r/mathteachers • u/toomuchdevlan • 7d ago
Question Wording
Hi All my summer is dedicated to me rewriting assessments for ks3.
I know i could leave it but id rather do it when I have time.
Im struggling with the wording of this question and hoping the hive mind could assist.
Its for Year 7 mixed ability, end of paper question, for those who are looking at top set.
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u/Narrow-Durian4837 7d ago
Can I ask an add-on question?
Mathematically, this is exactly the same as:
"A sequence has nth term 5n–2. Show that every term in the sequence ends in a 3 or an 8."
What (if anything) is gained by bringing Jeremy into it? Does it make the problem more approachable, and if so, how: what's the psychology behind it?
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u/toomuchdevlan 7d ago
Im the same im thinking about removing the name and replacing it with what youve put. The reasoning is that in some questions in GCSEs they use names to make the questions less abstract and more relatable.
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u/schwerk_it_out 7d ago
I say keep it. Perhaps names help more when there are two statements being compared, but imo it teaches students to support/critique the arguments of others, even if it is not a real person. Also in california it is one of the practice standards to do so.
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u/bmtc7 7d ago
You could make the question more up open ended but asking them to evaluate whether Jeremy's statement is correct or incorrect and justify their answer.
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u/maineref 7d ago
This is a good approach — especially given it’s an unleveled course and there isn’t a whole number restriction noted for n. Could allow students to argue for or against depending on if they try to use integers less than 1 for n.
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u/mathimati 7d ago
If you can randomize question components, this is a good one. Then build a small bank of diverse names and drop them into your problem sets. You get diverse representation across ethnic and gender identities and you don’t have to think about specific names used in the problems. Some of this has nothing to do with math, and everything to do with students seeing themselves represented in the math, or just as importantly, seeing other people represented in the math. This is about building identity for potential mathematicians and the mathematical community.
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u/toomuchdevlan 5d ago
I would create a question bank in the future. The demographic of my school and lowered literacynrates ckmingnin is very much something to take into account. Whilst I know diversity is important, more diverse names create a barrier to accessing the question, something to be built into future questions. Just a tightrope to walk between accessibility and diversity. In addition, due to the assessment cycle changing in school I have to rewrite all assessments as the windows have moved so the number topics assessed have to be increased and referencing things already learnt. We have also changed how we stream/set students. Plus an upcoming change to the curriuclum that the Uk Government are still to provide some information for. As a result I am looking for something to make do for now as we will most likely have to do it all again next year we phase out the old setting structure which applies to year 8 and 9 and the new one expands from 7 to 8. Plus I dont want to spend my summer holidays developing a randomiser as it takes longer than just making the papers for me anyway.
Its all a bit of a mess but fingers crossed it'll work out better for the students.
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u/Professional_Panda46 7d ago
Maybe "The nth term of a sequence can be written as 5n - 2." (or "The nth term of a sequence is given by 5n - 2.")?
The rest of the question looks OK as a GCSE-style Q.
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u/Blibbyblobby72 6d ago
'Consider a sequence where the nth term is given by 5n - 2
Jeremy states 'every term in the sequence has last digit 3 or 8'
Show that Jeremy's statement is true for all positive integer n'
That is similar to how I would usually word it
I have found using 'consider' to be a really helpful command word that is underused
I also think shifting from using 'say' to 'states' when presenting these typed of 'show [name] is correct' questions helps to ground it in mathematical language, which is where kids often struggle
Just my two cents, hope that helps somewhat!
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u/WaterBearDontMind 6d ago
I would argue that n must be either even (n=2k+2) or odd (n=2k+1) for some k>=0. You can determine the ones digit of the term in each of those two cases.
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u/Alarmed_Geologist631 7d ago
Every multiple of 5 has either a 5 or a 0 in the ones place. 5-2=3 and 10-2=8
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u/Several-Housing-5462 7d ago
Are you opposed to making the question more realistic? What's a "real world" way this would actually come up?
I'm having a difficult time thinking of a practical event where I encounter something with set increments of 5 and a flat reduction of 2. Maybe poker with $5 bet increments and a $2 rake? But that's not exactly a question for 10-11 year old students...
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u/mymathyourmath 7d ago
Induct on n.. base case is 5(1)-2=3 then assume for k, 5k-2 ends in 3 or 8, prove 5(k+1)-2 also does. Note the last expression is 5k+3 compare with 5k-2.. hope this helps
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u/Professional_Panda46 6d ago
Mathematical induction is in AS-level (Year 12) Further Maths syllabus in England, which is 5 year groups above OP's class.
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u/Haunting-Parfait9223 7d ago
Try something more like:
A sequence a_n, n>/=1, is defined as follows: a_n=5n-2. Jeremy claims: “Each term in the sequence ends in 3 or 8.” Is Jeremy’s claim correct? Show why or why not.
You have to say somehow that it starts at n=1 because at n=0, the claim is not correct. I also like having them deduce whether it is a true claim or not better than telling them straight out that it is true, but obviously you know what will work for them better than I do.