Myths about teaching can hold you back
- Year 10•
- Foundation
Problem solving with the laws of indices
I can use my knowledge of the laws of indices to solve problems.
- Year 10•
- Foundation
Problem solving with the laws of indices
I can use my knowledge of the laws of indices to solve problems.
Lesson details
Key learning points
- The base could be a number, letter or combination of the two.
- The laws are another way you can simplify an expression.
- Plotting numbers against their squared values can help you estimate unknown amounts.
Keywords
Power - An alternative word for exponent or index. Used when reading exponents above 3. E.g. 2^4 is read as “2 to the power of 4”.
Vinculum - Vinculum is the horizontal line placed over an expression to show that everything below that line is one group.
Common misconception
Using the laws of indices, when dividing by a number with a negative exponent pupils can incorrectly subtract the negative exponent.
When the bases of all the numbers are the same, forming an equation with the exponents can reduce errors.
To help you plan your year 10 maths lesson on: Problem solving with the laws of indices, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Problem solving with the laws of indices, 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 Arithmetic procedures: index laws unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Evaluate $$16^\frac{1}{2}$$, giving the positive solution where necessary.
Q2.Evaluate $$9^\frac{3}{2}$$, giving the positive solution where necessary.
Q3.Evaluate $$25^\frac{1}{2}$$, giving the positive solution where necessary.
Q4.What is the value of $$b$$ for $$b^7 \div b^5 =9^2$$?
Q5.What is the value of $$k$$ for $$0.2^5 \div 0.2^k = 0.2^7$$?
Q6.What number is written as $$2^3 \times 5 \times 7$$ as a product of its prime factors?
Assessment exit quiz
6 Questions
Q1.What is the value of $$x$$ for $$(3^3)^4 \times 3^2 = 3^x$$ ?
Q2.What is the value of $$x$$ for $$\frac{2^{12} \times 2^4}{2^{10}} = 2^x $$?
Q3.What is the value of $$x$$ for $$\frac{5^{14} \times 5^5}{5^{-2}} = 5^x $$?
Q4.What is the value of $$x$$ for $$3^2 \times 3^6 = 9^x$$ ?
Q5.What is the value of $$x$$ for $$2^3 \times 4^3 = 2^x$$ ?
Q6.What is the value of $$x^{4x}$$ for $$2^x \times 2^{3x} = x^{4x}$$ ?