Elementary Album Review

One of the first choices that a homeschooling parent has to make is what curriculum they will use.  These choices are informed both by state/national requirements, your family preferences, and your child’s interests, strengths, and weaknesses.  In Montessori, curricula is usually delivered in the form of topical “albums”.  If you were formally trained in Montessori, you would actually write your own albums during your training or there are some available for purchase.  I am constantly asked what albums I use because there are several choices out there and they’re all pretty pricey so people want to make the “right choice”.  Montessori albums are, by nature, somewhat complex because of the integrated nature of the curriculum; a topic like biomes may be covered in science, geography, botany, zoology, history, and cultural curriculum.    So, just a last disclaimer that I don’t think it’s “easy” to produce albums, I empathize with everyone who’s ever attempted this and I’m so grateful for what’s available to us as homeschoolers without formal training.

 

As with anything, album choice is personal preference but in this blog, I’ll share my personal experience and what’s worked for us.  I’ll present the options and rate them on aspects that are important to me.  I hope other bloggers will chime in with their opinions too, I have seen many, many people who LOVE albums that I don’t care for.  In fact, here’s my favorite blogger’s opinion on this same topic: “What did we do all day” Blog.

 

Here are the albums I currently have access to:

  • Keys of the Universe – complete set
  • Cultivating Dharma – math, language, geometry (all that’s available)
  • NAMC – Math 1 & 2 (which includes geometry), language, 5 Great Lessons (and I have seen all the other Lower El albums they have available)
  • Montessori R&D – Language Arts 2 & 3 (I have seen samples of others – these are available on their website)

 

Also, there is a scope and sequence that I sometimes refer to at Montessori Compass , it is free but is not printable or customizable unless you purchase a subscription (I have not).  Although this seems maybe extraneous, a scope and sequence is actually really important; there are, for example, 6+ strands of math at any given moment and the albums are arranged topically so you have to jump around to present things in an appropriate order and to know when the stopping point is for each topic at each approximate age.  No matter which albums you choose, I highly recommend that you acquire and review a scope and sequence regularly.

 

Keys of the Universe

  • Keys Albums
  • Price: $240 for complete set of albums ages 6-12 + $120 for online support
  • Printables Included: Yes, if you buy the online support, a large library of printables for almost all albums including cosmic timelines, grammar boxes, etc. that can be very pricey to buy
  • Organization: Can be a little difficult to follow and find every topic, table of contents not always up-to-date
  • Scripted: Very little scripted though sometimes key phrases are listed to remind the child of prior work
  • Scope/Sequence available: Yes, in the online support forum, provided in multiple formats in Excel documents (by topic, by suggested age, etc).  Can be a little hard to follow but the only album that provides this.
  • Support available: In theory but not recently
  • Physical album available: Not unless you print it yourself

Keys is the most affordable way to buy an entire set of albums for ages 6-12.  They are also the only album with any support available in the form of a forum/Q&A from the writer of the albums.  Unfortunately, the writer Jessica is not currently available (she may be back in Aug 2019) so this really limits the support available.  Prior to her leaving (just as I was starting to homeschool elementary), I found her to be responsive and helpful in her forum and on Facebook.  I think her absence is a real blow to this curriculum because often once she provided an answer, I was able to proceed.

 

Keys is a popular album but I find it can be a little hard to follow sometimes.  I prefer the presentation layouts in Cultivating Dharma and some of the scripting I see in other albums.  I often have to read the presentations in Keys several times before I know what to do; my brain just must work differently than the writer’s does.  I also find that the organization can be hard to follow and it takes me a while to find things.  Does include some pictures/drawings to illustrate concepts.

 

Keys is also one of the few albums with printables included particularly of the timeline material.   The quality of the printables can be quite low, I found the timeline images to be relatively low quality and there was not a finished picture or an order of the images so I was not able to put it together (this has since changed as someone posted pictures to the forum but the pictures are still lower quality).  The timeline images are basically hand drawings and in the age when many bloggers have high quality printables available, I didn’t get great value out of these printables.  The written printables for grammar/language are fine since these are typed pages.  Keys is also the only album to include videos (on the online forum); they aren’t the best lighting/quality but sometimes it’s helpful to see the presentation.

 

I mainly use these albums for math/geometry/some geography and the detailed scope and sequence that I can manipulate in Excel to create a scope/sequence that tracks what my daughter has completed presentation by presentation.

 

Cultivating Dharma

  • Cultivating Dharma Albums
  • Price: Free, but only math, language, geometry available (covers ages 6-12)
  • Printables Included: No
  • Organization: Relatively easy to follow
  • Scripted: Very little scripted though sometimes key phrases are listed to remind the child of prior work
  • Scope/Sequence available: No
  • Support available: No
  • Physical album available: Not unless you print it yourself

This is an incomplete set of albums available for free.  For the subjects available, it’s one of my favorite albums (particularly geometry).  I find the presentations easy to follow and clear.  It has good pictures for many concepts and I find the examples very helpful.  Given that this is an incomplete set of albums, it cannot be your only albums but I really, really like these.

 

NAMC

  • Lower Elementary Manuals
  • Price: $1,825 for the full package of lower elementary (14 manuals, DVD videos, printables); less for a smaller package.  I’ve heard rumors of a homeschool discount but I have no official confirmation of that.  Can also buy them a la carte for $149 each.
  • Printables Included: Yes, for a fee ($250 a la carte)
  • Organization: Topically organized, good table of contents, good theory notes/additional points beside some topics (teacher education)
  • Scripted: Almost nothing scripted
  • Scope/Sequence available: No
  • Support available: No
  • Physical album available: Yes, in large binders in full color

This set of albums seems to be the most “controversial” amongst Montessori homeschoolers; people either love it or hate it.  I personally think it’s extremely, extremely pricey at $1,800+ for lower elementary only (traditionally ages 6-9).  This means you’d have to buy a second set of albums for upper elementary (9-12).

 

I admit, I want to love this option because it comes in full color manuals and they’re really pretty.  The presentations are step-by-step though they’re not scripted.  They tell you what to do but not what to say.  This can be helpful for parents who want every single step written out.  There are also suggestions for “extensions” on materials to deal with special cases (e.g. a zero in a multiplication problem).

 

The printables for math/language are mostly “worksheet” style which can be good for checking understanding at the end (that’s how I use the math ones) but not necessarily for introducing concepts.  They do include some printables to DIY things but I don’t think many of them would actually work in practice (for example, the checkerboard printable is a single page when the real thing is 2 ft x 3 ft).  There are also no printable timelines at least in the version I have.  There are no grammar box/sentence analysis materials included in my printables for language so you’ll have to buy those materials as well.

 

My real issue with this option though is that I don’t think it covers enough in Lower Elementary to be truly “Lower Elementary”, especially in math.  It starts with materials that are often used in primary (addition/subtraction strip boards) which is totally fine as many children may need to start with those but it simply doesn’t cover enough ground.  The Lower Elementary set doesn’t cover stamp game (intermediate step between golden beads and other materials), divisibility, any squaring/cubing prerequisites and only partially covers some topics.  An example is long division with the racks and tubes, the first 4 presentations (no abstraction/recording) are in the lower elementary album but the final 4 presentations are in the Upper Elementary album.  Thus, if you have a child of 7 who is capable/desires to continue on to abstraction, you run out of presentations!  This may not be a problem for every family, check out the complete tables of contents for each album on their website to reference the presentations you’ll need.

 

This set of albums would also exhaust my entire homeschooling budget but since it still assumes you own many of the Montessori classroom materials, you’d still need to spend more to acquire them all.  Still, it’s a good solution for those who want a full set of albums and don’t mind the price.

 

Montessori R&D (“MRD”)

  • Elementary Albums
  • Price: $1,000 for the full package of elementary but they are available a la carte for $20-$50; also available online for slightly cheaper at Montessori Parent (with limitations on how many devices you can use them on).
  • Printables Included: No but you can DIY
  • Organization: Topically well organized
  • Scripted: Completely scripted
  • Scope/Sequence available: No
  • Support available: No
  • Physical album available: Yes, in bound books and the company worked with me on media mail shipping to save on shipping costs.

The MRD albums are very nicely scripted.  The scripting includes references to prior lessons (e.g. “remember when we learned about compound words, suffixes also contain a root word”).  I really like the clear layout and tables of contents available on their website and their samples are very reflective of the material covered.

 

I also really like that they come in small albums at an affordable price so you only pay for what you need.  For example, I had already DIYed grammar work from a prior source so I didn’t have to pay for their Language 1 album.

 

Another feature I really like is that some of the materials contain enough information that you could DIY some of the work yourself even though it doesn’t come as a “printable”.  For example, their language album covering word study (Language 3) includes all the “suffix sets” required for a study of suffixes.  The language album covering sentence analysis (Language 2) includes pages of example sentences that you could easily type up yourself or write on a white board.  So although it’s not “printable”, it does feel like you have enough material that you wouldn’t have to purchase more materials in order to provide a full sequence of lessons.

 

My only dislike with the language albums so far is that Language 2 seems very, very redundant.  The first 40-50 pages of lessons are very similar.  Since I have some other albums, this doesn’t seem necessary to me but that’s because I have other albums to compare.  Also, Language 2 doesn’t appear to cover any advanced sentence analysis (adverbial clauses) and from what I can tell from their TOC on their other language albums, I’m not sure it’s every covered.  By that point, I don’t think I’ll need an album (or I’ll consult another one) but it would be a downside if I didn’t have the free ones from Cultivating Dharma to consult.

 

My ability to assess their math albums is limited but from their samples, I can see similar scripting and a really thorough coverage of the material.  I did ask for a sample lesson I was specifically interested in via email and they provided it promptly.  I also know that their botany/physical geography manuals include the charts printed in color (I have friends who have these manuals) so you may not have to purchase a full set of charts to use those materials.  I am planning to purchase the physical geography manual this summer.

 

So What Do I Do?

Short answer: Bounce around like a crazy person and find the presentation I like.

Longer answer: I use MRD for sentence analysis/word study, Cultivating Dharma for Math/Geometry also consulting Keys for Math/Geometry.  I use Keys for some cosmic/history/science but have also gone to other curricula because I need something easier to follow.  Going forward, I have plans to purchase a few more MRD albums and then I’m probably good on albums.  I’m also interested to see how Keys changes when Jessica returns.

 

I think if I were starting over today, I’d consult Cultivating Dharma to see where I should start my child in math/language and then use those plus MRD albums.  Because we are somewhat eclectic in our Montessori journey (using other science/history curricula), I probably didn’t need to buy an entire set from Keys because we just don’t use the printables or the albums beyond math/language/geometry; that being said, the scope/sequence from Keys is hugely helpful and I might be lost without it.  It’s almost like, I needed a combination of albums to “find my way”.

 

Disclaimer: This is an honest review and represents only my opinion based on my family’s experience; every family will be different.  I have not been compensated in any way or received any free albums, everything I reviewed was purchased by me.  I have represented each option to the best of my knowledge but as listed above, I do not have access to every single resource offered by each company.

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Feb 2019 TPT Sale: Our Favorite Sellers

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Teachers pay teachers is having their quarterly sale with discounts in the 20-40% range.  Not only that but some of my favorite sellers are matching/beating the sale on their own websites (where TPT doesn’t take a cut).  Sale ends at 11:59 PM (so midnight) Eastern Time on Feb 27th, 2019.  Use code TICKTOCK for the discounts (25+% off)

 

Math

I particularly like TPT for math task cards since you can adapt almost any word problem to using the Montessori materials.  And then there are the Montessori-specific sellers:

  • Montessori Kiwi (25+% off)
    • We love the number bonds worksheets shown above, the hundred board task cards, etc.  If you want a review of how we use a lot of these materials as “transitional” from primary to elementary, you can read my blog post here: Learning Math Facts: Addition and Subtraction
    • For my oldest, I started this year (her elementary 2 year) with a review of place value using these materials: Advanced Place Value Cards
  • Rachel Lynette TPT sale (25% off)
    • We have her 3-4 grade and 4-5 grade task cards bundle.  I like that this resource is more analogous to what my daughter might experience on our state-mandated tests so it provides exposure
    • Topics covered include factoring, divisibility, operations with fractions, etc.
  • Montessori Math Command Cards (Gr 1-3)
    • Shown above with blue outline
    • These cards use a lot of Montessori materials (stamp game, golden beads, etc).  They are not our “go to” right now because she’s beyond some of these materials but I’ll be breaking them back out in the fall for D.
  • Divisibility Bundle
    • This bundle was absolutely EXCELLENT for working though the mastery of divisibility.  Divisibility isn’t the most flashy topic but I thought the creator did a great job of really making this resource fun and varied

 

I have these on my wish list for additional number sense work: Number Talks – Grade 4 (Full Year Curriculum)  . In case you want to read about my obsession interest with number fluency and number sense, I wrote an entire post here: Number sense & Montessori

 

Geometry

We love these angle measurement cards which get the child using their protractor: Angle Measurement Cards

And these are on my wish list (50% off) for more advanced geometry task cards: Geometry Task Cards Bundle

 

Science:

I don’t use a ton of science printables but we have really enjoyed these Science Anchor Charts . They provide good information but stick very much to what an elementary student might need to learn about science topics (energy, food chains, ecosystems, water cycle, etc).  I have found them easy to adapt and a nice reference.  They also come in black and white so a younger child could use as a coloring sheet.

 

Cosmic:

If you’re planning on teaching the Great Lessons next year (here’s my entire series on that: Great Lessons), there are several resources you could consider stocking up on now:

  • Grooving Through the Grades has 3 Part Cards that match the Prehistoric Toobs:
  • Montessori Kiwi (25+% off)
    • Too many to link specifically.  Materials on Clock of Eras, each Era (Mesozoic, Cenozoic, etc.), etc.  There are also PowerPoints and scripts to help you get started writing your own stories.  I won the Great Lesson giveaway from this store in the fall and it was very helpful to me especially in Great Lessons 4/5.

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My items on sale (20-30% off):

I don’t make many printables; I usually just upload them when someone asks me where I got them so my offerings are way less fancy than many but I am participating in the sale as an FYI:

DIY Equivalency Cabinet

As a homeschooler, I try to make thoughtful decisions about what materials to buy and what to try and make myself.  This decision is different for every situation and includes considerations of budget, space, the number of children, and the children’s interests, to name just a few.

 

One of the important materials in the Montessori geometry curriculum is called the Equivalency Cabinet (also called the Iron Materials).  This includes equivalency materials and the Pythagoras plates.  These materials are typically made of metal and they are simply gorgeous:

Equiv Figure

 

But as you can see, that’s only the material, doesn’t include the Pythagoras plates for that price OR the cabinet it comes in.  Together, they can cost between $400-$1,000.  For me and many (all?) homeschoolers, that’s simply not feasible.  I also particularly struggled with the fact that I learned geometry mostly abstractly in 10th grade (non-Montessori) so I figured that I could always teach my children a more standard geometry curriculum.

 

Being the crazy person researcher that I am though, I did hunt for alternatives.  The usual DIY blogs and sources turned up nothing that anyone made on their own except for a handful of people with very sophisticated computer-aided wood carving machines.  Finally though, I did find this printable version (note that the Pythagoras “plates” actually come in their fraction bundle): Making Montessori Ours Printable Equivalence file

 

I wanted to find a way to make these more manipulative than printed paper so I began thinking about how to approach this.  First, I had the materials printed on glossy cardstock legal size (larger than a standard sheet of paper) – total cost $19:

This treatment made them thicker and larger which helps with durability and sensorial impact.  Please note that each “plate” comes with 3 pictures: a picture of the cabinet “tray” (don’t need to print), inset plate (print), and pieces that go into the insets (print).

 

Then over a series of evenings, I cut out each of the insets and matched them into their plates.  Then, using Modge Podge (could also use glue) and red push pins I created “knobs” by applying the Modge Podge to the base of the push pin and then pushing it into the inset while it was aligned in its plate.  It was extremely simple to do this as I pushed them all into styrofoam.  After each piece dried, I separated the pieces from the plate.  I’m storing the plates flat and the pieces all on styrofoam.

I tested it to see how “strong” it was.  Also the Modge Podge dries clear so you don’t have to worry about wiping it off too perfectly.

 

In terms of the styrofoam, I used the thin styrofoam from my Pin It Maps or you can get it from a craft store.  If you buy from Pin It Maps, it’s about $10 to get their nice foam shipped to you in the US (under the replacement tabs); it doesn’t seem to “shed” styrofoam as much as the craft store version does.  I’m storing them directly on the styrofoam mat as well when they’re not in use.

 

My foam took a beating from an overexcited 2 year old but it works great for this purpose!

 

So how did it turn out?  GREAT!  We were able to get the sensorial experience of the pieces matching/fitting together and it was definitely far more affordable.  It’s fine for 1-2 children at a time but obviously it’s not going to stand up to 35 children at a time.  I’m very encouraged though because of course pieces are easily “replaced” just by printing them again.  I hope this helps someone!  It’s not the most common thing to DIY but it can really save you a lot of time and $$.  Oh and if for some reason your pieces needing “re-gluing”, I’m sure superglue or similar would also work but I just didn’t have any at the time.

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Oh and how did we do the Pythagorean theorem part of it?  So the Pythagorean theorem plates show how two types of right-angled triangles (isosceles or scalene) both follow the Pythagorean Theorem.  You can prove the scalene one with Legos (legs are 6 and 8 legos long, hypotenuse is 10) which works great and delighted her.  After I showed her the triangle, she built out the squares and showed how they could overlap the square formed by the hypotenuse:

This does not work for isosceles (or I couldn’t make it work) because I couldn’t figure out what length to make the two legs to make the square of the hypotenuse an even number.  So what we did instead is to create them in card stock and prove it that way.  This isn’t a concept she’s meant to totally understand right now but the sensorial experience will stick with her when she encounters that proof again.

I cannot take credit for this idea,  it’s widely available online but it worked well so I’m happy to share it with you.

Learning Math Facts: Addition and Subtraction

One of the things that I found very stressful initially was how to teach math facts to my daughter.  The nice thing about Montessori is that it does not force full memorization before moving on to different math activities (the children either partner up with someone who does know the facts or use a chart of facts) but this is still an important skill.  C (age 7) has now learned almost all her math facts but D (age 5.5) is just starting so I’m going back to the approaches that worked for us the first time around two years ago.

 

The traditional way to learn math facts in Montessori is to fill out a variety of tables using an equation box.  The child selects an equation from the box and using tiles or paper fills in the equation table which they then check against a classroom table.  There are several steps in this process that you can see here: Using an Addition Chart .  Long story short, it did not work for us.  My daughter completed each chart exactly once and then was wholly uninterested in repeating the work enough times to actually memorize anything.

 

So, I got to research other ways to teach math facts and came across the idea of number bonds or fact families.  Number bonds emphasize the idea that addition and subtraction are related (and multiplication/division) so that “fact families” can be learned as followed:

For the numbers 2 and 4, this is the fact family:

  • 2 + 4 = 6
  • 4 + 2 = 6
  • 6 – 2 = 4
  • 6 – 4 = 2

Once the child is taught how the numbers in a fact family will relate, the can easily learn (or reason out) their math facts.

 

So I set out teaching my oldest number bonds to 10 when she was 5:

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She looks so little (2016)!  (Wooden disks = 0)

You can see that we simply used cuisenaire rods and wooden numbers.  It was easy to start and I used what I had.  Number bonds are often shown as a 3 circles in a relationship (addend, addend, sum on top) so you can see that we progressed to that.  I would write the sum and one addend and she would figure out the missing one:

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She likes to check her own work (backwards checks are hers)
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C checking her own work using an addition table (age 5.5)

 

In this way, she learned her addition/subtraction facts in concert.  A few years later and we’ve gotten more materials so you can see more Montessori incorporated into what I’m doing with D but it’s the exact same idea:

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Bead houses (number fact families)

 

And here’s our current version of number bonds:

 

I prefer these newer versions because they match our Montessori materials but they would work with any manipulative.  Here are the printables used:

  • Bead “houses”
    • I printed on colored cardstock and then used an exacto knife to cut the “slots”.  I also painted the “10 house” gold with gold colored paint.
  • Colored bead “fact families”
    • These show the entire set of the number bonds (so the addition and subtraction) and we will be using these next for D
  •  Number bonds cards
    • These are print and go, I printed 2 per page

 

In addition to teaching addition facts, it’s also very, very useful for a child to learn “doubles” (3+3, 4+4, etc) so I teach them explicitly.  This is useful because they can apply this knowledge to problems with “near doubles”: if you know 3+3=6, you know 3+4=7 because it’s simply one more than the double.  I made a really simple DIY version of this flip chart to introduce doubles.  Mine shows bead bars but you can use whatever rods/manipulatives that your child would be familiar with:

 

And now we’re using these task cards on adding doubles: Doubles Task Cards

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It’s almost Valentine’s Day here and she LOVES using these little heart markers on her work.

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These approaches have been really helpful for my children and more engaging than repeatedly using the tables.  I’m certain those tables work for some children but they just weren’t a good fit for our family.

 

FYI, many of these activities and the hundred board activity cards (shown below) that we LOVE are available (Feb 2019) as a bundle here.  I already purchased most of these a la carte but they’re bundled here at big savings: Junior Math Bundle

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Disclosure: Last week I became an affiliate for Montessori Kiwi so some of the products linked above are affiliate links (at no additional cost to you).  However, all but one of these materials (the colored bead fact families) I purchased prior to that arrangement at full price and have used for years in our homeschool.  My posts are meant to be informative and helpful; you can count on me to always recommend the best product I’ve found whether or not I am an affiliate.

Daily and Weekly Rhythms

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2016 – Our rhythms have changed a lot since then!  That was 2 zip codes ago.

Before I started homeschooling, I was very interested in what a “normal” day looked like for homeschoolers and how homeschoolers prepared to teach their children each week.  Now that I’ve done it for 18 months, I’ve settled on what works for us (at least for now) so I decided to share how we approach our weekly and daily rhythms.

 

Weekly

 

As previously discussed in this post, I have a pretty good sense of our upcoming lessons so the first thing I do each weekend (usually Sunday afternoon) is consult 1) my lesson plan and 2) the prior week’s work journal.  Our work journal is laid out by subject so this allows me to see what (if anything) was left over from the prior week.  If a lesson wasn’t finished, it is added to the upcoming week’s work plan but if it was, then I know that I’ll give the next lesson in my lesson plan.

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All my books for a planning session.  I know it looks like a lot but I’m only skimming.  It goes quickly!

 

I can already anticipate that there would be questions as to why something would be unfinished in a prior week’s work plan.  The short answer is that it’s relatively rare but if it happens, it happens by agreement.  We informally review (literally by glancing at it) the work plan during the week so if it is clear that we’ve run out of time/decide to pursue other work at the expense of something on the chart, we discuss bumping that item to the next week.  It is a shared decision between C and I to do so.  Typically, this happens because I’ve planned too much work; since I’m not a trained guide, I’m never quite sure how long follow-ups and rabbit holes will take.

 

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Meeting White Board (Jan 2018) – Black are my notes, blue are her additions
Meeting (today) – black are my notes, blue are her additions

I copy my rough plan for the week onto a white board (shown above) and then we have our “meeting”.  C and I meet together quickly and we run through the lessons/topics for the week.  I show her any new material (not demonstrating it, just physically showing it to her) and tell her what we will be studying in history, science, etc. The meeting gets her excited about work that is coming up.  It is not uncommon for her to choose the first few things she wants to work on during the meeting, even if she won’t start work on them until the next day.  Sometimes, we modify the plan based on her feedback.  For example, she recently declared that she “already knew everything” (gotta love the confidence of a 6 year old) in our science lesson because we had discussed those items during the Great Lessons earlier in the year; after asking her to explain the topic to me, I determined that we could skip over that particular science lesson.  This is uncommon but it has happened.

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Dec 2018 Work Journal

Once we’ve agreed on the weekly lessons, I copy them into our work journal.  We use a short-hand notation of “(p)” if something requires a presentation from me before she can work on that independently.  The number of lines represents the number of times that something should be accomplished and we date each activity as it is completed.  The “number of repetitions” is the most often thing we debate during the weekly meeting but we have a minimum family requirement of 5 “problems” or “practice opportunities” before each line is satisfied and receives its date.  Either of us can date an activity after it is finished; now that’s she’s accustomed to the system, I trust her to complete the agreed upon activity.

 

Daily

I thought I might do this section as a time diary of one of our days.  I work PT from home in the afternoons so that section won’t apply to all families but this is a faithful documentation of our day on Tuesday, Jan 8th, 2019.  Please keep in mind that Tuesday is a heavy presentation/minimal independent work day in our homeschool because it’s our first day of the week (we do coop on Mondays).  Weds-Fri is generally significantly “quieter” in terms of fewer presentations and C working independently.  There are a lot of pictures…

 

5:30 AM: Run and Bible study/prayer time.  I have been a runner for 10 years and I love starting my day this.  And doing my prayer/Bible study time as I cool down has meant I do it more consistently.  No pictures of sweaty me, no one wants to see that.

7-7:30 AM: Kids awake and eating breakfast

7:30-8:40 AM: Getting dressed, mama showering, getting D and R (ages 5 and 2.5) ready for preschool

8:45-9:15 AM: Preschool drop off

9:15 AM: Bible study/prayer time with C.  We are currently in Mark, chapter 15.

9:15-9:45 AM: Flags of Africa.  She reviewed the 10 flags she knows so far and selected 10 new flags to learn this week.  Her follow-up work is practicing the flags and then checking them against the key.  For more on our use of Pin-It-Maps, please see this Pin It Maps

She’s chosen to start with the flags of southern Africa

9:45-10:45 AM: Science presentation on distinguishing materials.  We are using the curriculum from Building Foundations of Scientific Understanding. We don’t have a great follow-up from this lesson, I really need to get better about planning follow-up options for them.

We began by reviewing that all “human-made” objects are made from natural or biological materials (prior lesson in the curriculum).  Then we categorized the materials we could find in our homeschool room or around our home (metal, wood, plastic, stone, rubber, etc).

Then we determined some properties of these materials and made some observations in a chart form (we’re very visual so lots of things get “chart-ified”); observations included the strength, flexibility, magnetism, and weight of material.  This led to a discussion of why certain materials are used to make certain human-made objects and not others (e.g. we don’t see glass cars driving around).

When I asked for her permission to share the entire day including lots of pictures, she agreed but she wanted me to be in a picture. So here is her photo of me and our list of materials in our homeschool room.
Determining the magnetism of our stair railing
Our comparison of different properties of materials

Lastly we finished with an extremely popular old video from Mr. Rogers about how crayons are made and the materials that go into that.  She was fascinated and is now very interested in the many, many videos on YouTube of how things are made.

 

10:45-11:05 PM: Geometry presentation on the nomenclature of lines (line, ray, line segment, vertical, etc).  She categorized lines by their positions during the lesson and the follow-up work is the line task cards from ETC Montessori.

11:05-11:30: Language presentation on alphabetization.  This is review for her as we did some work with dictionary skills last year but it was a good refresher.  She did two drawers and will complete more for follow-up.

11:30-12 PM: History presentation on the Indus River Valley Civilization.  We are using the guide from History Odyssey for our focus on Ancient Civilizations this year.  It includes readings from the encyclopedia, Story of the World, and map work.  She completed her initial follow-up (drawing/writing a sentence about what she remembers from the lesson).  As another follow-up, we also plan to look up modern day India in our “Children Like Me” reference which is excellent.

She remembered the Indus River valley civilization was the first cultivation of cotton but wanted to use our encyclopedia to double-check all of her spellings.

So that was our morning! I’m going to publish this now because the rest isn’t going to change; afternoons are all the same around here and it’s all in big blocks of time.

 

12:00 PM: I begin work by checking my emails, C goes downstairs to eat her lunch.  She delights in the quiet of lunch and reads her book while she eats.

12:30 PM: Our nanny arrives and she and C head off to preschool to collect D and R.

12:30-5:30 PM: I work and our nanny plays with the kids and/or drives them to activities (soccer, swimming, dance).  C often completes follow-up in the afternoons as well for 30-60 minutes but this is optional and completely at her discretion.

5:30-7:30 PM: Dinner, bath, Bible with Daddy, read-alouds (currently read Anna Hibiscus – highly recommend!). My husband is usually home around 6 PM which is a huge blessing after years with him working very late.

7:30-9:30 PM: My husband and I clean up, eat dessert (I have a big sweet tooth!), and watch TV before bed.  I sometimes am laminating/preparing new materials though I try to take a break and not do that every night.

Hope that helps anyone who is curious! Feel free to leave me questions in the comments.

So how did that “yearly plan” work out?

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Weekly work journal – Week 14

Some of you may remember that I wrote a post about our 2018-2019 Curriculum Choices and I promised I would update you on how my annual planning went.  This year, for the first time, I attempted to lay out all the lessons I would give in the upcoming year.  Well, as expected, things have not gone to plan.  When I looked at my yearly plan in week 14, we were on week 22 in math, 18 in geometry, and 9 in geography.  The nice thing about this plan is that that is not a disaster, you just tack more lessons on at the end if you finish a subject early but the main point of the plan still holds.

 

Why did I do this planning at all?  Well, because though I harbored no illusions that I would actually get the plan exactly right, it helped me see what was coming next and allowed me to prepare. This is extremely valuable if you need to buy materials, create materials on your own like task cards, etc. but also just to know what lesson you need to prep for next week.

 

Additionally, because the curriculum has so many threads, it allowed me to try and find the natural stopping points in each thread and commit to what I wanted to cover.  What do I mean by this, well as referenced in this excellent post: What Did We Do All Day Blog, there are twelve “threads” or math topics covered in Montessori math ages 6-12.  Many (all?) of these threads are spread across multiple years so you have to make choices about when to stop one thread and move on to another.  It is possible/desirable to do a few threads at once but certainly not all 12!  These threads are related and build on each other (for example, you clearly don’t want to cover decimal multiplication before integer multiplication).

 

Here’s a concrete example – Here you can see that you cover the thread “squares and cubes” in Y1-3.  As the diagram shows, you can introduce in Y1 or Y2 of elementary and then finish in Y2-3.  This seems confusing at first but it actually allows a lot of flexibility.  For example, last year, we did not cover ANY squares/cubes lessons so I chose to introduce this concept in Y2.  The blue shows what I’m hoping/planning on covering this year which will leave the orange to cover in Y3.  As you can see, I’m making the choice to stop at “Paper Decanomial” because I’ve found a natural stopping place; I never would have known when I should stop unless I was planning in advance.

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By the way, if you utilize the Keys of the Universe albums/lessons, I posted this math sequence by year in the math section of the discussion board (it’s an Excel doc).  Figuring out that lessons overlapped was a HUGE breakthrough for me because I didn’t realize the overlap between years in when you could address something.  If anyone creates something similar for any other subjects (particularly language or geometry), please let me know!

 

So how did I mis-plan so “badly” on some topics and not on others.  It appears to me that certain subjects (math, geometry) are broken down into very, very small increments and when I planned, I assumed each lesson was a single week.  For example, in the picture above, you can see (in the blue highlight) that Lesson 1 is “introduction to the squares” and that Lesson 2 is “labeling the squares”.  In practice, however, many lessons are combined because I’m only teaching one child.  If I explain what a square is (example: 4×4 = 4^2) and then end the lesson, that has taken 2 minutes and should not be all the math we do for a week.  So of course I combined Lessons 1 and 2.  This means that I’m covering some topics much faster than the others.  This is much less of an issue in history or science for example where an idea can be fleshed out significantly more deeply depending on the time/interest of the child.

 

This is my original vs. revised math plan.  The revised shows what we actually covered in math in weeks 1-15.  As always, the caveat when I show something is that every child is different and to follow the child; just because we covered something in a certain number of weeks doesn’t mean that you should feel any pressure to go slower or faster.

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We also added a parallel math thread called “Number sense/Challenge cards”.  This is an independent math thread that utilizes many of the task cards/number sense materials that I discussed in this post: Number sense & Montessori

 

I’m still probably being conservative in the number of lessons we can cover because as you can see above, I’m already planning on combining weeks 16/17 into a single lesson since we recently reviewed factors this year and Week 17’s cube extension lesson involves factors.  The nice thing though is that I’m prepared with the next lesson whenever it happens because I’ve planned in advance!

 

Although this post focuses mostly on math, I did this for all subjects and have my revised plan (including going slower in geography because I was way too ambitious there) for the remainder of the school year.  The yearly plan was a lot of work but I’m really pleased that I did it because it’s so much easier to know where I’m going and what to tackle next.  How about you?  Did you plan weekly, monthly, yearly?

Number sense & Montessori

I was speaking to a good friend of mine who teaches middle school math about elementary school math and I asked her what the most important elementary math skills were that translate into math fluency later in life.  Without hesitation, she said place value and “number sense”.  I immediately ran off to google “number sense” so let me first define it for you:

  • Number sense means a fluidity and flexibility with numbers including an understanding of what numbers mean and an ability to manipulate numbers to perform mental math

Ah, so number sense is the thing that I observed when I did interviews for my consulting company and people would ace the mental math.  The interviewees who could just easily manipulate numbers in their head and seemed comfortable with things like estimating, mental math, and manipulating large numbers.

Still lost?  Ok, here’s an example: If I asked you to multiply 15 x 28, what do you do? Seriously, play along….think before you scroll….

 

 

 

 

 

 

 

 

 

 

 

 

I’ll tell you what I would do, because I don’t have great number sense, I’d stack 28 x 15 and begin doing “long multiplication”.  But what someone with great number sense might do would be to say:

  • Consider if it was 15 x 30…
  • 15 x 3 = 45
  • Now multiplying 45 by 10 = 450
  • Now subtract  2 x 15 = 30 (because you were multiplying by 28, not 30)
  • Final answer = 420 …. No pen and paper needed and can be done very quickly, mentally because you have a construct that 28 is simply 2 less than 30

Ready for another strategy?

  • 28 x 15 is the same as 14 x 30 (you can halve the multiplier and double the multiplicand and it’s the same result)
  • So 14 x 3 = 42
  • 42 x 10 = 420

So, once I knew what number sense was, I knew I (badly) wanted my children to have it.  Then, serendipitously, I read this excellent article on “math strategies”: Math Strategies in a 6-12 class . While some of these strategies were familiar to me (using doubles in addition), others were completely new (like the halving/doubling strategy above).  It seemed clearly to me though that working problems forward AND backward was one way to start so I started demonstrating that immediately in my work with my daughter.   But what about other resources or approaches?  Below are a couple more things that worked for us.

Montessori Materials

Many of the classic materials like the association of bead colors in a Montessori classroom are a great start (for example, the 2 bead bar is always green, the pink bead bar is always 3).  If you’re looking to incorporate early learning with bead bar work, I highly, highly recommend using these printables to help drive this home for the children: Helpful Garden Bead Bar Printables.

Another helpful thing for me was to remember with my elementary aged child was to ask her “why” when she was using Montessori math materials.  So when she’s working with the checkerboard, ask her “why” the second row starts with a blue square (because it represents the tens place) and if she can demonstrate that mathematically.  Asking her questions helped me understand what she knew “by rote” vs. what she had actually internalized.  Another example might be “why do you add a zero when you multiply by 10?” (answer: because 45 x 10 is asking you to take 45 ten bars and because we know that 10 ten bars = 100, we know that 45 ten bars = 450)  This probably comes naturally to a trained teacher but I am learning to be significantly more pro-active in asking her to explain her reasoning or “how could we prove that”?

So many people just memorize the steps of math even in Montessori (I know I did and I was a Montessori child) so it was eye opening for me to remember that if she couldn’t explain it, she probably didn’t deeply understand.  This is, of course, the ENTIRE point of multi-age classrooms because older children would further solidify their understanding by teaching younger children but in a homeschool, that doesn’t always happen.  Another idea would be to see if your child can teach the approach to a “naive” adult (anyone other than the homeschooling adult); your observation of this will tell you if they know more than the memorized steps.

Games

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We regularly play “race to 100” and “race to 0” but I began working it into our day more.  This simple game involves a 10 sided dice (found here: 10 Sided Dice).  You throw a dice and either add up to 100 or subtract to 0, keeping score on a piece of paper or a white board.  The first person to 0 or 100 wins.  The important part of this as the adult is that you model using number sense by solving the problem out loud.  For example:

  • You have 35 points, you roll a 9 so you say “35 + 5 is 40, plus 4 more is 44” (this uses the strategy of making a 10)
  • You have 57 points, you roll a 7 so you say “7+7 is 14 so the answer is 64” (this is using doubles as a strategy)

These are just some ideas.  But you ask that the child do it the same way so that you can observe what strategies they’re using.  You can use this approach to modeling other addition/subtraction strategies once your child gains comfort with some.  You can see above that we were playing with actually golden beads to keep count but as she got older, we just kept score on paper.

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Another of our favorite math/number sense games is: Prime Climb.  This game is excellent because it is a race to 101 but allows for the utilization of all math operations plus incorporates prime numbers.  In the same game, you might do all four operations in your quest to get your pieces to land on 101; I particularly like it because it teaches you to do operations forward and backward.

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In addition to playing the rules as designed, we’ve also added a twist to prevent them from simply counting when they’re doing addition/subtraction.  It was frustrating me that instead of practicing her facts, she was just simply counting on a turn where she decided to do addition or subtraction.  So we instituted a rule that if she correctly did the addition/subtraction mentally (out loud), she could choose to advance one additional place if she chose (sometimes it’s not advantageous to advance your piece so it is a choice, not a requirement).  If your child doesn’t have their multiplication/division facts memorized, the game is actually color coded so you can figure out the relevant facts, it’s completely brilliant!  Lastly, it also teaches multiplication facts as factors with its color coding (for example 6 is reflected with the colors scheme as a multiple of 2 x 3 and then 18 is reflected as 2 x 3 x 3; in the picture above 6 is shown as half orange and half green to represent 2 x3).  I love how many layers this game has an it fits perfectly within the Montessori schema of teaching the big picture concept but not limiting the child if they don’t have their facts 100% memorized.

Apps

We do very little screen time in our home but once I started reading about the Native Numbers app, I definitely wanted to try it.  This app is for a younger child (maybe 4-7); my just turned 5 year old loved it and begged to play it daily.  You can read more about it here:  Native Numbers.  It’s a curriculum with 30ish levels (I liked that it didn’t go on forever) that gets kids to begin to associate numbers, quantity, relative size.  For example, it discretely teaches the skill of “counting on” (if you’re adding 4 + 3, you say “4 plus 5, 6, 7” to find the answer, you don’t start at 1).  My 5yo worked through the levels in about a month playing probably 2 hours a week and it was definitely valuable.  I almost cannot believe I’m recommending an app but this one is so good that I feel compelled to share it.

 

Printables

Number lines:

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One of the ways that made the most sense to me to approach number sense is using number lines.  In order to use number lines, you need to understand the relationship between numbers, how to decompose them, etc.  If you compare two similar lines and are trying to determine the value of a dot somewhere along that line, you need to understand the relationship and relative size of the numbers that are already placed on the line in order to estimate.  It’s also great math fact practice to understand how to place values between numbers; for example, to be able to figure out that 500 is halfway between 200 and 800.

The examples above are from an excellent bundle on TPT but of course you could make your own:  Number Sense Bundle.  We are working through the numbers 1-1000 bundle (also sold separately) right now and I really thought that some of this might be too easy for her but it’s been a nice challenge.  I look forward to moving on to the 1-1,000,000 and fraction/decimal bundles

Strategies by operation: (free printable linked below)

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Another way to approach this is to look for materials/printables by each operation and teach all the different strategies as options.  An excellent example is this FREE printable that teaches multiple multiplication strategies: Multiplication Strategies

Other Inspiration

This post K-3 Number Sense Ideas shows photographs and explanations of many, many options for grades K-3.  These activities are available for purchase but you could also make any of these things very, very easily and substitute things like Montessori beads or cuisenaire rods for the “snap cubes”.

What are other ideas?  Would love to hear how you’re approaching number sense in your homeschool.