A1 SEQUENCES & FUNCTIONS 6h Autumn Term
KEY OBJECTIVES: 1 Represent unknown numbers / variables with letters
Objectives   And see...
1. SEQUENCES & FUNCTIONS: Generate simple integer functions; describe in words  
2. SEQUENCES & FUNCTIONS: Generate simple sequence from a rule (term-to-term; position-to-term) A3, A5
3. SEQUENCES & FUNCTIONS: Generate sequences from practical contexts; describe general term A3, A5
4. SEQUENCES & FUNCTIONS: Express simple functions - words, then symbols A3, A5
5. SEQUENCES & FUNCTIONS: Represent simple functions in mappings A3, A5
6. FORMULAE & IDENTITIES: Represent unknown numbers / variables with letters A2, A4
7. PROBLEM-SOLVING: Suggest extensions using 'What if ...' A5
8. PROBLEM-SOLVING: Begin to generalise & to understand significance of counter-example A5
 
 
 
 
A3 SEQUENCES, FUNCTIONS & GRAPHS 6h Spring Term
KEY OBJECTIVES: 1. Graphs of simple linear functions
Objectives   And see...
1. INTEGERS, POWERS & ROOTS: Multiples, factors (divisors), CF, LCM, primes (<100); simple divisibility tests N5
2. INTEGERS, POWERS & ROOTS:
Recognise 1st few triangular nos, squares nos (at least 12 x 12); square roots & key		  
3. SEQUENCES & FUNCTIONS: Generate simple sequence from a rule (term-to-term; position-to-term) A1, A5
4. SEQUENCES & FUNCTIONS: Generate sequences from practical contexts; describe general term A1, A5
5. SEQUENCES & FUNCTIONS: Express simple functions - words, then symbols A1, A5
6. SEQUENCES & FUNCTIONS: Represent simple functions in mappings A1, A5
7. SEQUENCES & FUNCTIONS: Generate coordinate pairs satisfying a simple rule & plot graphs of simple linear functions (y explicit)- paper & ICT A5
8. SEQUENCES & FUNCTIONS: Recognise straight-line graphs parallel to x- or y-axis A5
9. SOLVING PROBLEMS: Solve problems & investigate in a range of contexts: Number & Algebra  
10. PROBLEM-SOLVING: Identify info necessary to solve problem  
11. PROBLEM-SOLVING: Represent problems mathematically - symbols / diagrams / tables / graphs A2
 
 
 
 
A5 (SEQUENCES, FUNCTIONS & GRAPHS part) 6h of 8h total Summer Term
KEY OBJECTIVES: 1. Graphs of simple linear functions
Objectives   And see...
1. SEQUENCES, FUNCTIONS & GRAPHS: Generate sequences from practical contexts; describe general term A1, A3
2. SEQUENCES, FUNCTIONS & GRAPHS: Express simple functions - words, then symbols
A1, A3
3. SEQUENCES, FUNCTIONS & GRAPHS: Represent simple functions in mappings A1, A3
4. SEQUENCES, FUNCTIONS & GRAPHS: Generate coordinate pairs satisfying a simple rule & plot graphs of simple linear functions (y explicit)- paper / ICT A3
5. SEQUENCES, FUNCTIONS & GRAPHS: Recognise straight-line graphs parallel to x- or y-axis A3
6. SEQUENCES, FUNCTIONS & GRAPHS: Begin to plot / interpret real-life linear graphs  
7. PROBLEM-SOLVING: Suggest extensions using 'What if ...' A1
8. PROBLEM-SOLVING: Begin to generalise & to understand significance of counter-example A1
 
 
 
 
Note on Strand A1> A3 > A5
INTRODUCTION: This strand focuses on sequences & functions & graphs, whilst the A2 >A4 strand focuses on equations, formulae & identities. However, the autumn term unit A1 includes elements of both strands, for a balanced introduction to Y7 Algebra. Also, the final unit, A5, reintegrates the 2 strands in the summer term.
  • HOW TO REPRESENT A FUNCTION? There is a common core of L.O.s to units A1, A3 & A5, all relating to the representation of functions: words, symbols, (general term and, later, equations,) mappings - and also graphs from A3, onwards. In parallel with the approach used with FDPRP in Number, the aim here is to support learning of a challenging concept such as a function by using an interlinked set of ideas. Words, symbols, mappings, nth terms, equations & graphs not only offer a range of conceptual 'handles' for approaching functions, they also provide for pupils with differing levels of maturity in abstract thinking. For example, some pupils find it easy to produce an equation from a mapping, other pupils from the nth term and others again from a word equation or from the original diagram / context. Therefore, overhead sheets included in the units have been designed to allow an open-ended use by the teacher.

  • The basic pattern for each unit is as follows:
 
A1 6h Autumn Term Key L.O.s: 1. Represent unknown numbers & variables with letters
Unit A1 develops further the Y5/6 Programme on sequences to include simple functions. Terms of a sequence can be generated from previous term (term-to-term) or from its position (position-to-term). Following extensive experience of a range of contexts, pupils may begin to describe the general term, in either words or using symbols. The key L.O. is common also to the both units of the A2 > A4 strand and the emphasis in this unit to achieve sufficient confidence in using words, then letter symbols, to describe a broad range of generated sequences. Because A3 follows A1 very closely, progress in A3 next term depends very much on the finishing point reached at the end of A1. Also, although the time allocation appears to be generous for these 2 units, the rate of progress seems to be quite demanding. Therefore, A carefully assessed starting point for each teaching group is likely to be particularly beneficial in this strand.
Problem-solving L.O.s ('What if ...?' and generalisation) support a investigative approach to this unit.
 
A3 6h Spring Term Key L.O.s: 1. plot graphs of simple linear functions

Representation of functions is continued from unit A1 & extended to Cartesian coordinates & graphs, from mappings, general terms and/or equations. The scope of contexts used to generate sequences is enlarged by the introduction of multiples, factors & their derivatives, square and triangular numbers. Divisibility tests are also included here. These special numbers are also included in the summer term Number unit, N5.
Problem-solving L.O.s in A3 (identify initial information and mathematical representations) support pupils' decision-making during an investigation.
 
A5 8h Summer Term Key L.O.s: 1. plot graphs of simple linear functions

By now, pupils will have experienced a rich variety of contexts for representation of unknown numbers & variables with letters. They will have used sequences in A1 & A3 to extend sequences term-to-term, & position-to-term. These experiences can now be used to explore more deeply the concept of a function in A5. There is only one new L.O. in A5 relating to sequences, functions or graphs. Rather, unit A5 provides an opportunity to consolidate pupils' understanding of sequences through the general term, mappings, coordinate pairs and graphs, and then to link this to equations and formulae work from A2 and A4.
As noted earlier, this summer term unit reintegrates the two strands, A1 > A3 > A5 and A2 > A4 > A5 so that equations & formulae are re-linked with sequences, functions & graphs. The very positive outcome of this integrated approach to algebra then allows pupils to use and apply their learning to problems involving a range of contexts. The problem-solving L.O.s from A1 are repeated in A5 ('What if ...?' and generalisation), but can be explored more deeply in the final unit.