United States
Hong KongCompetency 3: Algebraic thinking and the coordinate plane
Competency 3 has seven skills, the joint most of any competency on the Mathematics subtest, and about 12 of the 35 questions on our split. Equivalence, modeling a situation, solving equations and inequalities, graphing linear equations, functions, and comparing slopes.
Seven skills, and only one of them is about solving an equation in the abstract. Read them and the emphasis is unmistakable.
The seven skills as the rule states them
1. Determine whether two algebraic expressions are equivalent by applying properties of operations or equality. 2. Identify an algebraic expression, equation, or inequality that models a real-world situation. 3. Solve equations and inequalities (e.g., linear, quadratic) graphically or algebraically. 4. Determine and solve equations or inequalities, graphically or algebraically, in real-world problems. 5. Graph and interpret a linear equation in real-world problems (e.g., use data to plot points, explain slope and y-intercept, determine additional solutions). 6. Identify relations that satisfy the definition of a function. 7. Compare the slopes of two linear functions represented algebraically and graphically.
Section 82, Mathematics, incorporated into Rule 6A-4.0021, F.A.C.
Count the appearances of "real-world": three of the seven. Skills 2, 4 and 5 are all about translating a situation into algebra rather than manipulating algebra you have been handed. That is a different preparation from the one most people default to.
Size
| Competency | Skills | Our estimated questions |
|---|---|---|
| 1. Number sense, concepts, and operations | 3 | 5 |
| 2. Geometry and measurement | 4 | 7 |
| 3. Algebraic thinking and the coordinate plane | 7 | 12 |
| 4. Probability, statistics, and data interpretation | 7 | 11 |
FLDOE publishes 35 questions for this subtest and no split beneath it. We apportion the 35 in proportion to the skills the rule states under each competency. Algebra and statistics both have seven skills, so they tie; the 12 and the 11 differ only because the column has to sum to 35. Anyone presenting algebra as clearly the biggest block is over-reading the arithmetic, including us if we did not say this.
What is and is not here
Quadratics appear once, inside brackets, as an example of a kind of equation you might solve graphically or algebraically. They are not a named skill. Neither are polynomials, logarithms, exponential functions, matrices or sequences.
What is named: equivalence, modeling, solving, graphing linear equations, functions, and comparing slopes. Five of the seven touch linear relationships in some form. If you learn one thing properly for this competency, learn the straight line.
Skill 6 is the odd one out
"Identify relations that satisfy the definition of a function." That is a definition question, not a calculation, and it has a one-line answer: a relation is a function when every input has exactly one output.
On a graph that is the vertical line test. On a table it means no repeated input with different outputs. On a set of ordered pairs it means no first coordinate appears twice with different partners. Same rule, three presentations. Patterns, sequences and functions covers it.
Skills 3 and 4 look identical and are not
Skill 3 is solving equations and inequalities. Skill 4 is doing it in real-world problems, and it adds the word determine: you have to work out what to solve before you solve it.
That is why word problems carry so much weight in this competency. The algebra in them is rarely hard. Setting them up is where candidates lose marks, and it is also where the 2.86 minutes a question that this subtest allows on our division of the published figures actually goes.
Where to start
- Solving linear equations, because everything else assumes it
- Slope and the equation of a line, because five skills touch it
- Translating word problems into equations, because three skills say real-world
- Functions, which is a definition worth twenty minutes
The concession we would make on this page: our 12-question figure and the 11 for statistics are separated by a rounding decision and nothing more. Treat the two competencies as equally weighted and revise both.
Common questions
What algebra is on the FTCE General Knowledge Test?
Equivalence of expressions, modeling a situation with an expression or equation, solving equations and inequalities, graphing and interpreting linear equations, identifying functions, and comparing slopes. Quadratics appear only as an example inside one skill, not as a topic.
How many algebra questions are on the math subtest?
FLDOE publishes 35 for the subtest and no breakdown. Our estimate is about 12, apportioning the total by the number of skills stated under each competency. Algebra ties with statistics on seven skills, so the two are effectively equal in weight.
Is quadratic factoring tested?
The rule mentions quadratics once, in brackets, as an example of an equation you might solve graphically or algebraically. It is not a named skill, and no skill statement mentions factoring, the quadratic formula or completing the square.
What makes a relation a function?
Every input has exactly one output. On a graph that is the vertical line test; in a table it means no input appears twice with different outputs; in a set of ordered pairs it means no first coordinate repeats with a different partner.