Grade 4. A table, a line plot, some questions.
You could decide to have your students complete the page as is:

Put an x in a box. Put a number in the blank. 
Or you could decide to let your students make their own line plots:

Things may get a little messy. 

Rulers will help. 

He started at 0 and ran out of room on his paper! Now what? 
There were many false starts. Some first drafts got crumpled up and thrown away. But it was a productive struggle with many benefits, the majority coming from the decisions that the students had to make:
 Which way should I hold the paper?
 Where should I start?
 What if I don't have enough room?
 How many intervals do I need? How far apart should they be?
 Which fractions go where?
Did everyone get to all the questions? No. Is the opportunity cost worth it? Yes. We can't continue to bemoan the fact that students have trouble persevering and solving problems when what they mostly do in class is put x's in boxes and fill in blanks with numbers. And in case you're wondering, rather than starting all over, the student who started at zero and ran out of room simply taped another piece of paper onto the end of his original sheet. Lesson learned.
Amen, brother! I was just looking at our 6th grade texthistograms. Every single example gave the kids a frequency table complete with intervals and totaks firceach, then asked the student to create a histogram with the data. The kids didn’t need to look at the range, figure out evenly spaced intervals (I think the hardest part), make their tallies, count them up  or basically think. They just had to draw some lines and then make some boxes up to those lines. Yuck!!
ReplyDeleteLove reading your posts, even when I end up saying yuck!!
Thanks Debbie!
DeleteWhen teaching these skills and understandings to my third and fourth graders the ability to think through the parts and make mistakes and correct them built such greater understanding of looking at graphs and all of the parts and pieces that go with them. Thanks for another great post!
ReplyDeleteThanks Mary. I agree that the process of building the graph (or line plot, table, whatever) puts you in a much better position to understand how all the parts operate together. It's a rich experience with many benefits.
DeleteBrilliant!
ReplyDelete