The common core expects students to be able to use multiplication to solve a word problem by using equal groups, arrays and drawings so that is what this portion of the lesson is aimed at addressing. Yesterday we did a similar lesson, taking numbers and creating word problems to match them. That's when I noticed that although my students used drawing groups and putting an amount in each group to help them solve problems, they relied heavily on the traditional algorithm in proving their work. They were able to articulate their understanding of place value when multiplying, so today I will spend additional time ensuring they can articulate that their multiplication problem represents groups of objects.
I put 2 more numbers on the board and ask students to take a minute to think about what type of problem they could create to match these numbers. I'm deliberately selecting numbers that we have worked with frequently (up to 12) for these examples so that the real thinking goes into creating the problem, and not solving the multiplication problem.
I always pull sticks to call on students so that kids are always prepared to answer any question I ask. I give each pair of students a white board and marker, but you can also use pencil and paper to check for understanding.
Ok, now what type of story can you tell me about these 2 numbers? Turn to your partner and think about the story you will tell. You have 3 minutes! As the student is speaking, I’m listening to make sure their problems involve groups. With the common core it is important for students to develop fluency in multiplying and to have a range of strategies to rely on in doing so (MP1).
Alright, I’m impressed! I saw some really great thinking and math problem solving going on. Who would like to teach us how they solved their problem?
I ask the students why they chose to represent the problem in that way, what their model or numbers show, and what their product represents (MP2, MP3, MP4). I like to lead students back to answering the questions beyond giving me a number. I want them to be able to articulate their mathematical reasoning (MP3).
I call on another student to share a different way, so that many different ways of problem solving are shown and explained by the students. I think this is important because other students may see a strategy they may not have considered and students are prompted to defend their solutions and their work (MP3).
My lesson yesterday with creating word problems provided me with some great information about what students know and are able to do, but I did notice that a lot of students relied on the traditional algorithm to show their work. This may be because we just learned steps for using it, or that it is faster when solving larger multiplication problems involving larger groups of objects. While it is important for students to use a range of strategies, I will ensure my questioning today pushes them to defend why they chose a particular strategy and challenge them to show their work in more than one way.
Yesterday we created some great stories involving groups to represent multiplication, but I think you’re ready for more! Yesterday I gave you numbers to work with, but today I know that you can create your own numbers and problems. In your group it will be important to decide on your numbers and the story you will tell with your numbers. I challenge you today to show your work in more than 1 way, because you may teach your classmate about a new way of thinking about multiplication. Great experts are always able to teach others about all that they know!
Students are dismissed back to tables to begin their work. As I’m walking around the room and looking at their problems, I question students who may be creating an addition word problem instead of a multiplication problem.
It requires a deeper understanding of multiplication when students are expected to actually write out a problem that involves groups of objects, which is what I’m expecting them to do. Although students are strong at recalling multiplication facts, it is always a bigger challenge for me to get them to recognize multiplication within word problems. By writing the problems, they are required to construct a problem with equal groups, and if they can do that thinking, it will lead to a better understanding of when to multiply when they read other problems.
The common core emphasizes a lot of problem solving, making and defending arguments, modeling and the need for students to communicate precisely with others. Providing students with the opportunities to share their work and question one another, and for you to ask clarifying questions, is a great way to address these things.
I pull sticks to call on groups to come and share their posters.
I have them read the problem, defend why it is a multiplication problem, show us and explain how they solved the problem and why they chose to represent it in the way that they did (ie: drawing out the groups, setting it up with numbers only or using an array).