Download Lesson Plan - Dr Frost Maths

Lesson Plan
8th Feb 2012 - Year 8 P1 – Laws of Indices – J Frost
Learning Outcomes
Topic Specific:
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To understand the three main laws of indices, recognising the scenarios in which we can
add, subtract and multiply powers respectively.
To be comfortable with expressions which require multiple rules to be used or multiple
applications of the same rule.
To initially reflect on what happens when we have a power of 0, or a negative power, or
when we multiply exponentiations with different bases. This will be cemented in further
lessons.
Abstract skills to develop:
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For students to independently (in groups) leverage existing knowledge (i.e. the three
laws they have learnt) to solve unfamiliar types of problems.
For students to be able to communicate their solutions clearly in front of others.
Provide difficult extension problems to challenge the brighter/more inquisitive students
and encourage further investigation.
For students to understand the general means by which we can avoid mathematical
errors by reflecting on the laws that they apply.
Plan:
1. Introduce myself. Briefly discuss the topics I teach at university and how school maths can
be applied to interesting research problems.
2. Display the kind of problems we wish to solve by the end of the lesson (implicitly showing
learning objectives).
3. Check their knowledge of terminology: base, power/exponent.
4. Ask for how we would write out 3^6 as a multiplication. Based on this, ask how we might
then solve 3^6 x 3^2. Ask for a verbal explanation of what we can conclude (clearly
indicating the result on the board).
5. Present the first rule of indices on the slides (and indicate that they should write it down in
their books). Emphasise the importance of being able to express mathematical laws both
verbally and formally using notation.
6. Now ask about 4^6 / 4^2, indicating we can use a similar technique to the previous problem.
7. Present slide for the second law of indices.
8. Present interactive questions on the board to test this knowledge, using
http://www.edumonkey.org/demo/resource-view.php?id=10
9. The last of these questions is a trick question: emphasise the need to keep the reason why
we can apply certain laws at the back of our minds to avoid careless errors. Relate to
experiences of Oxford undergraduate interviews.
10. Finally, explore rule of raising a power to a further power, using example of (4^3)^4 before
presenting the general rule.
11. (Approx 15 mins after start of class) Ask if there are any questions, before distributing the
class worksheet.
12. (Approx 15 mins before end of class) Bring the class back together to examine some
unfamiliar problems. Assign into groups of 3-4, with 4 different tasks distributed between
the groups (one task for each group). Indicate that they only need to use the three rules they
have learnt, and ensure these rules are on the board for the duration of the task. Use
http://www.edumonkey.org/demo/resource-view.php?id=11 to assign tasks to groups.
a. 4^2 = 2^x (as an interesting aside, mention after the solution is presented that the
only whole-number values we can plug into the general equation a^b = b^a is 2 and
4; there is no other solution except when a = b).
b. x = 4^0
c. x = 9^3 * 3^5
d. x = 5^(-1)
13. After most groups have found an answer, come back together and ask a representative from
one of the groups assigned to each task to explain their solution (they can write on the
board if they wish).
14. Mention that students will have further lessons to explore these new types of problem (to
avoid them being intimidated by the large quantity of new material).
15. Thank the students and close.