Algebra – We started Chapter 2 and have been working with algebra tiles for most of this week. Monday the lesson was on zero and negative exponents – I really liked how CPM has the kids think about the zero exponent. It asks them to write down what they know about x squared/x squared. Some kids do the “division rule” they figured out, and end up with x to the zero power. Other kids see that it’s the same thing in the numerator and denominator so that simplifies to 1. We talked about if doing both things is correct then x to the zero power must equal 1. I also expanded out from 2 to the 4th power down to 2 to the zero power – but instead of just writing 2 times 2 times 2 times 2, I put a 1 in front of it: 1(2)(2)(2)(2). So the exponent “4” tell you the number of 2’s to write. Therefore when you get to 2 to the zero power, you write the 1 and no 2’s! I said Math People are Efficient (lazy lol) so we don’t want to write the “1” each time in front of the expansion, but if we did then it is easy to see why anything to the zero power is 1.

With the algebra tiles we solved equations using an equation mat so we could see it visually and then also wrote the equations algebraically so we could see how the “legal moves” of moving the algebra tiles compared to the written expressions. All of this was getting us to exploring the Area Model and multiplying binomials to create an area model. It was challenging and fun today – challenging for me to not get frustrated when some kids want to do the minimum… but it all worked out.

Math 7CP – This has been an interesting week. Monday we had a Team Quiz to get ready for our Unit Test, which was Wednesday. Before we started I had the kids do the 100 Number Challenge, which promotes working together as a team.

I took pictures of all of the teams and they’re up at the front of the room to “show” what team work looks like – everyone participating, everyone engaged, helping each other. (We talked about them on Tuesday before I hung them up – all of the other classes asked why THEIR pictures weren’t up!) So then on the Team Quiz I heard a couple of groups saying “okay, let’s each do one problem.” Later, when I thought about it I realized that technically, this is team work, they were going to share their answers, but when we have a Team Quiz we make the problems harder, so they need to work together and help each other do the problems. Apparently the 100 Number Challenge was one thing, and working on a Team Quiz was another on “how they did it”. So I had them take them home to finish….and they’re not good. On Tuesday I collected them and then we did all of the problems together in class and reviewed a little more for our Rational Numbers Unit Test. The test wasn’t great either. On the quiz I had highlighted all of the errors, and the kids could work together and do corrections (on a separate page, showing all the work) and improve their quiz grade. I really don’t know if this helped – I know it helped that grade, but the test had the same mistakes. Huge problems with fractions and integers – which was the main part of the test. Today I’m going to do some fraction multiplication and division using rectangles with them – which could be either a disaster or helpful. Something has to help! I’m passing back the tests today too…. at the end of the period I think. I don’t want to spend a lot of time correcting in class. I want to just keep teaching these concepts and then do a retake in a couple of weeks.

Thursday was fun because we worked on Balance Puzzles after we went over the homework. This time I assigned certain homework problems to a table and they had to go over them together, then decide who was going to come up and present their problem to the class, on the doc camera. It worked really well! If they were wrong other students raised their hand (I was sitting with the class) and I just said “someone has a question” and the other student would explain what was wrong and it got fixed. After each person we did one clap (a la Andrew Stadel). Here are the Balance Puzzle sample pages I have.balance-puzzles-and-more. They are from SolveMe Puzzles – and there is super fun app for your phones from the same place with fun balance puzzles and more on it!

Math 7 Accelerated – They’ve also been working all week with algebra tiles and equation mats – in much more detail than the algebra kids. We’ve compared expressions, simplified and recorded the work, and solved equations. There are 3 “legal moves” that can be used to remove the tiles from the mats to simplify or solve the problems: 1) remove “zero pairs” from one of the sections = combining like terms when doing the problem algebraically. 2) moving tiles from the “opposite” (negative) section to the positive section – the tiles need to be flipped over when they move from one section to the top/bottom. So if you had x + 3 in the “opposite” section, and moved it to the positive section you’d flip them over, and they’d become -x – 3 in the positive section. This is the same as distributing the negative algebraically. For example: -(x + 3) = -x – 3. 3) Taking the same tile away from 2 related sections. If there is an x-tile in the positive section and an x-tile in the opposite section (on the same side – left or right – you can’t go “across the equal sign” on the mat) you can remove them both, because x and the opposite of x is zero. You can also remove two tiles that are the same in corresponding sections across the “equal sign” on the mat – so if you have 3 unit tiles in the positive section on both the left and right sides of the mat you can take them both off. Algebraically it’s combining like terms if they’re on the same side of the mat (left or right) and removing the same amount from both sides if they’re in the same section, but on opposite sides of the mat. Some kids want to combine everything in their heads and just write the problem and the answer (that’s a surprise) so while I’m walking around I’m asking them for their answer and just saying “right, wrong, wrong, right” – and telling them to show me their steps. Regardless of the materials some kids want to do the minimum (I can relate).

Today is the closure activity – they have to make up a problem, then on the Activity Page they have to explain the steps as if they were teaching it to a student that hadn’t used algebra tiles before. Then they make up a “test problem” for their student. When they finish, and I see it, they can start their Closure Problems (the chapter review). Which reminds me, we need to finish making the tests for this chapter – a group quiz and individual test!

Algebra tiles! You’ve mentioned them before in prior blogs, but this time you had sufficient info about how the students used them, for even me to figure it out. Great tool – I wish I had them when I was in these grades. Love, Mom