We have been working really hard on figuring out how multiplication and division share a relationship. I want you to warm-up your brain with these examples. Work together at your tables so that everyone is helping one another get stronger!
I have placed triangle cards at each table with 3 numbers and students must identify the relationship between the 3 numbers to create multiplication and division equations.
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 do a quick warm-up to review the relationships between multiplication and division with fact families and students will create a model to represent the relationship between the equations (MP4). Each set of numbers is on a triangle card and the students choose cards and solve using their understanding of the relationship the 3 numbers share in multiplication and division (MP1). My goal here is to ensure students can develop fluency (3.OA.C.7) by quickly recognizing relationships.
As we prepare for common assessments, we are practicing one word problem that requires students to determine which operation is needed to solve every day. I have a problem written on the board and I ask students to help me solve it.
I have noticed how great we are doing with understanding when we need to multiply and when we need to divide. I want to show you this problem that I have and I want to see if you can help me solve this using the things we have learned about problem solving.
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). I teach my students songs and other rhymes to help them remember different patterns in math, and they used the following song to help them solve this problem.
We have already done some great work with multiplication and division. We’ve learned about their relationship, we’ve written word problems and we’ve been practicing getting faster and stronger at solving! Today we are going to push ourselves to think about real world problems that will be asking us to multiply or divide, and we will have to decide which is needed!
What kinds of problem solving tools do we have in our tool box?
Here I expect students to share creating pictures, models, arrays, reciting the songs we use (there are plenty!) and eliminating answers they know are incorrect.
I created word problems, and then cut up the problems. There is a set at each table. Students will have to alternate between the operations when reassembling the problems in different ways. Students must understand what it means to create groups and what it means to divide things equally. Students must show how they solved the problem and write a sentence to justify their answers. It is important that students are able to justify their reasoning (MP3, MP4, MP5, MP6). When students must show their work and write out how they know their work is true, the strategy/strategies used to solve, or what thinking helped them figure it out - it helps the teacher to identify misconceptions, and it helps students to become aware of their own problem solving processes and strategies.