Tables and Input Output

Overview

In this sixth lesson of the 26-lesson unit, students connect visual linear patterns to input-output tables and machine diagrams. Building on prior work with pattern rules, students identify the operation linking an input to an output, complete missing values, and explain their reasoning using concrete materials, diagrams, tables, and equations.

Learning intentions

Students will:

• Connect a pattern rule to an input-output table.
• Use a machine diagram to show the operation applied to an input.
• Complete missing input or output values.
• Explain the relationship between input and output orally, visually, and symbolically.
• Check answers using mental mathematics, a calculator, or substitution.

Success criteria

• I can put an input through a number machine and find the output.
• I can complete missing entries in an input-output table.
• I can state the operation connecting the input and output.
• I can explain or show how I know my answer is reasonable.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — constructing and interpreting tables of values from a relation.
• Mathematical processes — communication, connections, mental mathematics and estimation, problem solving, reasoning, and visualization.
• Report card evidence — Knowledge and Understanding, Mental Math and Estimation, and Problem Solving.

Lesson structure (50 minutes)

1. 0–5 min · Attention hook and retrieval. Teacher displays the opening section of the input-output introduction deck and asks, “If a number enters a machine and the rule is add 4, what must happen every time?” Students use mini whiteboards to solve two quick examples, such as 3 → 7 and 10 → 14, then explain the rule to a partner.

2. 5–13 min · Concrete number machine. Teacher places a labelled “input” and “output” space on the table, introduces arrows, and models a rule such as “multiply by 2, then add 1”; teacher refers to the machine diagram and worked example. Students physically place number cards into the input space, apply the operation with counters or a calculator when appropriate, and place the output card beside it. Pause after each example to ask, “What stayed the same? What changed?”

3. 13–22 min · Guided notes and connection to tables. Teacher plays a short, age-appropriate input-output table video selected from the prepared classroom search, pausing to emphasize the input, operation, output, and repeated rule. Using the guided-notes slides, teacher models transferring 2 → 5, 4 → 7, and 6 → 9 into a table and identifies the rule as “add 3.” Students complete corresponding sections in the input-output tables practice worksheet and state the rule orally or in writing.

4. 22–31 min · Mathology table investigation. Teacher gives pairs the relevant Mathology table activity and models the first row without completing the rest. Students complete tables using visual arrows, number cards, and the worksheet prompts; each student must explain one row using the sentence frame, “I put in __, I ____, and I got __.” Teacher checks that students distinguish between the input and output columns and records observations.

5. 31–38 min · Supported digital practice. Teacher demonstrates the assigned Mathletics activity using the Mathletics instructions and checking slides. Students practise independently or with a partner, selecting an appropriate support level. Teacher circulates, prompting students to predict an answer before entering it and to check whether the same operation works for every row.

6. 38–47 min · Independent evidence checkpoint. Teacher distributes the final section of the missing-values evidence checkpoint. Students complete tables with missing entries and write or record the operation connecting each input and output. Include examples such as “multiply by 3,” “subtract 2,” and “multiply by 2, then add 1.” Students may use arrows, counters, guided notes, or a calculator, but must show or explain the rule.

7. 47–50 min · Share and exit check. Teacher displays the closing discussion and exit prompt and asks students to compare two answers, identifying whether the same rule was used consistently. Each student responds to: “For 4 → 12, one possible rule is ____. I know because ____.” Collect responses and note whether the student can complete a table and communicate the rule.

Resources

• the input-output introduction deck
• the input-output tables practice worksheet
• Mathology table activity and student materials
• Prepared input-output number cards
• Cardboard or magnetic number-machine spaces
• Arrows, counters, mini whiteboards, and markers
• Classroom video access and speakers
• Mathletics access
• Calculators for selected students
• Guided-notes copies and pencils

Assessment

• Knowledge and Understanding: During the machine and Mathology tasks, record whether each student identifies input, output, and the operation connecting them, and completes tables accurately.
• Mental Math and Estimation: Note whether students predict simple outputs, use known facts, and judge whether an answer is reasonable before checking with a calculator or digital tool.
• Problem Solving: Use the independent checkpoint to document whether students apply a rule to missing values, maintain the same relationship across a table, and explain their strategy. Record progress as beginning, developing, or demonstrating.
• Use oral explanations, diagrams, number cards, or scribed responses as valid evidence where written output is a barrier.

Differentiation

• Provide colour-coded input and output columns, large visual arrows, one operation at a time, and a worked example that remains visible. Use the sentence frame, “The rule is ____ because ____.”
• For students with a math disability or modified programming, use smaller numbers, concrete counters, partially completed tables, and repeated practice with addition or subtraction rules before introducing two-step rules.
• Offer dyslexia-friendly copies: clear sans-serif font, generous spacing, minimal text, bold operation symbols, uncluttered tables, and instructions read aloud. Permit oral responses, pointing, manipulatives, or speech-to-text.
• Seat distractible students close to the teacher, give them an active role such as operating the number machine or checking a row, and use short timed chunks with specific praise for focused mathematical talk.
• For students ready for challenge, provide a completed table and ask them to determine a possible rule, then create a second table with the same rule and explain whether more than one rule could fit limited data.