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Thursday, August 14, 2014

ACT Readiness- pt 5- Numbers and their Properties

The next set of standards will be Numbers and their Properties.  I hate to think that this is an area of weakness, but after years of seeing students counting on their fingers and the difficulty which my students have with factors (both prime factorization and factoring standing out as examples) I can't say that it isn't a possible source for student struggling.

Why does this first problem start with y not equal to 0?  Do you agree with the asterisk'ed answer?

How could you "work out" this second problem?  Would a list or table simplify calculating the answer?  How would you set up one of these to do this?

I look at the first column and seeing fractions, even equivalent ones leaves me wondering.  Also, I look at one of the higher columns and I see rules of exponents and complex numbers, and I know these are skills my students can accomplish.  Makes me feel like more and more that I need to know exactly where our students have struggled in the past.

I have a couple of ideas for my lovely students to do on this one.  First off, Beginner , That's COOL! and (if you use IoS, then FactorMan).

One more thing...on paper please list out the numbers 10 - 25.  For each number list out possible ways to multiply two numbers to get that number as an answer and then find the sum of those factors. (you need only do the positive factors and stick with whole numbers)

For example 24:
1*24: (sum) 25
2*12: (sum) 14
3*8: (sum)  11
4*6:  (sum) 10

Please keep the work from these "challenges" until after school starts.  Details will be given as to why before the end of the first week of school...