WitCH 123: Blockheads

Ok, I’ve started to look more carefully, and my conclusion will come as no great surprise to the “I told you so” readers: NAPLAN still really sucks. Clearly, my informant was drunk.

Over the next few days, I will be posting a number of WitCHes, on questions from the post-2016 tests to which I currently have access. I’ll then try hard to find the time to write on NAPLAN more generally. I have also updated The ACARA Page with internal links, to make it easier to access all the NAPLAN posts and articles from over the years.

The following question is from the 2021 Year 9 test, calculator section. The test was bad, worse, it seems to me, than 2018. I will only WitCH this one question from the test, but there were numerous close calls, and a general feeling of nausea.

18 Replies to “WitCH 123: Blockheads”

  1. So, we just define 3+3=7 and all is good.

    Because, defining addition differently is now OK, according to WiTCH 120.

  2. What is the point of the blocks? They appear misleading and from my glance, don’t appear to be to scale?

    Writing tests is hard. Given how tests have multiplied: NAPLAN, PAT, etc etc (not so subtle mathematical pun), my guess is that the resources required have not been allocated and clearly the people devising such tests do not appear to have the skill sets needed.

    Remind anyone of anything?

    1. Scale is the least of the issues. If you have a SQUARE base of 9 cm^{2} then each side must be 3.

      If the rectangles have an area of (EDIT) 21 cm^{2} then the long sides must be 7.

      So why do (EDIT) two of the short (3cm) sides magically now align in the diagram with one of the long (7cm) sides?

        1. Yep. Thanks. Typo.

          The diagram may not be to scale, but I would hope that the scale was consistent within each dimension…

          1. I’ve corrected your comment with a note of the edit.

            I don’t think a poorly placed “not to scale” notice remotely excuses that diagram.

      1. Another typo – I meant to say TWO of the short sides making one long side.

        Hence my earlier comment that 3+3=7.

          1. Thanks Marty – I was busy trying to look interested in the PD session. Your blog is way more interesting though…

  3. Since the question describes a physical object, it is entirely reasonable that an accompanying diagram somehow illustrates the object. This diagram is a shambles. It looks like all the blocks have relative dimensions 1 × 1 × 2, which would mean the the sides of the blocks (to fit the top area) would be 0.75 × 0.75 × 1.5. But using those dimensions would give a side total of 6 × 0.75 = 4.5, which is not 7. Alternatively, the diagram shows a construction with relative dimensions 4 × 4 × 6, which is very far from 3 × 3 × 7. Saying “not to scale” is pathetic. The diagram is at best not to scale, at worst it is actively giving prospective solvers the wrong idea. This is inexcusable.

  4. Just a really bad diagram… the arrows look like they point to the “small wooden blocks”, but the smaller blocks are just a distraction in this question.

    1. Yep, and also wrong, as people have point out. But I spent a *long* time pondering this, assuming the arrows were pointing to the faces of the blocks.

      1. Sorry for the slow reply. I don’t see it is necessarily wrong, just badly misleading. If you ignore the blocks, then the problem is easy and probably what was intended.

        The blocks are not all multiples of the same cube which was implicitly or explicitly assumed in the calculations in the comments. eg see the front face – the middle top block and middle bottom block are both “2×1″s but not clearly the same size. Lucy was pretty smart to be able to build a square prism from such misshapen blocks…

        Anyway, happy to agree it was a bad question. 21cm^2 should be replaced with 18cm^2 then there could be no fewer complaints. Or just throw away the pseudocontext and have a diagram that represents what is really being tested.

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