In this topic, students will:
write expressions using whole-number exponents to represent real-world and mathematical problems
evaluate expressions with whole-number exponents
find the prime factorization of a whole number
find the greatest common factor (GCF) and the least common multiple (LCM) of two whole numbers
use the GCF and the Distributive Property to add
use the GCF and the LCM to solve problems
evaluate expressions using the order of operations
insert grouping symbols in a numerical expression to affect the value of the expression
write an algebraic expression to model a pattern
write an algebraic expression from a word phrase
use precise mathematical language when identifying parts of an expression
evaluate algebraic expressions, including those with whole numbers, decimals, and fractions
use mathematical modeling to represent a problem situation and to propose a solution
test and verify the appropriateness of their math models
explain why the results from their mathematical models may not align exactly to the problem situation
write equivalent algebraic expressions
identify equivalent algebraic expressions
justify whether two expressions are equivalent
use properties of operations to simplify algebraic expressions by combining like terms
Vocabulary:
Base - the number that gets multiplied when using an exponent
Evaluate - to find the value of the expression when the variable is replaced by a given number
Exponent - tells the number of times the base is used as a factor.Â
Power - a base number raised to the exponent
Composite numbers - numbers that have more than two factors
Factor tree - a diagram that shows the prime factors of a composite number
Greatest common factor (GCF) - the greatest factor that two or more whole numbers have in common
Least common multiple (LCM) - the smallest multiple that two or more non-zero whole numbers have in common
Prime factorization - finding which prime numbers multiply together to make the original number
Prime number - a number greater than 1 that has only two factors, 1 and itself
Numerical expression - a combination of numbers, and integers combined using mathematical operations such as addition, subtraction, multiplication, or division
Algebraic expression - an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.)
Coefficient - a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
Term - either a single number or variable or the product of several numbers or variables
Variable - a letter or symbol that represents an unknown quantity
Substitution - A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable
Equivalent expressions - expressions that have the same value