Simplifying expressions (Förenkling av uttryck)

Lektionssteg / Steps in the lesson: 

1. Lektionsuppvärmning / Lesson warm up / Hook / Review from previous lesson

Warm-up - Accessing prior knowledge

1. Which of these representations does not tell us to multiply?

a. 3(4)                                c. 6 . 7

b. 2m                                  d. 8 x 10

2. Use mental math to compute (learners explain reasoning when sharing answers).

a. 3 + (17 + 38)                  d. 2(13) + 2(7)              

b. 1 + (1/2 + 4 + 1/2)        e. 5(3 + 10)

c. 5 x 26 x 2                         f. 231 . 8 . 0

3. Compute using the correct order of operations (learners explain reasoning when sharing answers).

3 + 5^2 (9 - 3 (-1 + 4))

2. Introduktion till lektionen / Introduction to the lesson content 

The main part of the lesson, will start with the learners watching a video on simplifying expressions (see attached).

While the video is playing, the teacher will stop it at various points and ask learners questions on what was said, to gauge their understanding and keep them active in the lesson.

3. Aktiviteter / Key Activities 

Collecting Like Terms 

A term is an individual part of an expression and typically appears in one of three forms:

• A number by itself

• A letter by itself

• A combination of letters and numbers

Like terms have the same combination of letters. To add or subtract terms with the same letter, we add or subtract the numbers like usual and just put the letter back on the end.

Skill 1: Linear Expressions with a Single Variable

Linear expressions are those in which all variables (i.e. the letters) are to the power of 1 so there are no squared or cubed terms.

Example: simplify the following, 2a+3+a+5

We have to group the terms that are similar; all the terms that are just numbers need grouping together and simplifying, as do the similar algebraic terms.

This gives, 

2a + 1a=3a

3 + 5=8

Skill 2: Like Terms With Different Letters

Sometimes terms have more than one variable (letter) multiplied or divided together:

xy + y + 2xy

in this instance, 

xy and 

2xy, are like terms that can be added together to simplify the expression, hence we find,

3xy + y

Skill 3: Identifying Like Terms with Powers

Terms of certain powers have to be grouped with terms of the same power. Such terms can also include multiple letters and powers.

2x²y + xy² + 3x²y + 5xy² 

= 5x²y+6xy² 

2x²y and 3x²y are like terms xy² and  5xy² are like terms.

Example 1: Two Variables

Simplify the expression 3y + 2x + 4x − y.

3y and −y are like terms

2x and 4x are like terms 

• Example 1: (Teacher led example)

• Whenever a problem can be simplified, you should simplify it before substituting numbers for the letters. This will make your job a lot easier! To simplify an algebraic expression: (2 . 3) + 2(x) + x(1) -x(4x) + 5

• Clear the parentheses. 2 . 3 + 2 . x + x . 1 - x . 4x + 5

• = 6 + 2x + x - 4x² + 5

• 
  

• Combine like terms by adding coefficients. 6 + 2x + x - 4x² + 5

= 6 + 3x - 4x² + 5

• Combine the constants. 

6 + 3x - 4x² +5

= 11 + 3x - 4x²

Example 2: (Teacher led example with student discussion)

Before you evaluate an algebraic expression, you need to simplify it. This will make all your calculations much easier. Here are the basic steps to follow to simplify an algebraic expression:

• remove parentheses by multiplying factors

• use exponent rules to remove parentheses in terms with exponents

• combine like terms by adding coefficients

• combine the constants

Let's work through an example.

When simplifying an expression, the first thing to look for is whether you can clear any parentheses. Often, you can use the distributive property to clear parentheses, by multiplying the factors times the terms inside the parentheses. In this expression, we can use the distributive property to get rid of the first two sets of parentheses.

Now we can get rid of the parentheses in the term with the exponents by using the exponent rules we learned earlier. When a term with an exponent is raised to a power, we multiply the exponents, so (x2)2 becomes x4.

The next step in simplifying is to look for like terms and combine them. The terms 5x and 15x are like terms, because they have the same variable raised to the same power -- namely, the first power, since the exponent is understood to be 1. We can combine these two terms to get 20x.

Finally, we look for any constants that we can combine. Here, we have the constants 10 and 12. We can combine them to get 22.

Now our expression is simplified. Just one more thing -- usually we write an algebraic expression in a certain order. We start with the terms that have the largest exponents and work our way down to the constants. Using the commutative property of addition, we can rearrange the terms and put this expression in correct order, like this.