Session Three of Mathematical Flow.
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Flow
.http://2015byod.wikispaces.com/Flow+Course
Session 3
Algebra as requested  at the end of session 2.
Manipulation and word problems.
What is algebra? (Answers are from around the web, some reworded).
a. Algebra is the part of mathematics in which letters and other general symbols are
used to represent numbers and quantities in formulae and equations.
b. Algebra is about finding the unknown or it is about putting real life problems into
equations and then solving them.
c. Algebra is a branch of mathematics dealing with symbols and the rules for
manipulating those symbols. In elementary algebra, those symbols represent
quantities without fixed values, known as variables.
d. Algebra is a branch of mathematics that deals with properties of operations and the
structures these operations are defined on.
e. Algebra is a Language - The Language of Mathematics.
f. Algebra is a tool for solving problems.
g. If you succeed in Algebra people think you are smart and hardworking, hence,
algebra can be the secret to success in life.
How would YOU describe agebra?
Session Three of Mathematical Flow.
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MCAT 2015: applying algebraic procedures in solving problems.
• selecting and using procedures in solving problems.
• demonstrating knowledge of algebraic concepts and terms.
• communicating solutions using appropriate mathematical symbols.
• Show working, no guess and check.
• Always simplify your answers.
• Turn word problems into algebra problems.
Quadratic functions warm up:
Sketch a quadratic function with the roots of 1 and 3.
Sketch another one, with the same roots, mirrored through the x axis.
How many quadratic functions have the roots of 1 and 3?
If the coefficient of the x squared term is 1, what are the coordinates of the vertex?
What is the equation of the graph?
Now take a look at the quadratic functions below, can you match up the equations with
the graphs?
Mark had worked twice as many hours as James. If James had worked another 48 hours
he would have worked twice as long as Mark. How many more hours had Mark worked
than James?
Write your own problem like the one above using different names and numbers and
context. How did you do that? Did you start with the answer and work backwards to the
question?
Explain why (where n= 0,1,2,3,4…)
U = n2 – n – 6
will never give a positive prime number value for U.
If you knew it was possible, then could you do it?
Session Three of Mathematical Flow.
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Emma tells her friend that her height is at least as much as her younger sister’s plus a
quarter as much again. Her sister’s height is 96 cm. Compare Emma’s height with her
sister’s.
What is the quadratic function that only has a positive output using inputs between 3 and
5, and has a maximum output of 1?
MCAT NCEA Level One Check List:
A milk drink costs $1.50 more than a fruit drink.
5 fruit drinks and 4 milk drinks cost a total of $24.
What is the cost of 1 milk drink?
How many real solutions does this equation have?
Session Three of Mathematical Flow.
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Fun and games algebra: What can or should you do with these?
1
1
1
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bc ac ab
3
3
3
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bc ac ab
5n 5n 10n

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bc ac ac
1 1 1
 
bc ac ab
3bc 3ac 3ab

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bc
ac
ab
16n 2 8an 2acn


bc
abc ac
3 x 2  3a 2
2b 2  2c 2
5d 2  5e 2


 x  a  x  a   b  c  b  c   d  e  d  e 
The answer is 2, what is the scary looking algebraic question? What did you learn
today? What do you understand better now? Are you more confident?