Math for ESL Students
This session will introduce math activities that integrate
mathematics and English vocabulary using hands-on
manipulatives that engage collaborative learning. We will
explore free resources; engage numeracy by providing a
balance between skill building and functional need; and
demonstrate that games, hard-copies, and computer-based
interactions can create a rewarding instructional balance.
Example activities begin with a problem-posing point (e.g.
mistake on a paycheck), then provide a context for learning
new skills (e.g. subtracting decimals), provide detail (e.g.
Adding decimals), and conclude with practical application (e.g.
adding sales tax for fast food bills).
Presented by: Michael Matos
Albany Park Community Center – Chicago, Illinois
matosmichael2@gmail.com (access to Google Docs)
2016 Forum for Excellence Conference
Wednesday, September 28, 2016 — 2:30 PM – 3:30 PM
This session is sponsored by IACEA.
1
Math for ELA
Web-marking site “Summon Up” at delicious.com/apccctc
2
Math for ELA
Teaching Strategies in Math for ESL Students
The integration of the English language within math content is essential for assisting
ESL students to develop a good understanding of mathematics.
1. Teach mathematical vocabulary and language structures daily.
2. Post math vocabulary cards around the classroom on completed problems, number
lines, rulers, fraction diagrams, and other objects.
3. Model the problem solving process by talking aloud while solving problems on the
overhead, chalkboard, or interactive white board to demonstrate thinking processes.
4. Use math Cloze exercises or sentence prompts for students to copy and complete when
they enter class or during reviews.
5. Give students a computation problem to solve and then have them write the steps they
used to solve it in complete English sentences.
6. Design multi-sensory lessons that address various student learning styles, i.e., visual,
auditory, tactile, and kinesthetic.
7. Use visuals whenever possible to reinforce auditory instruction, i.e., charts, graphs,
manipulatives, diagrams, models, real objects.
8. Provide explicit instructions and practice with reading and writing word problems. Teach
students to identify key words for solving word problems and identifying mathematical
operations.
9. Use graphic organizers to visually represent mathematical concepts.
10.Simplify the language used rather than the mathematical concepts taught by using
known vocabulary and simple sentence constructions.
11.When ESL students speak, focus on their message rather than their grammatical skills
and accuracy. Respond using the proper grammatical form rather than overtly
correcting their mistakes.
12.Integrate reading and writing about math through the use of journals, learning logs, and
literature.
13.Give ESL students alternate ways to participate in whole-class discussions and respond
to questions, i.e., think/pair/share, flashcards to raise over head, hand and/or body
movements, individual chalkboards for solving computations.
14.Integrate hands-on activities by using manipulatives, real life materials, and calculators.
15.Integrate educational technology tools, i.e., Web 2.0 online tools, interactive math
websites, and interactive computer games.
16.Teach math note-taking skills, because copying notes is an effective way for learning
English writing conventions.
17.Review mathematical vocabulary and concepts using math games, examples include TicTac-Toe, bingo, and concentration.
3
Math for ELA
Mnemonics
are useful language devices that improve our memory and
help us to remember.
I.
Order of Operations
Please
Excuse
My Dear
Aunt Sally
1st solve what is in Parentheses
2nd do the Exponents
3rd Multiply and Divide
4th Add and Subtract
II.
Dividing One Fraction With Another
Keep the first fraction, Change the sign from divide to multiply, Flip the last fraction.



Kentucky Chicken Fried
Kangaroo Candy Flowers
Koalas Chasing Ferrets
http://www.onlinemathlearning.com/pre-algebra-mnemonics.html
III.
Simple Interest Formula
Interest = principle × rate × time
• I = prt
read as “I am pretty”
IV.
Distance Formula
Distance = rate × time
• d = rt
remember as dirt
4
Math for ELA
KEY OPERATION WORDS
For Solving Word Problems
ADDITION
SUBTRACTION
Add
All together
And
Both
Combined
How many in all
In All
Increased by
Increase
More
More than
Plus
Sum
Total
Change (for money)
Decrease
Decrease by
Difference
Farther
How many more
How many less
How much left
Larger
Left
Less than
Nearer
Reduce
Remain/remaining
Smaller
So on
MULTIPLICATION
DIVISION
In all
Of
Multiply
Product of
Times (as much)
Total
Twice
Whole
Average
Cut
Divide
Each
Equal pieces
Every
One
Quotient
Split
EQUALS/IS EQUAL TO
Is
The result is
Yields
Is equal to
Is the same as
5
Math for ELA
MATH WORD SORT
From the Word Bank on the other side of the page, choose at least five words
with similar meanings that you can group. Choose three different groups of math
words or phrases, title and explain below why they belong in each group.
Complete with sentences preferred.
Word Group Title 1: _________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
Word Group Title 2: _________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
Word Group Title 3: _________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
6
Math for ELA
Word Bank
add
change (for money)
left
all together
Decrease
less than
and
decrease by
nearer
cut
Total
is equal to
both
Difference
reduce
combined
Farther
remain/remaining
twice
the result is
average
how many in all
how many more
left
is
Whole
multiply
quotient
Smaller
every
in all
how many less
so on
increased by
how much left
each
split
times (as much)
yields
is the same as
Increase
less than
in all
More
nearer
more than
reduce
product of
Plus
remain/remaining
divide
Sum
Total
of
7
Math for ELA
Money Stories, Poems, and Songs
To develop activities and practice for ESL Math
One a Penny
One a penny,
Two a penny,
Three a penny,
More,
Four a penny,
Five a penny,
That's a nickel more.
Six a penny,
Seven a penny,
Eight a penny,
More,
Nine a penny,
Ten a penny,
That's a dime for the store!
Money Rhymes
Twenty five cents,
Money that rhymes,
Take one nickel
Add two dimes.
Three fat nickels,
One thin dime.
Makes twenty-five cents
Every time.
Five fat nickels,
No thin dimes.
Makes twenty-five cents
Any time.
Penny, penny,
Easily spent.
Copper brown
and worth one cent.
Nickel, nickel,
Thick and fat.
You're worth five cents,
I know that.
Dime, dime,
Little and thin.
I remember,
you're worth ten.
Quarter, quarter,
big and bold.
You're worth twenty-five
I am told.
The Penny
See the shiny penny, brown as it can be,
With two maple leaves for all of us to see.
It's made out of copper at a mint,
A penny's worth one whole cent.
The Nickel
A resting beaver will be found
On a nickel, shiny, smooth, and round.
The Queen is on the other side.
A nickel is worth five cents. Say it with
pride.
The Dime
A dime is the smallest coin of them all,
With the Bluenose sailing nice and tall.
A dime is worth ten cents. Don't you
agree?
Which makes me happy as can be!
8
Math for ELA
Smart –Poetry and Math
Read the poem below and answer the questions that follow.
Part I: Smart Poetry Reading
Instructions:
Smart
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!
And then I took the quarters
And traded them to Lou
For three dimes—I guess he don’t know
That three is more than two!
Just then, along came old blind Bates
And just ‘cause he can’t see
He gave me four nickels for my three dimes,
And four is more than three!
And I took the nickels to Hiram Coombs
Down at the seed-feed store,
And the fool gave me five pennies for them,
And five is more than four!
And then I went and showed my dad,
And he got red in the cheeks
And closed his eyes and shook his head--Too proud of me to speak!
--- Shel Silverstein From Where the Sidewalk Ends HarperCollins Publishers: 1974
Instructions: Type or write correct letter on the line.
Show the amount of coins that the character gets when he trades his money and add them up.
Part II: Multiple Choice “Smart” Questions
1)
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!
a. Two quarters = .50 cents
b. Six quarters = $1.50
c. One quarter = .25 cents
9
Math for ELA
DRAW and WRITE about the NUMBERS
1.
Draw a table or chart that represents 9/11.
2.
Shade in 3/6
3.
Write the fraction for
4.
Write the alphabetic expression for ¼ (example 1/2 is one-half)
5.
Write the alphabetic sentence for example
2+2=4.
2 + 9 = 17 - 6
5.
Write the alphabetic expression for 7/9. Type or write below.
10
Math for ELA
Drag the boxes to make a flow chart with examples on how to solve equations.
Copy the arrows you need.
Isolate the Terms that
Contain the Variable
Steps for Solving
Equations
Combine Like Terms
Isolate the Variable
You Wish to Solve For
Substitute Your
Answer into the
Original Equation
Combine like terms and
simplify
3z + 5 +2z = 12 + 4z
Solve the following equation for
the variable in the equation.
Solve the equation
for x.
(2/5) x = 8
9x + 3 = 8x + 19
Result:
72 = 72
Result:
5 = 12 – z
Result:
Result:
Result:
x = 16
23 = z
x = 20
a + 12 = b, and a = 9, find the value for b.
Solve the following equation for the
variable in the equation.
38 = z + 15
11
Math for ELA
2 by 2
Try to fill in the missing numbers in the puzzle below.
Use the numbers 1 through 4 to complete the equations.
Each number is only used once.
Each row is a math equation. Each column is a math equation.
Remember that multiplication and division are performed before addition and subtraction.
2 to the right and 2 forward
Try to fill in the missing numbers in the puzzle below.
Use the numbers 1 through 4 to complete the equations.
Each number is only used once.
Each row is a math equation. Each column is a math equation.
Remember that multiplication and division are performed before addition and subtraction.
Created with Puzzlemaker at DiscoveryEducation.com
12
Math for ELA
11-11-11
Pairs – Subtraction to 11
A game for 2 players
Players take turns to cross off a pair of adjoining numbers with a difference of 11, e.g. 15 and 4
(15 - 4=11). The pair of numbers must be in squares that are joined by a side, not joined by
corners. Once a number has been crossed off, it cannot be used again. The last player who is
able to cross off a pair is the winner for that game.
13
Math for ELA
Celebrate 11-11-11 w/ Equations
To celebrate this special date, can you make 11, three times by putting the
given digits into the equations below?
1. Fill in the boxes with these digits to make a true equation – 2, 4, 5, 6.
2. Fill in the boxes with these digits to make a true equation – 3, 8, 8, 9.
3. Fill in the boxes with these digits to make a true equation – 3, 4, 6, 8.
14
Math for ELA
11-11-11 scoring table
Player 1
Player 2
15
Math for ELA
Multiplication Table
Multiply the column number by the row number and fill in the answer
number to complete the multiplication table.
0
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
10
11
12
16
Math for ELA
Value the Place Table
9923471
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
9
9
2
3
4
7
1
1173812
4239710
4786650
1129798
4332144
1254493
6679054
2257904
5577231
17
Math for ELA
Number Line Use this number line to help you when adding and subtracting signed numbers.
(-)
-40
-35
-30
-25
(+)
-20
-15
-10
-5
0
5
10
15
20
25
30
35
40
I
I______I_______I_______I_______I_______I_______I_______I_______ ______I_______I_______I_______I_______I______I_______I______I
Number Line Use this number line to help you when adding and subtracting signed numbers.
(-)
-40
-35
-30
-25
(+)
-20
-15
-10
-5
0
5
10
15
20
25
30
35
40
I
I______I_______I_______I_______I_______I_______I_______I_______ ______I_______I_______I_______I_______I______I_______I______I
18
Math for ELA
Student Height: Mean, Median, Mode, and Range
Student Name
Height (in Feet and Inches)
1.
‘
“
2.
‘
“
3.
‘
“
4.
‘
“
5.
‘
“
6.
‘
“
7.
‘
“
8.
‘
“
9.
‘
“
10.
‘
“
11.
‘
“
12.
‘
“
13.
‘
“
14.
‘
“
15.
‘
“
16.
‘
“
17.
‘
“
18.
‘
“
19.
‘
“
20.
‘
“
Mean Class Height
Median Class Height
Class Height Mode
Height Range of Class
19
Math for ELA
How much does a gallon cost?
Most of us are aware of the cost of a gallon of gas or
milk. However, it would be interesting to calculate the
cost of a gallon of other frequently used items.
Complete the chart below.
Fill in the Price Per Gallon column.
Remember, like in real life situations units of
measurement are not always the same.
Look at the conversions below the table for help.
Item
Price per container
Diet Snapple
Half & Half
Ice Tea
Gatorade
16 oz. for $1.29
1 pint for $ 1.99
16 oz. for $1.19
20 oz. for $1.59
Tomato Juice
Ocean Spray
Pint of milk
Olive oil
STP Brake Fluid
Vick’s Nyquil
Pepto Bismol
1 quart for $3.99
16 oz. for $1.25
16 oz. for $1.59
1 pint for $3.99
12 oz. for $3.15
6 oz. for $8.35
4 oz. for $3.85
Whiteout
Clorox Bleach
Scope
Evian water
7 oz. for $1.39
1 quart for $1.50
1.5 oz. for $0.99
9 oz. for $1.49
Price per Gallon
1 pint = 16 ounces (oz.)
1 quart = 32 ounces
1 gallon = 128 ounces
1 gallon = 4 quarts
20
Math for ELA
Penny Heads or Tails
Ten Toss Probabilities: Use the interactive coin toss at Shoder.org website
Hold down CTRL key and click on link
http://www.shodor.org/interactivate/activities/Coin/
Complete the table below with results from tosses.
Heads (Blue)
Tails (Red)
1
2
3
4
5
6
7
8
9
10
Click on the boxes below and type your answer or write your answer in the boxes below.
What are your odds of tossing heads when you flip a coin? Express your odds as a
fraction.
Express it as
out of
. Express it as a percentage:
%
21
Math for ELA
It’s Raining Quarters, Dimes, Nickels, and Pennies
In column A. is the amount of money; in column B. is the number of coins that make up the first
column’s amount. In the spaces provided in under column C., write the number of coins that make
up column A.’s amount. The coins are quarters (Q), dimes (D), nickels (N), and pennies (P). The
first question has been completed as an example.
#
A. Money Amount
B. Coin Amount
1.
25¢
5
2.
35¢
7
3.
33¢
8
4.
46¢
5
5.
56¢
7
6.
17¢
4
7.
43¢
6
8.
29¢
7
9.
54¢
8
10.
57¢
7
11.
48¢
7
12.
34¢
8
Q
0
D
0
N
5
P
0
22
Math for ELA
The Penny Worksheet
One a penny,
Two a penny,
Three a penny,
More,
Four a penny,
Five a penny,
That's a nickel more
One a Penny
Six a penny,
Seven a penny,
Eight a penny,
More,
Nine a penny,
Ten a penny,
That's a dime for the store!
Day & Pennies
Exponent
Total Amount
1
11
22
33
$ 0.01
$ 0.04
$ 0.27
2
.
3
4
5
6
7
8
9
10
11
12
Answer
12
23
1212
$8,916,100,448.12
Math for ELA
Cha.. Cha.. Cha.. Cha.. Changes
Below are three groups of coins. Your challenge: As coins are shuffled in and out of
these groups, see if you can figure out how much money is in each group each time.
Each numbered challenge tells you some necessary information and then asks you to
fill in the omitted numbers to solve each problem.
Coins used: Pennies
, Nickels
, Dimes
, Quarters
Write your answers in the spaces provided. The first question group has been completed as an example.
1.
GROUP 1
GROUP 2
GROUP 3
GROUP 4
2 coins
3 coins
4 coins
9 coins
11¢
16¢
12¢
39¢
The total number of dimes in the three groups above is
2.
.
GROUP 1
GROUP 2
GROUP 3
GROUP 4
coins
coins
5 coins
12 coins
45¢
26¢
¢
The total number of nickels in the three groups above is
3.
.
GROUP 1
GROUP 2
GROUP 3
GROUP 4
7 coins
coins
3 coins
coins
¢
31¢
¢
The total number of quarters in the three groups above is
4.
89¢
91¢
.
GROUP 1
GROUP 2
GROUP 3
GROUP 4
coins
5 coins
5 coins
coins
37¢
27¢
¢
The total number of pennies in the three groups above is
$1.10
.
24
Math for ELA
NUMBER GAMES WITH CARDS
Skill: Addition or Multiplication
Purpose:
 Addition: To get three cards which add up to exactly 16.
 Multiplication: To get three cards that have a product of exactly 72.
Players: 2
Directions:
1. Mix the cards and place in front of the players
2. Players take turns drawing cards.
Addition: The first player to have exactly 3 cards that total 16 is the winner. If the
first three cards chosen do not add up to 16, the players continue to choose cards
until one person gets it.
Multiplication: The first player to have 3 cards with a product of 72 wins.
Variations:
For most variations, the basic 3-down-1-up battle pattern becomes 2-down-2-up.
For advanced games, however, the battle pattern is different: in case of a tie, the
cards are placed in a center pile. The next hand is played normally, with no cards
turned down, and the winner of that skirmish takes the center pile as well.
25
Math for ELA
Money - What’s Probable?
Money – Coin and Paper - Click or check off the correct answer below.
1. In two tosses of the same penny, what are the chances they will both be heads?
a. ☐ 1/8
b. ☐ 1/4
c. ☐ 1/2
d. ☐ 1/16
e. ☐ 1
2. In two tosses of the same penny, what are the chances that you will get a combination of
one head and one tail?
a. ☐ 2 out of 4
b. ☐ 3 out of 4
c. ☐ 1 out of 8
d. ☐ 4 out of 4
e. ☐ 4 out of 8
Click inside the box and type in your answer or write in your answer in the boxes below.
3. Beth has 14 coins in her pocket. The probability of pulling out a penny is 1/2. How many
pennies are in her pocket? Express the probability in three ways:
a. Express as a fraction
b. Express as a decimal
c. Express as
out of
4. Tom has less than 12 nickels, dimes, and quarters in his pocket. The probability of pulling
out a nickel or a quarter is 3/4. The probability of pulling out a dime is 1/4. How many
coins does Gene have in his pocket?
How many of each does he have?
a. Nickels
c. Quarters
b. Dimes
26
Math for ELA
Recipe for Four - Breaded Steak for One
What would the recipe look like if you were only making enough breaded steak to serve one?
Please write the correct measurement conversions and translation on the lines below.
This bachelor has to convert a recipe his mother gave him for breaded steaks recipe that serves four to a
recipe that will serve one. Usually a bachelor fridge just has a few half-empty jars of condiments, a flat 2liter Coke and some old pizza in it, but you need a big fridge for beer parties. A bachelor’s cooking utensils
are also limited. There are no tablespoons and measuring cups in this house. Teaspoons and shot glasses
have to be used as substitutes.
Breaded Steak recipe (Bistec Empanizado) - serves 4
Conversions (changes)
4 steaks (1/4 inch thick)
1/2 cup onion, chopped
1 tbsp fresh garlic, minced
1/4 cup sour orange juice
1/4 tsp salt
4 eggs, beaten well
1 cup finely ground crackers, salt to taste
1/2 onion, sliced into rings
Olive oil
Sprinkle steaks with chopped onion, garlic, orange juice and salt. Rub garlic into meat. Marinate for a few hours in the
refrigerator. Brush off the onion pieces and dip each steak into the egg to make sure it’s fully coated. Dip the steak into
the crackers, making sure that the ground crackers completely cover the steak. Fry the steaks in cooking oil on medium
heat until golden brown and well done. Serve with a few onion rings.
 1 US tablespoon = 3 US teaspoons
 One shot = one ounce
 One cup = eight ounces
27
Math for ELA
Shopping (clothes, shoes, and accessories)
Read the word problems carefully. Work through and answer
questions below.
1. Marian took her two sons back-to-school shopping in August.
They went to the Mall of America in Bloomington, MN.
Minnesota does not charge sales tax on clothing. First, Marian
bought shoes for her children. One pair of shoes cost $29.99 and
another pair cost $36.99. Next, she bought two pairs of jeans,
each for $27.99. Finally, she bought each boy three new shirts
(two dress shirts and a T-shirt). The dress shirts cost $14.99 each. The T-shirts cost
$7.99 each. How much did Marian spend on her back-to-school purchases?
2. Alex was looking for a good sale on soccer gloves, but he did not
want to buy poor quality. He was hoping to find gloves that he could
use for at least two outdoor seasons. He visited three different
sporting goods stores. At the first store, he found gloves that he
liked for $26.99, but in a sale box at 20% off. The sale price would
be given at the cash register. At the second store, he found gloves
that he really liked for $45.00, but on sale at 25% off. The sale price
would appear at the cash register. At the third store, he found the same gloves for
$40.99, but on sale at 10% off. Again, the sale price would appear at the cash
register. Alex decided that the gloves at the first store were too cheap and probably
not very good quality. He had to decide if he should buy the gloves at the second or
the third store. The gloves were exactly the same brand, color, and size, but the price
of each pair of gloves was a little different. At which store did Alex probably
purchase his gloves?
28
Math for ELA
Pay Check Deductions
Using the paycheck information below; calculate what percent each of the following
is of the gross (pretax) income and write it on the lines after the questions:
29
Math for ELA
Use paycheck information to answer questions below.
1. Federal Income Tax
2. State Income Tax
3. FICA
4. Medicare Tax
5. Total Deductions
True or False Paycheck Quiz
Check your understanding of taxes by answering the following questions.
1. Net pay is the total amount of income you receive during a pay period before
taxes.
☐ True
☐ False
2. FICA Federal Insurance Contributions Act
☐ True
☐ False
Looking at it from the employer’s math
An employer has one employee, Bob Jones, who is paid $1800.00
per month before deductions. Bob is married and claims two
exemptions. His net paycheck is $1478.10. The details of his paycheck are:
 Gross pay $1800.00
 Federal income tax -145.00
 State tax -39.20
 FICA tax -111.60
 Medicare tax -26.10
Net pay $1478.10: In addition, the employer must pay $111.60 for FICA and $26.10 for
Medicare.
Question: What is the employer’s total labor expense for this month?
30