Writing Algebraic Expressions Lesson 2-3

CCS: 6.EE.2. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) 6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Objectives: To write and apply algebraic expressions Solve problems by making a table and finding the algebraic rule

Word phrases can be written as algebraic expressions. Use the words to determine what operation you are using. Use a variable for the phrase “a number.”

Adding Phrases Plus More than Sum Increased by

Subtracting Phrases Minus Difference Subtracted from Decreased by Less than

Multiplying Phrases Dividing Phrases Times Product of Quotient Divided by

Example: 7 decreased by b “Decreased by” means subtract. 7 - b

Example: The product of 19 and k “Product” means multiply. We show multiplication by placing the factor right next to the variable. 19k

Less than, more than Some word phrases contain the words “less than” or “more than.” When you see those words, start with the second part of the phrase. Example: 23 less than m m - 23

Example: 32 less than 5 times c The 32 is less than the 5 times c, which means we subtract 32 from the 5 times c. So, start with 5 times c. 5c - 32

Tables When you are given a table of values, determine how to get from the first column to the second column. Describe that pattern with an algebraic expression.

Example n ? 3 12 7 28 11 44

Compare from left to right. How do we get from 3 to 12? Add 9 or multiply by 4. How do we get from 7 to 28? Multiply by 4. If we multiply 11 by 4, we get 44. The pattern is to multiply our number, n, by 4. The algebraic expression to describe this is: 4n

Describing Unknown Numbers When you don’t know what a number is, let a variable stand for that number. Use an algebraic expression to describe what you’re looking for.

Example Write an algebraic expression to describe Jerry’s age. Use the following information: Jerry is 4 years younger than his brother Steve. First, we have to know how old Steve is. We do not have an age for Steve, so we will use a variable: Let s = Steve’s age. Now that we have determined Steve’s age (s), we can use it to determine Jerry’s age. Jerry is 4 years younger than Steve. s - 4

If Steve is 22 years old, then how old is Jerry? Jerry is 18 years old. 22 - 4 18

Make a table and Look for a Pattern Lesson 2-4

Use a Chart or Make a Table Sometimes putting information into a table with rows and columns makes it much easier to keep up with numbers or spot missing numbers in a problem. Sometimes you can even discover relationships and patterns among the information.

Sample Problem Wheels, Inc., is gearing up for its annual bicycle race. This year’s race will involve bikers from three different towns. For every eight bikers from Glendale, there will be 12 bikers from Glenbrook and nine bikers from Glenwood. If 72 bikers from Glenwood will be at the race, how many bikers from each of the other two towns will be there?

Solution

Look For a Pattern Looking for patterns is often useful in solving problems. Sometimes a pattern may need to be extended or the information put into a table to reveal the pattern.

EXAMPLE A CAR DEALER SELLS AT LEAST 3 CARS A DAY. ON MONDAY MORNING THERE ARE 50 CARS IN THE LOT. BY FRIDAY, WHAT IS THE GREATEST NUMBER OF CARS THE DEALERSHIP CAN EXPECT TO HAVE?

Make a table Day of the week Number of cars Monday Tuesday Wednesday Thursday Friday 47 44 41 38 35 THEY SHOULD EXPECT TO HAVE 35 CARS ON FRIDAY.

Classwork Homework TIME PG. 76, 2-34 EVEN & PG. 81, 2-16 EVEN Patterns are sequences that repeat or change in an orderly way. You can use patterns to predict the next step in solving a problem. In Crack Hacker's Safe, the player must complete a sequence of patterns to crack Hacker's safe. ALGEBRAIC EXPRESSIONS MILLIONAIRE This Algebraic Expressions Millionaire Game can be played online alone or in two teams. For each question you have to identify the correct mathematical expression that models a given word expression. Homework TIME PG. 76, 2-34 EVEN & PG. 81, 2-16 EVEN