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