Simplifying Algebraic Expressions by Combining Like Terms Lesson 6.2.3 Attention… Be sure to look at notes section of each slide for answers and additional instructions. 6.EE.2b, 6.EE.3, 6.EE.4

In Chapter 4 We learned… 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.

In Chapter 4… Example 4x + y + 9 + x² We learned that an algebraic expression is a mathematical expression built from numbers, variables, and operations. There are no equal signs in an algebraic expression. Example 4x + y + 9 + x²

Today… We are going to learn about the parts that make up an algebraic expression. We are also going to learn how to simplify an algebraic expression by… “combining like terms”

Let’s Get Started… Section 1 – Vocabulary Section 2 – “Like” Terms Section 3 – Simplifying Expressions by combining the “like” terms

Terms 4x + y + 9 – x2 Terms are the small parts (or chunks) that make up an expression. This expression has 4 terms. Do you notice anything that might help you identify where each new term starts? Terms are separated by either a + or – sign!

How many terms are in this expression? 9x – 5 + x2 Answer: 3

Coefficient: 5x + y + 8 A coefficient is the number that multiplies the variable. ALL variables have a coefficient. If you don’t see a number in front of the variable, it is assumed to be 1. 5 is the coefficient in front of the x 1 is the coefficient in front of the y

Constant 5x + y + 8 A constant is a term that has no variable. It is the plain number. 5x + y + 8 Constants are constantly alone!

Naming Coefficients and Constants When naming coefficients and constants, the sign directly in front goes with it. 3m – 2n + n – 4 Coefficients: 3 -2 1 Constants: -4

x + 5x – 2 + y3 A) coefficient B) term C) constant Name the item in blue x + 5x – 2 + y3 Choose one… A) coefficient B) term Pick student volunteer to answer. Then ask… “What kind of 5 is it?” Answer: positive 5 C) constant

12 + k3 A) coefficient B) variable C) constant D) term Name the item in blue 12 + k3 Select all that apply… A) coefficient B) variable Pick student volunteer to answer C) constant D) term

Write a word to describe the blue item. 7a2 + 3b – 1 term Pick student volunteer to answer

-m – 12 + 4n How many terms are there? 3 Name the coefficients: -1 4 Name the constants: -12

Moving On… Section 1 – Vocabulary Section 2 – “Like” Terms Section 3 – Simplifying Expressions by combining the “like” terms

Like Terms are terms that have the same What are “Like” Terms? 5x and 10x n2 and 7n2 14 and 19 Like Terms are terms that have the same variable and exponent.

Yes, they have the same variable and exponent. Are these like terms? 6b and 9b Yes, they have the same variable and exponent. guided practice

No, they do not have the same variable. Are these like terms? 5x and 2y No, they do not have the same variable. guided practice

Yes, they have the same variable and exponent. Are these like terms? x2 and 8x2 Yes, they have the same variable and exponent. Have students record the answer on their student notes if you printed them out.

No, they do not have the same exponent. Are these like terms? 7x and 5x² No, they do not have the same exponent. Have students record the answer on their student notes if you printed them out.

Yes, they are both constants. Are these like terms? 6 and 15 Yes, they are both constants. Have students record the answer on their student notes if you printed them out.

No, they do not have the same variable. Are these like terms? 3x and 1 No, they do not have the same variable. Have students record the answer on their student notes if you printed them out.

Yes, they have the same variable and exponent. Are these like terms? 2m and 6m Yes, they have the same variable and exponent. Have students record the answer on their student notes if you printed them out.

Moving On… Section 1 – Vocabulary Section 2 – “Like” Terms Section 3 – Simplifying Expressions by combining the “like” terms

Steps for Simplifying an Algebraic Expression Use the Distributive Property to remove any parentheses 3(x + 5) + 4x Step 2 Identify the “like” terms 3x + 15 + 4x Step 3 Combine the “like” terms by adding or subtracting the coefficients 3x + 4x 7x + 15 Encourage the use of shapes to identify the like terms. When combining the like terms, remind students that the sign in front goes with the coefficient. Notice that the sign is included in the highlighted shape. ALSO… point out that the answer can be written in a different order. 7x + 15 is the same as 15 + 7x per the Commutative Property. Answer: 7x + 15

Simplify the Expression. 9m + n2 + 4m – 2n 9m + 4m 13m + n2 – 2n Teacher Guided Practice Encourage the use shapes to identify the like terms. Point out again that there are various correct ways to write the final answer per the Communitive Property. Example… a multiple choice might have the answer as: n² + 13m - 2n Answer: 13m + n2 – 2n

Simplify the Expression. 6x2 – y + 12 + 5 12 + 5 6x2 – y + 17 Teacher Guided Practice Encourage the use shapes to identify the like terms. Answer: 6x2 – y + 17

Simplify the Expression. 15 + 6x³ + 8y – 3 – 5x³ 6x3 – 5x3 15 – 3 12 + x3 + 8y Teacher Guided Practice Encourage the use of shapes to identify like terms. x³ + 8y + 12 is another correct way to write the answer Answer: 12 + x3 + 8y

Now Watch Me x2 + 3 + 12y – 4y + 4 + 5x2 Teacher is to work this out on board for students. Use circles, squares, underlines, triangles or hearts to identify the “like terms”. Answer: 6x2 + 7 + 8y or 6x² + 8y + 7

Now Watch Me 10 + 3(x + 2) Answer: 16 + 3x or 3x + 16

Simplify the Expression. 8x2 + 7x – 25 – 5x2 8x2 – 5x2 3x2 + 7x – 25 Have students record the answer on their student notes if you printed them out. Answer: 3x2 + 7x – 25

Simplify the Expression. 15y + y + 11 – 2y 15y + y – 2y 14y + 11 Have students record the answer on their student notes if you printed them out. Answer: 14y + 11

Simplify the Expression. 4x2 + 8y + 6x2 – y – 22 4x2 + 6x2 8y – y 10x2 + 7y – 22 Have students record the answer on their student notes if you printed them out. Answer: 10x2 + 7y – 22

Simplify the Expression. 5(a+6) – 2a 5a + 30 – 2a 5a – 2a 3a + 30 Have students record the answer on their student notes if you printed them out. Answer: 3a + 30

End of PowerPoint