Why does my child keep getting negative number problems wrong even though they know the rules?

Usually they know a rule but not which rule applies. The sign rule for multiplication and the rule for subtracting a negative sound similar out loud, so problems get sorted into the wrong box under time pressure. Sessions focus on identifying the operation first, then choosing the reasoning.

What is the difference between an integer and a rational number?

Integers are the whole numbers and their negatives: -3, 0, 12. Rational numbers include all of those plus any number that can be written as a fraction of two integers, so 0.75, -2 1/3, and 0.666... are rational but not integers. Every integer is rational; not every rational number is an integer.

What grade is this topic taught in?

Negative numbers and absolute value are usually introduced in grade 6, operations with signed numbers are the core of grade 7, and grade 8 assumes all of it while working with irrational numbers and linear relationships. Students often need this reviewed in grade 8 or early algebra.

Can Evelyn help if my child is behind and still struggling with fractions?

Yes. Signed fractions require both skills at once, so sessions can slow down and rebuild fraction operations as they come up, rather than pushing ahead on sign rules the student can't apply to anything but whole numbers.

Integers & Rational Numbers

Middle School (6-8) · Mathematics

Integers and rational numbers is where the number line grows to the left of zero and stays crowded with fractions and decimals in between. In grades 6-8, students move from recognising negative numbers in temperature or elevation contexts to computing with them fluently: adding and subtracting signed values, multiplying and dividing them, and treating any fraction, terminating decimal, or repeating decimal as a rational number that can be located, compared, and operated on. Sessions work through the reasoning behind the sign rules rather than only the rules themselves, since most later algebra errors trace back to a shaky moment here.

Start a session on Integers & Rational Numbers

What this covers

Placing and comparing integers, negative fractions, and negative decimals on a number line, including ordering statements like -5.2 < -5 < -4 3/4
Absolute value as distance from zero, and finding the distance between two points as |a - b|
Adding and subtracting signed numbers, including rewriting subtraction as adding the opposite and using zero pairs or number-line jumps to justify the result
Multiplying and dividing integers and rational numbers, with the sign rules explained through patterns and repeated reasoning
Converting between fractions, decimals, and percents, and using long division to show why some fractions terminate and others repeat
Applying signed numbers to context: temperature change, elevation below sea level, bank balances and debt, and net gain or loss over several steps

Where learners get stuck

Applying "two negatives make a positive" to addition, so -4 + -6 becomes 10: The phrase is learned as a chant about multiplication and then transferred to any problem containing two minus signs. Students need to see that -4 + -6 means two moves in the same direction, while 5 - (-3) is where the double-negative reasoning actually applies.
Ordering negatives by their size, deciding that -8 is greater than -3 because 8 is greater than 3: Years of practice have tied "bigger digit means bigger number" to magnitude. The fix is repeated reference to position on the number line, and separating the question "which is further from zero?" from "which is greater?"
Treating absolute value as "drop the sign" and then writing things like |-7 + 2| = 9, or claiming -|4| = 4: The shortcut works for a bare negative number, so students never learn that the bars are a grouping symbol. Problems where an expression sits inside the bars, or a negative sits outside them, expose the gap.

What a session looks like

Sessions are spoken conversations. Evelyn poses a problem, waits for the student to talk through it, and probes the reasoning aloud: "you got -2, tell me which direction you moved from -9." Because signed-number errors are usually one specific slip repeated many times, the tutor tracks which slip a student is making and returns to it with fresh numbers rather than moving on. Number lines, zero pairs, and context stories (temperature drops, debts paid off) are described verbally and can be sketched by the student on paper alongside. A typical session mixes quick mental computation, one or two multi-step context problems, and a check on fraction-decimal conversion.

Helpful to know first

Fluent addition, subtraction, multiplication, and division with whole numbers
Comfort with fractions and decimals as positive quantities, including equivalent fractions and comparing decimals by place value
Long division with a remainder, used later to convert fractions to decimals
Reading a number line with whole-number and fractional tick marks

Questions

Why does my child keep getting negative number problems wrong even though they know the rules?: Usually they know a rule but not which rule applies. The sign rule for multiplication and the rule for subtracting a negative sound similar out loud, so problems get sorted into the wrong box under time pressure. Sessions focus on identifying the operation first, then choosing the reasoning.
What is the difference between an integer and a rational number?: Integers are the whole numbers and their negatives: -3, 0, 12. Rational numbers include all of those plus any number that can be written as a fraction of two integers, so 0.75, -2 1/3, and 0.666... are rational but not integers. Every integer is rational; not every rational number is an integer.
What grade is this topic taught in?: Negative numbers and absolute value are usually introduced in grade 6, operations with signed numbers are the core of grade 7, and grade 8 assumes all of it while working with irrational numbers and linear relationships. Students often need this reviewed in grade 8 or early algebra.
Can Evelyn help if my child is behind and still struggling with fractions?: Yes. Signed fractions require both skills at once, so sessions can slow down and rebuild fraction operations as they come up, rather than pushing ahead on sign rules the student can't apply to anything but whole numbers.