Balance addition equations - up to two digits

Learning Objectives Define an arithmetic sequence and its relationship to balanced linear equations. Translate a problem involving missing terms in an arithmetic sequence into a balanced algebraic equation. Solve for a single variable in a linear equation involving addition and two-digit integers. Apply the principle of equality to isolate variables in multi-step equations derived from sequences. Verify the solution to a balanced equation by substituting the value back into the context of the number sequence. Model real-world patterns of constant change using arithmetic sequences and balanced equations. Imagine a ladder with a missing rung. 🪜 How could you use the position of the rungs above and below to calculate the exact position of the missing one? While balancing simp...

TermDefinitionExample Balanced EquationA mathematical statement asserting that two expressions are equal, represented by an equals sign (=). The value of the expression on the left side is exactly the same as the value on the right side.In the equation `x + 15 = 40`, the expression `x + 15` must have the same value as `40`. Arithmetic SequenceA sequence of numbers in which the difference between any two consecutive terms is constant.The sequence `8, 11, 14, 17, ...` is an arithmetic sequence because you add 3 to each term to get the next. Common Difference (d)The constant value that is added to each term to get the next term in an arithmetic sequence.In the sequence `50, 45, 40, 35, ...`, the common difference `d` is -5. VariableA symbol, usually a letter like x or n, that represents an u...

Common Difference Equality For consecutive terms `a_1, a_2, a_3`, the relationship is `a_2 - a_1 = a_3 - a_2`. This rule states that the difference between the second and first term is equal to the difference between the third and second term. This is the primary way we create a balanced equation from an arithmetic sequence. Arithmetic Mean Property For consecutive terms `a_1, a_2, a_3`, the relationship can be rearranged to `a_1 + a_3 = 2a_2`. This is a rearranged version of the Common Difference Equality. It shows that the sum of the outer two terms is equal to twice the middle term. It's a useful shortcut for setting up a balanced addition equation.