Talking about the area of a circle...

Dear Families,

Today we started talking about the area of a circle... that's the space that covers a circle. And we started by talking about some vocabulary that we can use to describe the circle's area. Students made a foldable today that in which we defined segments, semicircles, sectors, and quadrants of circles. 

For homework tonight, students are just supposed to share their foldable with you and get your signature on the page. Then they are finishing a small project where they are making the area in a circle's quadrant one color (or pattern) and the area outside the circle's quadrant a different color or area. This is to help us anchor on the idea that we are examining the amount of space between a circle's center and its circumference.

We are examining how many radius-squares (squares that are the same size as a circle's radius) can fit inside a circle. Students have four different colors of radius squares and we are in the middle of cutting them apart to physically fit them into the circle.

Tomorrow we will formalize a model-building project that we started today and will find that we can fit 3 radius squares... and a little more into the circle. That means that we can fit... well... pi radius squares into it! But that is tomorrow. For today we just started seeing that about three of those radius squares can fit into a circle.

Thanks!

Brian MacNevin

Become a "Maker Scout" at DIY.ORG

Dear Families,

I ran across this website and I thought it was too cool not to pass along. My own kids are only 3 and 5, so we're not this far yet, but if your child loves to tinker and make things (ANYthing!) the website http://www.diy.org lets them earn virtual "badges" for learning how to make stuff and learning how to do things!

It's like merit badges for everything under the sun.

Tie dye, typing, hacking, fence building... amazing stuff!

Sign-up requires parent consent, but if your child is curious about all sorts of things, you may want to point him/her in this direction!

Warm regards,

Brian MacNevin

The week ahead includes an author visit on Tuesday

Dear Families,

I hope you had a restful weekend. For the coming week, I wanted to let you know about a few goings-on:

Author Visit on Tuesday

This Tuesday, author Kirby Larson will be visiting our school to speak with students. Village Books will be selling copies of his books here at school. Please find a link to the flyer about purchasing his books here: [link].

Math Quiz on Wednesday: WRITE THOSE FORMULAS OUT!

This week in Math we will have a leveled practice day on Monday, a practice quiz on Tuesday, and a quiz on Wednesday all around calculating the circumference of a circle using diameter or calculating the diameter of a circle using circumference. It will also include finding the length of arcs that are 1/4 or 1/2 of a circle long. I have been very dogmatic that students first write down the formula, then replace the variables with numbers. They should always do this even when doing homework. Our quiz on Wednesday will cover these two learning targets:

• LT 1: I can identify the parts of a circle (vocabulary for circle, radius, diameter, chord, tangent, arc, circumference).
• LT 2: I can find the circumference of a circle or I can use the circumference to find the diameter and radius of a circle.

Science Retake Quiz on Wedneday

For the vocabulary around force and energy, I will offer a retake opportunity in class on Wednesday.

Continuing to Study Friction in Science

In science we are continuing to study friction. I have been very impressed at how many students referred to friction as a force because it seemed to push back against their pushes. That's a good sign, because friction is something we can't really see and is hard to describe unless you are looking at a very exaggerated difference between textured surfaces.

As part of our study into forces, students have been working on these learning targets:

1. I can identify forces as pushes or pulls.
2. I can write a conclusion to a question using evidence. 
3. I can draw a graph.

Thank you for everything you do to help your child.

Sincerely,

Brian MacNevin

WMS: Math update... Pi is in the air! That's 3.14159 Pi, not Apple Pie. :)

Dear Families,

We have packed a lot of exploration into a few days and I think it was important work for students to conceptually understand how circles and diameters and circumferences work. Here is the progression we've been through:

Tuesday

We learned about more parts of circles and practiced using that vocabulary in a homework assignment.

Wednesday

We investigated circumference and diameter and we found that circumference is *about* 3 times the diameter. So as a REALLY rough estimate, we decided we'd just use 3 for Wednesday. For homework, students had two word problems to solve using that approximation of 3.

Thursday

Today we did a more detailed analysis of circumference and diameter by building a foldable. Students recognized that the diameter was actually a *little* but more than 3 diameters... so we talked about the idea of pi. Pi is the idea of how many diameters there are in the circumference of a circle, so we represent it as C/d (circumference divided by diameter). But mathematicians throughout much of human history have struggled with describing exactly how many diameters can fit around the circumference of a circle... and the best estimates from a computer go on with an endless (infinite) non-repeating decimal (3.14159...). Today I introduced the idea that we can use an approximation of 3.14 or 22/7 for pi. But I stressed with them that 3.14 is not pi: it is just a approximation of how many diameters can fit on a circle. 3 is just a less precise estimate and other estimates can be more precise. 

Tonight's homework asks the students to compare their answers from last night's story problems to the answers they get when they replace our old estimate of 3 with a more precise one of 3.14.

Confusions for 6th Graders

For some reason, if we leave the estimate of pi at 3, kids have absolutely few problems conceptually answering these questions. But once we throw the decimal in there, students get confused about "should I multiply or divide?" If your child is confused in this circle work, have them go back to using 3 as their approximate number of diameters on circle. Once they know what to do, then they can try it again, replacing 3 with 3.14.

Formulas for Tomorrow

Do not worry if your child is not using the formula for circumference yet. We will formalize our understandings into a formula tomorrow. We started that work today with a foldable and we'll continue tomorrow with some calculation practice. 

Thank you for all the support you provide your child.

Sincerely,

Brian MacNevin

Tonight's Math Homework Resources

Dear Families,

I'm sorry to send two messages in a day. I promise I'm not trying to spam you. But I promised my students I would send along this stuff for tonight's math homework.

The red group still had a little bit to finish on their foldable before doing the assignment. I have included images of what belongs in their foldable. Please excuse some upside-down images. 

The information can be found here:
[link]

Thanks so much!

Brian MacNevin

WMS: Math and Science this week!

Dear Families,

Just a beginning of the week email to let you know what we're working on this week!

Math - NO CALCULATIONS YET, PLEASE! :) 

• TUESDAY: Okay, so we're doing circles. We have defined circles as the collection of points all equidistant from a center point. We have described and defined the radius and diameter of a circle and found a relationship between them. Today we added some vocabulary about arcs, chords, and tangents of circles. And tonight's homework asks students to do kind of a piece of artwork with a circle and its parts, then to try to find a way to measure the circumference. I asked students not to calculate the circumference (so no pi, no 3.14156, no 22/7... YET!). 
  
• WEDNESDAY: Tomorrow we will investigate how many diameters of a circle can fit around its circumference and we will have a rough estimate (about 3). Their homework will have them use that rough estimate.
• THURSDAY: On Thursday we will formalize pi as the ratio of circumference to diameter and we will begin using 3.14 and 22/7 as estimates of pi (just more accurate ones than the value of 3 we will use tomorrow) for calculating circumference... or for finding the diameter from the circumference... or for then finding the radius from the circumference.
• FRIDAY: We should be using circumference to find the perimeter of semi-circles and shapes that have semicircular (and quarter-circular) parts.

Science - FRICTION!

• TUESDAY: We introduced the word friction today and students brainstormed what they think it means to surface preconceptions.
• WEDNESDAY: We will investigate friction as it effects the force needed to move a wooden block over different textures (surfaces).
• THURSDAY: We will investigate the effects of load (mass) on friction. 
• FRIDAY: We will investigate the effect of surface area on friction.
• Throughout all of these investigations, students will be keeping careful notes in their science notebooks. There are specific CHECKOUTS throughout the lab where partners bring me over and I check on their progress and their understanding before the can move on. Your child is welcome to bring home his/her science notebook to share with you what we have been working on. 

A long weekend, a short week, and sunshine today! I hope you have a very pleasant Tuesday!

Sincerely,

Brian MacNevin

WMS: Math quiz tomorrow. Tonight's practice.

Dear families,

Tonight students have some homework to get ready for the quiz tomorrow. Tonight's homework asks the students to plot coordinates of shapes on a coordinate grid and then to find the area and perimeter of those shapes.

I asked students tonight to finish the Level 3.5 questions. They can use graph paper in their math notebooks to make a set of axes that go from -10 to +10 on the x and y axes. Students who seek to get a 4 should complete the level 4 questions to prepare.

Tonight's Practice: [link]

Answer Key: [link]

For perimeter estimates, students just use scrap paper to mark off the lengths of the sides, then compare those to the grid the shape is drawn on to estimate side lengths. I used the pythorean theorem to calculate those distances, so student estimates might not match these calculated sizes precisely. If students are 0.5 units under or 0.5 units above my calculated perimeters, their estimate is just fine. If they are farther off than that, they may want to recheck their measurements.

Tomorrow's quiz will NOT require points to be plotted. That is something that belongs to the common core state standards that we are moving toward and I will want to assess that separately. 

Thank you for your time and support of your child,

Brian MacNevin

WMS: Math quiz on Wednesday

Dear families,

We have a quiz coming up on Wednesday for these learning targets:

LT 3: I can find the area and perimeter of any triangle and I can use this to solve problems.

LT 4: I can find the area and perimeter of any parallelogram and I can use this to solve problems.

Today students are bringing home some practice problems and I have scanned in an answer key for them to use at home.

Practice Problems for Triangles: [link]

Practice Problems for Parallelograms: [link]

Answers for both: [link]

Side 1 of each represents a beginning level 3 (still at standard, but lacking any problem solving to it). The back questions represent a more solid 3 to level 4. 

I reminded my students that they don't have to work more than 45 minutes on these tonight. Of course, if they are enjoying the challenge, they are welcome to work longer. But I don't want anyone losing sleep over it. We will have more time to practice tomorrow in class and tomorrow night with homework.

Thanks!

Brian MacNevin