Unit 13 Algebra
Intent
The intention of this unit is to consolidate knowledge from Key Stage 3 and to revise and refresh concepts that will underpin the End of Key Stage 3 Assessment and future Assessments in Key Stage 4.
We want all students to become keen problem solvers and agile mathematical reasoners. This unit in particular develops these skills with:
Forming and solving linear equations from a variety of problems
Setting up and solving simultaneous equations
Implementation
For each strand in the unit students begin with lessons refreshing Year 7&8 knowledge before new concepts are introduced. At the end of each strand there are revision and mastery lessons to consolidate and ensure all students have picked up on new ideas.
From the 3rd week of the unit students will complete a weekly knowledge check so they can measure how their knowledge and expertise is building before the test.
During this unit there will be two longer written homework tasks which include a skills check as well as problem solving questions. Students will have an opportunity to follow-up and improve their work.
Impact
The impact of this unit of work will be measured through a 45 minute written assessment. The assessment will feature questions similar to the skills check and homework tasks. The assessment will cover every aspect of the unit of work and using the knowledge organiser together with this website is a great way to prepare for the test.
Topics covered in this unit:
Star / Star*
19a Evaluate symbols in place of numbers in one-step + - x ÷ equations
20a Evaluate letters in place of numbers
24a Writing expressions from simple descriptions like 4 more than n
25a Simplify expressions by applying standard algebraic notation
15a Evaluating the output of one-step function machines
17a Evaluating the output of multi-step function machines
18a Use a simple one-step formula in words
21a Determine the functions in 1/2 step function machines from a list of inputs and outputs
22a Use inverse operations to find the input of function machines
10a Continue a repeating sequence of colours or shapes
11a Recognise and name simple numerical sequences like even, odd or times tables from 1 to 5
13a Continuing arithmetic sequences
14a Filling in gaps in a sequence or on a number line, including steps of 2, 3, 5, 10, 50, 100
16a Writing out a sequence from a term-to-term rule
23a Recognising arithmetic, geometric, quadratic or Fibonacci patterns and continuing sequences
26a Recognise and continue sequences of patterns or diagrams
Core
34a Using BIDMAS to evaluate numerical expressions (without powers and roots)
27a Substitute positive whole numbers into simple expressions or formulae and evaluate
30a Writing and interpreting algebraic expressions from a written description
29a Simplify expressions by collecting terms
33a Simplify expressions by multiplying terms
47a Using the three index laws to simplify expressions
43a Listing integers that satisfy inequalities and representing inequalities on a number line
32a Solve equations formally by using 1/2 inverse operations
48a Solve equations with x on both sides and solving inequalities by algebraic manipulation
54a Forming and solving equations arising from shape, measure or word problems
42a Solve equations with brackets
51a Expand and simplify expressions with multiple single brackets
52a Expand and simplify pairs of brackets
53a Factorising into single brackets
28a Using a two-step formula written in words both forwards and backwards
38a Using an algebraic formula both forwards and backwards
49a Write algebraic formulae from a written description
44a Using the nth term rule of a sequence to find a given term
46a Finding the nth term of an arithmetic sequence
55a Changing the subject of a formula by using 1/2 inverse operations
Plus / Plus+
66a Simplifying expressions by applying index laws more than once or to several terms
60a Solve difficult linear equations with brackets and fractions
64a Solving linear simultaneous equations by elimination
65a Derive and solve simultaneous equations from word problems
56a Factorising quadratic expressions (unitary coefficient of x²)
63a Solving quadratic equations by factorising (unitary coefficient of x²)
78a Finding the nth term of a quadratic sequence