In Math...Using Cognitively Guided Instruction (CGI) for Problem Solving

 We read our first problem together, with no numbers. Jose and Khazjon are students in our class, and I picked Lego Ninjagos as our math currency because it didn't take me long to figure out where our interests lie. Once we read the story, I asked them what was happening in the story in their own words. "Jose has legos!" Mmhmmm....do we know how many Legos? "No! I think he has 5." hahahahah so funny this always happens! I can't tell you how many times I write a problem just like this, then when we finish reading "How many Lego Ninjagos does he have left?" I turn to find a forest of little hands, waving in the air, wanting to "answer" the question. LOVE

So what else do we know about our story? "He gives Khazjon some of his Legos." Do we know how many he gives him? "No! But maybe he gives him 10, I think." Maybe! What else do we know. "Jose has some left." How do you know that? "Because we have to count them." And what will that tell us? "How many he still has." Who is he? "....." It says "he" still has....who is "he" in this story. "...Jose!" Yes, we are finding out how many Jose still has. Our school is two-thirds English Language Learners, and I have learned that these referent pronouns are tricky...it is not always obvious who "he" refers to...is it Jose? Or Khazjon? They can figure this out, but asking the question surfaces it for them, and they sort it out, before we get into problem solving.

Next, I put two numbers on the chart, under the story, and we reread the story putting the numbers in order as they come up. We did 8 and 3, then we did 12 and 5, then we did 14 and 6. I have a small tub with a variety of tools, similar to their Math Bags, and two students (first Jose and Khazjon, then students acting as Jose and Khazjon...boys and girls alike....good times, good times!) act out counting out the starting number of Legos, then act out giving some to the other person, then we predict what is left in their hand, and I always ask, "How can we prove it?" I get either "because 3 and 5 is 8!" or else "we can count them!" and we always do. "So we think there are 5 in Jose's hand right now, let's count and see if we are right!"

Once we understand the problem, I set them off on their own with two final numbers. Because I'm a masochist, I gave them the numbers 22 and 7.

 They did a spectacular job! They grabbed their Math Bags and a tray, and with the vague instructions to "show me what the problem looks like", they got right to work. Here we see Dontrell and Jossah using two different tools to build the 22 units, and then they broke off or removed 7 tiles/cubes and counted what was left. Nice solid CGI strategy.

 

Now, I have worked with third graders who lost their collective minds when they built their numbers with base ten blocks and didn't have enough units to give them away. I've seen some seriously crazy stuff. But this Little One (second grade) took it in stride. She built her 22, pondered it for a few minutes, and quickly changed paths to make 22 unit blocks so she could give away 7. Please to note, she did not "exchange" one of then tens for the units, which would have sufficed, but instead completely rebuilt the number using all unit blocks. I see that efficiency is not on her mind! Good job, Abbs, you knock my socks off!