Introduction to Variables and Algebraic Expressions Lesson 4.1.1 Teachers: This lesson is designed to be used with mini-whiteboards. See the lesson plan for directions. There are student notes provided that will let the students know when it’s time to use the boards. Obj. 6.EE.2a

Number Shapes You will be given a set of cards. Each person is responsible for one card! You may tell your team exactly what your card has written on it, but you MAY NOT show your card to the team! Your challenge: Work together to determine what number is being represented by each shape. Set 1 can be used to model the task with the class. There are four puzzles in all and they increase in difficulty. The teacher may want to prepare all sets and once a team solves one version, the teacher can give the team the next version in the set.

Variables A variable is a letter that stands for an unknown number. Different letters indicate different values. For example, if X = 5, then the value of Y and Z will be a number other than 5.

Algebraic Expressions An Algebraic Expression is a mathematical expression built from numbers, variables, and operations. There are no equal signs in an algebraic expression.

Let’s Get Started… Expressions Involving Addition Expressions Involving Subtraction Expressions Involving Multiplication and Division Expressions Involving Exponents

Turn-and-Talk You have 1 minute to work with a partner and jot down as many words as you can that mean addition. (Write them on your four-door foldable in your notes!) GO!

Key Words for Addition ( + ) plus sum total increased by quantity of more than added to Here are some key words that indicate addition.

When writing an algebraic expression, you assign a variable to represent the unknown number. The variable can be any letter of your choice. The letters “x” and “n” are popular letters to use. Let’s take some addition phrases and see what the algebraic expression looks like...

Translating Addition (+) Phrases into Algebraic Expressions A number plus 3 The sum of a number and 5 The total of 6 and some number The quantity of 19 and a number, n A number increased by 2 n + 3 c + 5 6 + x 19 + n p + 2 Normally, you write the expression in the order that it is presented in the phrase.

If you think about it though, the expression makes sense. “Turn Around Words” than, from, to PHRASE Algebraic Expression 10 more than a number A number added to 11 k + 10 11 + t Emphasize the words THAN and TO. When you see the words than, from or to, the expression is turned around from how it is written in the phrase. If you think about it though, the expression makes sense.

Match the phrase to the correct expression x plus 25 25 + x x + 25 Mini-Whiteboard: Have the students write their answer on a mini-whiteboard. On cue have the students hold up their answers.

Match the phrase to the correct expression 50 increased by x 50 + x x + 50 Mini-Whiteboard

The total of 17 and a number, n Match the phrase to the correct expression The total of 17 and a number, n n + 17 17 + n Mini-Whiteboard

Match the phrase to the correct expression The sum of c and 7 7 + c c + 7 Mini-Whiteboard

Match the phrase to the correct expression 12 more than x x + 12 12 + x Mini-Whiteboard Circle 10 and draw arrow to the back! Emphasize the word THAN. This is a turn-around word. The Tricky One!

Moving On… Expressions Involving Addition Expressions Involving Subtraction Expressions Involving Multiplication and Division Expressions Involving Exponents

Turn-and-Talk You have 1 minute to work with a partner and jot down as many words as you can that mean subtraction. (Write them on your four-door foldable in your notes!) GO!

Key Words for Subtraction ( - ) minus difference decreased by less less than fewer than subtracted from Here are some key words that indicate subtraction.

Translating Subtraction ( - ) Phrases into Algebraic Expressions A number minus 7 The difference of 3 and a number 9 less a number A number decreased by 12 b – 7 3 – n 9 – h x – 12

6 subtracted from a number “Turn Around Words” than, from, to PHRASE Algebraic Expression 4 less than a number A number fewer than 21 6 subtracted from a number x – 4 21 – m r – 6 Emphasize the words THAN and FROM.

Match the phrase to the correct expression 10 decreased by a number, w 10 – w w – 10 Mini-Whiteboard

Match the phrase to the correct expression The difference of 60 and p p – 60 60 – p Mini-Whiteboard

Match the phrase to the correct expression 75 less x x – 75 75 – x Mini-Whiteboard

Match the phrase to the correct expression Subtract c from 12 c – 12 12 – c Mini-Whiteboard Circle the “c” and draw arrow to the back. Emphasize the word FROM. It is a turn-around word! Hmmm…One of those tricky ones again!

Match the phrase to the correct expression 45 less than a number, n n – 45 45 – n Mini-Whiteboard Circle the “c” and draw arrow to the back. Emphasize the word THAN. It is a turn-around word. Help! Which one is it…

Moving On… Expressions Involving Addition Expressions Involving Subtraction Expressions Involving Multiplication and Division Expressions Involving Exponents

Which of the following correctly represents multiplication? Select All that Apply 6 × 8 6(8) (6)8 (6)(8) 6•8 All choices represent a correct way to illustrate multiplication.

Turn-and-Talk You have 1 minute to work with a partner and jot down as many words as you can that mean multiplication. (Write them on your four-door foldable in your notes!) GO!

Key Words for Multiplication ( x ) times product twice; double triple of (when finding part of a number) half (times 1 2 ) You can take half of something by either multiplying by ½ or dividing by 2, so half will be a key word for both multiply and divide.

Translating Multiplication, (x), Phrases into Algebraic Expressions There are 4 ways to write multiplication. Can you fill in the missing ways? PHRASE Algebraic Expression 8 times a number 8n 8 • n 8(n) 8 x n The product of 14 and a number 14 • n 14(n) Twice a number; double a number 2n 2 x n Triple a number 3 • n 3(n) A number multiplied by 6 n • 6 n x 6 Three-fourths of a number ¾ n ¾ (n) Half a number ½ • n ½ n Explain the “algebra way” of expressing multiplication: the number is written in front of the variable with no symbol in between. In algebra if a number is right next to a variable, 8n, it is understood to be multiplication.

Turn-and-Talk You have 1 minute to work with a partner and jot down as many words as you can that mean division. (Write them on your four-door foldable in your notes!) GO!

Key Words for Division ( ÷ ) quotient divided by half (÷ 2 ) separated into ratio

True or False These all mean the same thing. True

Translating Division (÷) Phrases into Algebraic Expressions The quotient of a number and 7 n 7 n ÷ 7 10 divided by a number 10 x 10 ÷ x Half a number, n 2 n ÷ 2 The ratio of a number to 15 15 n ÷ 15 Explain that the “algebra way” of expressing division is with a fraction bar.

The product of a number and 19 Match the phrase to the correct expression The product of a number and 19 n ÷ 19 (n)(19) Mini-Whiteboard

The quotient of 60 and a number Match the phrase to the correct expression The quotient of 60 and a number 60 ÷ n n ÷ 60 Mini-Whiteboard

Match the phrase to the correct expression Twice a number, n 2 + n 2n Mini-Whiteboard

Match the phrase to the correct expression 50 divided by x 50 ÷ x x ÷ 50 Mini-Whiteboard

Match the phrase to the correct expression A number divided by 75 75 y y 75 Mini-Whiteboard

Match the phrase to the correct expression Half a number, x 𝑥 ÷ 1 2 1 2 x Mini-Whiteboard

Moving On… Expressions Involving Addition Expressions Involving Subtraction Expressions Involving Multiplication and Division Expressions Involving Exponents

Key Words for Exponents

Match the phrase to the correct expression Mini-Whiteboard

Match the phrase to the correct expression A number, x, squared 2𝑥 Mini-Whiteboard

Match the phrase to the correct expression A number, y, cubed 𝑦 4 Mini-Whiteboard

Find the turn around words… Closure Add Subtract Multiply Divide sum plus increased by more than total quantity of added to difference minus decreased by less than less fewer than subtracted from product times twice double triple of half quotient divide by separated into ratio half Go over the key words for each operation. Point to the “Add” column and have a student name the “turn around words”. Answer: more than, added to Point to the “Subtract” column and have a student name the “turn around words” as well. Answer: less than, fewer than, subtracted from Which key words indicate that the expression is turned around from how it is listed in the phrase? Find the turn around words…