I like to vary the start of my math block to keep kids thinking about numbers and relationships, especially related to multiplication. Yesterday we did work with 2-by-1 digit multiplication, and today we will apply what we know to word problems. The common core expects students to be able to use multiplication to solve a word problem involving equal groups, arrays and drawings so that is what this portion of the lesson is aimed at addressing. I will use this lesson for 2 days so that students have additional practice reinforcing these skills.
I have a word problem written on the white board and have students come join me on the carpet. I ask students to think about the ways they can solve this problem, and then I ask a student to come teach their class about the way they would solve it.
Watch the video here.
The common core requires deeper understanding of multiplication as a total number of objects in groups and for students to be able to communicate that understanding, so I will be guiding students through this process using the creating of word problems and presentations of their work at the end.
Who can tell me what the factors in multiplication represent? What is another way we can think about multiplication to make it easier to understand and solve?
One thing that I love about multiplication is that I can tell stories and create word problems with my numbers. I always have to be careful of 2 very important things when I tell my multiplication story. The 1st thing is that I must have groups of things, and then the next thing is that I must have a number in each group.
I have 2 numbers on the board today, 27 and 3. I’m going to tell you a story about these numbers so I need your listening ears open and your math thinking caps on.
As I’m telling this story to students, I’m also writing it on the board. Mr. Andrews has 3 fish tanks in his house. He needs to clean each tank out, and he has 27 fish in each tank. How many fish will have their tanks cleaned?
Here I ask students what kind of tools we have that will help us solve this problem. Here I expect students to tell me that they can repeatedly add 27 up, 3 times. That I can draw my 3 tanks and draw 27 fish in each one, or that I can multiply the numbers using the traditional algorithm. I record all 3 ways on the chart so students are able to refer back to the strategies when they complete their group work.
Each table has a 2 digit and 1 digit number turned over, markers, scratch paper and a larger poster piece of paper to show their completed work. It is important with the common core that students are able to explain themselves and the meaning of their problem, so this activity will give them practice in this skill.
I think that you’re ready to construct and build your own word problems, solutions and examples for the rest of us to see. When you return to your seats, please work in your groups to create a problem to match your numbers. All of you must agree on the problem and the solution, and you can show your work in any way that your group members used to solve it.
Students are dismissed back to their tables to get started. I walk around the room and question groups about their work.
Key questions: Why does this problem represent a multiplication problem? How are you going to be able to prove your answer? What type of model, picture or number sentence can you draw to make solving this problem easier? Can you show me another way to solve this?
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). Watch a group presenting their work.
I will display student work in the hallway after this assignment so that students can see their hard work displayed for others.