Checking and securing understanding of solving with simple algebraic fractions
I can solve equations involving simple algebraic fractions.
Checking and securing understanding of solving with simple algebraic fractions
I can solve equations involving simple algebraic fractions.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- The product of a number and its reciprocal is 1
- The product of a term and its reciprocal is 1
- Equivalence can be maintained by multiplying the connected statements by the same reciprocal.
- This step can help you simplify an equation so you can solve it.
Keywords
Solution - A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1
Common misconception
When solving equations with fractional coefficients, pupils may divide by the reciprocal rather than multiply. E.g. $$\\frac{1}{2}x = 8$$ pupils may just halve $$8$$
Start with integer coefficients, and get pupils used to the idea of multiplying by the reciprocal (not just dividing by the coefficient). This step should be written as part of the working. Answers can be checked by substitution.
To help you plan your year 11 maths lesson on: Checking and securing understanding of solving with simple algebraic fractions, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Checking and securing understanding of solving with simple algebraic fractions, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Algebraic fractions unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
$$2$$ -
$$1\over 2$$
$$1\over 2$$ -
$$2$$
$$3\over 2$$ -
$$2\over 3$$
$$-{1\over 2}$$ -
$$-2$$
$$-{2\over 3}$$ -
$$-{3\over 2}$$
$$1\over 6$$ -
$$6$$
$$2(3x-6)$$ -
$$6x-12$$
$$6(x-1)$$ -
$$6x-6$$
$$2(x-6)$$ -
$$2x-12$$
$$-6(-2-x)$$ -
$$6x+12$$
$$3(2x-6)$$ -
$$6x-18$$
$$6(3-x)$$ -
$$-6x+18$$
Exit quiz
6 Questions
$${1\over 4}a + 3 = 10$$ -
$$a = 28$$
$${1\over 4}(a + 3)=10$$ -
$$a = 37$$
$${4\over 7} a = 1$$ -
$$a = {7\over 4}$$
$${7\over 4}a=14$$ -
$$a = 8$$
$$\frac{a+3}{7} = 2$$ -
$$a = 11$$
$${2\over 3}x$$ -
$$2x\over 3$$
$$2\over 3x$$ -
$$2({1\over 3x})$$
$${2\over 3}\times {1\over 3x}$$ -
$$2\over 9x$$
$$2x \times {1\over 9}$$ -
$$2x\over 9$$
$${3\over 2}\times {1\over x}$$ -
$$3\over 2x$$