Today, I will explain how we act on a part-part-whole problem using our hands. The next two entries will focus on change and comparison problems.
I am sure I am not the only one with students who can understand the math concept and can listen to a story problem but then have a difficult time managing and connecting all of those pieces together when asked to solve a problem. For example, my students understand the part-part-whole concept and can draw and solve the pieces of a number bond like nobody's business. They can also listen to a word problem and understand the general gist but when asked to assign meaning to the pieces in a word problem (Do you know both parts? How would you solve to find the total? Are we missing a part or the total?) They are completely overwhelmed. These hand motions allow them to "see" the action of the problem and merge their knowledge together in a much easier way.
Here is a quick video showing how the hand motions look in practice. A more detailed explanation is written below!
For a part/part/whole problem students use their two hands with palms facing up to show the "parts" and then they clap their hands up and together to show the "whole". When they hear a problem, they act out the pieces they hear with their hands and then can easily figure out where the missing information is and which operation they can use to solve.
For example: Tony has 12 red t-shirts (one hand out, palm up) and 8 blue t-shirts (the other hand out, palm up). How many does he have altogether? (Clap hands together for "altogether") Students know that they are missing the total so they should add.
A missing part example might look like this: Tony has 12 red shirts (one hand out, palm up) and some blue shirts (students would put their other hand into a fist and gently shake it back and forth to show missing information). Altogether, Tony has 20 shirts. (Students would clap hands together). How many blue shirts does Tony have? (Students would go back and shake the missing part hand). They would then know that they are missing a part and should use subtraction to find the missing part.
here are times when students begin to use motions for a problem but then notice that they have made an error. They are trained to re-read the problem and re-act out the problem with their hands. For example, if the problem said: Tony has 20 shirts. 12 are red and the rest are blue. How many shirts are blue? A student may start by putting out a palm up hand for Tony's 20 shirts. By the time they finish reading the problem they quickly realize that the 20 shirts were actually the total rather than a part. They re-read and fix their error.
I am, actually, thrilled when a student makes this initial error and then fixes it up because, previously, some of my students with speech needs would read through this type of problem and just "pick" + or -. With the motions, they realize that if their hand motions aren't lining up with the action of the problem that there is a mis-understanding and they need to go back to clear it up!
I have created "Sort & Solve" packs for my kids to use when practicing these techniques. Some days we de-emphasize the solving of the problems and spend the majority of our time discussing how we would solve a problem and how we know that strategy is sound. Sort & Solves have been an amazing addition to my classroom!