Missing Terms and Errors

Overview

In this tenth lesson of the 26-lesson unit, students use tables, concrete balance models, and written rules to find missing terms in linear patterns. They also diagnose and correct incorrect rules, building on previous work with constant change, input-output tables, and algebraic expressions.

Learning intentions

Students will:

• identify the constant change in a linear pattern;
• use a table, balance-style model, or rule to find a missing term;
• explain why a pattern rule is correct or incorrect;
• communicate a correction using words, symbols, manipulatives, or an oral explanation.

Success criteria

• I can find the constant change in a pattern.
• I can use a rule or table to find a missing term.
• I can identify and correct an error in a pattern rule.
• I can explain what changed and why my correction works.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — construct tables of values from relations, graph values, and analyse patterns to solve problems.
• Patterns and Relations — preserve equality when modelling and solving equations.
• Mathematical processes — communication, connections, mental mathematics and estimation, problem solving, reasoning, visualization, and appropriate technology use.

Lesson structure (50 minutes)

1. 0–5 min · Attention hook and retrieval. Display the hook and retrieval slides with the pattern 4, 7, 10, 13, __ and ask, “What could someone do wrong when finding the next term?” Students write the next term and the change on mini-whiteboards, then briefly explain their thinking. Quickly revisit the meaning of term, position, and constant change.

2. 5–13 min · Explicit teaching. Use the worked-example slides to model the pattern 6, 10, 14, 18, __, __ in a table. Show that each term increases by 4 and connect the table to the rule “start at 6 and add 4 each time.” Model a second example with a missing middle term, such as 9, __, 17, 21, and demonstrate checking from both directions. Students complete guided notes by recording the table, change, rule, and check.

3. 13–21 min · Concrete balance modelling. Give pairs a small set of counters and the algebra balance mat. Model how equal changes must be made consistently when checking a rule or solving a missing-term situation. For example, compare the claimed rule “add 3” with 5, 8, 12, 14; students place counters or record terms on the mat, locate the break in equality, and state that 8 to 12 changes by 4 rather than 3. Each student explains one check to a partner using the sentence frame: “The rule is incorrect because ____. The corrected change is ____.”

4. 21–30 min · Error-analysis investigation. Organize four students into pairs and distribute the sequence rule cards for sorting and discussion. Present three teacher-prepared error examples on the error-analysis slides:

• 3, 8, 13, 18 with the rule “add 4”;
• 20, 17, 14, __ with the rule “add 3”;
• 2, 6, 10, 14 with the rule “multiply by 2.” Students identify the first incorrect claim, correct the rule, and find the missing term. Require each pair to justify one answer with a table, counters, symbols, or an oral response. Confer closely with students who need prompts.

5. 30–41 min · Guided and independent practice. Work through the first two questions on the missing terms and errors worksheet together, emphasizing “find the change, apply the rule, check the result.” Students then complete the remaining selected questions independently. Include missing terms in different positions, an incorrect rule to repair, and one question requiring a short written explanation. Students who finish may use Mathletics for a matching linear-pattern activity or complete the larger-term challenge on the worksheet. Keep the teacher-led group at a reduced number range with counters and a partially completed table.

6. 41–47 min · Evidence checkpoint and corrections. Ask each student to correct one deliberately incorrect pattern rule from the worksheet or a teacher example. Students must explain what changed using words, symbols, manipulatives, a labelled table, or an oral response recorded by the teacher. Use the checking and explanation slide to prompt the sequence: “What was wrong? What is correct? How do you know?” Students independently correct any earlier worksheet errors in a different colour.

7. 47–50 min · Plenary and exit check. Display the final reflection slide and ask students to solve 7, 11, __, 19 and identify the rule. Students hold up answers and complete the sentence, “I checked my answer by ____.” Collect the worksheet and record the evidence checkpoint for reporting and next-lesson grouping.

Resources

• the Missing Terms and Errors slide deck
• the missing terms and errors worksheet
• the algebra balance mat
• the sequence rule cards
• Mini-whiteboards, markers, and erasers
• Linking cubes or counters
• Pencils, coloured pencils, and highlighters
• Teacher device and display for a short teacher-selected missing-terms video
• Mathletics access
• Guided-notes page or exercise books

Assessment

• Knowledge and Understanding: Observe whether students identify terms, constant change, and an accurate pattern rule. Record progress when a student correctly completes at least three of four selected pattern items and explains one rule.
• Mental Math: During retrieval and guided practice, note whether students mentally recognize and apply common constant changes without counting one-by-one. Record strategies such as counting on, using a known difference, or checking by subtraction.
• Problem Solving: Use the evidence checkpoint to record whether each student locates an error, makes a correct change, and justifies the correction using a representation or oral explanation.
• Use worksheet responses, questioning, and the final pattern as formative evidence. Record achievement in PowerSchool descriptors for Knowledge and Understanding, Mental Math, and Problem Solving as beginning, developing, or independently demonstrated.

Differentiation

• Provide step cards, colour-coded tables, worked examples, and a completed first row for students who need scaffolding. Keep numbers small and use counters before moving to symbols.
• Offer dyslexia-friendly presentation: clear sans-serif font, generous spacing, minimal text, one question at a time, uncluttered worksheet sections, read-aloud directions, and oral or scribed responses.
• For students with a math disability or modified programming, assess recognition of “same change” with two- or three-term patterns and accept matching, pointing, building, or oral explanations.
• Seat highly distractible students close to the teacher, assign a short role such as checker or model builder, use brief timed work intervals, and provide immediate feedback. Challenge ready students with larger terms, negative or decreasing changes, or a pattern with two plausible-looking but different rules that must be checked against a table.