• Home
  • About Me
    • Reviews & Advertisements
    • Affiliations, Disclosure, and Privacy Policy
  • Notebooking
  • Lapbooking
  • Homeschool
    • Teaching Writing
    • Homeschooling an Only Child
    • Homeschooling Middle School
    • Homeschool for High School
    • Curriculum Reviews
  • Charlotte Mason
    • Narration
    • Charlotte Mason Homeschooling Q & A
    • Artist Study
    • Composer Study
    • Living Math
    • Nature Study

Jimmie's Collage

lifestyle blog of a single mom who works from home

  • BUY THE BOOK: Notebooking Success
  • BUY THE BOOK: Essay Tune Up

Living Math with Angles

December 10, 2009 By Jimmie Quick 11 Comments

Taking a break from our intense multiplication study, we’ve moved on to a new topic — angles.  With living math, I do use our Singapore textbook. I browse through it to find another topic to study. (grin) Actually, I do have Sprite do a workbook exercise now and then.

Angles was one such topic that we hadn’t touched on this year, and it seemed easy enough to learn in a hands-on approach. (This is the face she wanted on the blog.)
sprite with angles

Above and below you can see our most important tools:

  1. a home made protractor in 360°
  2. an angle maker
  3. a store bought protractor

our finished page plus tools

I find that in planning living math activities, I often have to reverse engineer the workbook exercises. I look at the problems and ask myself, “How can I convert this skill or concept into a hands-on or real problem solving activity?” And that’s where these activities came from.

First of all, I knew that the entire concept of degrees was important. Sprite needs to understand what an angle is and that it can be big or little and that the size is measured in degrees.

[The technical terms such as acute and obtuse are not vital at this point, so I didn’t use them.  Vocabulary can come later after the concepts are cemented. However, we had already learned about right angles (90°) with Pythagoras, so it was easy to talk about smaller than and larger than a right angle.]

So I had Sprite make a 360° protractor by simply marking degrees on a large circle. (Got to sneak in some x9 facts too — 90°, 180°, 270°, and 360°.)

The angle maker is simply two strips of cardstock connected at one end with a paper fastener. Using these two tools together, we arranged the angle maker in various positions and measured the resulting angle, approximately, with our protractor. We did this for a couple of lessons so that Sprite would get a feel for the sizes of angles — a 20° angle is tiny and a 280° angle is big. A 100 ° angle is a tad larger than a right angle, and so on.

Then come the bits of paper. (It seems we can’t do a math activity without loads of cut up paper.) I used some scrap paper to make circles. I made sure to mark the center with a pen so Sprite could cut out angled sections. Some circles were cut in two pieces, others in three.

cutting circle angles in circle
IMG_9038
Then she measured. First I asked her to estimate visually the degree of angle. Her skill at estimating got better and better. Then I had her use the homemade protractor and then the official one.

homemade protractor measuring angle

measuring with homemade tool clear protractor measuring

IMG_9031I had her label each angle with its measurement. And then we verified the rule that each circle has 360° by adding up the total of the angles. It worked each time!  Of course. But letting a child discover rules rather than dictating them is a halmark of living math.

It all made its way onto a notebooking page.
circle has 360 degrees notebooking page

Next approach — triangles.
triangles

I gave Sprite some triangles and asked her what she thought we’d find when we measured the angles and totaled them. She wasn’t sure, but she felt certain it wouldn’t be 360° like the circles.

measuring angles

Oops… she ended up with several triangles whose angles totaled over 180°. She somehow sensed that 181° and 182° must be wrong and that the triangles that were measured at 180° must be correct. It actually was easy enough to go back and remeasure and find her small errors. It ended up that some of our “right angles” were not actually 90°.
triangles 181 degrees

We corrected the measurements on the backsides, and put a few sample triangles onto a notebooking page.
triangles notebooking

Just to be clear, these angle lessons were spread over about a two week period. Interspersed in with these hands-on activities were some workbook exercises and at the end I used this BBC worksheet as an overall wrap up.

More You Will Like

Top Picks for Hands-on Math Manipulatives and Games
Living Math Update - Fractions
Learning x8 Facts

Filed Under: living math Tagged With: angles, hands-on, living math

Comments

  1. Tammi K says

    December 10, 2009 at 12:36 pm

    Great Ideas! I love to see how you put things into action.

    I did teach the names of the angle types. We used word association: 90 degree (Roight angle) He’s an ‘upright’ kind of guy. Acute – little, tiny baby angles….awwwww, cute!
    and, while it’s not politically correct – big fat angles , Obtuse, are obese. It works well for him. He actually gets a kick out of saying Awwwwww, cute in his best ‘talking to baby’ voice.
    .-= Tammi K´s last blog ..A Little More Music (Part 2) =-.

    Reply
    • Jimmie says

      December 10, 2009 at 8:57 pm

      @Tammi — Great ideas for learning the names of the angles! And anything that makes it FUN is a winner in my book.

      Reply
  2. Maureen says

    December 10, 2009 at 9:01 pm

    Love this Jimmie! I will be using this w/ my kids for sure!
    .-= Maureen´s last blog ..So much to blog but not enough time =-.

    Reply
  3. Dana says

    December 10, 2009 at 9:59 pm

    We’ve done the “this angle is so CUTE” bit, too. 🙂

    Anyway, I LOVE, LOVE, LOVE this post!!! We will definitely be doing this. I think it might be a great way to do math as it gets harder & harder to do school with Christmas approaching. THANKS for posting!!!
    .-= Dana´s last blog ..Dickens on the Strand =-.

    Reply
  4. Kris says

    December 11, 2009 at 4:01 am

    LOVE it! Please, please, please submit this one for the upcoming Homeschool Showcase. It totally makes me want to send my kids to your house for school…except, well, international transportation expenses would get pretty high. 😉
    .-= Kris @ Weird, Unsocialized Homeschoolers´s last blog ..Happy Birthday, Buddy! =-.

    Reply
    • Jimmie says

      December 11, 2009 at 4:38 pm

      @Kris — Your children are welcome to come, but on one small condition. YOU have to come too! 🙂

      Reply
  5. Nadene says

    December 11, 2009 at 11:23 pm

    These are great ideas! I am inspired to develop more hands-on time and take ideas from my Singapore maths books (instead of sticking to the workbook) and have more FUN! 🙂
    .-= Nadene´s last blog ..New Sonlight Stone Age Lapbook and Hands On Activity Page =-.

    Reply
  6. Barb-Harmony Art Mom says

    December 12, 2009 at 5:06 am

    I can remember doing similar projects with my boys years ago…great way to learn about triangles and angles and using a protractor and compass.

    This would be a great entry for the Hands-On Homeschool Carnival as well which I am hosting on Monday…hint, hint.
    http://blogcarnival.com/bc/cprof_6064.html

    Barb
    .-= Barb-Harmony Art Mom´s last blog ..Winter Birds – So Lovely =-.

    Reply
  7. Alexandra says

    December 12, 2009 at 12:43 pm

    Neat!

    Reply
  8. Angie says

    December 15, 2009 at 10:10 am

    Awesome post, Awesome lesson!!! Thank you so much for sharing this!! Be Blessed, Angie in GA
    .-= Angie´s last blog ..Lord, I am so Thankful! (Gratitude Community…1000 gift list cont’d) =-.

    Reply
  9. Cindy says

    December 27, 2009 at 9:06 pm

    This is such a fun living math activity! Caleb will enjoy it when I steal it from you! LOL
    .-= Cindy´s last blog ..Christmas Train Ride =-.

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Welcome!

jimmie lanley
So glad you clicked over. You are welcome here. I'm Jimmie, a single, work from home mom of one teen.

Get This One FREE!

My books

Notebooking Success eBook

Copyright © 2023 · Lifestyle Pro Theme On Genesis Framework · WordPress · Log in