Grade 8 Mathematics: Algebra and Patterns Assignment

Vocabulary practice flashcards covering pattern concepts, repeating units, linear and non-linear patterns, initial values, rates of change, and real-life algebraic models from the Grade 8 Algebra-patterns unit assignment.

K/U-Observation

An assessment category that evaluates a student's knowledge and understanding of pattern concepts and terminology through observed written work.

T/I-Observation

An assessment category focused on thinking and investigation, where students analyze patterns, determine rules, complete tables, and calculate missing terms.

Application - Conversation

An evaluation category where students apply algebraic pattern concepts to real-life word problems and explain their reasoning orally to the teacher.

Communication - Conversation

An evaluation criterion assessing a student's ability to clearly and independently articulate their mathematical strategies, calculations, and rules to the teacher.

Curriculum Expectations C1.1–C1.4

The specific set of Grade 8 curriculum expectations evaluated across all 19 student versions of the patterns assignment.

Repeating Unit

The specific sequence of numbers or terms that recurs identically in a cycle, such as $(\frac{1}{2}, \frac{1}{4}, \frac{3}{4})$, $(\frac{1}{3}, \frac{2}{3}, 1)$, $(0.2, 0.4, 0.6)$, $(0.5, 1, 1.5)$, or $(2, 5, 8)$.

Repeating Pattern

A sequence of elements that cycles continuously without changing its core values, such as $1, 3, 1, 3, 1, 3$.

Linear Growing Pattern

A numerical sequence that increases by a fixed, constant rate of change from one term to the next, such as $2, 5, 8, 11$ or reading $18$ pages on the first day and adding $4$ pages each day after.

Linear Shrinking Pattern

A numerical sequence that decreases by a fixed, constant rate of change between consecutive terms, such as $10, 7, 4, 1, -2$ or $100, 90, 80, 70, 60$.

Constant Rate of Change

The steady amount added or subtracted between consecutive terms in a linear sequence, such as $-3$ in the sequence $20, 17, 14, 11, 8$.

Initial Value

The starting amount or base quantity in a linear relationship before any regular changes occur, such as a setup fee, registration fee, or starting bank balance.

Geometric Doubling Pattern

A non-linear growing sequence where each successive term is multiplied by $2$ rather than increasing by addition, such as $2, 4, 8, 16, 32$ or $3, 6, 12, 24$.

Geometric Halving Pattern

A non-linear shrinking sequence where each term is multiplied by $\frac{1}{2}$, such as $10, 5, 2.5, 1.25, 0.625$ or $1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}$.

Square Number Pattern

A non-linear pattern formed by consecutive squared integers, exemplified by $1, 4, 9, 16, 25$, which does not have a constant rate of change.

Pattern Equation

An algebraic rule relating the term value $T$ to the term number $n$, such as $T = 4n - 3$, $T = 7n - 5$, or $T = 30 - 2n$.

Term Value ($T$)

The algebraic variable representing the output or numerical value of a specific position within a sequence.

Term Number ($n$)

The algebraic variable representing the position, step, or input index of a value in a pattern.

Savings Account Linear Model

A real-world application starting with an initial balance of $20$ dollars and increasing by regular weekly deposits of $7.50$ dollars.

Tree Growth Linear Model

A growing situation where a tree has an initial height of $45\,\text{cm}$ and increases at a constant rate of $3.5\,\text{cm}$ per month.

Pool Drainage Linear Model

A shrinking situation where a swimming pool starts with $500\,\text{L}$ of water and empties at a constant rate of $22.5\,\text{L}$ per minute.

Candle Burn Linear Model

A shrinking situation where a candle starts at a height of $24\,\text{cm}$ and decreases by $1.5\,\text{cm}$ for every hour it burns.

Taxi Fare Linear Model

A real-world linear equation model with an initial starting fee of $6$ dollars and a rate of $2.75$ dollars per kilometre.

Water Tank Linear Model

A linear shrinking relationship where a tank holds $90\,\text{L}$ of water initially and loses volume at a rate of $4.5\,\text{L}$ each minute.

Delivery Service Fee Model

A linear cost relationship consisting of a fixed $12$ dollar service fee plus a variable charge of $1.80$ dollars per kilometre.

Phone Battery Depletion Model

A linear shrinking scenario beginning at a full charge of $100\%$ and declining at a constant rate of $8\%$ per hour.

Gym Membership Cost Model

A linear cost model starting with a $25$ dollar registration fee and increasing by a regular rate of $18$ dollars per month.

Car Rental Fee Model

A linear relationship that charges an initial cost of $40$ dollars plus an ongoing rate of $35$ dollars per day.

Bank Account Withdrawal Model

A shrinking linear model where an initial account balance of $300$ dollars decreases by regular withdrawals of $17.50$ dollars per week.

Printing Company Cost Model

A linear equation application consisting of a $15$ dollar setup fee and a variable cost of $0.25$ dollars per page printed.

Bicycle Rental Cost Model

A linear cost equation featuring an initial rental charge of $8$ dollars and an additional hourly rate of $4.50$ dollars.

Fuel Consumption Linear Model

A linear shrinking relationship where a truck begins with an initial $80\,\text{L}$ of fuel and consumes $6.5\,\text{L}$ per hour of driving.

Negative Balance Account Model

A linear growing model starting at a negative balance of $-50$ dollars and increasing by weekly deposits of $12.50$ dollars.

Fundraising Budget Linear Model

A linear shrinking situation where a campaign begins with $120$ dollars and loses $7.50$ dollars daily due to expenses.