Grade 6 · Grade 6: Expressions and Equations · Expressions, Equations and Relationships
Expressions, Equations and Inequalities
Translate words into algebra, generate equivalent expressions, solve one-step equations and graph inequalities.
Learning objectives
- Write and evaluate expressions with variables and exponents.
- Generate equivalent expressions using properties of operations.
- Solve one-step equations of the form x + p = q and px = q.
- Write and graph inequalities of the form x > c and x < c.
- Relate dependent and independent variables in tables, graphs and equations.
AERO Mathematics alignment
AERO.M6.AE.1
Write and evaluate numerical expressions involving whole-number exponents.
AERO.M6.AE.2
Write, read and evaluate expressions in which letters stand for numbers, using correct terms such as sum, term, product, factor, quotient and coefficient.
AERO.M6.AE.3
Apply the properties of operations to generate and identify equivalent expressions.
AERO.M6.AE.4
Solve real-world and mathematical problems by writing and solving one-step equations of the form x + p = q and px = q.
AERO.M6.AE.5
Write inequalities of the form x > c or x < c to represent constraints, and graph their solution sets on a number line.
AERO.M6.AE.6
Use variables to represent two quantities that change in relation to one another, and analyse the relationship using tables, graphs and equations.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion B — Investigating patterns
- Criterion C — Communicating
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
A delivery service charges 10 QAR plus 3 QAR for each kilometre.
Think about it
How would you write a rule that gives the cost for any distance, and how would you find the distance when the cost is 34 QAR?
Hint: Use a letter for the distance you do not know yet.
EXPLAIN
From words to symbols
A variable is a letter standing for a number that is unknown or that changes. An expression such as 3d + 10 has no equals sign: it is a recipe for calculating. An equation states that two expressions are equal.
| Word | Meaning | Example in 3d + 10 |
|---|---|---|
| Term | A part separated by + or − | 3d and 10 |
| Coefficient | The number multiplying a variable | 3 |
| Constant | A term with no variable | 10 |
| Factor | Something multiplied | 3 and d |
Exponents
An exponent records repeated multiplication: 5³ = 5 × 5 × 5 = 125. Note that 3d means 3 × d, while d³ means d × d × d — they are completely different.
Solving one-step equations
Keep the equation balanced by doing the same thing to both sides. For 3d + 10 = 34, subtract 10 from both sides to get 3d = 24, then divide both sides by 3 to get d = 8 kilometres.
Inequalities
x > 20 describes infinitely many values. On a number line, an open circle at 20 shows that 20 itself is not included; a filled circle would include it.
Where this is used
Dependent and independent variables appear everywhere: cost depends on distance, wages depend on hours, and fuel used depends on kilometres driven. The independent variable is the one you choose.
INVESTIGATION
Try it yourself
Invent a pricing rule for a small business, write it as an equation, build a table for five inputs, then graph the pairs. Identify which variable is independent and explain how the graph shows the fixed charge.
Watch
Solving Basic Equations
Math Antics · 9:00
Models the balance idea you will use for every equation from now on.
Before you watch: If x + 7 = 12, what undoes the +7?
- Solve 4x = 36.
- Write an equation for: a number increased by 9 is 21.
Interactive simulation · PhET
Expression Exchange
Build expressions with coin values, then collect like terms and check equivalence.
While you explore
- Which of your expressions are equivalent, and how do you know?
- How does the simulation show that 3x is not the same as x³?
Key vocabulary
- Inequality
- A statement that one amount is bigger or smaller than another.
- Coefficient
- The number in front of a variable.
- Variable
- A letter that stands for a number.
Practice questions
0/1 correct
Level 1 · Criterion A
Which expression means "7 more than triple a number n"?
MYP criterion tasks
Level 2 · Criterion D
A taxi charges 12 QAR plus 2 QAR per km. Write an equation and find the distance for a 30 QAR fare.
Reflect & track
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