Monday, April 13, 2026

Fraction Skill-Building

After our Introduction to Fractions in March, we will work during April and May on skill-building. Children will continue to add concepts to their MLBs.

The Introduction to Fractions needs to be done very slowly and carefully to ensure there aren't enduring misunderstandings that show up later on!


I wanted to share the rest of my fractions planning for the year now since it is ready. If I make any changes to this as we go along, I will update it.

You will see that even though we went very slowly at the start, they will end up doing standard fifth grade fraction problems by the end of the ten weeks!


Themes Covered in Week 1

    Mon - K/W/L Chart

    Tue - 1/2, 1/4, 1/8

    Wed - Making Thirds & Halving Thirds

    Thu - Fractions of a Group, Equivalent Fractions (Houses on a Street)


Themes Covered in Week 2

    Mon - Fractions of a Number

    Tue - Puddle Question

    Wed - Reading a Ruler, Fractions in Lowest Terms

    Thu - Build-an-Animal


Themes Covered in Week 3

    Mon - Restaurant Simulation

    Tue - Coins as Fractions & Decimals

    Wed - Basic Operations with Fractions

    Thu - Converting Improper Fractions to Mixed Numbers


Themes Covered in Week 4

    Mon - Converting Mixed Numbers to Improper Fractions

    Tue - Elapsed Time

    Wed - Making Arrays

    Thu - Using Arrays to Simplify Fractions


week of April 6

Mon - Comparing Fractions

    recall Thursday's work with arrays

    look back at Fraction of a Group and find the equivalent fractions (2/4, 4/6) visually but also "prove it mathematically" on the board

    look back at Colorful Fraction Circles and see if you can find the equivalent fractions (4/8, 2/4, 5/10, 2/10)

    have children come up to the board to demonstrate the steps in how to convert each of these fractions to their simplest form

    what happens if you reduce 4/8 by dividing both numbers by 2? nothing, you'll just have to simplify it again by repeating the process

    so if there are multiple things you can divide the top and bottom number by, you should choose the largest one because that'll save you the most time

    notice that a unit fraction (with a 1 on top) is always in simplest form because its only factors are 1, and 1 isn't allowed in factor trees (YCCOM)

    have children work independently on Comparing Fractions worksheet
    https://www.superteacherworksheets.com/fractions/comparing-fractions-tape-diagrams_QWERT.pdf

    for the two equivalent fractions on that worksheet, we then used the chalkboard to "prove it mathematically"

    notice that for 6/8 = 3/4, we divide the top and bottom by 2

    but for 4/5 = 8/10, we multiply the top and bottom by 2

    we can make them larger by multiplying the top and bottom by the same number, and there are times in math when we want to do that!

    it's like Alice in Wonderland; you can make her bigger and smaller by nibbling and sipping, but she's still Alice while her size is changing

    why does it work? remember that the top number is how many and the bottom number is what kind. if you have a plan to eat 5 pieces of cake, but your mom cuts them in half to make twice as many (so now there are 10 and they are smaller) but you just adapt by eating twice as many, you have still had the same amount of cake!

    Arnold Schwarzenegger and the 2 ply toilet tissue fiasco!

    he switched to 1 ply at the government offices in California to save money during the budget crisis, and everyone promptly switched to using twice as much toilet tissue

    "if you're going to give half as much, I'm going to take twice as much"


    Carlyn Beccia book - which 6 of these 9 cures for Wounds worked? that's 2/3!


Tue - Add to MLB

    add the steps in making equivalent fractions to the MLB

    add new observations and new questions about fractions


Wed - Alice in Wonderland

    practice making equivalent fractions by either multiplying the top and bottom number by the same thing or dividing them

    go bigger and smaller just like Alice in Wonderland

    assignment: write three fractions that are equivalent to one another


Thu - Fact Families

    as I watched children working on yesterday's assignment, I realized that the class needed a review of Fact Families

    I had each child just choose a few multiplication facts that they were having trouble with and write out the fact families for them


week of Apr 13

Mon - +/- Fractions with Common Denominators

    have students practice addition and subtraction of fractions with common denominators by creating problems for classmates to solve (an answer key must be provided)

    a fun spin on this is "Secret Code," where the children come up with a fraction to represent each letter of the alphabet and then write a series of math problems for a friend to solve

    the answers to the problems spell out a secret message!

    this works best if improper fractions ("top-heavy fractions") are allowed and the answers do not have to be put in simplest form

    note: a very good way to see if children understand a skill is to have them create their own problems; if children understand that the denominator of a fraction is its name and does not represent an amount, they will resist the temptation to add or subtract them


Tue - Rounding Fractions

    practice Rounding Fractions to 0, 1/2, or 1

    observe, can children visualize the fractions in order to round them?
    or do some kids still need to see them, draw them, or build them?


Wed - Simplifying Fractions Mandala


Thu - "Of" Means "Times"

    explain that, in math, the word "of" means "times"

    sing the song,

      "Multiplying fractions
      Is no big problem
      Top times top over
      Bottom times bottom"

    do Fractions of a Group (a whole number has a denominator of 1)

    do Multiplying Fractions (notice that the answers are very tiny! 1/3 of 1/4 is 1/12! cut up the Comparing Fractions worksheet to prove this)


week of Apr 20

Mon - First to 50


Tue - Dividing IS Multiplying by the Reciprocal


Wed - Reciprocals of Mixed Numbers


Thu - Add to MLB

    add adding and subtracting fractions (with common denominators) and multiplying and dividing a fraction by a fraction to the MLB

    add new observations and new questions about fractions


week of Apr 27

Mon - Factor Trees

    read the introduction to YCCOM

    have fun by drawing factor trees and creating the artwork for them!


Tue - Finding the GCF

    do Simplifying Fractions

    how have you been solving these? have you ever found an equivalent fraction but it was still the wrong answer because it wasn't in lowest terms? how can you be absolutely sure you're dividing by the biggest possible number that goes into both, and there are no more steps?

    explain how to write factors in parentheses to find the GCF


Wed - Add to MLB


Thu - Factors for Numbers 1 to 100

    write out the factors for the numbers from 1 to 100 (in parentheses)


week of May 4

Mon - Finding the LCM

    this is it! our final fractions skill! and then you will be able to do anything you ever need to with fractions

    what would happen if we wanted to add fractions from different sections of the box together?

    what if I ate half of my birthday cake during the daytime and then I got really hungry in the middle of the night and went back and ate 1/5 more?

    yes, you could do it... but how would you express the answer?

    if you say well, 1/2 + 1/5 = 1/2 and 1/5 more, then you have basically just repeated the question

    the answer has to have only one denominator; therefore,
    you need those two fractions to share a name before you add them

    is this possible mathematically?

    absolutely! we know how to make fractions smaller by dividing both parts by the same number but we can also make them bigger by multiplying, and the fractions will still be equivalent

    here we need to figure out not what factors but what multiples two numbers have in common

    as we will still have to simplify our answer at the end of the process, it saves time to go with the smallest common multiple (if I turn 1/2 into 50/100 and 1/5 into 20/100, I will get 70/100 and then reduce... if I turn 1/2 into 5/10 and 1/5 into 2/10, I will get 7/10 right away)

    practice with Least Common Denominator task cards


Tue - Task Cards


Wed - +/- Mixed Numbers with Unlike Denominators


Thu - Add to MLB

    write in adding and subtracting fractions with different denominators to the MLB

    add new observations and new questions about fractions


week of May 11

Mon - Brain Drawings


Tue - Multiples for Numbers 1 to 100

    using another paper that goes from 1 to 100, write out as many skip counts as you want for each number


Wed - Word Problems


Thu - Quiz


week of May 18

Error Analysis



This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Posted by at No comments:

Sunday, April 12, 2026

Local Industry - Salt

Our second Local Industry for Southern Illinois!


timing:

    Great Salt Spring is a prehistoric site first occupied around AD 800 along the Saline River in southern Illinois. Here, Native Americans extracted salt from the naturally occurring salt springs, mainly as a seasonal activity during the autumn months. (source)

    Temple and Castle owned and operated the mine from 1854 to 1873. They are said to have made five hundred bushels every twenty-four hours. About the beginning [of] 1873 they thought the brine could be transported easier than the fuel, so they started to build a larger and newer plant nearer the coal mine. The work of construction was started but hard times, caused by the panic of 1873, came on and work stopped. Salt became cheaper when the crisis passed over and they never finished the new plant. (source)


resource list:


artifacts:

examples of sea salt


follow ups:

it would be fun to

Explore the Water Cycle!
Water Cycle Mat from Waseca Biomes

Design a Science Experiment!
The Curious Kid's Science Book by Asia Citro

Asia's book is the best for Science Experiments because she has them create their own instead of just replicating an experiment design she has provided.

We have done this in the past to explore questions about evaporation (dishes of water with food coloring or sugar dissolved in them, left out covered or uncovered, left in places in the house of different temperatures).

Even though they know intellectually that the water will "go back up into the clouds," it's fun to watch it happen firsthand!

They are often interested in how quickly evaporation will happen, what else will evaporate up along with the water and what will be left behind (sugar? food coloring?), and if water can successfully get out of a closed container.


This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Posted by at 1 comment:

Saturday, April 11, 2026

Art History - Maurizio Cattelan

In my 2025-2026 school year plan, I decided that our April artist would be Maurizio Cattelan. (Here is the complete list of all the artists we've learned about so far.) Now on to some resources and my planning notes:


Maurizio Cattelan
1960 -


Unique in that this is the first artist that we have done by student demand! They became intrigued by his work when Comedian was in the news.


I think our plan of attack for Cattelan is to choose one piece of art to study each time and look at what its message might be (symbolism, satire).

some possibilities:

Oblomov Foundation Scholarship (1992)

Working Is a Bad Job (1993)

Love Lasts Forever (1997)

A Perfect Day (1999)

Not Afraid of Love (2000)

The Wrong Gallery (2002)

America (2016)

Comedian (2019)
the famous Sotheby’s auction was in 2024


I also think that it would lay a foundation for Maurizio Cattelan's work if we learn about Marcel Duchamp. I have resources about Duchamp in

Discovering Great Artists by MaryAnn Kohl (available at Internet Archive)

Vincent's Starry Night by Michael Bird

Encyclopedia of Artists, vol. 2


also

Maurizio Cattelan
Wikipedia page

Maurizio Cattelan: Beware of Yourself by Maurizio Cattelan
2026

Maurizio Cattelan: All by Nancy Spector
2016

So, a Banana Walks into an Art Fair
frieze.com

Maurizio Cattelan: Houdini of the Art World
"Modern Art Is Rubbish" podcast notes

Maurizio Cattelan
domusweb.it



A lot of this will take the form of us looking at the artwork during Snack and having a discussion about what we think the artist is trying to say.

I've yet to figure out any art inspired by him that we can make on our own!


week of Apr 13:

Mon

    read "The Bremen Town-Musicians" from Favourite Grimm's Tales illustrated by Anastasiya Archipova (p.143)

    act out story with our collection of wooden figures:
    tree, house, donkey, dog, cat, rooster, robber, dining room table!

    look at and discuss Love Lasts Forever (1997)

    use this to kick off our new Philosophy topic, Love


    RNS - Why is this piece called Love Lasts Forever?

    CB - They're working together to get food because they're all hungry. That's love, when it's teamwork.

    AAR - They died but they're still together. That's the forever part. They didn't split up, they stayed together in that house.

    EF - They are all friends. They all stayed in the house together; it's their home now. They are all friends. That's a kind of love. You can see it in their skeletons. They are still friends, even when they died.

    RNS - Why did he choose to have them in this position? It could have been four animal skeletons standing side by side -- donkey, dog, cat, rooster -- and it would still be referencing Bremen-Town Musicians.

    AAR - It's a tower, a strong tower.

    RNS - Have you ever seen an animal skeleton before in real life? When is a skeleton just a skeleton and when it is symbolism?


Tue

    discuss Oblomov Foundation Scholarship (1992)

    explain the cultural reference to Oblomov

    tie in with our SWI lesson on < they >


Thu


week of Apr 20:

Mon

    look at and discuss Not Afraid of Love (2000)

    tie in with our Philosophy discussion of Love


Tue


Thu

    look at and discuss The Wrong Gallery (2002)

    measure out 2 1/2 square feet with masking tape on the floor


week of Apr 27:

Mon

    learn about Marcel Duchamp and discuss his ideas

    read #54 "Spinning a Story: Marcel Duchamp"
    from Vincent's Starry Night by Michael Bird, p.249

      Rue de Bicyclette, 1913

      "Duchamp decided that the really essential thing about being an artist was having interesting ideas that make people see things differently."

      "'I'm the artist, not you,' thought Duchamp. 'I'm the one who decides what is art.'"


    read "Marcel Duchamp"
    from Encyclopedia of Artists, volume 2, p.50

      Fountain, 1917

      "He created an artwork out of ordinary materials (in this case a bicycle wheel and a stool); only the idea to do it was his own."

      "'Whether Mr Mutt with his own hands made the fountain or not has no importance,' Duchamp contended. 'He chose it.'"


Tue


Thu


This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Posted by at No comments:

Block Beeswax Crayons in Primary Colors

I was looking through the Clearance section of A Child's Dream yesterday when I spotted individual Stockmar block beeswax crayons.


Sieglinde de Francesca recommends these for children in grades 1 & 2. It can be a very interesting exercise to work only with the primaries, and have to carefully blend and layer them to get the effect you want. And far cheaper than a set of 32 crayons for $72.00!


Sigi has two books about this lovely method of drawing:


They used to be available on Amazon but she just has them in her online shop now at teachwonderment.com.

Her Fables book is my absolute favorite resource for this classic Waldorf grade 2 block!


I was looking back through my previous posts to see what I had written about working with Block Beeswax Crayons in Primary Colors. I found a post from 2012 which states that single crayons (you only need carmine red, lemon yellow, and ultramarine blue) were available for $1.50 each. So the current clearance price of $1.57 apiece is pretty inflation-busting!

And here is my 2013 post: Book Review - Coloring with Block Crayons. (Naturally, instead of a CD she now offers streaming videos.) I still have a few of the little pouches my students sewed!

the Stockmar color numbers are

carmine red - 01

lemon yellow - 05

ultramarine blue - 10


This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Posted by at No comments:

Friday, April 10, 2026

Our Final Philosophy Discussion of Reality

The final in our series of four chats about Reality. The first three are here:


This week I introduced the class to the philosopher René Descartes.

I started by explaining one of his major contributions to mathematics (Cartesian geometry) using the anecdote described on page 39 of Luetta and Wilbert Reimer's Mathematicians Are People, Too - vol. 2.

Complete details on this series and a list of all the mathematicians included may be found here.


We then moved on to his six meditations. I read them Mister Descartes and His Evil Genius, a picture book by Jean Paul Mongin which gives a quick overview of the series of logical deductions that Descartes goes through before reaching the conclusion that he himself is real, as is the world around him!

note: it is useful to have a piece of modeling beeswax on hand


I then wrote a quick overview of the book -- which is itself a quick overview of his writing -- up on the board so that we could discuss it. Our focus was on whether we found each stage of his thought experiment persuasive. Descartes' goal was to build up from assuming that nothing was real, and create a chain of wholly logical arguments.

* Because one of the links in his chain is God, we had to figure out how to talk about that in the classroom in a way that was respectful of all beliefs. *

If the children felt like there was a break in the chain for them, where was it and why?

His reasoning goes basically like this:

I know for sure that I have thoughts so I exist; my mind is real

my thoughts are built on things that are real; I recognize wax as wax both when it is cool and hard and also when it is warm and gooey because I have a central concept of wax which both of these thoughts connect back to

it's not my senses that I am using to tell that it is wax because it appears so different in every sense, therefore, it must be the idea of wax that I'm using

the ideas that stand as the basis of my thinking are real, and whatever created those ideas is likewise real; those ideas come from a deep, eternal, infinite and perfect source and that source is called by the name "God"

God is all things and contains all things and that includes being real

God is also love and truth and would not be tricking me as an Evil Genius

my dreams are not real; I can tell my dreams from being awake because I can use my memory to connect the past and the present; ie. when I awake from a dream I see my bedroom and my sheets and my family and the trees outside and they are the same as what was there when I fell asleep


By the way, I made a blog post that lists all the titles in this series by Plato & Co.

Now, on to our discussion!


I would like to hear some of your thoughts.

CB - I kind of don't agree with him. I think that dreams are real, that it's your imagination. I've had dreams that I'm in my bedroom and it's my same bedroom. I think that they're real because of the dreams that I've had, they are literally me in my bed watching TV and that's what I do.

EO - I agree with CB that dreams are real. Some dreams are a mix of your imagination and a memory. Or maybe a memory that you don't remember because it's from too far back but it pops up in your dream and you're like, why do I recognize that but I don't really recognize that?

AAR - My mom told me, and I believe her, that dreams are memories. Dreams are built off of the memories so something you don't remember pops up in your dream. And sometimes you dream that same dream but just slightly different. I had a dream that I had again but it's just different people.

Z - I had a dream one time that we were having a party and I just got this feeling that I just knew what was real and what wasn't. I just knew. That only happened that one night but in that moment I knew what was what. And dreams are built on actual things, I agree with you. I had a nightmare a couple days ago that I was in the laundry room, the actual laundry room, and that was scary but it was the actual place.

CB - I had a dream last week that I was two and I asked my mom about it that morning and she said that it actually happened.

EO - I strongly disagree with him about never having the same dream again. I know I'm a lucid dreamer so I can put it on replay or put it in my memory bank and say, I'm going to dream this again tomorrow night. I've also had the same nightmare again.


Let's look at his chain of reasoning from the very beginning. Do you agree that this is a true statement, that your mind does exist?

Z - No, your mind gives you images that sometimes are real and sometimes are not. Like if you dream that there's a unicorn in your bathroom. That isn't real. So how do you know that everything else also isn't real, like the sofa or the handwork baskets. We are fiction, and there is somebody else who is real and they tell our stories around campfires. And we are the fiction. And then we think that they are the fiction. Gnomes would tell our stories as giant stories but we would tell their stories as fae folk.

AAR - I do agree about that one but I don't agree on the God thing. We have no proof I feel. How is he real? How is he controlling? He could be your mind tricking you. How do we know he's real? We never have seen him before. We are the cause of our ideas. Our brain is the cause of our ideas.


How far along the chain do you go? Does he persuade you all the way to the end?

CB - If there's no Jesus and no God, then what's church?


Descartes is saying that "God" is the word that we use to refer to mysterious and infinite and eternal. You don't have to believe in God or not believe in God to be part of the thought experiment. He's playing a game. Are we here? How do you know we are here?

CB - We are living and breathing.

EO - I don't want to offend anybody who does believe in God.


I think when people get offended, it's when someone is saying "you are wrong; don't believe that." But if you say, "in my mind, this is how I think about it," then I don't think that would offend anyone.

EO - Okay. On the chain, I think that I believe in the "memory past to present" and "in my mind, I exist" but not "cause of ideas, God." How I think about it is that somebody hundreds of years ago thought of God and then sprouted a religion. That's where the chain would break with me.

AAR - He didn't persuade me about the God thing, it's your mind. And then "perfect" [in the chain] would be erased for me because nobody's perfect; "infinity," I'm not 100% sure about that; "love and truth"...


Love and truth, are they real?

AAR - YES. And shapes and textures are real but not colors. That color of the floor is just the color your eyes are letting in. So actually everything is every color. Scientifically. I believe that because there's a video that my mom watched. Why are the prime colors different on computers and paints?


Are you real? [to the people who haven't spoken yet]

EF - I consider yes, because it goes back to our first discussion. How do you know if it's real? I can see EO right now. I can feel her. If she talks I can hear her. So that confirms to me that she's real.

LL - I don't know. I hear things a lot. That aren't actually there. My mind is real but not always the things that it tells me.


Explain the difference between a thought that isn't real and your mind not being real.

LL - Even a false thought is proof that you have a mind. Because you can think so it must be there.



EF bringing things back to our very first discussion, "The Velveteen Rabbit," reminded me that I had wanted to tell the children that I think the Velveteen Rabbit was real the whole time... because he is the only one who asks the Skin Horse about being real. Only someone who is real would have quesions about being real. That's my response to "The Velveteen Rabbit" and to Descartes! I remember when I was a little girl and my rabbit died. I asked my father if rabbits have a soul. He told me that only creatures that have a soul wonder if they have a soul. Asking the question is itself the proof.


The children have requested that we do Love as our next Philosophy topic!


This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Posted by at No comments:

Thursday, April 9, 2026

Local Industry - Shell Buttons

Our first Local Industry for Southern Illinois!


timing:

    Beginning in 1891, mussels were harvested to manufacture shell buttons for clothing. (source)

    The last independent buttonworks in the U.S., the Wilbur E. Boyd Factory at Meredosia on the Illinois River, closed in 1948. (source)


resource list:


order the poster here!


a lovely quote from Minn of the Mississippi by Holling Clancy Holling

    "Minn walked sometimes on a clay-sandy bottom paved with punched-out, lace-holed shells...." (p.34)


artifacts:

buttons made of natural materials (shell, wood, horn)

and an example of buttons sewn on a card


follow ups:

it would be fun to

Play the Button Game!

Sew a Button Tree!


This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Posted by at No comments:

Special Things I Never Want To Do Again!

A few things stand out to me as being wonderful, special, lovely, fantastic, and VERY elaborate... and I never want to do them with a class again!!!

Homemade Pasta


Cardboard Boat Regatta

Posted by at No comments:
Subscribe to: Comments (Atom)