A1.1 • Sec 1 MOE

Numbers & Algebra

Algebraic Expressions

Simplify expressions by collecting like terms — core Sec 1 algebra skill.

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Learning objectives

• Identify like terms and coefficients
• Simplify expressions with multiple variables
• Substitute values into expressions
• Form expressions from word descriptions

Before I teach you, attempt the warm-up. Even wrong answers activate your brain — then my explanation will stick better.

Learning methods:CRAI-We-YouSpaced reviewRetrievalMetacognition

Brain warm-up (try before we teach)

Try first, then learn step by step

Simplify

4 x + 2 x

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Foundation — I Do → We Do → You Do

I Do — Learn

Step 1 of 28

What is a variable?

A variable (like $x$ , $y$ , $n$ ) stands for an unknown number.

$3 x$ means 3 × $x$ .

$x + 5$ means a number $x$ , then add 5.

Algebra lets us write maths rules that work for any number.

I Do — Learn

Step 2 of 28

Like terms

Like terms have the same variable part.

- $3 x$ and $5 x$ are like terms → sum to $8 x$

- $3 x$ and $3 y$ are NOT like terms

- $2 x^{2}$ and $4 x$ are NOT like terms (different powers)

Only like terms can be combined.

I Do — Learn

Step 3 of 28

Worked example: 5a + 3b − 2a + 7

Group like terms:

( $5 a - 2 a$ ) + $3 b + 7$

= $3 a + 3 b + 7$

Constants (plain numbers) are like terms with each other too.

I Do — Learn

Step 4 of 28

Worked example: 8x − 3x

Subtract coefficients when variables match:

$8 x - 3 x = (8 - 3)$ x = $5 x$

Think: 8 bananas − 3 bananas = 5 bananas.

I Do — Learn

Step 5 of 28

Fractional terms in algebra

Expressions can have fractional coefficients.

$\frac{x}{2}$ means half of $x$ .

$\frac{3 x}{4}$ means three-quarters of $x$ .

To add $\frac{x}{2} + \frac{x}{4}$ :

1. Both fractions need the same denominator (here, 4).

2. Rewrite $\frac{x}{2}$ as $\frac{2 x}{4}$ (multiply top and bottom by 2).

3. Add: $\frac{2 x}{4} + \frac{x}{4} = \frac{3 x}{4}$

We Do — Guided

Step 6 of 28

Guided: Simplify 4x + 2x

Simplify

4 x + 2 x

We Do — Guided

Step 7 of 28

Guided: Simplify 9a − 4a

Simplify

9 a - 4 a

We Do — Guided

Step 8 of 28

Guided: Are these like terms?

Are $2 x^{2}$ and $5 x$ like terms? Answer yes or no.

We Do — Guided

Step 9 of 28

Guided: Simplify 5m + 3m + 2

Simplify

5 m + 3 m + 2.

We Do — Guided

Step 10 of 28

Guided: Simplify 7y − 3 + 2y + 5

Simplify fully:

7 y - 3 + 2 y + 5

We Do — Guided

Step 11 of 28

Guided: Two variables

Simplify

4 x + 3 y + 2 x - y

We Do — Guided

Step 12 of 28

Guided: With negatives

Simplify

12 p - 5 - 3 p + 10

You Do — Practice

Step 13 of 28

Practice: Simplify 6x − 2x + 3 − 7

Simplify fully:

6 x - 2 x + 3 - 7

You Do — Practice

Step 14 of 28

Practice: Three terms

Simplify

2 a + 5 b - a + 3 b + 1

We Do — Guided

Step 15 of 28

Guided: Simplify x/2 + x/4

Simplify $\frac{x}{2} + \frac{x}{4}$ fully.

First rewrite $\frac{x}{2}$ with denominator 4, then add the fractions.

We Do — Guided

Step 16 of 28

Guided: Simplify 3x/2 − x/6

Simplify $\frac{3 x}{2} - \frac{x}{6}$ fully.

Rewrite both fractions with denominator 6, then subtract.

You Do — Practice

Step 17 of 28

Practice: Fractional expression

Simplify $\frac{x}{3} + \frac{2 x}{3} - \frac{x}{6}$ fully.

Add the thirds first, then subtract $\frac{x}{6}$ .

I Do — Learn

Step 18 of 28

Substitution

To substitute means replace a variable with a number.

If $x = 3$ , then $2 x + 5$ becomes:

2 $(3) + 5 = 6 + 5$ = 11

We Do — Guided

Step 19 of 28

Guided: Substitute x = 3

x = 3

, find the value of

2 x + 5.

We Do — Guided

Step 20 of 28

Guided: Substitute a = 2, b = 5

a = 2

and

b = 5

, find

3 a + b

You Do — Practice

Step 21 of 28

Practice: Substitute x = 4

x = 4

, find

5 x - 2.

I Do — Learn

Step 22 of 28

Forming expressions from words

Translate English into algebra:

- "5 more than a number n" → $n + 5$

- "Twice a number" → $2 n$

- "7 less than x" → $x - 7$

We Do — Guided

Step 23 of 28

Guided: Write an expression

Write an expression for: 5 more than a number n

We Do — Guided

Step 24 of 28

Guided: Twice a number

Write an expression for: twice a number x

You Do — Practice

Step 25 of 28

Practice: Rectangle perimeter

A rectangle has length l and width w. Write the perimeter formula. (Use

2 l + 2 w

)

You Do — Practice

Step 26 of 28

Practice: Evaluate perimeter

Using

2 l + 2 w

, find the perimeter when

l = 6

and

w = 4.

We Do — Guided

Step 27 of 28

Guided: Write a fractional expression

Write an expression for: one-third of a number x

You Do — Practice

Step 28 of 28

Practice: Evaluate algebraic fraction

x = 7

, find the value of

\frac{2 x + 3}{5}

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