How would my child, who hasn't been introduced to algebra yet, solve this problem?

[u/NoHunt5050]

This is a question on my kiddos homework and I can't, for the life of me, figure out how to solve it without using algebra. My kiddos in 6th grade and he hasn't started to learn algebra yet.

Solved! Thank you so much for the quick replies! At least it was a good opportunity for me to teach my child about algebra:).

[u/aprg]

There are five stores. If the average is 55, then the sum is 55 × 5 = 275.

If you then subtract all the number of cereal varieties, you get to the answer.

I think this is a case where knowing about algebra eclipses the simpler solution.

[u/ClownUniversityPhD → u/aprg]

There’s a way with no multiplication either. Just a running count of difference from 55.

K is +19.

S is -4 so the running count is +15.

B is +4 so we’re back at +19.

S is -18 so we’re at +1

G needs to be -1 from the average to bring us to 0.

[u/TeaSimilar5714 → u/ClownUniversityPhD]

OMG, do you also count cards?

[u/TheKaptinKirk → u/ClownUniversityPhD]

This is how I thought of it first.

[u/NoHunt5050 → u/aprg]

Omg...thats...duh 

Haha thank you!!

[u/johnpeters42 → u/aprg]

Algebra is just a more compact/flexible notation for word problems or fill-in-the-box problems, which can generally be boiled down to a single unknown that only appears once.

[u/nmrk → u/johnpeters42]

That is precisely the point. This is about the point in the math curriculum where the students start to discover algebra on their own. There was much preparation to get to the point where the kids start to see the underlying algebra.

[u/Han_Sandwich_1907 → u/aprg]

I disagree with your last statement. This sort of reasoning comes from the sort of intuition you get once you know algebra and become comfortable with "working backwards".

[u/Dodger7777 → u/Han_Sandwich_1907]

There are lots of little things in math where it does benefit you to do it the long hard way before you are taught the simple easy way just so you can know how to do it.

For example 5*20 is 100. Simple right? But if you say to most cashier's today 'Can I get change for a dollar? I want it in nickles' they look at you like you just spoke an alien language.

It drives my Dad nuts, because he likes to use exact change. He'll have a total read 8.40, and give them 13.00 then he'll give them .40 cents and say 'you can just give me a 5 back', and you can see their brain clunk to a stop like he just asked them about their parent's secret mustard recipe. I've legit watched people brain fart for like 5 minutes over this exact conundrum. It doesn't help that my Dad tries to walk them through it, but is getting mildly angry about being made to explain basic 2nd grade math.

[u/MERC_1 → u/Dodger7777]

I have done the same thing as a kid, some 30+ years ago. Except I gave the cashier some change when she was supposed to give me the same amount. This was me making a mistake. But the cashier was utterly confused and gave me the wrong amount back.

[u/chmath80 → u/Dodger7777]

Paid cash for a purchase of $41.10 recently. Put down a 50c, and 3 × 20c, followed by a $50 note. Girl on the till took the note, and immediately pushed the coins back to me. I had to stop her from just giving me change on the note.

Then there's the older woman at the fish and chip shop, who uses a calculator to work out change, and still tried to give me too much the last 3 times I was there.

[u/prawnydagrate → u/Han_Sandwich_1907]

Nah I was more comfortable with this method before I learned about algebra

[u/aprg → u/Han_Sandwich_1907]

I mean simple in terms of prior knowledge; the problem for a lot people who are good at maths when trying to teach kids is that they forget what it's like to do these problems without the knowledge that they have. Case in point, this very thread: it's the instinct of OP to use algebra to solve this problem but their kid doesn't know that yet.

This problem lays the groundwork for motivating algebra -- we're looking for an unknown -- using some prior knowledge that should hopefully be well established (the most complex idea here being mean average). I fully expect a strong 11 year old to be able to use those tools to solve this problem without understanding algebra and then later to see why understanding algebra makes solving this problem even quicker.

[u/TheKaptinKirk → u/aprg]

I thought of it this way.

74 - 55 =19
51 - 55 =-4
59 - 55 =4
37 - 55 =-18

19 - 4 + 4 - 18 =1

So, 55 - 1 =54

[u/ExpensiveFig6079 → u/TheKaptinKirk]

I thought of it this way.

If you smear then all out like concrete... that is piled to high in some paces and too low in otehrs

74 - 55 =19

19 extra in the first bucket

51 - 55 =-4
59 - 55 =4

These two smear out to the av 15 by taking 4 out of one pile and putting it inthe other

37 - 55 =-18

The 19 from before fill this up to 55 with 1 left over

19 - 4 + 4 - 18 =1 (not used or done as single operation)

so with 1 left over from levelling all the above to 55. Thuis one with 54 will with the extra 1 also be 55.

All thatsaid this is in some ways HARDER than algebra, BUT is also good thing to teach first.

Specifically in MY explantion I would be tryign to get students to see that takignthe average

*IS*
*The same thing*

as when you spread out piles of concrete and make them all even heights.

WHY?

The entire functionality of math is not in classrooms but is in the fact that the entire universe works

*just like*

math.

\\\\\\\\\\\\\\\\\\\\\

and for the non nerds out there get all the way to group theory and find out the SU3 group works for baryons AND for the corners of rubics cubes

Corners of rubics cubes are NOT baryons, but they

"work like A"

and that is DEEP math and goes allthe way back to fractions and signed numbers and averages.

BTW i have szero idea what an electron is... BUT I know it works like wave when it goes through a slit (or two)

[u/Pitiful_Lie4818 → u/aprg]

Isn’t that just algebra? 😅 Where am I going wrong

[u/aprg → u/Pitiful_Lie4818]

Yes; you're looking for an unknown.

But going from this to full-fledged algebraic manipulation of the problem, e.g.
_x_ = 55 × 5 - (74 + ... ), is not something most 11 year olds will have seen yet, and you need to show them problems that motivates them to learn algebra, otherwise they don't understand why they should bother using letters to label unknown quantities... (source: I'm a secondary school teacher.)

[u/ztexxmee → u/aprg]

algebra just makes this so much simpler to structure. it’s literally just solving for x in (74+51+59+37+x)/5 = 55. your last statement is false. algebra shows true structure. while the math is the same process overall, algebra just makes it easier to see and solve than working with pure numbers.

[u/aprg → u/ztexxmee]

I meant simpler as in "requiring less prior knowledge". The most complex idea the pure numbers approach needs is understanding what a mean average is.

There exists a bias amongst mathematicians that makes some excellent mathematicians terrible teachers: they think that because they know the maths, they must teach over-advanced technique to a young pupil. It's wrong and counter-productive: the best maths teachers aren't people who hold a PhD in Maths, but people who understand how the slow evolution of knowledge builds up in pupils' understanding. If this kid hasn't learned algebra then introducing algebra now might just confuse them.

[u/ironclad_packetship → u/aprg]

I am having that exact problem right now with my children in elementary school where their homework uses simple methods taught in their grade level but my mind jumps right to solutions that involve algebra/geometry/trigonometry.

[u/Kuddel_Daddeldu → u/aprg]

Yes, (5*55)-74-51-59-37=54.

[u/Neither_Berry_100 → u/aprg]

This is the answer. I don't even understand how you could use algebra here.

[u/visceralviceroy → u/Neither_Berry_100]

(x + 74 + 51 + 59 + 37)/5 = 55

And then that gets you to the formula they outline above to find x.

[u/Neither_Berry_100 → u/visceralviceroy]

Is that even algebra? Just one x. Not like matrices or solving systems of equations.

[u/davideogameman → u/Neither_Berry_100]

Yes, it's algebra.  It's simpler algebra hence possible to solve without needing to learn algebra first but it is the way to phrase the problem from the algebraic point of view

[u/y2khardtop1 → u/aprg]

My kids were doing this in 4th grade, unfortunately their teacher was an idiot and almost in-taught them.

[u/Zarakaar]

55x5 minus the current total.

Algebraic thinking before symbolic algebra.

I wish average middle school students knew enough about what a mean was to even attempt this.

[u/igotshadowbaned → u/Zarakaar]

They're meant to, mean/median/mode is usually taught like 3rd/4th grade

Or it used to be precovid, I don't know where shits at now

[u/Kuildeous]

One way is to reason it out individually. If the average is 55, then the first row is off by 19. The subsequent rows are off by -4, 4, and -18. If you add them all together, you get 1, which means to offset that difference, you add -1 to the average: 55-1=54 is the missing value.

[u/aprg → u/Kuildeous]

While this is correct, you will probably confuse a lot of 11 year olds by introducing the idea of offset here unless they're more capable at maths. The offset approach is clear to anyone who already understands how mean averages work, but this problem is trying to build that basic understanding first.

[u/igotshadowbaned]

Kids are indirectly taught algebra concepts pretty early on, before the word is ever introduced

Its not that complicated for a 6th grader who has probably been introduced to the idea of averages a few years ago to realize the solution will be the difference between the sum of the 4 cereals, and 4•55

[u/FanMysterious432]

I don't think this problem needs algebra. I think this problem is designed to get your child used to the kind of thinking algebra will use.

[u/somet31721]

If average is 55, the 55 x 5 = 275 is all the stores added together. Adding together the first 4 gets 221, therefore the last must be 54.

[u/Kirbeater]

55x5=275-(74+51+59+37) =54

[u/JDHPH]

You can solve this problem using addition, division, subtraction and multiplication. I recommend you show what average means using arithmetic.

[u/ephemere_sloboda]

Kiddo would know that if the average of 5 numbers is 55, the sum of the five numbers must be 55x5 = 275.

4 numbers are known and add up to 221, so the missing number must be 275-221=54.

[u/mrjeanette]

5*55-(74+51+59+37) = 54

[u/ruffryder71]

If the average of 5 data points is 55 then the sum must be 275. Subtract the amounts from that total to find the missing amount.

[u/green_meklar]

There are 5 shops. Multiply 55 by 5. That's how many total varieties there need to be. Add up the 4 counts stated in the list. Subtract that from the 5*55. That's how many would need to be at the 5th shop.

[u/Another_Timezone]

Taking one step back, these questions don’t come out of nowhere. Your child would solve it the way the teacher demonstrated in class.

I’d be very surprised if this is the first time this “determine the value given the average and n-1 values” was presented.

The story and values have changed, but they’ve been given a strategy to figure this out that is in line with the current lessons.

[u/Dazzling_Music_2411]

74 varieties of cereals in a U.S. grocery store? Really?

I think I can see why the country has problems.

[u/Ok_Hope4383 → u/Dazzling_Music_2411]

That actually sounds a bit high but still plausible for a typical large supermarket here...

[u/ctoatb]

You find the average by adding numbers then dividing by how many numbers you added. (A+b)/2, (a+b+c)/3, etc. Here, you have the average and know four out of 5 numbers. (A+b+c+d+e)/5 = x. Solve for e

[u/michaelpaoli]

First to make it easy, look at the last digits of the 4 values given, add them and repeat until one has a single digit. Now, how many more to make an even multiple of 5?

Great, use that as a first guess for ?, and calculate the average.

So, how far off is that result? Multiply that error offset by 5, add it to the guess, and there's your answer - and can check by recalculating the average.

Or, 5 items, must average 55, what's 5 times 55? Now subtract the sum of the 4 that are given - the difference must be what's needed for the unknown item.