Open Middle®
Directions: Using the digits 1 to 9 exactly one time each, place a digit in each box to make the sum as close to 1000 as possible.
Hint
How do you know you can’t get any closer to 1000? What should be true about the hundreds places of your three numbers? How do the tens places affect your answer?
Answer
Lots of answers will get you 999. One would be 247 + 563 + 189.
Is exactly 1000 even possible? Here’s a Geogebra tool you can use to check your answer.
Is exactly 1000 even possible? Here’s a Geogebra tool you can use to check your answer.
Source: John Ulbright and Robert Kaplinsky
One would be 189+247+563
Hi, I’m a 1st time visitor. We are just really getting started recording various levels of DOK questions within our common lessons. I found your site via a Goggle search. However, I have a question. How can I confirm if a question is a DOK 2 or 3? They do not seem to be identified. Are the levels noted somewhere?
Thanks,
Laura
Hi Laura. You can see it in the gray tags area just above the comments section. This problem is DOK 3.
173 248 569
600+300+100=1000
DDDDDDDDDDDDDDEEEEEEEEEEEEEEEVVVVVVVVVVVNNNNNNNNNNNN YO SISSY
Devn, that isn’t true. You cannot use 0s.
176+534+289=999
152+368+479=999
583+167+249=999
To pique student interest and involvement, I put a leaderboard on the classroom whiteboard. This showed first, second, third and fourth places of who in the class could get closest to 1000. It was great to see so many students taking up the challenge to get first place.
By the way, where do I find the DOK that goes with this resource? I’m having trouble finding it on the website.
The DOK is listed in the tags just below the question and just above the comments section.
I was wondering if we could extend the problem by adding closest to 1,000 meaning above or below it. It doesn’t specify, but wondered if that would be another option to use?
234+324+401=959
152 + 528 + 329 = 999
250 + 250 + 500 would get 1,000.
cant use 0 and cant use the same number more than once
169+452+378=999
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179+452+368=999
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584+236+179=999
584+239+176=999
584+276+139=999
584+279+136=999
586+134+279=999
586+139+274=999
586+174+239=999
586+179+234=999
586+234+179=999
586+239+174=999
586+274+139=999
586+279+134=999
587+143+269=999
587+149+263=999
587+163+249=999
587+169+243=999
587+243+169=999
587+249+163=999
587+263+149=999
587+269+143=999
589+134+276=999
589+136+274=999
589+143+267=999
589+147+263=999
589+163+247=999
589+167+243=999
589+174+236=999
589+176+234=999
589+234+176=999
589+236+174=999
589+243+167=999
589+247+163=999
589+263+147=999
589+267+143=999
589+274+136=999
589+276+134=999
594+137+268=999
594+138+267=999
594+167+238=999
594+168+237=999
594+237+168=999
594+238+167=999
594+267+138=999
594+268+137=999
597+134+268=999
597+138+264=999
597+164+238=999
597+168+234=999
597+234+168=999
597+238+164=999
597+264+138=999
597+268+134=999
598+134+267=999
598+137+264=999
598+164+237=999
598+167+234=999
598+234+167=999
598+237+164=999
598+264+137=999
598+267+134=999
may I ask for the code used to find these combinations? thanks.
yea
598+267+134=999
you forgot 999+0+0=999
597+238+164=999
564+121+311=996
should be 247+563+180
how many problems do you have
589 + 276 +134 = 999
I gave this to my 7th grade math team after seeing in it the Open Middle Math book. I made it a three step investigation. Fist was find the largest sum, then the smallest then get as close to 999. The loved it, especially the third challenge. It lead us into some counting theory discussion regarding permutations. One kid even observed that the ones column adds to 19, the tens adds to 18 and the hundreds adds to 8. They searched for different solutions that each had 216 permutations. And they are at 5 as of now.
I love how something that seems so simple can become so engaging and complex.
One would be 365 + 426 + 198
Does anyone have a way to prove that getting exactly 1000 is impossible using only elementary math?
Thanks.
not again!