Solving One-Step Linear Equations, Part 1

This lesson will introduce students to the concept of solving simple equations. The big ideas are:
- The solution to an equation is the number that makes it true.
- You can write a different yet related equation to make the problem simpler.

Step one, bring on the fact families. Remember these?
3+5=8
5+3=8
8-3=5
8-5=3
As long as students have a decent grasp of what addition and subtraction mean, you can use some kind of manipulative to show how the different facts fit together. Using a rectangular array, the same can be done with multiplication and division fact families. When leading students to write out the fact families, ask them to find the patterns about where the largest number is in the addition/multiplication and subtraction/division problems. Is it the part or the whole of the group?

Then, replace one of the numbers in a family with a variable or empty box.
3+[ ]=8
[ ]+3=8
8-3=[ ]
8-[ ]=3
Ask students to fill in the spaces, and then pick out which fact is easiest to "solve" for. They might choose one of the addition facts and solve by counting on, or they'll choose the subtraction fact with all numbers and operations on the left-hand side (LHS) of the equation, and the unknown isolated on the right-hand side (RHS). Whichever one they choose, make sure they check their answer by taking the solution and replacing it in the equation they chose; if it turns out true, then their solution is correct.

Next up, write an equation that has one unknown/blank, such as:
[ ]-6=4
Ask students to write the other three equations that will be in the same fact family (What numbers? What operations? What are the parts and whole?) Circle the equation that has all numbers on one side of the equal sign, and the unknown isolated on the other side. Repeat with similar equations that have the blanks in any of the three spaces until students can identify what different but related equation they would use to solve it.

Resources and Extras:
This worksheet from math-drills.com has algebraic equations with small numbers and the basic operations, with one number blanked out. Have students choose their problems, then write the fact families for them, choose the "easy" equation to solve, then fill in the blank. Other versions of this worksheet have symbols or variables in place of the blank.

Dice are a good tool for getting more tactile with this lesson, especially in the addition/subtraction fact families for lower-skilled students. Roll two dice, place the dice next to each other, and write the addition fact that's shown. Physically change the place of the two dice to show the second addition fact. For example, if they rolled 4 and 5, that gives you 4+5=9 and 5+4=9. Start writing the subtraction fact as 9-[ ]=[ ] and remove one of the dice. Ask, "How many did I take away? How many are leftover? Where do each of those numbers go in the sentence?" Students can practice drawing out each of the problems they do with the dice along with the fact family. Slightly higher-level students can do the same with multiplication/division problems by drawing the array.

I'm one month into my second year of tutoring math at an urban high school, serving almost all ELL students. Now that I have a degree and a year of school-specific experience under my belt, there are some aspects of my tutoring that I want to improve.

1. Spiral Review daily.
   Our official curriculum has built-in review days, but they are designed to target only the skills that we taught that past week. I've been slowly creating review cards with questions from every topic we've studied so far, so I can pull them out and let students choose a random card (skill) to practice.
2. Teach note-taking and note-using skills.
   Even if my students are technically placed in 9th or 10th grade, due to possible interrupted schooling, many of them are not used to "doing school", or what they need to do other than just sit and learn in order to succeed in high school. With some of my younger students, or those with major organizational issues, I write out a set of notes as the lesson goes on, and tell them, "Make your notes look like mine." Then, as we accumulate more lessons in their notebooks, I encourage them to look in their notebooks for answers before they ask me.
3. Create cumulative vocabulary sheets.
   I'm still undecided whether it'd be better to create a long list of words at the back of their notebooks (or on a separate sheet), or to make an outline before each section with the words and phrases written in, with space for them to write definitions and translations, and show examples. The latter worked excellently last year for the Algebra I unit on linear equations, so I might try that again this year, even if it requires more upfront work on my part.
4. ELL support, even for English speakers.
   By the nature of this particular high school, every student in the academy is enrolled in an ELL class along with their content classes. Even if the students are comfortable with spoken, social English, all of them need help practicing the academic language structures that will let them be successful in their content classes, and eventually be able to transfer into one of the other academies (that isn't specifically designed for newcomers and ELLs). These techniques could include writing sentence stems into their notes; encouraging students to discuss problems with each other in English or Spanish and responding to them in English; and pre-teaching the vocabulary needed for an upcoming section.

As the year goes on, I also intend on keeping detailed notes on how I teach all of the different topics, and what did/didn't work for various students. Even though I can remember most of the techniques for myself the next time I see that topic, my notes could possibly help some of the new tutors this year and in the future.

How I (Will Have) Spent My Summer Vacation

The next few months are going to be very different from what I've gotten used to as a college student. Just as soon as I got the hang of being a decent student, I end up teaching instead. It's all for the better, anyway; according to my professors, I haven't actually learned any useful teaching skills yet. I have to get those on the job. Well, here's that there job.
For the next four weeks, I will be teaching two elementary school-aged math classes at a community summer program (where I previously worked as a counselor, and was a camper before that >_< ). My first class each day is "Math Fun and Games," where I'll try to convince students entering 3rd-6th grade that there's more to math than worksheets and drills by encouraging them to look for patterns and think creatively. The class for kids entering 1st-3rd grades is called "Number Sense," and I hope to give the younger students an idea of what different physical quantities look like by learning how to measure and record.
Classes start on Monday, and I honestly have no idea what to expect:

• The kids are outside of my typical age range for teaching or tutoring.
• This is my first time in charge of an actual class.
• I've come up with the lesson plans myself, and don't know how good they are.
• I don't yet know how old the kids that signed up are, or why they're signing up.

I'm pretty sure I find out part of that last one tomorrow. It's only really an issue for the younger class, because there's such a wide range in what I can do with a 5 y.o. fresh out of kindergarten, and a 7 y.o. who just finished 2nd grade. (All made more annoying by the fact that NJ doesn't have statewide math standards, nor does my school district across schools.) There will be a lot of modifying to do after the first day or two of class, but I feel like I'll manage to not screw up my campers too badly the first time I teach this. 

Fun- and preparation-filled weekend ahead. I'll keep all y'all posted. 

(Looking at past posts, I'm good about writing at the start of a "semester". I'm going to break that habit this summer.)