One of the things that math experts must do is use what they know to problem solve. We have so many tricks and tools in our math toolbox to help us solve problems, and we’re going to need them now to figure out what’s missing here.
I have a missing number problem on the board that we will solve together. I usually start the day off with 1 or 2 questions on the white board that we break apart and solve as a group.
The common core requires that students interpret products of whole numbers (3.OA.A.1) and interpret whole number quotients (3.OA.A.2) so we will apply what we know to a missing number problem. Students should be able to see the relationship between the 2 known numbers to determine the value of the unknown number. My goal here is to ensure students can develop fluency (3.OA.C.7) by quickly recognizing important information and the relationships between multiplying and dividing.
We discuss how we will solve, we show our steps and then we justify why the other answers are wrong (MP1, MP3). This allows students to understand what the question is asking of them and why the other answers will not be correct (MP2).
We have practiced accountable talk since the beginning of the year so students must always frame their speech (and thinking) using a full sentence structured in this way:
“I believe the answer is ____ because ____.
I solved it by using ____ and found the answer was _____.”
If a student shares an answer without their proof I always go back to them to stretch their thinking, using questions such as, "why do you think that", or "how do you know that", or "prove your thinking".
I heard some great ideas about how to solve problems when I don’t have all of the numbers! When I'm looking for something missing in a problem, I find it helpful to see the relationship between the numbers that I have.
I want you to practice with your table to not only find what’s missing, but to find the other numbers that complete this family.
Here I expect students to use the relationship between multiplication and divisions to determine the unknown number. They should also be able to quickly record and model the other 3 equations with these 3 numbers.
One way we are going to become better at solving math problems is to keep working hard at it. You’ve shown me how to find relationships in numbers and we’ve been working very hard at problem solving. Today you’re going to have to read problems that require you to problem solve. It might be multiplication and it might be division, there might be missing numbers and they might be tough- but I want you to use your problem solving tools to help you solve your problems and show your work!
I have cut up word problems on their tables and students will have to alternate between the operations. In order for students to develop fluency in solving problems they must be given time to practice applying the skills they have learned. Students choose problems, show their work to solve and then move on to another problem. If they have tried using their tools and are having trouble, I will help them get on the right track, but it’s important not to give them the answers. It is important that students are able to justify their reasoning and the validity of their answer (MP3, MP4, MP5, MP6) so I expect to see their steps for solving written out. I do not accept a single answer to justify their work, they must also show me their steps.
(pictures of ind work)