Algebra – On Monday we finished the last lesson this chapter – and the kids used Desmos to graph the equations of the lines they’d written, along with domain/range restrictions to make the ‘logos’.

I thought they did a really good job! Tuesday I wasn’t here, Wednesday was a final day of clarification and review, Thursday was the chapter 2 test, and today we started chapter 3, “Simplifying and Solving” with the first section on exponents. It was interesting because the problems had the kids factoring the exponential expressions so they had what they could simplify out written separately. So the second step was simplifying what they could to 1, then what was left they multiplied across the numerators and denominators. A lot of them wanted to use the “rules” but this was teaching them WHY the rules work, and what is happening to the parts that are “cancelled”. I will pass back the tests on Monday.

Math 7CP continued working on the Rational Numbers Unit. We did a lot of problems together and in their groups – word problems that involved decimals and fractions. I really tried to have them draw pictures of the problems that involved fraction division. (pic on left) We had a discussion today about subtracting with mixed numbers. The problem I was using said “the weight of the basket is 58/3 pounds”. I said, “This shouldn’t be written this way, who says 58/3 pounds?” It also had the weight of the fruit as improper fractions. So we changed everything to mixed numbers. Then wrote the problem – which was now a subtraction problem with mixed numbers. I asked “Who now wants to change everything back to improper fractions?” and several hands went up. After not shooting myself, I went up to the front of the class and had a big talk with them about how this is SO MUCH HARDER than just subtracting the whole numbers and subtracting the fractions (it wasn’t borrowing, thankfully – another topic). I asked them if they go to the store with a $5 bill and ask the cashier to change it all to nickels because they’re going to buy something for $1.25. I told them that I knew teachers taught them to do it the improper fraction way, because it would always work, but it was SO MUCH HARDER,and they could do it with mixed numbers. So we did the problem together. We all lived!

When I was gone on Tuesday they did “fraction squares”. I gave them a fraction and they had to represent it in a drawing (I’m irritated with myself that I forgot to have mixed numbers and improper fractions in it), on a number line, as a ratio written 3 ways, as a percent, decimal and then as 3 equivalent fractions. I had the first example drawing as a circle. One of my fractions was 1/6. When I came back I was checking their fraction squares and a few kids had drawn a circle, and made 5 vertical lines in it and colored in one section. Which was not the same size as the other sections! I asked the kids why they’d done it this way and they said, “The sub said we had to draw it as a circle.” I’m sure she didn’t notice that they’d drawn the lines like that! And interesting to know that some of the kids don’t understand that the pieces need to be the same size! We’re having a group quiz on Monday, so I’ll see how much they know then.

Math 7 Accelerated – We started Chapter 2 in our supplementary text, which is on expressions and equations, using algebra tiles. On Tuesday one of the problems had them writing the perimeter of a complex shape made with algebra tiles. We went over it again on Wednesday because they weren’t labeling all of the little sides, so were doing it wrong. Wednesday and Thursday we used Expression Mats and the algebra tiles and they were building them and simplifying them. Today we learned the “legal moves” that can be used to simplify the expressions, and used the Expression Comparison Mat to simplify then compare the expressions. We also wrote what was happening algebraically. It was confusing to some at first, but I think by the end everyone was doing it correctly.

Debbie, this is SO DIFFERENT than when I was in school. Your students are very lucky to have you as their math teacher, notwithstanding your comment below “After not shooting myself”, which made me laugh. Your reaction to the couple of raised hands wanting to go back to improper fractions was great – you gave good examples. How times change, Love, Mom

Thanks Mom! What’s so frustrating to me is having teachers at my school, who I’ve talked to and worked with that still teach adding and subtracting mixed numbers by having the kids changed everything to an improper fraction. Then get a common denominator. They say it’s “just easier for the kids”. I wonder if they don’t understand how to do it using mixed numbers. It’s bringing it down to the lowest level – something everyone can always do, but isn’t efficient and doesn’t make the kids think. It’s like always taking the surface streets instead of the freeway, because the street is outside your door. Sure it takes 3 times as long to get from LA to San Diego, but you’ll get there.

And, since I’m on a roll, they also teach multiplying fractions by “multiply first, then simplify your answer”. They won’t make the kids simplify first “They don’t want to, they like simplifying the answer.” Well, make problems with larger numbers so it’s EASIER to do them if they simplify first! Of course the kids won’t do it if they don’t see the need…. and neither will the teachers. I need to figure out how to get the teachers to see the need!