If I ask them to translate "the sum of a number and five," they can usually come up with "x + 5." No problem. But if I ask them to translate, "the product of a number and the sum of the number and five," they shut down.
I know there's a lot of talk in the MTBoS about not teaching kids which words mean which operation. And, I see where they are coming from with this. Half of can mean multiply by 1/2 or divide by 2. Per can mean multiply or divide. But, if students don't know what the word quotient means, how am I supposed to help them without giving them a chart???
Here's this year's attempt at teaching this topic.
In the past, I've had students make foldables and list the key words. This was time consuming, and I often found myself giving students a lot of the words because they couldn't come up with them on their own.
Here's a pic of a foldable from a couple of years ago:
I knew I wanted to try something new this year. I thought about doing a card sort to glue in, but a million little pieces to glue in and my Algebra 1 students don't mix well. Then, I remembered how @druinok had modified a statistics card sort I had made to be a coloring activity.
I decided to make a coloring page for my students to complete.
The kids kept trying to classify the words that mean equals as add/subtract/multiply/divide which was frustrating. We did this as a class. I asked them to suggest words for addition. We colored all those. Then, subtraction, etc.
We drew arrows over the "turn around words." This wasn't enough, however, to make it stick for my students. This needs some more work for next year!
I think I'll keep the coloring aspect for next year. I missed some phrases when putting this together quite hastily. (Read: during first hour plan to teach third period!) So, I definitely want to try and make it more comprehensive.
I also want to come up with a way to signify that some words can mean multiple different operations. Still working out the best way to do that. Any suggestions on improving this lesson would be greatly appreciated!
Another area my kids have struggled with in the past was knowing when to use parentheses. I decided to try a new approach this year.
I had students draw ovals around all of the operation words. Then, I had them draw a rectangle around the equation/inequality word, if applicable. If there are 2+ ovals on one side of the rectangle, I told them they needed to use parentheses.
Now, you and I both know that these parentheses are sometimes redundant. But, I'd rather my students putting parentheses and not needing them than needing them and not putting them.
Note to self for next year: TYPE THESE!
A common question type my students struggle with is writing expressions that match a scenario that builds on itself. I put one of these on the quiz, and it was still the most missed question. I think my mistake was not giving students independent practice with this question type. That's another thing to fix for next year!