## The One with the Linear Representations Scaffold

### Image

One thing I’m finding, 3 weeks (to the day) into summer school, is that when in doubt, lean on your routines (I’m fairly certain I read this in Carl Oliver’s blog, to give credit where credit is due). We have about 5 weeks with 50 minute classes, so there is not much time to teach or to plan (let alone condense everything into a cohesive, project-based unit that may or may not sync with the biology class next door).

It’s taken me a while to remember this, and to get back into it.

I do recall that one of the structures that was most successful from our linear functions unit is the multiple representations paper (It says “Different Representations” on the actual paper and that is how the kiddos largely refer to it. Change it? Leave it? The eternal dilemma…)

For some reason, the kiddos love this one. There’s enough to talk about, there are different sections, and (added benefit of teaching summer school to some awesome multilinguals, many of whom I taught some portion of the year to) enough kiddos know something about the things that we’re seeing that most kiddos have some access to the content but still need to practice what goes where in the table or why we don’t just put the y-numbers from the table on the y-axis.

I’m also fairly certain that only our school talks about “Figure X” as I had to stop class and review it every time. It’s sometimes a bit too complicated for my tastes, anyway (but makes a nice stretch point).

Photo: Different Representations Paper

What do you notice? What do you wonder?

# The One with the Big Numbers

We’re doing linear functions for summer school and pulling hard from last year’s curriculum. This means using CPM’s pile patterns (which I cheat and just refer to as “patterns”. Who wants to explain what “pile patterns” is to a class of (amazing) emerging multilinguals, when there’s so much else you could be teaching).

Kiddos glom on to the idea of patterns pretty readily, which is great. They’re visual and you can ask “how many?” and point without requiring too much language (my big takeaway this week).

I get to tinker with this class a bit more and we have less time (5 weeks, 5o minutes a class), so I cut some stuff.

For the patterns, we usually jump from finding the 4th and 5th figure to finding Figure 99. This has always been a bit of a jump for me, especially for kiddos with Interrupted Education who may not make connections to the idea of repeated addition and multiplication.

Photo: How many squares in Figure 15?

I spend quite a bit of time in class saying, “Sit down, Jeronimo” (not the kiddo’s real name). But he really grabbed on to this task. While many kiddos struggle to anticipate the figures beyond the ones they can see (or ones one or two our), this kiddo made his own chart to help track numbers. Pretty awesome.

What do you notice? What do you wonder?

## The One with the Patterns

### Image

Week 3 of Summer School, though I don’t know if the first 3 day week actually counts.

In what is maybe not the most cohesive move, we start a new unit on linear functions and graphing this week (Goodbye area and volume). I largely pull from our linear functions unit from this year which largely pulls on CPM (credit where credit is due).

Photo: Student Work on PatternsEduardo has been in my class for 2 years, which makes me somewhat wonder why he’s in my summer school class, but also thankful that he’s there to help support other kiddos as we go. He catches on to the patterns quick (and also has a helpful habit of saying “Wait, we learned this already”, which gives me some hope that what I teach may stick around for longer than the 65 minutes I usually see kiddos) and is quick to point out that the sentence structures for the opening are the same for this entire week (thanks, Estimation180).

He also carries over some unusual conceptions from the school year (that many other kiddos carry), including how to generalize figures with more squares. Admittedly not the most useful skill and probably not Common Core-approved, but it reminds me that I need to push kiddos to explain what the square represents and ground them in familiar concepts like base and height.

What do you notice? What do you wonder?

## The One with Individual Tangent Practice

### Image

I’m a bit more into individual practice, these days. A few years ago, I think I was more “all groupwork, all the time”, but I’m appreciating the fact that a decent culture of groupwork at our school helps support our kiddos when they’re working individually while also allowing them to spend time on what they need.

We’re still working through how reference angles are related to tangent ratios (without really calling them that – most kiddos are sticking with opposite and adjacent sides). Also trying to balance procedural work (especially with ratios) and conceptual thinking. Someone made a decision with this curriculum to round some of the tangent ratios to numbers that made it easier to solve for unknown numbers. While this may take away from the actual ratios (which are a calculator button push away, anyway), it did give a lot of kiddos access who weren’t familiar with solving ratios. Lots of struggle today and I’m hoping kiddos got something out of it.What do you notice? What do you wonder?

## The One With Ratios

### Image

We’re onto right triangle trigonometry. This year is flying by (and we’re a few days in at this point).

One of the many tricky things about right triangle trigonometry is that ratios are big. For classes where some kiddos don’t really know how to divide (let alone when it’s written as a fraction) while some (one) roll their eyes because the conceptual trigonometry we’re using has an approximation rather than the actual tangent ratio, the need to differentiate is real.

We took a bit of time today to talk about how to solve ratios. How many kiddos did we actually reach? Unclear, but the first step is important.

It’s fascinating for me to see the 4 papers I used (one per period) to show how to solve an with a variable in the denominator. By the end of the day, I’d realized that writing fewer steps cleanly is more important. I’ve also decided on “one finger if you understand, two fingers if you’d like to hear it again” is a nice way to hear what the class is thinking without being too judgemental (I’m so used to thumbs up/thumbs down, but that feels weighted).

We also did a reading guide where the kiddos used calculators to find the tangent ratio. It’s actually something that I remember relatively vividly from student teaching. I’m feeling a deep appreciation for this unit the third time I teach it.

Photo: 4 iterations of solving the same ratio

What do you notice? What do you wonder?

## The One with Process over Aesthetics

### Image

New unit on exponents, about to be differentiated like whoa.

We started off with a group task (with varying levels of success) about a pyramid scheme. Lots of modeling. Sometimes I wish I’d done more, though frankly the class where I opted to not do modeling got the furthest.

Photo: We made posters. I told them I cared more about their process than their aesthetics. (One kiddo pays the first kiddo on a list \$3, then makes 8 of their friends the next kiddo \$3. Those 8 kiddos choose 8 friends to pay the next kiddo \$3 and so on)

What do you notice? What do you wonder?

## The One with the Angle Measurements

### Image

We do some more work measuring angles, but this time with protractors. It feels like quite a few kiddos have some traction and understanding here. We do some more individual work with measuring lines and angles, which feels worthwhile.

Fun fact: the Spanish word for “protractor” is “transportador”. Wild.What do you notice? What do you wonder?

## The One with the Angle-o-Meters

### Image

Is it clickbait if the content and photos don’t actually match the title?

Back from Professional Development to start talking about angles (so that we can talk about similarity, eventually). We measure with angles and give directions using turns and degrees.

Teaching similarity is still a bit of a mystery to me, but we get some good thinking done about sides and angles and how they change.What do you notice? What do you wonder?

## The One with the Complex Instruction Professional Development

### Image

We’re fortunate enough to have a strong mathematics Curriculum and Instruction department in our district. Once a year, we take a day to do some district learning and site-based learning.

Gotta shout out my school here (even though I don’t think they read this – am I subtweeting?) because we were short several subs and lots of (amazing) teachers filled in so that our departments could go and work together. Thank you thank you thank you.

We spent the first part of the day doing math and then thinking about how we could assign competence (recognize smartness) in each other. So many ways to talk about this and think about this. We also got a chance to talk about some best practices in our work at our school, which was cool.

Photo: Poster form teams assigning competence to each other:What do you notice? What do you wonder?

## The One with the Dilated Logo

### Image

Our similarity unit doesn’t really have a project. We had a picture project where we dilated candy bar wrappers when we taught the course 2 years ago, but it was more a project than mathematics (and they aren’t mutually exclusive, though we didn’t strike that balance here), so we shortened it to one day. Fascinating to watch students take art and grapple with how to make it bigger. Not pictured: Sailor Moon or an elephant.What do you notice? What do you wonder?