# FSMQ: developing confidence with algebra

**Steven Walker, Maths Subject Advisor**

#### Adding value through algebra

One of the unintended consequences of the increased unstructured problem-solving requirement of the reformed GCSE (9–1) Mathematics is the reluctance of some talented students to apply their algebra skills to the process of constructing algebra expressions from word problems. This limits the amount of experience they can gain of forming and solving equations to determine the answers to problems set in context. For the students that are confident enough to solve the problems set, the fact that their solution routes are not the most efficient is not a barrier to GCSE success.

One of the main reasons why algebra is important is that it provides a foundation for understanding more complex mathematical concepts. Trial and improvement or multiplicative relationships can successfully solve one off problems, but algebra allows a series of problems to be solved efficiently.

The algebra section of the FSMQ focuses on manipulating expressions and solving equations and inequalities. This leads into the sections of enumeration, coordinate geometry, trigonometry, calculus, and logarithms. The section on numerical methods covers ideas around where solutions cannot be determined through solving equations directly but still requires strong algebra skills.

#### Decoding the letters

Studied solely in the abstract, algebra may seem like just a bunch of letters and symbols on a page. However, when it is linked to real life scenarios, students can develop an understanding of both what these letters and symbols represent. It also helps them overcome many of the misconceptions that can inhibit progression. Although algebra is about manipulating equations and finding patterns in numbers, these skills are essential in many fields, including science, engineering, finance, and computer science and can be useful for everyday life.

#### Supporting algebra development

Algebra can be a difficult subject for many students, but with the right activities and practice, students can develop strong algebraic skills. Here are some suggestions of activities to help improve algebra skills for the FSMQ (and for GCSE students and those students just starting AS/A Level):

1. Simplifying expressions: The first skill in algebra is simplifying expressions. Teachers can give students practice problems that require them to simplify expressions by combining like terms and using the rules of exponents. This can be a good way to develop strong algebraic skills and improve problem-solving skills. See LibreTexts Mathematics for an example of some interesting challenging questions.

2. Solving equations: Equations are at the heart of algebra, and solving equations is an essential skill. Teachers can give students practice problems that require them to solve equations using a variety of methods, such as substitution and elimination. This can be an effective way to develop fluency and reinforce algebraic concepts. See the CIMT GCSE site for an example of some interesting questions.

3. Identifying the variables: One of the key skills in algebra is identifying the variables in an equation or expression. A key misconception to avoid is the Fruit salad algebra issue. Matching sets of equations to a set of word problems can help reinforce an understanding that the letters actually represent numbers. These may be unknown, standard constants, or variables. Unstructured word problems where the student must define their own variables and create the equations to be solved can be an effective way to develop a solid foundation in algebraic understanding. The Warmsnug Double glazing challenge, on Nrich, requires students to define the variables and create the formulae needed to calculate the cost of different windows and frames.

4. Using algebra to solve real-world problems: Students can often struggle to see the relevance of algebra in the real world, but often the understanding of the real-world scenarios can be a barrier to accessing the maths to be solved. Problems involving physical artefacts can help students understand the practical applications of algebraic ideas and improve their problem-solving skills. Kinematics provides a familiar environment for teachers to provide practice problems that apply algebraic concepts to real-world scenarios, such as calculating the distance travelled by a car given its speed and time. There are many questions that directly use Pythagoras Theorem and trigonometry identities. These geometrical problems that involve circles and triangles allow teachers to set a variety problem that involve a simple diagram rather than lines of text. Transum has some interesting questions in level 7.

5. Collaborative problem-solving: There are some good algebra themed maths games on-line that are great for paired or small group challenges to introduce algebra concepts. Puzzles and unstructured problems that students can work through in small groups, perhaps as team challenges, can be an effective way of developing algebraic skills. These activities encourage communication and collaboration, while also reinforcing algebraic concepts. Nrich has a good collection of puzzles to choose from, such as How old am I?.

#### OCR support

In addition to past papers, you will also find two practice papers on Teach Cambridge.

The Algebra delivery guide has some teaching ideas and links to third party resources.

The Algebra Check In test provides a set of 10 questions, with fully worked solutions, focused on this section.

Don’t forget to join us for the termly FSMQ Teacher Networks and look out for professional development events throughout the academic year.

#### Stay connected

Share your ideas for promoting confidence with algebra in the comment box below, with any links to on-line material. For some interesting maths puzzles, see our weekly #OCRMathspuzzle each Friday.

If you have any queries or questions, you can email us at maths@ocr.org.uk, call us on 01223 553998 or tweet us @OCR_Maths. You can also sign up to subject updates and receive information about resources and support.