12 of 32 Items .... Type: Raw Pure Math

Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Algebra 2:
Write a function for this graph ...

Estimation:
What are some possible values for a,b,c,d?
If I told you it also went through (0,54), what might the leading coefficient be?


.: [ALG2], [Jennifer Wilson], [Raw Pure Math].

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If we stipulate that

\( (x+12)^2+(y+4)^2+(z+3)^2=0\), then

\( \sqrt{x^2+y^2+z^2}=?\)

Should we brute-force this or is there a more beautiful or subtle way of getting what we want?




.: [PRE-CALC], [David Marain], [Raw Pure Math].

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Is there enough information to determine the least possible value of y?


.: [PRE-CALC], [SAT], [Raw Pure Math].

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Can you find values for y that will make each answer true? Generalize the rules in effect here.


.: [ALG2], [SAT], [Raw Pure Math].

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Raw, pure math. Ummmmmm, tasty.

But can you make the question harder by rearranging the variables?


.: [GEOM], [mathsjem], [Raw Pure Math].

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For the last couple of days, I've been asking you to create a new puzzle. Today, I'd like you to describe HOW to create a puzzle with a unique solution, or two solutions, or three. How did Don Steward create these and KNOW that they only had one solution?


.: [ALG2], [Don Steward], [Raw Pure Math].

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Put algebraic expressions into the cells so that the product is as indicated. That's for warm-up.

That's not what I'm going to ask you to do, though ...


Make a new puzzle with two solutions.


.: [ALG2], [Don Steward], [Raw Pure Math].

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Put integers into the cells so that their product is as indicated.


.: [MS Math], [Don Steward], [Raw Pure Math].

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If a and b are both positive integers, \(a^{a - b}=10^6\),
list all possible ordered pairs (a,b).

What are a couple of different ways to approach this nugget?

What are the "obvious" answers that everyone will miss?


.: [ALG2], [David Marain], [Raw Pure Math].

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Is this enough information to find the equation?


.: [ALG2], [T.R.Milne], [Raw Pure Math].

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Let's examine the function g(n):


g(n) = smallest integer such that g(n)*n! is a perfect square.


How should we go about finding if there's a pattern in that?


.: [PRE-CALC], [James Tanton], [Raw Pure Math].

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Is there an easy way to tell if those lines will have one solution, no solution, or an infinite number of solutions?


.: [ALG1], [T.R.Milne], [Raw Pure Math].