Myths about teaching can hold you back
- Year 10•
- Foundation
The laws of indices - multiplication
I can use the laws of indices to multiply two powers where the bases are the same.
- Year 10•
- Foundation
The laws of indices - multiplication
I can use the laws of indices to multiply two powers where the bases are the same.
Lesson details
Key learning points
- When multiplying two terms, you can sometimes write this more simply.
- If the powers have the same base, then the powers can be combined into a single power.
- The exponent or index of the new power reflects this combination.
- By studying the structure of multiplication, you can see how the index will change.
- a^b × a^c = a^(b+c)
Keywords
Power - 16 is the fourth power of 2. Alternatively this can be written as 2^4 which is read as “2 to the power of 4”.
Index - An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices).
Coefficient - A numerical coefficient is a constant multiplier of the variables in a term.
Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.
Associative - An operation is associative if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.
Common misconception
When multiplying terms with coefficients, pupils also add the coefficients as well as the exponents.
Pupils should be encouraged to rewrite their expression using the associative and commutative laws, with the number parts grouped and powers grouped. This hopefully avoids this error as they can see it is the product of the numbers.
To help you plan your year 10 maths lesson on: The laws of indices - multiplication, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: The laws of indices - multiplication, 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
Loading...
Prior knowledge starter quiz
6 Questions
Q1.Calculate $$-3 \times 5^2$$
Q2.Calculate $$-3 \times 4^2$$
Q3.Calculate $$-3 \times 2^2$$
Q4.Calculate $$-4 \times 4^2$$
Q5.Calculate $$3^2 + (-4)^2$$
Q6.Calculate $$9^2 + (-5)^2$$
Assessment exit quiz
6 Questions
Q1.What is the value of $$a$$ for $$3^3 \times 3^a = 3^{20}$$?
Q2.What is the value of $$a$$ for $$3^3 \times 3^a = 3^7$$?
Q3.What is the value of $$a$$ for $$5^8 \times 5^a = 5^{10}$$?
Q4.What is the value of $$a$$ for $$3^3 \times a^7 = 3^{10}$$?
Q5.What is the value of $$a$$ for $$3^7 \times a^8 = 3^{15}$$?
Q6.What is the value of $$a$$ for $$6^3 \times 6^8 = 6^a$$?