Multi-Step Scattered Terms / Variable Multiple Times is a fully resourced secondary maths teaching pack. This is Lesson 3 of Unit 3 (Linear Equations 3), engineered around atomisation, explicit instruction, cognitive load shaping, variation theory, and schema-aware progression.
Tackling high-tier algebraic structures, this lesson introduces complex equations where the variable is scattered across different components and trapped within fractions, such as x/(3x+2)=11. Students are explicitly taught to clear the binomial denominator as their primary structural move. This transformation intentionally generates a variable-on-both-sides scenario, forcing students to synthesize their prior grouping schemas with advanced balancing mechanics to systematically collect and isolate the unknown.
What Is Included in This Pack?
- 1. Lesson Slides.pptx: Presentation featuring diagnostic mini-whiteboard questions, atomised check-teach-recheck sequences, silent teacher modelling blocks, and an intelligent variation expansion sequence. Visualiser ready.
- 2. Worksheet.docx: Fluency-building 25-question progression sheet interleaving denominator clearance, algebraic term collection, and fractional solutions. Includes a Live Marking Key for immediate feedback.
- 3. Exam Style Questions.docx: Targeted assessment paper containing 15 formal exam questions with a mark scheme mapping method (M1), accuracy (A1), and independent (B1) marks.
- 4. Lesson Guide.docx: Pedagogical handbook detailing delivery strategies, 60/75-minute lesson timings, anticipated misconceptions, and precise metacognitive scripts.
Linear Equations 3 (Full Unit 3 Outline)
- Lesson 1: Fractions and Brackets Recap
- Lesson 2: Unknowns on Both Sides (ax+b=cx+d)
- Lesson 3: Multi-Step Scattered Terms (e.g., x/(3x+2)=11)
- Lesson 4: Changing the Subject (Isolating via Factorising)
- Lesson 5: Mixed Interleaved Practice Capstone
This unit strictly excludes non-linear equations, simultaneous systems, and quadratic factorising.
All lessons include as standard:
- Atomisation & CTR Sequences: Prerequisite verification of discrete mathematical atoms using a structured Non-example/Positive-example (NPPPN) delivery method.
- Metacognitive Modelling: Side-by-side comparative modelling via silent teacher execution under a visualiser to isolate structural barriers and preserve cognitive capacity.
- Intelligent Variation: A paired mini-whiteboard sequence systematically altering operations, signs, and coefficients to guarantee 100% conceptual clarity.
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