Unpacked Content
Knowledge
Students know:
- a number and its opposite have a sum of 0.
- A number and its opposite are called additive inverses.
- properties of operations.
- Absolute value represents distance on a number line, therefore it is always non-negative.
- Every quotient of integers (with non-zero divisor) is a rational number.
- If p and q are integers, then -(p/q) = (-p)/q = p/(-q).
- The decimal form of a rational number terminates in 0s or eventually repeats.
Skills
Students are able to:
- add rational numbers.
- Subtract rational numbers.
- Represent addition and subtraction on a number line diagram.
- Describe situations in which opposite quantities combine to make 0.
- Find the opposite of a number.
- Interpret sums of rational numbers by describing real-world contexts.
- Show that the distance between two rational numbers on the number line is the absolute value of their difference.
- Use absolute value in real-world contexts involving distances.
- Multiply and divide rational numbers.
- Convert a rational number to a decimal using long division.
Understanding
Students understand that:
- p + q is the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.
- Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
- If a factor is multiplied by a number greater than one, the answer is larger than that factor.
- If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
- Multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
- Integers can be divided, provided that the divisor is not zero.
Vocabulary
- Integers
- Rational numbers
- Additive inverses
- opposite quantities
- Absolute value
- Terminating decimals
- Repeating decimals
