Apply a Newly Defined Operation
A new symbol or rule is defined, and the task is to evaluate or solve by substituting carefully into that definition and respecting order of operations. Learners meet symbol-coded equations they solve in order, then defined operators over whole numbers and fractions. The skill is reading a rule precisely and executing it. A function rule such as f(a + b) = f(a) + f(b) is the grade-8 form: plug in the inputs the rule makes easy and build outward.
grade 2–8 FractionsOperationsFunctionsExpressions Convert to AlgebraIdentify Subproblems
Progression (11)
g3 1. Solve shape-coded products in order Operations
g3 2. Evaluate a custom-defined operation symbol Operations
g3 3. Set up an expression and compute in order Operations
g5 4. A new symbol can define a custom operation Operations
g4 5. Apply a defined symbol to compute with fractions Fractions
g5 6. Evaluate a newly defined operation symbol Operations
g5 7. Define a custom operator and evaluate it Operations
g7 8. Peel a nested defined operation from the outside Expressions
g8 9. Find the x that makes the input right FunctionsExpressions
g8 10. Build values up from the sum rule FunctionsExpressions
g8 11. Plug special inputs into the identity FunctionsExpressions
Bridges to competition (5)
Reasoning problems that extend this idea toward competition:
Old multiplication methods Pattern & rule
Convert ancient symbol numerals Pattern & rule
Discover the hidden operation rule Pattern & rule
Decode the shape-to-number rule Pattern & rule
Apply a newly defined symbol rule Pattern & rule