This is an image from our smart-board today, and what students took notes on in the their journals at the beginning of class. We were exploring strategies for solving word problems. Our focus right now is word problems involving multiplying fractions, and will change to dividing fractions later this week.
Students often do what I call smooshing the numbers together. Students will pull out numbers and add, subtract, multiply, or divide without taking the time to understand the situation. This strategy causes students to arrive and unreasonable solutions, and also makes it difficult for students to evaluate for reasonableness.
A way to avoid this is to start with asking: “What do I have?” Students can then draw a picture of what they have. This helps the student to understand what is happening. To explore this we did numberless word problems. These are problems that start with no numbers at all, and then gradually give you more information.
This is an example halfway through our word problem, and a model that was created to go with it.
Notice that the 1/2 a gallon is also the full bucket. This allowed us to have a conversation about what the word “whole” means, which we will continue tomorrow.