Numerical Reasoning
Georgia Standard: 7.NR.1: Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).
Expectations
Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.
Show and explain p + q as the number located a distance |q| from p, in the positive or negative direction, depending on whether q is positive or negative. Interpret sums of rational numbers by describing applicable situations.
Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems.
Show and explain subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in contextual situations.
Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
Make sense of multiplication of rational numbers using realistic applications.
Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.
Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation.
Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.
Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.
Examples
3 + (−3) = 0
3 and (−3) are additive inverses of each other.
6 + (– 4) is 4 units to the left of 6 on a horizontal number line or 4 units down from 6 on a vertical number line.
Create a model and realistic situations for each of the products. Write and model the family of equations related to 2 × 3 = 6.
(-1/2) – (-2) is the same expression as (-1/2) + – (-2), which is 2 units to the right of (-1/2) on a horizontal number line or 2 units up from (-1/2) on a vertical number line.
(-8) + 5 + (-2) may be solved as (-8) +( -2) + 5 to first make (-10) by using the Commutative Property.
If yellow counters represent positive amounts and red counters represent negative amounts, you can model 3 * (–2) as three groups of two red counters.
(-8) * 2 * (-5) may be solved as (-8) * (2*(-5)) to multiply by negative ten, using the Associative Property.
1/2 is the same as 0.5 and 50%
3/5 is the same as 0.6 and 60%
If Sara makes $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50.