United States
Hong KongCompetency 1: Number sense, concepts and operations
Competency 1 is the smallest on the Mathematics subtest: three skills, about five of the 35 questions on our split. Compare real numbers and locate them on a number line, solve real-world problems with the four operations on rational numbers, and evaluate expressions using order of operations.
Three skills. The whole of what most people think of as arithmetic, compressed into the smallest competency on the paper.
The three skills as the rule states them
1. Compare real numbers and identify their location on a number line. 2. Solve real-world problems involving the four operations with rational numbers. 3. Evaluate expressions involving order of operations.
Section 82, Mathematics, incorporated into Rule 6A-4.0021, F.A.C.
Notice what is not there. No prime factorization, no exponent laws as a topic, no roots, no absolute value as a named skill. Those can appear inside an order-of-operations expression, and none of them is a skill in its own right.
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 the Mathematics subtest and no split beneath it. We apportion the 35 in proportion to the skills the rule states under each competency, which gives about five here. The three is the state's; the five is ours.
Skill 1: comparing and locating
"Real numbers" is broader than it sounds: integers, fractions, decimals, negatives, and irrationals like the square root of 2 or pi. An item may ask you to order a mixed set or place one on a marked line.
The technique is conversion. Put everything into the same form and compare. Three fifths converts to 60 percent and seven tenths to 70 percent, so three fifths is the smaller of the two. The calculator makes this mechanical, which is the point of having one.
Negatives are where errors cluster. Negative 8 is smaller than negative 3, and the larger the digit the smaller the number. Say it out loud once and it stops being a trap.
Skill 2: four operations, real-world
The phrase "real-world problems" is doing the work. These are word problems, and the difficulty is translation rather than computation: reading a situation and deciding which operation it calls for.
| The situation says | The operation is |
|---|---|
| total, combined, altogether | addition |
| difference, how many more, left over | subtraction |
| per group, times as many, of | multiplication |
| shared equally, per unit, how many fit | division |
That table gets you most of the way and it will occasionally mislead you, because a well-built item can use more in a subtraction context. Read the sentence, not the keyword.
Skill 3: order of operations
Its own skill, in a competency of three, which is a strong signal that it is worth practicing rather than assuming. Order of operations and number properties covers it, including what the calculator will and will not do for you.
Where fractions and percents live
Inside skill 2, as rational numbers. The rule never names fractions, decimals or percentages as separate topics, which is a useful thing to know: they are not a fifth of the subtest, they are one skill of twenty-one, appearing wherever a real-world problem uses them. Fractions, decimals and percents works through the conversions anyway, because they turn up in the other three competencies too.
Our read
This is the competency to get right rather than the one to study hardest. On our estimate it is about five questions, the pass mark is around 22 of 35, and these are the questions you cannot afford to drop because they are the ones a calculator plus care will settle.
Spend an hour on negatives and order of operations. Then move to algebra, which is more than twice the size on the same estimate.
Common questions
What is Competency 1 on the FTCE Mathematics subtest?
Knowledge of number sense, concepts and operations. Three skills sit under it: comparing real numbers and locating them on a number line, solving real-world problems with the four operations on rational numbers, and evaluating expressions involving order of operations.
Are fractions and percentages tested separately?
No. The rule folds them into skill 2 as rational numbers rather than naming them as topics. They appear wherever a real-world problem uses them, including inside the geometry, algebra and data competencies, which is why they are worth practicing.
How many number sense questions are there?
FLDOE publishes 35 for the subtest and no breakdown. Our estimate is about five, apportioning the total across the four competencies in proportion to the number of skills the rule states under each. The figure is ours rather than the state’s.
Does the FTCE test prime factors or exponent laws?
Not as named skills. Competency 1 lists three skills and none of them mentions primes, roots or exponent rules. Those can appear inside an order-of-operations expression, but no skill statement makes them a topic in their own right.