math activities for esl/ell students · 3. model the problem solving process by talking aloud while...
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Math Activities for ESL/ELL Students
Presented by: Michael Matos Senior Director of Adult Education, Employment and Training Programs; Instructor Albany Park Community Center – Chicago, Illinois Doc sharing and email: [email protected] Web sharing: http://del.icio.us/apccctc Twitter: @mmatos02 Forum for Excellence Conference September 25-26, 2018 Marriott Hotel & Conference Center, 201 Broadway Avenue, Normal, IL. Session V: Wednesday, September 26, 2018 — 9:45 AM – 10:45 AM Fell C IACEA Sponsored Session
Math Activities for ELL/ESL Students
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Teaching Strategies in Math for ELL/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 Tic-
Tac-Toe, bingo, and concentration.
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Mnemonics are useful language devices that improve our memory and
help us to remember.
I. Order of Operations
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
Please
Excuse
My Dear
Aunt Sally
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KEY OPERATION WORDS
For Solving Word Problems
ADDITION
Add
All together
And
Both
Combined
How many in all
In All
Increased by
Increase
More
More than
Plus
Sum
Total
SUBTRACTION
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
In all
Of
Multiply
Product of
Times (as much)
Total
Twice
Whole
DIVISION
Average
Cut
Divide
Each
Equal pieces
Every
One
Quotient
Split
EQUALS/IS EQUAL TO
Is Yields Is the same as
The result is Is equal to
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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: _________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
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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
of more than reduce
product of Plus remain/remaining
divide Sum Total
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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!
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.
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.
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!
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Smart –Poetry and Math
Instructions: Read the poem below and answer the questions that follow.
Part I: Smart Poetry Reading
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
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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.
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Drag the boxes to make a flow chart with examples on how to solve equations.
Copy the arrows you need.
Steps for Solving
Equations
Combine Like Terms
Isolate the Variable
You Wish to Solve For
Substitute Your
Answer into the
Original Equation
Solve the equation
for x.
(2/5) x = 8
Solve the following equation for
the variable in the equation.
9x + 3 = 8x + 19
Combine like terms and
simplify
3z + 5 +2z = 12 + 4z
Result:
72 = 72
Isolate the Terms that
Contain the Variable
Solve the following equation for the
variable in the equation.
38 = z + 15
a + 12 = b, and a = 9, find the value for b.
Result:
x = 20 Result:
x = 16
Result:
23 = z
Result:
5 = 12 – z
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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
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Value the Place Table
Millions Hundred
Thousands Ten
Thousands Thousands Hundreds Tens Ones
9923471 9 9 2 3 4 7 1 1173812 4239710 4786650 1129798 4332144 1254493 6679054 2257904 5577231
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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
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Student Height: Mean, Median, Mode, and Range
Mean Class Height Median Class Height Class Height Mode Height Range of Class
Student Name Height (in Feet and Inches)
1. ‘ “
2. ‘ “
3. ‘ “
4. ‘ “
5. ‘ “
6. ‘ “
7. ‘ “
8. ‘ “
9. ‘ “
10. ‘ “
11. ‘ “
12. ‘ “
13. ‘ “
14. ‘ “
15. ‘ “
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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 Price per Gallon
Diet Snapple 16 oz. for $1.29
Half & Half 1 pint for $ 1.99
Ice Tea 16 oz. for $1.19
Gatorade 20 oz. for $1.59
Tomato Juice 1 quart for $3.99
Ocean Spray 16 oz. for $1.25
Pint of milk 16 oz. for $1.59
Olive oil 1 pint for $3.99
STP Brake Fluid 12 oz. for $3.15
Vick’s Nyquil 6 oz. for $8.35
Pepto Bismol 4 oz. for $3.85
Whiteout 7 oz. for $1.39
Clorox Bleach 1 quart for $1.50
Scope 1.5 oz. for $0.99
Evian water 9 oz. for $1.49
1 pint = 16 ounces (oz.) 1 quart = 32 ounces 1 gallon = 128 ounces 1 gallon = 4 quarts
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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/
1. Predict: How many heads and how many tails will show up if you flip the coin 10 times?
Why?
2. 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: %
3. Make a bar graph in Excel representing the results of your first 10 flips. Do this bar graph on the
worksheet provided click here. Make the number of heads red and the tails green.
4. Compare your results with the rest of the class. Were their results according to your prediction?
Next, add the results of the whole class. How do the results compare now?
Heads (Blue)
Tails (Red)
1 2 3 4 5 6 7 8 9 10
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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 Q D N P
1.
25¢
5
0 0 5 0
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
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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
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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 2-
liter 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
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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?
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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:
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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?
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Floor Area – Square feet and yards
Find the floor area in square feet for each of the following floor plans. Omit the
closet area in #1 and the bathroom area in #3. Use measuring tape as needed.
Formula for area of rectangle: A = L x W
Floor plan 1. Floor plan 2. Floor plan 3.
Find the floor area in square yards for each of the following floor plans. Omit
the closet area in #1 and the bathroom area in #3.
One square yard = 9 square feet
Floor plan 1. Floor plan 2. Floor plan 3.
1. 2.
3.
Bedroom # 4
CL.
24'-0"
16
'-0"
Living Room1
6'-0
"
32
'-0
"
24'-0"
20'-0"
Office #1
Office #2
WaitingRoom
5'1
1
15'9
9'6
20'
24'
32'
16'
27'
8'
22'8
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How much paint?
The Perez Family on a budget wants to paint two bedrooms in their home. They want to
make sure that they have enough paint to finish the project but not a lot leftover because
they are trying to keep cost low. The two rooms are identical in size, so we really only need
to calculate the area to be painted in one room and multiply it by two. Calculating the
amount of paint you’ll need for any project is simply a matter of coming up with the square
footage to be covered. Below are some illustrations to help with visualization and
calculations. The floor plan has the dimensions for each numbered wall and ceiling. Use
the spaces below to record measurements and solution. Remember for painting you should
round to the nearest foot. To make sure you have enough paint do not subtract any square
footage for windows and doors unless they significantly reduce the square footage of that
wall. One gallon of paint generally covers about 400 square feet. The area formula below
will be helpful.
Formula: Area = Length x Width Width
Length
Walls
Using all the information provided on this page.
How many gallons of paint will the Perez Family
have to buy to complete their project? Remember to
use all information and draw to help evaluate. The
walls are 9 feet high. One gallon of paint covers 400
square feet of surface.
Area to be painted:
Number of gallons needed:
Wall 1 width:
Wall 2 width:
Wall 3 width:
Wall 4 width:
Wall height: 9 feet
________
Ceiling
Ceiling length: ___________
Ceiling width: ___________
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Length:
How much carpet?
Tammy and Mike want to carpet their living and dining room area. They want to
come up with a quick estimate to make sure they could afford the project. They also
want to make sure that they have enough carpet to finish the project. Getting a
rough idea of how much carpet you will need for a project is pretty simple, but a
precise figure is a little more difficult to come by. Calculating the amount of carpet
you’ll need and what it costs means coming up with the square footage and
multiplying this measurement by the price per square yard. The price of carpet is
usually expressed in square yards.
A yard is 3 feet so a square yard equals 3 feet by 3 feet or 9 square feet.
Find the area in square footage for the Living/Dining room. After converting to
square yards, calculate how much the carpeting will cost. One square yard of
carpeting is equal to $9.99. Below are some illustrations to help with visualization
and calculations. The floor plan has the dimensions needed to calculate the square
footage of the area to carpet. Use the spaces below to record measurements and
solution. You should round up to the nearest foot. The area formula below will be
helpful.
Formula for area of rectangle: A = L x W and square: A = Side2
Rectangle Width Square Side
Length Side
How many tiles?
Width:
Square feet needed:
Square yards needed:
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How many tiles?
John wants to completely tile all the walls of his master bathroom. He wants to make sure
that he has enough tiles to finish the project with only a few extra tiles for mistakes and
replacement. Calculating the amount of tiles you’ll need for any project is simply a matter
of coming up with the square footage to be covered and the size of the individual tile.
Below are some illustrations to help with visualization and calculations. The floor plan has
the dimensions needed to calculate the square footage of the walls. Use the spaces below to
record measurements and solution. Remember for tiling you want to over-estimate so you
have a few tiles extra. You should round up to the nearest foot. To make sure you don’t
buy too many tiles subtract any square footage for windows and doors. The area formula
below will be helpful.
Formula: Area = Length x Width Rectangle Width Square Side
Length Side
Formula for area of rectangle: A = L x W and square: A = Side2
Estimate the number of tiles you will need to complete your project.
Using all the information provided on this page. How many tiles will John
have to buy to complete his project? Your results will show both the number
of square feet of tile you'll need and also the actual number of tiles in the size
you specified.
Remember to use all information and draw to help evaluate.
4” inches
4” inches
Width:
Length:
Tile size:
Total area:
Total number of tiles:
Tile
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How much wallpaper?
The Jasper Family wants to wallpaper their living room. They want to make sure they have
enough paper with the least amount of waste. To estimate the amount of standard
American wallpaper they will need to first add up the lengths of all walls to get the distance
around the room and enter this figure as the perimeter of the room. Round off to the
nearest foot. Next, enter the number of single doors (about 20 square feet), the number of
double doors (about 40 square feet), small windows (10 square feet) and large windows (25
square feet). Also enter the square footage of any other openings or areas not to be
wallpapered -- such as a fireplace.
To make sure you have enough paper with the least amount of waste subtract any square
footage for windows and doors that significantly reduce the square footage of that wall.
Fill in the information below. Use floor plan below for measurements for calculations.
Note the size of the roll of the paper you're using in square feet. A standard American roll
of wallpaper gives you about 35 square feet.
Rolls needed:
:
10 sq. ft. 25 sq. ft. 40 sq. ft. 20 sq. ft
Room
perimeter:
ft.
Wall height:
ft.
Single doors:
20 sq. ft.
Double doors:
40 sq. ft.
Small windows:
10 sq. ft.
Large windows:
25 sq. ft.
Other areas:
sq. ft.
Roll size:
35 sq. ft. per
roll
Living Room
16
'-0
"
32
'-0
"
24'-0"
20'-0"
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Complete the table below with the selected shape, ruler, and scale assigned.
Name the Shape Draw the Shape Perimeter Area or Volume Surface Area Weight
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Formulas Perimeter of a: Square P = 4s
Rectangle P = 2l + 2w
Triangle P = s1 + s2 + s3
Circumference of a Circle C = 2 r OR C = d
≈ 3.14
Area of a:
Square A = s2
Rectangle A = lw
Parallelogram A = bh
Triangle A =
bh
Trapezoid A =
h(b1 + b2)
Circle A = r 2
Surface area of a: Rectangular Prism SA = 2lw + 2lh + 2wh
Right Prism SA = ph + 2B
Cylinder SA = 2 rh + 2 r2
Pyramid SA =
ps + B
Cone SA = rs + r2
Sphere SA = 4 r2
Volume of a: Rectangular Prism V = lwh
Right Prism V = Bh
Cylinder V = r2 h
Pyramid V =
Bh
Cone V =
r2h
Sphere V =
r3
(p = perimeter of base with area B; ≈ 3.14)
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Egyptian Multiplication
Egyptians used a hieroglyphic system for numbers in which each character was a picture of an
object which in turn represented a number. Numbers are written
by using the symbols additively, starting with the smallest numbers on the left and moving
toward the largest on the right.
The Egyptian number system used these symbols:
Math Activities for ELL/ESL Students
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First read and write an equation to solve for each word problem below. Re-write the
equations with answers using the hieroglyphic system and the characters that
represent the numbers.
1. The price of a hamburger is 3 dollars. What is the price of 6 hamburgers?
2. Yesterday we ate 23 apples, 20 mangos and 17 blueberries. How many fruits did we eat altogether?
3. There are 25 students in my class. 12 of them have black hair. How many students do not have black hair?
4. Patrick has 40 dollars. Jess has 20 dollars less than Patrick. How many dollars does Jess have?
5. James is 175 centimeters tall. Tommy is 10 centimeters shorter. How tall is Tommy?