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Use a blank function table with input, rule, and output columns to organize substitution practice. Includes worked example, rubric, and four self-contained tasks.
A blank function table helps students slow down substitution: choose inputs, apply a stated rule, and record outputs in a clear column structure. This instructional set defines a simple convention for handwriting and table layout, then gives a worked example, common mistakes, a rubric, and four practice tasks. Each task is solvable from the text alone. Numerical values in examples are hypothetical teaching choices, not equipment specifications. The planned printable would place three tables per page with a small coordinate grid beside each for optional plotting, but that resource is not yet built.
Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.
Draw three columns labeled Input, Rule, and Output. Write the rule once at the top of the Rule column, for example multiply by 2 then add 1. Each row uses one input value. The output cell shows the result after applying the rule exactly as written.
Use a consistent handwriting convention: x-height is the distance from baseline to midline. Letter styles vary, so accept any legible style that keeps digits distinct and aligns columns. Do not require a single universal letterform. Keep units consistent within a table; if a rule uses centimeters, label the input and output columns with centimeters.
Rules are read left to right unless parentheses appear. For the rule multiply by 3 then subtract 2, an input of 4 gives 4 times 3 equals 12, then 12 minus 2 equals 10. Writing intermediate results beside the table reduces order errors.
When a rule contains two operations, test a small input and a larger input. This reveals whether the table is consistent. Keep arithmetic simple and checkable: use whole numbers and single-digit multipliers where possible.
A small grid beside each table lets students plot input-output pairs without turning the task into graphing instruction. Label the horizontal axis Input and the vertical axis Output. Choose a scale that fits the largest output in the table.
Plot each row as one point. If a point falls outside the grid, adjust the scale rather than changing the data. The grid is optional; the table itself is the required record.
Complete a table for the rule multiply by 4 then add 3 using inputs 1, 2, and 5. Label columns Input, Rule, Output.
Input 1 gives 1 times 4 equals 4, then 4 plus 3 equals 7. Input 2 gives 8 plus 3 equals 11. Input 5 gives 20 plus 3 equals 23. Outputs are 7, 11, and 23.
Complete a table for the rule multiply by 2 then subtract 1 using inputs 3, 4, and 6.
Input 3 gives 6 minus 1 equals 5. Input 4 gives 8 minus 1 equals 7. Input 6 gives 12 minus 1 equals 11. Outputs are 5, 7, and 11.
Why: Apply multiplication first, then subtraction, for each row independently.
Check: Reverse one row: add 1 to the output, then divide by 2. For output 11, 11 plus 1 equals 12, and 12 divided by 2 equals 6, matching the input.
Complete a table for the rule add 5 then multiply by 3 using inputs 0, 2, and 4.
Input 0 gives 0 plus 5 equals 5, then 5 times 3 equals 15. Input 2 gives 7 times 3 equals 21. Input 4 gives 9 times 3 equals 27. Outputs are 15, 21, and 27.
Why: Addition occurs before multiplication because the rule states add then multiply.
Check: Reverse one row: divide the output by 3, then subtract 5. For output 21, 21 divided by 3 equals 7, and 7 minus 5 equals 2, matching the input.
A table has inputs 1, 3, and 5 with rule multiply by 10 then add 2. Complete the outputs and state the unit if inputs are in centimeters.
Input 1 gives 12. Input 3 gives 32. Input 5 gives 52. Outputs are 12, 32, and 52 centimeters.
Why: Multiply each input by 10, add 2, and keep the centimeter unit on outputs.
Check: Subtract 2 from an output and divide by 10. For 52, 52 minus 2 equals 50, and 50 divided by 10 equals 5, matching the input.
Complete a table for the rule divide by 2 then add 7 using inputs 4, 8, and 10. Use whole-number outputs only.
Input 4 gives 2 plus 7 equals 9. Input 8 gives 4 plus 7 equals 11. Input 10 gives 5 plus 7 equals 12. Outputs are 9, 11, and 12.
Why: Divide first, then add 7. All chosen inputs are even, so outputs are whole numbers.
Check: Subtract 7 from an output and multiply by 2. For 12, 12 minus 7 equals 5, and 5 times 2 equals 10, matching the input.
Use three to five rows for practice. More rows help reveal patterns but increase copying errors.
No. Write it once at the top of the Rule column so the table stays readable.
Yes, if the task allows it. Require at least one small input and one larger input to test consistency.
No. The grid is optional and supports plotting without changing the table task.