On Friday I had my students write their "math history" and then take a pre-test on factors and multiples. I know this is probably not revolutionary to many of you, but it was new for me and I am very happy with the results.
First I had my students tell me their "math history." I got the idea from Glenn Kenyon's blog. I just had them write one paragraph of how they did in math class in elementary school and how they feel about math as a subject. They were very honest about their past performance and grades. Many really like math and say that they are good at it. A few others have struggled and not surprisingly do not like math very much. None of them sounded like they have given up though, and were hopeful that they could be successful this year.
The pre-test was simply 7 questions covering the basic topics of our unit: prime and composite numbers, factors, multiples, LCM, GCF, and prime factorization. We did not review anything ahead of time so it was cold turkey. I could now compare my students self-assessment of their math abilities with their knowledge on our first unit. Most of their abilities matched what they said about themselves.
I also found out the overall strengths and weaknesses of the class. They did best on primes, composites, and factors. Some did not know multiples and only one student got the correct LCM of 4 and 5 being 20.
Based on their self-assessment and pre-test I know now where to spend my focus in this unit. Furthermore I have a good starting point of their math abilities whereas beforehand I had no clue of their level. I am now able to divide them into pairs for this week by their abilities.
I highly recommend both of these strategies to start a new class or new unit.