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Guiding Question: How can expressions support a generalized interpretation of number?
Order of operations
Order of operations
bedmas (sometimes called pemdas)
bedmas (sometimes called pemdas)
To ensure everyone gets the same answer, we follow a specific order:
Brackets: solve everything inside these first.
Exponents (powers): solve these next (e.g., 3ยฒ = 3 x 3 = 9)
Division/Multiplication: do these in the order they appear from left to right.
Addition/Subtraction: do these in the order they appear from left to right.
how to evaluate expressions
how to evaluate expressions
Look for parentheses. If there are operations inside, do them.
Look for powers. Solve them.
Step 3: Scan for x and รท . Don't do all firstโdo whichever comes first as you read left to right.
Step 4: Scan for + and - from left to right.
like terms & algebraic properties
like terms & algebraic properties
what are "like terms"?
what are "like terms"?
Terms are "like" if they have the exact same variable.
Constants (plain numbers like 5 or -10) are also like terms.
Example: In 3x + 5 + 2x, the 3x and 2x are like terms. The 5 is a constant.
how to simplify:
how to simplify:
Identify: Group terms with the same letter.
Combine: Add or subtract the coefficients (the numbers in front of the letter).ย
Example: 3x + 2x = 5x
algebraic properties (the rules of "rearranging")
algebraic properties (the rules of "rearranging")
Commutative Property: Order doesn't matter for x and +. (a + b = b + a)
Associative Property: Grouping doesn't matter for x and +. ((a + b) + c = a + (b + c))
Distributive Property: Multiplying a sum is the same as multiplying each part (3 (x + 2) = (3x + 6))
solving & verifying equations
solving & verifying equations
The Golden Rule of Equations: An equation is like a balanced scale. Whatever you do to one side, you must do to the other.
Simplified Forms: All simplified versions of an equation will have the same answer (solution). Itโs often easier to simplify both sides before you start solving.
How to Solve (The "Inverse" Method):
Simplify: Combine like terms on both sides of the equal sign.
Isolate: Use inverse (opposite) operations to get the variable by itself.
If the equation has +5, subtract 5 from both sides.
If the equation has รท3, multiply 3 by both sides.
One or two operations: In Grade 6, we focus on problems like 2x + 4 = 10.
Subtract 4 from both sides โ 2x = 6
Divide both sides by 2 โ x = 3
How to Verify (the check!)
Plug your answer back into the original equation. If both sides equal the same number, you are correct!
Example: if x = 3, does 2(3) + 4 = 10? Yes! 6 + 4 = 10.
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