Mathematics · Year 6

Active learning ideas

Describing Linear Sequences

Active learning helps Year 6 students grasp linear sequences because movement and discussion make abstract patterns concrete. Handling cards or racing to find sequences keeps pupils engaged while they internalise the idea of a constant difference between terms.

• National Curriculum Attainment Targets
• KS2: Mathematics - Algebra

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inquiry Circle
• 25 min · Pairs

Pair Sort: Arithmetic vs Geometric Cards

Prepare cards with sequence starts like 2,4,6 or 2,4,8. Pairs sort them into arithmetic or geometric piles, justify with differences or ratios, then write nth terms for arithmetic ones. Share one example with the class.

Differentiate between an arithmetic sequence and a geometric sequence.

Facilitation Tip

During Pair Sort, remind pairs to verbalise why each card belongs in the arithmetic or geometric pile using the visible differences and ratios.

What to look for

Present students with three different linear sequences (e.g., 3, 7, 11, 15; 20, 18, 16, 14; 5, 10, 15, 20). Ask students to write the common difference for each and then calculate the 6th term for the first two sequences.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Inquiry Circle
• 35 min · Small Groups

Small Groups: Sequence Hunt Relay

Groups visit school areas to find linear patterns, like tiles in corridors or steps on stairs. They photograph, note common differences, and derive nth terms. Regroup to present and critique findings.

Explain how sequences help us model real-life patterns like growth or savings.

Facilitation Tip

For Sequence Hunt Relay, circulate with a timer visible so teams feel the urgency but know the focus is accuracy, not speed.

What to look for

Give students the rule 5n + 2. Ask them to: 1. Write the first four terms of the sequence. 2. Explain what the '5' and the '+ 2' represent in relation to the sequence's pattern.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Inquiry Circle
• 20 min · Whole Class

Whole Class: nth Term Challenge Board

Project sequences on the board. Class calls out differences; teacher reveals nth term. Pupils vote on corrections for flawed rules, discussing as a group before confirming.

Critique a given rule for a sequence and suggest improvements if necessary.

Facilitation Tip

On the nth Term Challenge Board, ask students to explain their formulas aloud before writing them down to catch early overcounting errors.

What to look for

Pose the question: 'If a sequence starts with 10 and has a common difference of -3, is it a linear or geometric sequence? How do you know? What is the rule for the nth term?' Facilitate a class discussion where students justify their answers.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 04

• Inquiry Circle
• 30 min · Individual

Individual: Design Your Sequence

Each pupil creates a linear sequence from a real-life scenario, like plant pots in rows. They write the nth term and three peer-critique questions. Swap and respond.

Differentiate between an arithmetic sequence and a geometric sequence.

Facilitation Tip

In Design Your Sequence, remind students to include the nth term rule on their posters before swapping for peer review.

What to look for

Present students with three different linear sequences (e.g., 3, 7, 11, 15; 20, 18, 16, 14; 5, 10, 15, 20). Ask students to write the common difference for each and then calculate the 6th term for the first two sequences.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Teach linear sequences by pairing concrete actions with symbolic rules. Use number lines and counters to model why the nth term formula adjusts by one position. Avoid rushing to the formula; let students discover the pattern first through guided exploration and error analysis. Research shows that self-correction through peer feedback deepens understanding more than teacher correction alone.

Pupils will confidently identify common differences, extend sequences correctly, and write nth term rules without overcounting. They will also distinguish arithmetic from geometric sequences through clear reasoning.

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Watch Out for These Misconceptions

• During Pair Sort, watch for pupils assuming all increasing sequences are arithmetic.

  Have pairs physically group cards and justify each placement using written differences or ratios on the back of the cards. Ask them to create one geometric sequence deliberately to highlight the difference in growth.

• During nth Term Challenge Board, watch for pupils writing the nth term as first term plus difference times n without adjustment.

  Provide number lines and counters for students to model the sequence step-by-step, marking each jump. Ask them to compare their starting position to the formula, prompting them to adjust by subtracting or adding the extra step.

• During Sequence Hunt Relay, watch for pupils ignoring geometric sequences as irrelevant to linear work.

  Require teams to classify every card they collect as arithmetic or geometric, using ratio checks for the latter. After the relay, facilitate a quick discussion on why recognising ratios matters even when focusing on linear sequences.

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Methods used in this brief

• Inquiry Circle