"What the hand does, the mind remembers." - Maria Montessori

Research shows over 7% of students experience severe learning disabilities in math. Countless more struggle because of the way the language of math is spoken to them. You might as well be speaking Greek. Our goal at ShillerLearning is to make math understandable for every child with hands-on, exploratory learning – learning by doing.

Is your child struggling with math or would you like to avoid your child having math problems in the first place? The decimal material (also known as base ten blocks) paired with Montessori number cards are a game-changer for students young and old. I wonder how many parents, who themselves struggled with math as children, would have had an easier time learning (and even loving) math if they had worked with these tools.

As Dr. Maria Montessori so eloquently stated, "What the hand does, the mind remembers."

Together these hands-on tools make the decimal system and place value visually obvious and number sense easy to acquire – something with which many students struggle. These easy-to-use manipulatives and accompanying activities set your child up for math success and banish the tears and frustration. They provide a concrete introduction to the decimal system in an amazingly understandable way and can be added to any math instruction.

What are they?

The decimal material is introduced using the Montessori three-period lesson – a simple, but effective gap preventer that ensures the student understands the concepts and materials being used. The ShillerLearning YouTube channel features videos on the three-period lesson, as well as doing operations with the decimal material and number cards.

First the units are used to introduce and strengthen the recognition of quantities one through nine. The materials are then paired with number cards to learn the symbols – the numerals – 1 through 9.

The number cards help children recognize the numerical symbols for each place value category of the decimal system. One of the fringe benefits of the number cards for students with special needs is that they empower students to work with numbers without having to be able to write numbers. The number cards consist of four sets of cards for the first four different categories of numbers in the decimal system (base ten). The smallest sized cards are numerals 1 – 9 (units/ones), increasing in size algorithmically for place value with numerals 10 to 90 (tens), 100 to 900 (hundreds), and 1000 to 9000 (thousands). The cards are color-coded for place value in green, blue, and red with the color pattern repeating for each new place value family - everywhere a comma goes. If we were to create cards in higher place values, the color pattern would continue. Ten thousands would be blue and hundred thousands would be red.

With success achieved in numbers one through nine, students are ready to learn place value into the thousands! As they work with the material, they also discover that if we count beyond the number nine in any decimal (place value) category, we continue counting into the next highest category.

Abstract, sometimes difficult concepts become hands-on, concrete, interactive. This introduction and exploration of numbers is unparalleled in creating a solid number sense and understanding of place value – the cornerstone of a solid math foundation.

The magic continues as you work with operations: addition, subtraction, multiplication, and division. Students learns 4-digit static addition (addition without an exchange, commonly referred to as carrying), doing in the concrete with the materials and number cards what they will later do on pencil and paper. Once that skill is mastered, they learn to play the exchange game where various quantities of a place value are combined; when ten is reached, it is traded in the materials bank for the next place value, adding that to whatever is left over. Now the student is ready for dynamic addition – addition with an exchange (addition with carrying).

Here is a peek at 4-digit addition with exchange. The following is a summary of activities that are scripted in the ShillerLearning Math Kit I, Lesson Books 1 and 2.

You will be amazed at how quickly young children achieve conceptual understanding as well as success in performing operations – preventing math struggles from occurring. The activities are also a powerful remediation for older students struggling with math for a variety of reasons and crucial support for students with special needs. These are two math manipulatives that will promote the success of every student in homeschool math.

The decimal material and number cards are available separately and can be added to any math program. They are both included in Math Kit I (covers pre-k, kindergarten, 1^st grade, 2^nd grade, and 3^rd grade). To celebrate the new set of ShillerLearning color-coded decimal material, save $20 until October 31st. Because without them, math can be scary.

What is the Best Reaction When One Has Failed to Solve a Math Question?

Photo Credit @mythreedovesschoolhouse

Solving a homeschool math problem is only interesting and endorphin-releasing when it’s hard.

Solving a math problem requires an approach. If the approach is obvious and correct, the problem is easy. So hard problems don’t present an obvious approach. Elegance is not typically an adjective used to describe a successful approach that’s not obvious because you’re not likely to pick the best approach first: things are messy.

The beauty of math is that you can brainstorm all kinds of crazy ideas about how to proceed and you can actually try them out until one works. If you did this in real life, you’d probably get arrested.

As Thomas Edison realized, every failure is a step towards success. So one never fails to solve a math problem: you just haven’t solved it yet.

1. You think a dead-end is an obstacle. Until you realize it’s really a dead-end, you bang your head against the wall. But that’s not all bad: some useful things come out of that. When you finally realize it’s a dead-end and not an obstacle, you’re ready for a different approach.

2. You think an obstacle is a dead-end. You, therefore, try other approaches. When none of those works out, you begin to think, “Hey, maybe that wasn’t a dead-end, maybe it was an obstacle.” And you struggle until you make a breakthrough and solve it.

Self-awareness and the ability to let your negative emotions (frustration, anger, etc.) drive positive action will eventually result in success.

Encourage your child to ask for help when needed along the way, not letting his or her ego get in the way of seeking help from others. By constantly seeking advice from his peers, Albert Einstein ensured his theories were by and large bullet-proof (at least through the present).

If you’re a student, the best homeschool math curriculum - special needs students, gifted, and average learners included - doesn’t just show you what approaches work best; it teaches you how to think to come up with the best approaches.

When to Teach Fractions to Kids

I’ll never forget the joy in my son’s eyes when he shouted out- “Mom! Four quarters make one dollar, now I get this fraction thing!” It’s that moment of realization and understanding we absolutely love as homeschool parents. The moment when we realize our kids ARE getting it and we CAN thrive at home educators.  

For many children, making the connection between all those slices of pizza being the same as one whole pie is easy. Until you write it down on paper and take away the word pizza.

Or the child who can easily grab half a sandwich… but then stares at you like a deer in the headlights when you ask them to find the ½ written out.

It can be hard to translate real life into numbers on a paper- or even visual representations.

Homeschool parents are often frustrated by fractions. They see their children interacting with the “real life” examples and struggling to translate that over. Or parents worry the concept will be too difficult or confusing for their children. These are legitimate concerns.   Yet they shouldn’t stop you from teaching this important skill. We’re here to give you tips not only on when to teach this basic math skill but how to teach them in a way that won’t bring any tears or frustration.

The Best Way to Teach Fractions to Homeschoolers

The team at ShillerLearning discovered there was a gap in the fractions curriculum available to home educators. We saw this gap across all teaching modalities, especially among the Montessori-based home educators. Nothing truly hands-on existed for parents. We heard again and again from parents with no idea what to do. Our hearts broke for kids who cried over boring worksheets that didn’t make sense.

Something had to change

We created our Fractions Kit for exactly this purpose. It’s an open-and-go, 100% multisensory and engaging curriculum. You’ll discover it’s modeled just like our popular Math Kits I and II. We’ve used the same Montessori-inspired language, lesson structure, and manipulatives to bring this important basic math concept to life.

No more boring worksheets. Your children will use colorful pieces, real materials from home, and more. They’ll not only learn what a fraction is but why they matter. Your students will learn how to identify them in the real world. With joy and ease, they’ll complete equations, learn about denominators, and more. You will love not having anything to prepare but opening a book. Students will love learning and have a blast doing it. We’ve even heard from families whose children choose to work on this kit in their free time because they enjoy it so much.

When Should I Introduce Fractions??

Most children are ready around 2nd grade. However, fractions can be introduced from the time your children are very young. Give concrete examples in real life anytime you’re able. Count coins with them so they can see how 4 quarters, 10 dimes, 20 nickels, and 100 pennies all = 1 whole dollar. Cut up their sandwich and name the quantities. Discuss the percentage of sales and which fraction they match up to. If they have real-life situations in their brains already, they’ll be less intimidated.

Here at ShillerLearning, we don’t believe in putting an age limit on when children should be learning something. Isn’t part of what we love about the Montessori Method that children learn on their own pace? We have young children working in our kit, all the way through teens. We’ve even had a few adults work through the kit to help fill in gaps in their own education!  

If you don’t give age ranges, how do I know when to start my child on the kit?

This is a question we’re asked all the time. It can be confusing to not get a cut and dry answer. For most children, fractions are added in Kit I along with Book 2 or 3. Sometimes families will wait until they’re done with Kit I, others add the kit in alongside Kit II, Book 4. The overwhelming majority introduce fractions at Kit I Book 2 or 3.

Options and Tips for Introducing the Fractions Kit:

• Give your student a choice when they’d like to do fractions and how often.

Your student may want to work once a week on fractions, drop their current book, for now, to focus exclusively on fractions, rotate the kit book in at their leisure, or complete the entire book after book 3. These are only a few suggestions, your student may choose when they’d like to work on them

• At least through fourths needs to be introduced by the end of the second review test in book 3. Your student will need this information to move on to the next section.

• Foundational knowledge of division can be helpful, but not necessary

• As you progress through the Kit, you’ll eventually hit a point where you need to have completed specific lessons in our Math Kits to proceed.  

The Kit will last for several years! In general, it’s not something that’s worked all the way through because of this.

Want some additional help with this foundational & basic math skill? Love “real life” learning, games, crafts, etc? Make sure to grab our FREE Fraction Activity Pack for additional lessons. You’ll find lessons designed for all ages- toddlers through teens. As always, they’re full of the best of Montessori-inspired games, crafts, lessons, works, and more.

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