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Operators

The operator setting controls what type of arithmetic problems appear on the worksheet.

Options

`addition`

Only addition problems.

    47
  + 85
  ────

Scaffolding used: carryBoxes, answerBoxes, placeValueColors, tenFrames

`subtraction`

Only subtraction problems.

    72
  - 38
  ────

Scaffolding used: borrowNotation, borrowingHints, answerBoxes, placeValueColors

Note: Subtraction uses different scaffolding (borrowNotation/borrowingHints instead of carryBoxes/tenFrames) because the regrouping process is conceptually different.

`mixed`

Both addition and subtraction problems, randomly interspersed.

When to use:

Student has mastered both operations separately
Preparing for timed tests or real-world applications
Building operational flexibility

Caution: Mixing operations too early can confuse students who haven't automated each operation independently.

Pedagogical Sequence

Traditional Approach

Addition without regrouping → learn alignment
Addition with regrouping → learn carrying
Subtraction without regrouping → learn inverse operation
Subtraction with regrouping → learn borrowing
Mixed operations → build flexibility

Why Addition First?

Carrying is conceptually simpler than borrowing
"Making groups of 10" builds on counting knowledge
Errors are easier to check (count up to verify)

Why Not Skip Ahead?

Students who learn addition and subtraction together often:

Confuse carrying and borrowing
Make sign errors (adding when they should subtract)
Develop slower automaticity

Regrouping in Subtraction

Borrowing (subtraction regrouping) is cognitively harder because:

Requires recognizing "can't do this" situations
Involves reducing a digit (counterintuitive)
Changes two columns at once

Recommendation: Master addition regrouping to 90%+ accuracy before introducing subtraction regrouping.

Scaffolding Differences

Scaffolding	Addition	Subtraction
carryBoxes	✓	-
tenFrames	✓	-
borrowNotation	-	✓
borrowingHints	-	✓
answerBoxes	✓	✓
placeValueColors	✓	✓

When using mixed operator, all scaffolding types may appear depending on the specific problem.

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