOULD THIS MATTER FOR OUR ELLs?
(Slade, 2011)

5. Use certain color markers for teaching
Example: Write new content vocabulary words
always in blue, non-content vocabulary words in
red, write problems in purple, and steps to
solving it in orange, etc

6. Function is a relation for which each value from
the set; the first components of the ordered pairs
is associated with exactly one value from the set of
second components of the ordered pair
WHAT TROUBLE MIGHT ELLs HAVE WITH THIS
DEFINITION?

8. 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.
Provide visual cues, graphic representations, gestures, 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 ELMO or posted
throughout the classroom, and demonstrate the vocabulary in
front of the students.
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.
(Robertson, 2009)

9. Math Word Wall (No matter what grade level
you teach)

10. Frayer Model (Great for new vocabulary)

11. Choose a math vocabulary word that your
group can create a Frayer model with
Use the Frayer model that I have provided
for you
We will share out afterwards

12. WORD PROBLEM:
Maria has 24 marbles which is 8 fewer than
Pablo has. How many marbles does Pablo
have?
WHAT ACADEMIC AND
NONACADEMIC VOCABULARY
WORD(s) MIGHT NEED TO BE
INTRODUCED HERE FOR ELLs?
HOW WOULD YOU INTRODUCE IT?

13. 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.
Build knowledge from real world examples. Try to reinforce
concepts with examples that students can picture and talk
students through the situation.
Use manipulatives purposefully. This is important at all grade
levels.
(Robertson, 2009)

14. WORD PROBLEM:
Laura has a blue rope and an orange rope. The
blue rope is 14 meters shorter than the orange
rope. Laura also has 6 meters of duct tape. The
orange rope is 16 meters long. How many meters
of rope does Laura have in all?
WHAT MIGHT YOU NEED TO HELP ELLs WITH IN
THIS WORD PROBLEM?

15. Have students translate symbols into words, and write the sentence
out. 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.
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. 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.
Challenge students to create their own math problems. By creating the
problem and checking the answer they are reinforcing their own learning.
(Robertson,2009)

16. Teach students how to use a calculator. 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.
Look for educational resources that accompany your school's
technology tools and programs.
Look for interactive games that offer students a chance to
practice their mathematical skills.
(Robertson, 2009)

17. Each group come up with one myth and one
reality about differentiation.
Once you have one, come and put it up on
the chart that is provided on the wall.

18. MYTHS REALITY
Differentiation is another word for
“individualization”
Differentiation is not a synonym for
individualization
Teachers do not teach Teachers are the key to making all of
this work
Differentiation is only for the very
high students or the very low
students
Differentiation is for all students
No fair way to grade Teachers grade based on mastery
Students will not be prepared for
high-stakes testing
Students will be more prepared for
high-stakes testing
Students receive unbalanced
workloads
Students receive the same amount of
workload based on their own ability
Teachers teach so students should
learn.
Teachers must realize everyone
learns differently
Teachers have no time Saves time in the long run
(Wormeli, 2006)

19. Six ways to differentiate instruction
1. Process – how you teach
2. Product – what the students will produce
3. Content – different skills
4. Readiness – level the complexity of the skill
5. Interest – choice activities
6. Learning Modality – auditory, hands-on, etc

20. ( Lazzaro, 2010)

21. Dinner Menu
Main Dish (Select 1)
Measure the length of the objects in the measurement container using any of the
nonstandard units we have used in class.
Use the large paper clips to measure the pictures of the objects on the worksheet R
17.1
Complete the “Different Units of Measure” worksheet.
Side Dishes (Select at least 2)
Read the book The Biggest Fish. Measure the length of the fish in the fishing net to
the nearest inch. Then glue them onto a sentence strip from shortest to longest.
Complete the “What’s My Length?” activity.
Use a ruler to draw and label lines for the following measurements: 10 inches, 5
inches, 3 centimeters, 15 centimeters, 1 foot, 1 inch, 3 inches, and 10 centimeters.
Organize the pictures of the objects in order from smallest to largest.
Complete the “How Far to the Dragon’s Lair?” activity sheet
Dessert (Optional- Select 1)
Draw a map. Label 4 locations on your map with a large dot. Using you ruler draw
lines to connect these locations. Measure and label these lines on your map to the
nearest inch. Write a story problem on an index card that can be solved using your
map.
Read How Big is a Foot? Then pick 5 objects from the measurement container to
measure using a small paper clip, an eraser, and a ruler. Complete the worksheet for
this activity.
(Dill,2010)

22. WHY WOULD CHOICE ACTIVITIES BE GOOD
FOR ELLs?

23. Rotating Groups
20 minutes of direct instruction (vocabulary,
modeling examples)
20 minutes of a technology group
20 minutes of a project/hands-on group
20 minutes of skill practice
5 minutes for transitions between
groups (approx 1 minute each)
5 minutes at the end for closure
Total: 90 minutes

24. One-Step and Two-Step Equations Example:
First 20 minutes:
1. Introduce new vocabulary associated with equations (variables,
equation, inverse operations, etc)
2. Model ways to solve one and two-step equations (using the
color method)
Next 20 minutes and so on:
1. Activity on computer (mathxl, math-play, mathplayground,
quia, etc)
2. Worksheet solve and write steps in words
3. Cutting and gluing matching equations
Teacher walks around and facilitates learning.
Providing group roles may help groups work together better.
WHY WOULD TEACHING LIKE THIS HELP ELLs?

25. Think about a topic that your group would be
able to use in differentiating groups
What activities would each group do?
What vocabulary words would you have to
pull out for your ELLs?
What things would you have to model and
how would you model it?
Is there any other problems or questions that
ELLs might face in this section?
Share with whole group afterwards

27. Dill, J. (2010). Pinterest. Retrieved from Dinner Menu:
http://www.pinterest.com/pin/245305510926405429/
Lazzaro, T. (2011). Pbworks. Retrieved from ThinkTacToe:
http://2differentiate.pbworks.com/w/page/860118/ThinkTac
Toe
Robertson, K. (2009). Colorin Colorado. Retrieved from Math
Instruction for English Language Learners:
http://www.colorincolorado.org/article/30570/
Wormeli, R. (2006). Busting Myths about Differentiated
Instruction. LookSmart, 1-5.