I'm going to be teaching small (< 10 students) but very mixed group of middle schoolers (US system, ages 11-13) who have had varying amounts of pre-algebra and algebra instruction thus far. I need to give a placement test so that I know who has mastered which topics, to plan appropriately. I will probably then split the group into two subgroups, and also have enrichment activities available for students who have "tested out" of a topic the rest of their group needs to cover.

The problem is, they will show up on the first day of school rusty and not remembering much of what they learned last year. How can I quickly "de-rust" them to the point where I can get reasonable results on a placement test, preferably within one or two 45-minute sessions (with homework in between if helpful).

I'm thinking the homework might be a sample of problems like the ones they will see on the placement test, that they can hopefully remind themselves how to do. These are mostly above-average math students, but mostly lacking a parent who remembers algebra who could help remind them of what to do. So, if I could come up with (or find pre-made online) some kind of quick reference of pre-algebra and algebra topics (preferably not more than a couple of pages) that I could give them as a reference to refresh memories, that would probably be helpful.

  • $\begingroup$ Do you have time for in-class activities before this test? $\endgroup$ Commented Jul 14, 2014 at 2:41
  • $\begingroup$ @DavidButlerUofA I could use a couple of 45-minute in-class sessions toward "warm up" before the test. $\endgroup$ Commented Jul 14, 2014 at 3:48

2 Answers 2


I recommend devoting class time to helping the students review last year's content. I wouldn't recommend just telling them stuff, but getting them to identify things that they need to know themselves.

First I would get them to try to write down things they learned last year. Give them say 15 mins to write down everything they could think of individually without talking. The focus is on getting as much stuff down on the paper, and handwriting isn't important.

After they've written down as much as they can remember, get them in groups to compare notes. I recommend giving them guidance here or they might just argue. Tell them that at this stage they're looking for a list of topic headings (eg "negative numbers", "areas"). Maybe another 15 mins on that.

Finally get each group to share and collate it together to get a list of topics for the whole class. You can fill in any topics that are missing.

For homework, they can do the same "try to remember as much as you can" for each of those topics.

In the next class, get them into groups again to talk about each topic. The point here is to remember the main facts/rules from that topic.

You can give them a certain amount of time for each topic, then summarise these at the board.

This process ought to give you a feel for where the students are with regard to previous learning.

For homework the second day, they can try some example problems in preparation for the test.

  • $\begingroup$ Thanks, David. This is the kind of suggestion I was looking for. In my case, the whole group will not have covered all the same topics, but that is one of the things I need to find out. (I will also get information from last year's teachers on the topics covered.) $\endgroup$ Commented Jul 14, 2014 at 17:58

Presumably you have access to a class list over the summer? I would send the students a series of review problems in the mail once a week that form some sort of scavenger hunt. You can include a stamped postcard so they can send the answers back to you.

The answers to the review problems could correspond to letters of the alphabet (so a problem with the solution x = 1 would give the letter "A" as a "clue", the next week's problem could have the answer y = 3, which would yield the letter "C". By the end of the summer, the students would collect all the letters and solve the puzzle, which could be something like "ICE CREAM PARTY". This can then be their reward after the examination.

There's no guarantee the students will do the work, but the more motivated students will want to know the answer. Even if the students don't complete all the problems, they would still get some review out of it.

  • $\begingroup$ It's a bit of a wild idea, but I was inspired by all of those worksheets I had in middle school that were similar in nature. $\endgroup$
    – jonsca
    Commented Jul 14, 2014 at 3:27
  • $\begingroup$ I like the idea, but I'm not sure how much access I'll have before school begins. $\endgroup$ Commented Jul 14, 2014 at 3:57
  • $\begingroup$ @PurpleVermont Position it as a way of giving students early and optimal preparation for any standardized tests required during the year and the administration will gladly cough up the info ;) $\endgroup$
    – jonsca
    Commented Jul 14, 2014 at 4:06
  • $\begingroup$ It's an independent school, so we fortunately don't have to contend with the usual standardized testing requirements. I may have better luck with putting up a website and letting it be known that there is optional review and/or challenge material there for those who want to stay sharp over the summer. Partly, we don't know yet how the groups will be divided, but I can put up material applicable to a variety of levels. $\endgroup$ Commented Jul 14, 2014 at 4:12
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    $\begingroup$ The school has a facebook page, so I'll put a note there that I'm setting up a website, and let it spread by word of mouth. Not perfect, but it should catch most of them. It's a tight community. $\endgroup$ Commented Jul 14, 2014 at 4:31

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