Algebraic Expressions Slides MATH G.6 LESSON 1
Algebraic Expressions &
Substitution
Learn how to write, read, and calculate expressions with variables.
Srithammarat Suksa School English Programme
01 // INTRO ALGEBRAIC EXPRESSIONS
What is a Variable?
Read the code:
x + 5
Read as: "a number plus 5"
The Secret Number
In math, x is a letter that stands for a secret number . We call this a variable .
Example:
If x = 3, then
Focus: English Terminology Slide 2 of 6
02 // VOCABULARY ALGEBRAIC EXPRESSIONS
Parts of an Expression
x
Variable
Operation
5
Constant
Class Drill
Shout the name of each part!
Point to x: "VARIABLE!" Point to +: "OPERATION!" Point to 5: "CONSTANT!"
Focus: Key Vocabulary Slide 3 of 6
03 // SUBSTITUTION ALGEBRAIC EXPRESSIONS
How to Evaluate
Replace the letter with the number, then calculate the answer.
1
Substitute
Put the number in place of the letter.
2
Calculate
Follow the order of operations (PEMDAS).
Example Key: n = 4
Expression:
2n + 1
Step 1: Replace n with 4
2 × 4 + 1
Step 2: Solve
8 + 1 = 9
PEMDAS: Multiply first, then add! Slide 4 of 6
04 // PRACTICE ALGEBRAIC EXPRESSIONS
Variable Substitution Cards
Work with your partner to solve your expression cards!
1
Pick Cards
Draw one Variable Card (e.g., n = 4) and one Expression Card (e.g., 2n + 1).
2
Solve
Write the substitution on your mini whiteboard and calculate the answer.
3
Check
Compare answers with your partner. Do they match? Help each other correct any mistakes!
Activity Duration: 20 Minutes
05 // ASSESSMENT ALGEBRAIC EXPRESSIONS
Check Your Understanding
Assignment
Open Google Classroom and complete:
Week 14 : Lesson 1 : WS1
Practice Question
Evaluate this expression on your notebook:
3y - 2
when y = 5
End of Lesson 1 Slide 6 of 6
Variable Substitution Cards VARIABLE CARDS
CARD SET A
Teacher Prep: Print on cardstock and cut along the dotted lines. This page contains Variable Cards . Students draw one Variable Card to define their key (e.g., \(n = 4\)) for substitution.
01
x = 3
Variable
02
x = 5
Variable
03
y = 2
Variable
04
y = 7
Variable
05
n = 4
Variable
06
n = 6
Variable
07
a = 1
Variable
08
a = 10
Variable
09
b = 5
Variable
10
b = 8
Variable
11
z = 9
Variable
12
z = 0
Variable
13
x = 8
Variable
14
y = 3
Variable
15
n = 9
Variable
16
a = 5
Variable
Srithammarat Suksa School English Programme Page 1 of 2
EXPRESSION CARDS
CARD SET B
Teacher Prep: Cut along the dotted lines. This page contains Expressions to Evaluate . Students substitute their variable card's number into the expressions and solve.
01
2v + 5
Level 1
02
3v - 1
Level 1
03
v + 12
Level 1
04
10 - v
Level 1
05
5v + 2
Level 2
06
2(v + 3)
Level 2
07
3(10 - v)
Level 2
08
v/2 + 7
Level 2
09
v2 + 3
Level 3
10
4v - v
Level 3
11
v/3 + v
Level 3
12
(2v + 4)/2
Level 3
* Replace variable "v" with the value of your Variable Card (e.g., x, y, n, a).
Algebraic Expressions Worksheet Practice Sheet
Variables & Substitution
Srithammarat Suksa School
Name: ____________________
Class: G.6/_____
Date: ______________
Part 1: Match the Vocabulary
Write: Variable , Constant , or Operation in each box below.
x
1. __________________
2. __________________
9
3. __________________
Part 2: Calculate the Value
Replace the letter with the number, then solve. Show your steps!
Evaluate: y + 8 y = 5
Show work:
Evaluate: 3n - 2 n = 4
Show work:
Evaluate: 10 - a a = 3
Show work:
Evaluate: z/2 + 6 z = 10
Show work:
Part 3: Challenge Question
Solve: 2(x + y) - 5 x = 6, y = 1
Show step-by-step math (Do Parentheses first!):
Assignment: Week 14 : Lesson 1 : WS1 Pacing: 10 Minutes Max
Writing Simplifying Expressions Slides MATH G.6 LESSON 2
Writing & Simplifying
Expressions
Learn to write expressions from word phrases and combine like terms.
Srithammarat Suksa School English Programme
01 // VISUAL SETUP LIKE TERMS
Apples and Bananas
Why can't we add everything together?
Visual Example:
🍎🍎🍎 + 🍌🍌 + 🍎
🍎🍎🍎🍎 + 🍌🍌
We have 4 Apples and 2 Bananas total!
Algebra translation:
3a + 2b + 1a
↓ simplifies to ↓
4a + 2b
Rule: You can only add terms with the exact same letter !
Focus: Intuitive visual grouping Slide 2 of 6
02 // CLASSIFICATION LIKE TERMS
What are "Like Terms"?
Anatomy of a Term
3a
3 is the Coefficient (how many)
a is the Variable (letter)
Identify the Families:
LIKE TERMS (Yes)
3a & 5a
UNLIKE TERMS (No)
3a & 2b
Class Drill (Call & Response)
"Same letter? Combine them!"
"Different letter? Keep them separate!"
Oral Practice Protocol Slide 3 of 6
03 // DECODING CLUES ALGEBRAIC EXPRESSIONS
Translating Word Phrases
Learn how to translate English words into math symbols!
Addition
More than, Sum, Plus
"5 more than x"
-
Subtraction
Less than, Minus
"3 less than y"
×
Multiplication
Times, Product, Double
"Double n"
÷
Division
Divided by, Half of
"Quotient of z and 2"
⚠️ Remember: "Less than" changes the order! "3 less than y" is written as y - 3 .
04 // TEAM GAMEPLAY ACTIVE WORKSHOP
Like Terms Sorting Game
Classify term cards into columns and add them up!
1
Get Term Cards
Your group gets cards like: 4x, 3y, 2x, 7, 5y, 1.
2
Like Terms Sorting Cards LIKE TERMS SORTING MAT
GAME BOARD
Group Name: _________________
Date: ___________
How to Play:
1. Draw 6 random cards and put them on the board.
2. Sort each card into its correct column (the "Like Terms").
3. Add each column together to write the simplified expression at the bottom!
\(x\) - Family
Place Card
Place Card
COLUMN SUM:
________ \(x\)
\(y\) - Family
Place Card
Place Card
COLUMN SUM:
________ \(y\)
Constants
Place Card
Place Card
COLUMN SUM:
________
SIMPLIFIED EXPRESSION:
Srithammarat Suksa School English Programme Page 1 of 2
TERM CUTOUT CARDS
CUTOUT SHEET
Teacher Prep: Cut out these 15 algebra terms. Give one complete set to each student group playing the Like Terms Sorting Game.
01
4x
Coeff: 4 • Var: x
02
3y
Coeff: 3 • Var: y
03
7
Constant
04
2x
Coeff: 2 • Var: x
05
5y
Coeff: 5 • Var: y
06
1
Constant
07
5x
Coeff: 5 • Var: x
08
2y
Coeff: 2 • Var: y
09
10
Constant
10
x
Coeff: 1 • Var: x
11
y
Coeff: 1 • Var: y
12
4
Constant
* Vocabulary: "Like Terms," "Variable," "Coefficient," and "Constant."
Srithammarat Suksa School English Programme Page 2 of 2
Writing Simplifying Expressions Worksheet Practice Sheet
Writing & Simplifying Expressions
Srithammarat Suksa School
Name: ____________________
Class: G.6/_____
Date: ______________
Part 1: Translate Words into Math
Write the algebraic expression for each English word phrase.
English: 5 more than x
English: 4 less than y
English: Double n (2 times n)
English: Quotient of z and 3
Part 2: Combine Like Terms
Group the same variables together, then add their coefficients.
1. Simplify: 3a + 5b + 2a
Group "a" family: _________________
Final Answer: _________________
2. Simplify: 6x + 2 + 3x + 8
Group "x" family: _________________
Final Answer: _________________
Part 3: Challenge Question
Simplify completely: 5x + 3y + 4 + 2x - y - 1
Final Simplified Expression: __________________________________
Unit: Expressions and Equations Pacing: 10 Minutes Max
OneStep Equations Addition Subtraction Slides MATH G.6 LESSON 3
One-Step Equations:
Addition & Subtraction
Learn how to keep equations perfectly balanced on a scale.
Srithammarat Suksa School English Programme
01 // VISUAL SETUP BALANCE SCALE
Keep the Scale Balanced!
An equation is like a balanced scale. Do the exact same action to both sides!
Visual Scale Model:
x + 3 Left
8 Right
Equation: x + 3 = 8
What is an Equation?
An equation has an equal sign (=) . Both sides must always have the same value.
Isolate the Variable:
Your goal is to get the letter x completely alone on one side.
Rule: Maintain the balance scale! Slide 2 of 6
02 // INVERSE METHOD INVERSE OPERATIONS
Inverse Operations
"Inverse" means opposite. Use the opposite operation to cancel out numbers.
Undo Addition:
Equation: x + 3 = 8
Subtract 3 both sides: x + 3 - 3 = 8 - 3
Result: x = 5
Opposite Actions:
Inverse Operation:
Subtraction is the opposite of Addition.
Addition is the opposite of Subtraction.
Class Drill
"Plus turns to minus! Do the same to both sides!"
"Minus turns to plus! Do the same to both sides!"
Oral Practice Protocol Slide 3 of 6
03 // EXAMPLES ONE-STEP EQUATIONS
How to Solve
Always check your answers by substituting the number back into the equation.
Addition Equation
Solve: x + 4 = 10
x + 4 - 4 = 10 - 4
x = 6
✓ CHECK: 6 + 4 = 10 (True!)
Subtraction Equation
Solve: y - 2 = 7
y - 2 + 2 = 7 + 2
y = 9
✓ CHECK: 9 - 2 = 7 (True!)
Verification ensures accuracy! Slide 4 of 6
04 // PRACTICE CLASSROOM GAME
The Balance Scale Race
Solve equations step-by-step on your mini whiteboards!
1
Watch Screen
The teacher will project an equation on the board (e.g., x + 12 = 30).
2
Solve Both Sides
Write down the opposite operation on BOTH sides using your marker.
3
Balance Scale Equation Cards ADDITION EQUATION CARDS
ADDITION SET
Teacher Prep: Cut out these 12 addition equation cards along the dotted lines. Use them to display equations during the "Balance Scale Race" game, or give card packs to student groups to play.
01
x + 5 = 12
Keep Balanced
02
y + 3 = 10
Keep Balanced
03
a + 8 = 15
Keep Balanced
04
n + 12 = 20
Keep Balanced
05
b + 6 = 14
Keep Balanced
06
z + 9 = 21
Keep Balanced
07
x + 2 = 19
Keep Balanced
08
y + 15 = 30
Keep Balanced
09
w + 4 = 11
Keep Balanced
10
n + 7 = 16
Keep Balanced
11
c + 11 = 25
Keep Balanced
12
x + 20 = 50
Keep Balanced
Srithammarat Suksa School English Programme Page 1 of 2
SUBTRACTION EQUATION CARDS
SUBTRACTION SET
Teacher Prep: Cut out these 12 subtraction equation cards along the dotted lines. Use them for individual whiteboard practice or timed class games.
01
x - 3 = 8
Keep Balanced
02
y - 7 = 2
Keep Balanced
03
a - 5 = 10
Keep Balanced
04
n - 12 = 4
Keep Balanced
05
b - 1 = 15
Keep Balanced
06
z - 9 = 11
Keep Balanced
07
x - 4 = 18
Keep Balanced
08
y - 10 = 25
Keep Balanced
09
w - 8 = 3
Keep Balanced
10
n - 15 = 15
Keep Balanced
11
c - 2 = 19
Keep Balanced
12
x - 30 = 40
Keep Balanced
Srithammarat Suksa School English Programme Page 2 of 2
OneStep Equations Addition Subtraction Worksheet Practice Sheet
One-Step Equations (+ / -)
Srithammarat Suksa School
Name: ____________________
Class: G.6/_____
Date: ______________
Part 1: Solve Addition Equations (Subtract from both sides!)
1. Solve: x + 7 = 19
Show opposite operation steps:
Check: ____ + 7 = 19 x = _______
2. Solve: y + 11 = 30
Show opposite operation steps:
Check: ____ + 11 = 30 y = _______
Part 2: Solve Subtraction Equations (Add to both sides!)
3. Solve: a - 5 = 12
Show opposite operation steps:
Check: ____ - 5 = 12 a = _______
4. Solve: n - 8 = 15
Show opposite operation steps:
Check: ____ - 8 = 15 n = _______
Part 3: Word Problem
A physical balance scale has x + 8 marbles on the left pan and 20 marbles on the right pan. The scale is balanced.
Write Equation:
Solve x: x = ________________
Unit: Expressions and Equations Pacing: 10 Minutes Max
OneStep Equations Multiplication Division Slides MATH G.6 LESSON 4
FINAL STAGE
One-Step Equations:
Multiplication & Division
Learn how to solve multiplication and division equations using opposites.
Srithammarat Suksa School English Programme
01 // VISUAL SETUP INVERSE OPERATIONS
Undo Multiplication & Division!
Multiplication and division are opposites. One always undoes the other!
Undo Multiplication:
How to solve: 4x = 12
Explain: 4 times x equals 12
Divide both sides by 4:
→ x = 3
Multiplication is undone using division!
Undo Division:
How to solve: x / 2 = 5
Explain: x divided by 2 equals 5
Multiply both sides by 2:
→ x = 10
Division is undone using multiplication!
Focus: Opposite Actions Slide 2 of 6
02 // NOTATION DIVISION FORMAT
How we write division in algebra
In algebra, we write division as a fraction. Fraction line means division!
Algebra Fraction Format:
x 2
= x ÷ 2
We use a fraction line to express division.
Multiplication Format:
Multiplication has no symbol. 4x means 4 times x.
Class Drill (Call & Response)
"Multiply turns to divide! Divide turns to multiply!"
"Do the exact same action — to both sides!"
Oral Practice Protocol Slide 3 of 6
03 // EXAMPLES MULTIPLICATION & DIVISION
How to Solve
Practice both multiplication and division templates.
Multiplication Equation
Solve: 3x = 15
Divide both sides by 3:
(3x)/3 = 15 / 3
x = 5
✓ CHECK: 3(5) = 15 → 15 = 15 (True!)
Division Equation
Solve: y / 4 = 3
Multiply both sides by 4:
y / 4 • 4 = 3 • 4
y = 12
✓ CHECK: 12 / 4 = 3 → 3 = 3 (True!)
Always check with substitution! Slide 4 of 6
04 // PRACTICE PARTNER RELAY
Solve & Check Partner Relay
One partner solves, and the other checks the answer!
PARTNER A
The Solver
Pick an equation card, write it on your whiteboard, and perform the proper inverse operation to solve.
Solve Check Relay Cards RELAY EQUATION CARDS
DRAW PILE
Teacher Prep: Cut out these 12 multiplication and division equations along the dotted lines. In pairs, students draw a card to solve on their board, then pass to their partner to verify.
01
3x = 15
Solve & Relay
02
5y = 30
Solve & Relay
03
x / 2 = 8
Solve & Relay
04
y / 3 = 4
Solve & Relay
05
4a = 24
Solve & Relay
06
8b = 40
Solve & Relay
07
a / 5 = 5
Solve & Relay
08
b / 4 = 6
Solve & Relay
09
10z = 90
Solve & Relay
10
2n = 18
Solve & Relay
11
z / 10 = 7
Solve & Relay
12
n / 8 = 5
Solve & Relay
Srithammarat Suksa School English Programme Page 1 of 2
RELAY VERIFICATION SHEET
SUBMISSION MAT
Partner A (Solver): ___________________
Partner B (Checker): ___________________
ROUND 1 Partner A Solves • Partner B Checks
1. Original Equation:
Write here...
2. Partner A Answer:
x = ______
3. Partner B Check (Substitution):
Plug in variable to verify: ____ • ____ = ____
[ ] Correct [ ] Try Again
ROUND 2 Partner B Solves • Partner A Checks
1. Original Equation:
Write here...
2. Partner B Answer:
y = ______
3. Partner A Check (Substitution):
Plug in variable to verify: ____ • ____ = ____
[ ] Correct [ ] Try Again
How to debug if check fails:
- Did you use the correct opposite operation?
Srithammarat Suksa School English Programme Page 2 of 2
OneStep Equations Multiplication Division Worksheet Practice Sheet
One-Step Equations (× / ÷)
Srithammarat Suksa School
Name: ____________________
Class: G.6/_____
Date: ______________
Part 1: Solve Multiplication Equations (Divide both sides!)
1. Solve: 4x = 24
Show division steps on both sides:
Check: 4 • (____) = 24 x = _______
2. Solve: 8y = 40
Show division steps on both sides:
Check: 8 • (____) = 40 y = _______
Part 2: Solve Division Equations (Multiply both sides!)
3. Solve:
a 5
= 6
Show multiplication steps on both sides:
Check: (____) / 5 = 6 a = _______
4. Solve:
n 3
= 8
Show multiplication steps on both sides:
Check: (____) / 3 = 8 n = _______
Part 3: Challenge Question
Four friends share a box of pens equally. Each friend receives 6 pens. Write the division equation to find the total number of pens (p) and solve.
Write Equation:
Solve p: p = ________________
Unit: Expressions and Equations Pacing: 10 Minutes Max
