What are the challenges? To know how to translate word problems into a workable mathematical equation. To know where to start and how to go about figuring out the answer. To know the strategies needed to break down a word problem so it is clear and easy to solve.

6 Steps for Solving Math Word Problems

Step 1 Convert the words into an equation. Read through the entire problem first. Don’t try to solve it when you’ve only read one sentence. Read the problem completely in order to get the whole picture. Effectively translate and solve the problem.

Step 2 Go back to the beginning. Reread the first sentence. Write down what you know and what you don’t know. Use variables to stand for the unknowns and clearly label what they stand for. Do the same for the second sentence and each following sentence.

Step 3 Look for Signal Words that mean certain mathematical operations.

Signal Words Addition Subtraction Multiplication Division Equals

Step 4 Perform the required operations.

Step 5 Make sure you are answering the question that is being asked of you. One step may seem like it’s the answer, but it may take several steps to arrive at the final answer. Don’t lose sight of what the word problem is asking for or asking you to do. Label the answer with the unit of measurement or with the object the question is requesting.

Step 6 Mentally or on paper check your answer to make sure it is correct and makes sense. Replace the variable in each step with your answer. Calculate the equation with the now known variable to see if it satisfies the equation. If it does, then you’re done!

Practice, Practice, Practice! Mastering word problems requires practice!

Understanding Algebra Word Problems *Represent a given situation using algebraic expressions or equations in one variable. *Simplify and evaluate algebraic expressions.

The biggest challenge to solving word problems is figuring out whether to add, subtract, multiply or divide. Words Meaning Addition and increased more more than plus sum total Words Meaning Subtraction decreased difference less less than left lower than minus Words Meaning Multiplication double half (× ½) product times triple twice Words Meaning Division divide into half (÷ 2) divide by divide among quotient

To solve a word problem, you must first interpret the action you need to perform and then choose the correct operation for that action. Separate into equal groups Multiply How many more? How many less? Combine Combine equal groups Separate Add Subtract Divide Action OperationPossible Question Clues How many all together? How many equal groups?

a number plus 5 add 5 to a number sum of a number and 5 5 more than a number a number increased by 5 a number minus 11 subtract 11 from a number difference of a number and less than a number a number decreased by 11 3 times a number 3 multiplied by a number product of 3 and a number a number divided by 7 7 divided into a number quotient of a number and 7 + –   Word Phrases Expression n + 5 x  11 3m3m or a  7 a 7

TEST YOUR SKILL!! Match the phrase with the correct algebraic expression.

2 more than y 1.y y 3.y y / 2

16 divided into m m 2.16m 3.m m / 16

2 less than s 1.s s 3.s s / 2

Triple John’s age j j 2.j j 4.j ÷ 3

Twice the sum of y and y y (y + 15) 4.2(15) + y

n feet lower than than n 2.n n n

The quotient t and goes into t 2.t goes into 4 3.Multiply 4 by t 4.Add 4 and t

8) 18 divided by a number, g g 2.18 ÷ g 3.g × g

Setting Up Algebra Word Problems

To set up algebra word problems: 1.To complete an algebra problem, an equal sign must be added. 2.The words is or are as well as equals tell you that you should add an equal sign. Double Jake’s age, x, minus 4 is 22. 2x - 4 = 22

Translate the word problem into an equation. DO NOT find the solution yet. 1.Triple the original number, n, is 2, The product of a number, y, and 5 is equal to Four times the difference of a number, x, and 2 is The total, t, divided into 5 groups is 45. 3n = y = 15 4(x – 2) = 20 t ÷ 5 = 45

Translate the word problem into an equation. DO NOT find the solution yet. 1.The number of pants in the store, p, minus 54 pants sold today is One-half an amount, x, added to $50 is $ One hundred plants, divided by 5 rows, equals n number of plants per row. 4.A number, y, less than 50 is 82. p – 54 = 320 x/ = ÷ 5 = n y - 50 = 82

Translate the word problem into an equation. DO NOT find the solution yet. 1.Seventeen more than half a number, h, is The quotient of a number, w, and 4 is Six less a number, d, is Four times the sum of a number, y, and 10 is 48. h/ = 35 w ÷ 4 = 32 d – 6 = 12 4(y + 10) = 48

Word Problems

Solve the word problem: A number increased by 34 is 134.

Answer: n + 34 = 134 n = 100

Solve the word problem: Find the number Seventy-five less than a number is 62.

Answer: n - 75 = 62 n = 137

Solve the word problem: A number increased by 14 is 49.

Answer: n + 14 = 49 n = 35

Solve the word problem: Find the number Twenty-nine more than a number is 52.

Answer: n + 29 = 52 n = 23

Solve the word problem: Find the number One-half of a number is 9.

Answer: ½(n)= 9 n = 18

Solve the word problem: Find the number The sum of a number and 79 is 143.

Answer: n + 79 = 143 n = 64

Solve the word problem: Find the number A number decreased by 28 is 76.

Answer: n - 28 = 76 n = 104

Solve the word problem: Lisa is cooking muffins. The recipe calls for 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in?

Answer: 2 + c = 7 c = 5

Solve the word problem: How many packages of diapers can you buy with $40 if one package cost $8?

Answer: p(8) = 40 p = 5

Word Problems Multiple step

Solve the word problem: 331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? (assume each bus was equally filled)

Answer: 6b + 7 = 331 b = 54

Solve the word problem: Carter had $24 to spend on seven pencils. After buying them he had $10. How much did each pencil cost?

Answer: 7p + 10 = 24 or 24 – 7p = 10 p = $2

Solve the word problem: The sum of three consecutive numbers is 72. What is the smallest of these numbers?

Answer: x + (x+1) + (x+2) = 72 x = 23

Solve the word problem: The sum of three consecutive even numbers is 48. What is the smallest of these numbers?

Answer: x + (x+2) + (x+4) = 48 x = 14

Solve the word problem: You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?

Answer: 5 + 4e = 25 e = $5

Solve the word problem: The Math Team made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed four pies to the sale. Each pie was then cut into five pieces and sold. There were a total of 60 pieces to sell. How many pies did the Math Team make?

Answer: 5(p+4)= 60 p = 8

Solve the word problem: When the magic number is increased by 32 and this result is tripled, the final result is 246. What is the magic number?

Answer: 3(n + 32) = 246 n = 50

Solve the word problem: On a 30-question test, Makenzie earns 5 points for each correct answer and loses 3 points for every incorrect answer. If she answers all the questions, and her score was 6, how many did she answer correctly?

Answer: 5c – 3(30 – c) = 6 c = 12

Looking Ahead: we will eventually learn how two solve equations with 2 variables… looking at the previous problem… Lets assign variables: correct = c, incorrect = i Equation 1: c + i = 30 i = 30 – c Equation 2: 5c – 3i = 6 substitute previous value of i into 2 nd equation: 5c -3(30-c) = 6 5c -3(30) – 3(-c) = 6 5c c =6 8c = 96 c=12