Mid-Year Update: Math

In math, Gemma is almost done with Life of Fred: Fractions. There are 32 chapters and the final “Bridge,” and Gemma’s on Chapter 30. After she finishes LOF: Fractions, we’ll start LOF: Decimals.

We’re also both loving the game Prodigy. The online game is free and so much fun. For homeschooling parents, I recommend creating a Teacher Account by going to https://infl.tv/eCpl

You can set up a classroom with one or more students. If you have multiple children, I would set up a classroom for each of them, because the game asks for your class’s grade level. So, if you have a 4th grader and a 2nd grader, you can set up a 4th grade classroom and a 2nd grade classroom. (I also recommend creating your own account because playing in the same “world” and helping each other on quests and in battles is a fun way to bond. A really fun way.)

The game starts with the player customizing his or her avatar. You choose a hair style, hair color, eye color, and skin color. Then you choose a first name for your math wizard. As you battle creatures, you’re actually completing the game’s diagnostic test, which determines what grade level you’re working at. While this is going on, you get to choose math wizard last name - something high fantasy and multisyllabic (Gemma’s last name is Rivermaster, and mine is Windlemon), and a pet (I got a baby dragon named Dragic, and Gemma got a Peeko).

After you finish the Placement Test, the game will assign you math skills at your grade level. So, if you’re a 6th grader who placed in 4th grade, the game assigns you 4th grade skills, but if you’re a 2nd grader who placed in 5th grade, the game assigns you 5th grade skills. And the wonderful thing about having a teacher account is that you can see where your child placed and what skills he or she is working on. Even better, you can assign specific skill by creating a quiz. For example, tonight, I wanted Gemma to work on multiplying fractions to reinforce what she learned in LOF, so I assigned that skill. The student doesn’t get a message telling them that the teacher assigned them a quiz; they just keep having battles and going on quests, and as they play the game, they complete the assigned problems. It’s brilliant.

If you have any questions about homeschooling math with Prodigy, let me know. 😊

Three-Digit Number Scavenger Hunt

Here is a fun way I taught my daughter to read three-digit numbers...

Sunday, on our walk home after church, we went on a three-digit scavenger hunt.

Prior to this, she knew how to read two-digit numbers. On our hunt, I introduced the concept of place value, and she quickly got the hang of it.

We took turns spotting three-digit numbers, and then I would ask my daughter what digit was in the hundreds place, what digit was in the tens place, and what digit was in the ones place.

Next, I told her to cover up the first digit (the digit in the hundreds place). For example, in the above photo, she covered the 1 in 132. Then, I asked what number she had. She said, "Thirty-two." Finally, I told her to uncover the digit in the hundreds place and say the digit followed by "hundred."

We did this at every three-digit number we encountered for a mile. By the time we got home, she was a pro! I'm looking forward to trying this again with four-digit numbers. :)

Counting On: Adding Sums That Total Numbers Greater Than 10

Today we worked on "counting on." My daughter is working in Mathematical Reasoning Level B, a math book we both love. She has to solve the problems, but since she can't write yet, I write for her. Today she was adamant about doing the connect-the-dot portion of the lesson herself. (For fine motor practice, I've found that she really likes things like dot-to-dots and mazes, and we've recently started using Grapevine Traceables.)

She's already had quite a bit of experience adding and subtracting on number lines, and since we've now reached adding sums greater than 10, I figured it was time to teach her how to count on.

I explained that the first number was the SAYING number and the second number was the COUNTING number. (This made sense to her. When teaching her to add on a number line, I called the first number the BIG JUMP number and the second number was the TINY HOPS number. Whatever works.)

For example, for 7+4, the first number (the SAYING number) is 7, so she would say "seven" out loud. The second number (the COUNTING number) is 4, so she would hold up 4 fingers and count on (out loud) from 7. "Eight, nine, ten, eleven."

I like her thinking out loud because it helps me understand her thinking process. In an earlier post, I explained how this works with spelling too.

Right now, my daughter uses her fingers (or other counters) to do addition and subtraction. But there are some sums and differences that she has memorized because of repeated exposure, and over time, she will memorize more. She's also started to notice that certain numbers of counters can be divided into equal groups, and makes observations like, "Mommy, three groups of four makes twelve."

Math is fun. :)

Math with Rooster's Off To See the World

Earlier this week, I used the book Rooster's Off to See the World (Eric Carle) to introduce the concepts of addition and subtraction to our home(pre)school co-op.

This book is simple and predictable, and was perfect for our three and four year olds. The story is about a rooster who decides to go off and see the world. Along the way he "adds" 2 cats, 3 frogs, 4 turtles, and 5 fish to his entourage. I had the children stack Unifix cubes to represent animals.

• 1 rooster + 2 cats = 3 animals off to see the world
• 3 animals + 3 frogs = 6 animals off to see the world
• 6 animals + 4 turtles = 10 animals off to see the world
• 10 animals + 5 fish = 15 animals off to see the world

But then the animals realize that rooster hasn't planned the trip very well, and they "subtract" themselves from the group.

• 15 animals - 5 fish = 10 animals
• 10 animals - 4 turtles = 6 animals
• 6 animals - 3 frogs = 3 animals
• 3 animals - 2 cats = 1 rooster

The preschoolers enjoyed acting out the story with the Unifix cubes. Manipulatives aren't just for math!

What are your favorite math storybooks?

How to Add and Subtract on a Number Line

I've been using Mathematical Reasoning (Level B/1st grade) with my preschooler. (I LOVE Mathematical Reasoning. Best math books ever! We used half of Beginner 1, all of Level A, and are now using Level B.)

Mathematical Reasoning teaches children how to add and subtract using a number line. This is also something my public school fourth graders need to be able to do to meet Common Core standards, except instead of whole numbers, my fourth graders are adding and subtracting fractions.

The problem? When I surveyed my class, half said they'd never explicitly been taught how to use a number line. So, I taught my students how to use a number line the way I taught my daughter to use a number line...

Put your pencil on zero. That's the "starting line."

Make a BIG JUMP to the first number. (For example, in 4 + 3, the BIG JUMP is from 0 to 4.)

Next, make TINY HOPS (to the right for addition, or to the left for subtraction). (In the example 4 + 3, from the number 4, you make 3 TINY HOPS to the right.)

The number you land on is your answer. (In the above example, you land on 7.)

...BIG JUMP & TINY HOPS. That's all there is to it. (You can even do this on the sidewalk with sidewalk chalk and make it like hopscotch for your kinesthic learners.)

The half of my class that hadn't known how to use a number line smiled and made comments like, "Oh, now I get it!"

Here is yet another problem with Common Core: We roll out new standards, with the "expectation" that students in all grades will be able to meet those standards with the teaching they receive that school year.

But let's talk Charlotte Mason for a minute... Let's say you hadn't been a CMer with your child for grades 1 through 3, and then, in year 4, you made the switch. You had never taught your child to narrate, and - all of a sudden - you ask your child to narrate. Would your brand-new-at-narrating student narrate with the ease of a child who had been practicing this skill for three years? Or would your student find it difficult to organize their thoughts and give you more than a one sentence answer to "Tell me about the story."

I'll tell you that, from my own experience, it's work to teach fourth graders who aren't accustomed to narration how to narrate. Public school students are horribly used to being asked questions with single sentence answers, or being told how many sentences a paragraph must have, or being told what page they will find the answer to the question, or being given the answer "Yes" when asked "Is my work/answer good enough?"

We cannot expect students who do not have a foundation in New Program X to be successful in New Program X. It would be less unfair to start New Program X with a group of kindergarteners, and the next year have the first graders continue New Program X, and the year after that have the second graders continue, etc.

But to anyone just reading this because they were never taught to add or subtract using a number line - I wasn't - and is just curious as to an easy, fun way to teach it, I give you BIG JUMP & TINY HOPS. Happy hopping.

Make a Splash 120 Mat Floor Game

This game, from Learning Resources, has inflatable dice. The way we were playing, my daughter rolled the blue dice and found her number on the mat. In the picture above, she rolled 4 and 3 and then put the t-shaped frame on the mat with the number 43 in the center of the frame. Then she rolled the orange die. The orange die has -10 (look at the square above your number), +10 (look at the number below your number), +1 (look right), and -1 (look left).

Other info:

• You have to inflate the dice each time you play (if you want to pack everything back in the box). 
• Re-folding the mat reminded me of folding a road map - at which I am so completely terrible. I have an irrational fear of road-map-folding. I did figure it out. I didn't enjoy it. 
• If a die gets a hole, the box includes a tiny adhesive piece to patch it up.
• Static: every little speck clings to the mat. Vacuum the floor before playing.

That said, my daughter loved this.

Change a Mixed Number into an Improper Fraction

Here is a math hack I learned a few years ago from Danica McKellar's book Math Doesn't Suck:

In the textbook my school uses, improper fractions and mixed numbers are covered in one lesson. Students are expected to be able to change a mixed number into an improper fraction, and an improper fraction into a mixed number. These are separate skills. You use different processes. I like to start with changing a mixed number into an improper fraction. Here is how I teach it...

I start with MAdd Face.

MAdd stands for Multiply then Add. The x and the + are eyes. See the frown?

Here is this lesson's banner problem (a.k.a. the example problem).

First, I write the mixed number. Second, I draw MAdd Face sideways, in between the whole number (2) and the fraction (1/4).

Next, I'll multiply 4 x 2 (multiply the denominator by the whole number). That gives me 8. I'll take that 8 and add 1 (the numerator). That gives me 9, my new numerator. The denominator stays the same (4). Finally, I have my answer: 9/4.

Here it is again, with pictures...

Fractions in Simplest Form

Do your math backwards: A math hack for teaching fractions.

Here's how I taught today's math lesson...

First of all, I hate the way Fractions in Simplest Form is presented in the math textbook my school uses (Envision for 4th grade). Here's why: the banner problem (a.k.a. the example) is reduce 4/12 to simplest form. The banner problem tells students that because 4 and 12 are even you can divide both the numerator and denominator by 2, get 2/6, then divide 2/6 by 2 again.

If students aren't ready to learn how to find all the factors of a number so they can then find the greatest common factor, we shouldn't be teaching this concept yet. We should teach student how to reduce fractions to their simplest forms when students are ready to find the GCF.

Instead of teaching students the book's way, I reviewed the meanings of Factor, Product, and Greatest Common Factor. Then I reviewed how to find the factors of a number. I say "reviewed" because I've informally showed them this before, just for fun, for students who were ready for the concept. Then we found the factors of 24 (I like 24 as an example). But then-

And this was the part of the lesson that got me really excited. It was so simple, but I had never done it this way. I hadn't been taught to do it this way, and I haven't seen other teachers explicitly teach it this way (I'm sure some must!).

I had students fold their papers hot dog (lengthwise). I explained that the problems would go in the right column, but the factors (the show-your-work part) would go in the left column.

Doing it this way is backwards to the way students instinctively go about writing math problems. We write left to right, but I told them to write on the right and then the left. Backwards.

We did the first problem together and the students oohed and said  how it made so much sense.

Stuff making sense. Little victories. Yay!

Where We Are In Math

My 3 1/2 year old LOVES math. Part of me wishes she loved dollies and pretend food more, but nope. She wants to do math. I had hoped to follow a Charlotte Mason schedule in terms of when we started "schooling" (as in, not for another 2 1/2 years), but my daughter had different plans.

When I read the PNEU programmes, I was attracted to the way Mason believed math should be taught. It was gentle. It was hands-on. The sequence was logical (the PNEU programmes list Pendlebury Arithmetic: addition, subtraction, multiplication, simple division...). Little ones learned to add using beans and dominoes. Multiplication facts were learned using money (9 x 7 = 63, and one way to make 63 cents would be with 2 quarters, 1 dime, and 3 pennies, etc.). There was five minutes of drill daily.

I don't believe one must purchase a math curriculum for grades K through 3. That said, I think Mathematical Reasoning is really awesome, and I've written about that here.

My daughter has completed 150 pages of the 250-page Mathematical Reasoning Level A book. For the most part, we go in order, but if she doesn't understand a certain concept, we skip it and come back to it a few days later. Here are a couple of pages from Level A...

I'm not concerned with handwriting right now. She can learn to write Year 1 when she has more fine motor strength. But right now, she's capable of counting items in a set (one-to-one correspondence), and matching sets of items to numerals.

This page was fun because we used real pennies to "buy" candy by placing one penny over each piece of candy. This activity could also be done with real candy (like M&Ms or Smarties) and pennies!

Add this to the list of reasons we're homeschooling...

My public school teaching job informs the way I parent, and being a parent informs the way I teach a class of 30.

Today after school, I sat at my desk grading math tests. My fourth graders have just completed Topic 3, which is a chapter about the meaning of multiplication and division. The chapter includes lessons on drawing bar models to illustrate a multiplication or division problem (a concept I never learned in school - as a child who did well in math classes - but had to learn as an adult because I had to teach it as part of my employer's mandated math curriculum), the rules of division (n divided by n = 1, 0 divided by n = 0 [if I have nothing, and I want to share it with others, no one gets anything], n divided by 0 = impossible [it's impossible to share if there's no one to share with], n divided by 1 = n), distributive property (a lesson I LOVE teaching, thank you Danica McKellar*), etc.

Eighty-three percent of my class scored a 3 or above. (We have a 4 point grading scale in which 3 is Proficient and 4 is Advanced.) Half of those students scored 4s. Half of those 4s were high 4s: 100%.

Eighty-three percent! I was patting myself on the back. I must have done a really good job teaching this chapter. To public school teachers, 80% success is great; it's what we shoot for. To me as a homeschooler, this number is unacceptable. I don't want my child to turn the page in the textbook just because she scored "high enough." A student who scores 12/14 (86%) could possibly be missing two problems from the same lesson, meaning he or she does not understand a concept, and this will mean trouble later.

I want my child to learn to mastery, mastery being 100%. I don't want her to worry that she hasn't completed a textbook by a certain date. I don't want her moving on because a district's pacing plan says she should.

Eighty-percent isn't good enough. Add this to the list of reasons we're homeschooling.

*I got to hear Danica McKellar speak at Harvey Mudd College a couple of years ago, and her talk was wonderful.

Review: Mathematical Reasoning (Level A)

Mathematical Reasoning Level A by Linda Brumbaugh & Doug Brumbaugh can be used with kindergarteners as either a complete curriculum OR a supplemental resource. It's published by The Critical Thinking Co. 

The book I have is aligned with the National Council of Teachers of Mathematics (NCTM) standards. Lessons are divided into five categories: Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability.

The skills taught are addition, reading bar graphs, using a calendar, capacity, coins, counting, fractions, language, length, likelihood, matching, number line, odd/even, order, pattern, real world problems (word problems), shapes, subtraction, time, weight, whole numbers.

The topics spiral throughout the book. For example, the first eleven pages of the book are organized like this:

1 page of Geometry

1 page of Algebra

5 pages of Number and Operations

3 pages of Algebra

1 page of Number and Operations

A topic is dealt with, followed by a different topic or two, and then the topic comes back up later. The idea behind this is that a child will have time to let concepts sink in "before dealing with more complex aspects of the skill/concept" (from the Introduction). Because I teach full time, my job informs the way I teach my own child (and parent her), and my experience as a parent informs how I do my public school job. As a public school 4th grade teacher who uses a curriculum that does not spiral, I see a great value in spiraling.

The authors suggest that the buyer proceed page by page through the book. However, they also say that "if your child is interested in a given topic and seems to want more, it would not be unreasonable for you to skip to the next level of that topic and do more of it." This is what we've done. My three-year-old has done 87 pages in order. But she's also bounced around the book because she saw pages that caught her eye and wanted to do them.

The Mathematical Reasoning series offers books from Level A through Level G (kindergarten through 6th grade). There is also a Beginning 1 book (for 3 year olds) and a Beginning 2 book (for 4 year olds). I bought Beginning 1 when my daughter was 2. It was as wonderful as Level A, but Beginning 1 focuses only on numbers 1 through 5, and my daughter outgrew it by 2 1/2.  (She's got a mind of her own, this one. Mommy was thinking, Oh how lovely, we're following Charlotte Mason, so I have years before I have to think about teaching you addition. Years? Try nanoseconds.) Though Beginning 1 is designed for age 3, I would recommend it for children as young as 2. I would recommend Level A for children as young as 3 and 4.

The authors also suggest that you "keep learning fun and avoid frustrating your child. Work around your child's attention span." Hello, Charlotte Mason. If your child has a three minute attention span, work for three minutes. If your child has a twenty minute attention span, work for twenty.

The authors advise finding ways to relate the skills to your child's daily life. One way we did this was with the idea of even numbers. We talked about shoes, and how a shoe has a partner. One pair of shoes has two shoes, and when all the items in a set have partners, it's an even number, so two is even. What happens if you put Mommy's shoes with your shoes? Now you have four shoes. All the shoes have partners, so four is an even number. (It's all hands-on right now.) The authors also say that if your child has difficulty with a page, come back to it later or recreate the lesson with manipulatives. I also love the suggestion of making a number line that your child can walk on. We haven't tried this yet, but I plan to soon.

The book is available for $31.99 and does not require the additional cost of a Teacher's Manual. I have not used Saxon Math, but I have relatives who have and loved it, but the Saxon Math 1 Homeschool: Complete Kit is $107.35. I really, really, truly believe you should not need a Teacher's Manual for math in kindergarten or first grade. Arithmetic just isn't that complicated. The price difference is $75 I would rather spend on things like science kits. Your child does not have to write in Mathematical Reasoning (but certainly can), as many of the activities can be done by saying the answer or pointing to the answer; this means that the book can be reused with a second child. For activities involving tracing numbers, you can practice tracing with a finger, writing numbers on a whiteboard or a separate piece of paper, writing with chalk on the sidewalk, writing with bathtub crayon in the tub, printing handwriting pages off the internet, or - if you intend to only use the book once - writing in the book.

The book is full color and inviting. It has shapes, animals, clowns, fruit, sports equipment, dominoes, happy faces, etc. To view sample pages, click here and then click the tab that says "Sample Pages."

My daughter doesn't have the fine motor skills or the desire to trace numbers, so I don't force her to do this. Being able to write and being able to compute are separate skills, just as being able to write and being able to read are separate skills. A child learns to compute and read before being able to write. Charlotte Mason knew this, and that's why children gave answers orally and narrated orally instead of writing. Just because a child is a pre-writer doesn't mean you should put off teaching ideas. (My plan - which I reserve the right to change as needed - is to teach cursive when my daughter is six, earlier if she's interested.)

When my daughter finishes Level A, I will be buying Level B.

Not an affiliate link; I just think this book is awesome.

Math and Attachment Parenting: What do these have to do with each other?

My three-year-old likes math. A lot. Like she doesn't want to stop doing pages in Mathematical Reasoning (Brumbaugh & Brumbaugh). Mommy is the one who needs a break. Mommy is the one who says, "Okay, but just one more page. Then how about some TV?"

We watch a lot of TV. Today, in the park, my daughter pointed to a squirrel and said, "Mommy, if I had squirrel powers, I could activate that squirrel. And you could activate that squirrel over there." (This is a reference to the PBS show Wild Kratts, in which the main characters wear creature suits and "activate" their creature powers to learn more about various animals.) She wanted us to be able to dart across the park and speed up trees.

But math...
 
Mathematical Reasoning Level A (for kindergarteners) is 250 pages, and my daughter has done 100 of them (80 in order, from page 1 to 80, then about 20 scattered throughout the book). Prior to Mathematical Reasoning, we used dot-to-dot pages from a Kumon workbook, as well as Unifix cubes and a hundred grid, for practice counting and one-to-one correspondence, etc.

I just kept finding really fun resources. Keep finding.

 "Of all his early studies, perhaps none is more important to the child as a means of education than that of arithmetic."

Of all his early studies. Charlotte Mason just didn't mean this early.

I know this is very un-Masony of me, teaching my child to add before she's six. But children are born persons, and my person likes math. (And reading. And science. And...)

I think what drew me to Charlotte Mason were the same things that drew me to aspects of Attachment Parenting. I liked the idea of birth bonding, that my baby, a person with whom I'd spent the past nine months in the closest proximity possible, would be right there with me, not down the hall, out of sight, away from me. Sleep training had worked great for a friend of mine, and I read books on how to do it before my child was born. But then, there she was, a person who needed to be worn in a sling, needed to co-sleep, and needed to nurse on demand. So that's what we did. As she got older, it was about "appropriate responsiveness," saying no when she wanted to do something dangerous, and saying yes when I could say yes. (For example, at age two, when she wanted to stand over an open flame and saute shrimp in hot olive oil, my answer was yes - with me right next to you.) And my friend Anita gave me some of the best advice early on, which was to listen to my baby because she would tell me what she needed.

But math...

Right now she's telling me she needs numbers, shapes, and patterns.

Sometimes I think about the pace she's going, and if this continues, how she'll be finished with this book before she turns 4 (in seven months) and on to Level B (1st grade). I think about how I was in 1st grade the year I was ages 4/5. I think, okay, maybe this makes sense. Maybe this is what she needs. But I also think, Yikes, keeping up with you takes some doing.

If only I had squirrel power...

Review of "Lollipop Logic"

Lollipop Logic (Book 1) by Bonnie Risby and Robert K. Risby II is designed for use with children in grades K through 2. It features 52 lessons, each a single page, reproducible and easy-to-use.

The book includes activities in seven categories: 1)Sequences, 2)Relationships, 3)Analogies, 4)Deduction, 5)Pattern Decoding, 6)Inference, and 7)Criteria Analysis.

There are 8 "Sequences" activities. These activities ask the child to put a set of pictures in order. (The book is designed for pre-readers.) For example, the third lesson asks student to order 6 pictures of a pear tree and a basket of pears. The correct order for this lesson is 6 pears on the tree and 0 in the basket, 4 pears on the tree and 2 in the basket, 3 pears on the tree and 3 in the basket, and so on. At first, my three-year-old thought the tree with one pear came first, because she has learned to count 1, 2, 3... But then I told her a story about a person who went out with his empty basket to pick pears off his pear tree, and she was able to figure out the correct sequence after the prompt. (I had to remind myself that she wasn't taking an I.Q. test, she was learning to use logic.)

"Relationships" has 8 activities. Four of the activities ask students to find a picture in a set of four pictures that has something in common with an item. The next four activities ask students to find things that do not belong in a group of similar items (sports equipment, musical instruments, tools, round things). Examples: Find something that has something in common with a shoe (eye, foot, tire). Find something that has something in common with a cube (baseball, conical party hat, cube-shaped gift box). Find something that has something in common with a birthday cake (birthday party hat, book, pencil).

In the section on "Analogies," there are 8 activities. Again, because this book is for pre-readers, all analogies use pictures. Examples: Big fish is to little fish as big cat is to (dog, back of cat, kitten). Dog is to bone as bunny is to (carrot, Easter egg, hamburger).

"Deduction" has 7 activities. Each Deduction activity shows 4 characters (2 boys, 2 girls) and 4 items, and asks children to figure out which item belongs with which child, using 3 clues. For example, "Snack Time" asks children to figure out which character brought which food for snack time. (One clue is "Ron and the boy with the apple sat together under a tree to eat their snacks." Based on that information, the child knows that Ron did not bring the apple, but the other boy did.)

There are 8 "Pattern Decoding" activities. Examples: Moon, moon, star, moon, moon (sun, moon, star, raincloud). Plane, boat, boat, plane, boat (train, car, boat, plane).

The "Inference" activities are like putting together puzzles. In the first four activities, children are basically asked to put the last piece in a puzzle. These activities are followed by 2 activities in which children look at puzzle pieces and must determine what the pictures are on the puzzles; each puzzle has 5 pieces. The next 2 activities ask children to decide which pictures go together (in one column there is a snowman, rainclouds, a smiling sun and smiling flowers AND in the other column there is an umbrella, a kite, and a sled.) Lastly, there are 2 activities that ask children to guess what each item is by only showing part of it, like a "close-up." (For example, a pig body with a curly tail, but the child can't see the pig's face.)

Lastly, there are 3 Criteria Analysis activities. These puzzles show silly creatures and ask children to determine which creatures fit certain criteria. For example, Oggs all have tails. Creatures that are not Oggs do not have tails. The lesson presents 6 creatures and asks which are Oggs. (The activity does not tell children that all Oggs have tails. Children must look at the Oggs and figure out what they all have in common, and what they have that the non-Oggs do not have.)

My daughter likes all of the lessons. We got the book yesterday, did about a dozen activities, stopping while she was still loving it, and tonight she begged to do more lessons. There are 3 books in this series, and I'm sure I'll be buying the other two.

Lollipop Logic is stamped with a seal that says it "Aligns with the Common Core State Standards."* As a homeschooler, I don't care. I really don't care.

As a fourth grade teacher who must teach lessons aligned with the CCSS, who just so happened to be teaching a lesson on Patterning from our district mandated math curriculum today, I wondered if Bonnie Risby had written Common Core-aligned logic books for 4th graders. She has.

*(This book was "aligned" before there was a Common Core, which is why I bought it. In other words, it didn't start out CC. Nothing changed from its original publication other than a page at the back of the book that lists what standards it meets. In case you're curious - let's pretend you are - it meets kindergarten and 1st grade standards in both math and literacy.)

(This is not a paid review. I just think this book is awesome.) 

Puzzle Math

A fun preschool/kindergarten math activity you can make yourself.

Here's what you need:
Index cards
Do-A-Dot paints
markers
scissors

I wanted to introduce addition, so I took 4 index cards and made the following facts:
3 + 0
2 + 1
1 + 2
and I meant to make 0 + 3, but - oops - I made a second 3 + 0

Charlotte Mason used dominoes. I didn't have dominoes, and I didn't want to buy dominoes, so I made something with what was on-hand. The result? My daughter loved it. Who doesn't love puzzles?

Butterflies Are Free To Fly

Last night, one of the butterflies was quite intent on mating - quite - so I decided it was time to unzip their garden.

Day 19: When I got home from work, my daughter and I went onto the patio and watched them all fly away... high away...

(In the second clip, our most hesitant butterfly unfurls his proboscis.)

For earlier caterpillar posts, check out:
Day 1
Day 2
Day 3
Day 4
Day 5
Day 10
Day 13
Day 15
Day 16
Day 17

Caterpillars Day 17

They have all hatched. We came back from a birthday party to find the fifth Painted Lady flapping her wings.

For earlier caterpillar posts, check out:
Day 1
Day 2
Day 3
Day 4
Day 5
Day 10
Day 13
Day 15
Day 16 

And, if you like butterflies, here is our trip to the Los Angeles Natural History Museum's Butterfly Pavilion.

Caterpillars Day 16

 

Three more of the chrysalides were dark this morning, and the first-born butterfly was perched on the "garden's" netting.

Late last night (still Day 15)

Up close (late last night). How cool is this?!

This morning

The red spots on the paper towel are meconium - the waste that the "Painted Ladies" produce during the pupal stage. When a butterfly emerges, it pumps the meconium through its veins into its wrinkled wings.

A FEW HOURS LATER...

 We returned from the sandcastle competition to find that three more butterflies had emerged!

For earlier caterpillar posts, check this out.

Caterpillars Day 13

The paper under the plastic lid

This is before I removed the silk

Two caterpillars were not attached to the paper.

The caterpillars have been chrysalides for a few days now, so I watched the instructional video - which is actually very cool - and followed the directions.  It was terrifying. You have to remove all of the silk from around the chrysalides; it's really strong and you can hear it ripping. (Here are earlier caterpillar posts.)

Caterpillars Day 10

This is one caterpillar up close.  You can see he
(or she) is in the middle of changing into a chrysalis.

For earlier caterpillar posts:
Day One
Day Two
Day Three
Day Four
Day Five

Caterpillars Day 9

We returned home from visiting family to find our caterpillars pupating!  Four of them are hanging, and one is at the bottom of the cup.  When the caterpillars are done turning into chrysalides, I'm supposed to gently scoop it out with a spoon and put it on a paper towel on the floor of the butterfly habitat, and it will emerge there.

Here is a pic of our caterpillars just a few days ago.