This activity came about because my students get really bored with rounding off decimals for no particular reason. I’m sure you’ve seen these dumb “exercises” where kids get a bunch of random numbers and then are told to round them off to the nearest thousandth, hundredth or tenth, and really, who cares? So I adapted another set of activities that I developed for my younger students and came up with this!
But I have another item on my agenda: one of the things I have always advocated is giving children math problems that are interesting and challenging. I know, I know, this flies directly in the face of “well, if we give them hard things to do, then they’ll get discouraged and think math is hard.” Well, the truth is this: mathais hard! And let me say another thing: anybody, young or old, experienced or not, is either lying or has never done “real math” if they think it is “easy.”
In this activity, I’m pushing you to challenge your students in a few ways: the first is to give them 4 step problems. WHAT! How can 9 year olds solve a 4 step problem? Shouldn’t they first focus on a steady diet of 1 step “word problems” until they get to high school, and then maybe we can add another step somewhere along the way? NOPE, because waiting until high school is waaaaay tooooo laaaate!
Let me walk you off the ledge: the way to give a student a 4 step problem is to give them one step at a time. That’s why you cut out these little clue strips and assemble them into booklets, staple them together, and have students work on them one step at a time. That is called “scaffolding,” by the way.
This is an excellent activity because instead of throwing all 4 clues at once, the students can only reveal one clue at a time, and “solve” it before moving on to the next clue. By limiting the amount of information, we can allow students to work on highly complex problems in a structured and supportive way: first solve the first clue, then go on to the next clue, then the next.... it means that your students will be less likely to jump at any answer that pops into their carefully coiffed noggins and shows them that math can be done in an orderly way.
Now here’s why these are really cool: instead of giving kids decimals to round off, let’s do it backwards: tell them a decimal has been rounded off, and let them figure out the possible decimals it could be. So if you look at the sample problem, we start with a number rounded off to the nearest unit is 4, then it could be any number between 3.5 and 4.4, which means there are many, many decimals that go out to the hundreds place (actually, 900 if you go to the hundredths place.) The next clue, that it rounds off to 3.9 when rounded to the nearest tenth helps us narrow down the range: it could be any number between 3.85 - 3.94, which is only 90 different answers if you go out to the hundredths. The next clue, that it rounds to 3.85 means that the number has to be between 3.845 - 3.854, because all the numbers in between (3.845, 3.846, 3.847, 3.848, 3.849, 3.850, 3.851, 3.852, 3.853, 3.854 - 3.855 would round off to 3.86) . The last clue, that the “digit sum” is 18 means that the number could only be 3.852.
You can use these problems in a lot of ways: you can make the little booklets, put them in a jar and have students pick them out randomly, and then complete the answer sheet I’ve enclosed, or just work them out in their notebooks. It is important that they practice doing one clue at a time; it’s okay if they want to look at the entire problem first, but they should understand that one clue follows another, or else the problem won’t be solved properly.
I’ve also included a “Do It Yourself” sheet, where you and your students can make up your own 4 step clue puzzle booklets!