Formulas, equations and the root of an equation
Use the distance formula, find the unknown part of an operation, check a root by substitution, move terms across with the opposite sign and learn when ax = b has no root. Section: Grades 5-7, formulas, the root of an equation, ax = b; Grade 3-4 equations are in another studio.
- Ukraine: grade 5
Guide
This follows the Ukrainian books: Year 5 items 9 "Numerical and letter expressions. Formulas" and 10 "Equations"; Year 6 part 2 item 39 "Solving equations"; Algebra Year 7 item 2 "The linear equation in one variable". The child answers on the keypad under the exercise or taps the scale.
The equality s = vt is the distance formula (s distance, v speed, t time); from it v = s : t. A root of an equation is a number that turns it into a true equality when put in place of the letter; to solve an equation is to find all its roots or to see that it has none.
In Year 5 the unknown is found by rules: unknown addend = sum − known addend; unknown minuend = difference + subtrahend; unknown subtrahend = minuend − difference. In Year 6 a term moved to the other side changes its sign. For ax = b: if a ≠ 0 there is one root, b : a; if a = 0 and b = 0 every number is a root; if a = 0 and b ≠ 0 there is no root.