# How My Son Taught Himself to Learn Place Value

I'm no math teacher, we include mathmatetics as part of our everyday homeschool routine. Sometimes, even when we think we're prepared, our children throw us for a loop.

I had 218 written out on a piece of paper. “You may tell me this number.” I said to my seven-year-old.

- “Two thousand, one hundred and eighteen” he responded.

I was flabbergasted. We have spent SO much time working on place value. He knew it before our winter break and then- poof- it seemed to be gone.

It can be incredibly frustrating when we feel like our children have mastered something only to come back to it and find out they are in need of a refresher or they’ve forgotten it all together. It’s also totally normal. “Use it or lose it” exists for a while in these early years. They’ll get there. I took a calm breath, pulled out our number cards and built the number.

- “It’s not quite that number, let’s look at it together. How many units are there?”

- “Eight” he responded.

- “Yes, how many tens do you see?” - I asked

- “One.”

- “Yep, how many hundreds?”

- “Two,” he then got an incredibly confused look on his face. The ‘learning moment’ was happening and he was realizing that it was NOT 2,118.

- “Great, how many thousands do you see?”

- “None?” he responded slowly and cautiously.

- “I don’t see any either, what number do you see here?”

- “Two hundred eighteen!!!” He responded enthusiastically.

Yes!! Isn’t it a sweet moment when you’ve worked through it with your child and seen them generate their answer??

Place value will be something you’ll keep coming back to through the years. As you get into 3 & 4-digit numbers, decimals, and beyond; you’ll need to revisit this concept to make sure it’s cemented. It is a truly foundational math skill and something most children don’t pick up in one lesson.

# What is place value?

Place value is how we determine the value of a number. Our number system is based on groups. A single number (0-9) is referred to as a “unit” in Montessori teaching. Tens come next as two-digit numbers, hundreds help us make three-digit numbers and so on.

# Teaching Place Value

The best way for a child to learn place value is a lot of practice. In our curriculum, you’ll use place value materials throughout your student’s math education in numerous ways. Incorporating place value identification as part of your daily routine can also be helpful. Ask your student about place value for numbers you see on street signs, price tags, in books, etc. to help reinforce the concept.

# Decimal Material

Montessori decimal material is a foundation for teaching place value.

Providing children with something tactile for a concept that can be quite abstract is essential. Children begin by “building” numbers with unit cubes, ten rods, hundred flats, and thousand cubes. They can use these materials to “trade up” to the proper materials. For example, provide your student with 12-unit cubes and encourage them to trade to a ten rod when they get to ten units.

This is an excellent way for them to start grasping the concept of place value. As your student progresses, they can “trade” in for hundreds and thousands as well. Many children enjoy playing this like a shopping game where they “buy” the next decimal material for the proper amount of trade.

# Number Cards

Once a child is familiar with the unit cubes, they’ll begin using number cards. These helps provide a visual for creating numbers, the tactile experience of building numbers, and the auditory experience of hearing numbers. Children begin by matching the correct number card to the corresponding number of units. They then move into matching unit cubes to the proper number card. This helps create the foundation for place value by giving the child a visual and a number at the same time. The number cards will be incorporated with the decimal materials we discussed above as well. Eventually children will use number cards to build large numbers and will be able to tell the place value for each number, as well as build a number with verbal directions for which number card goes in each place value location.

# Number Tiles

Not be confused with number cards, number tiles are introduced after the student has a firmer grasp on place value. In our curriculum, number tiles are not introduced until Book 3.

These materials are used similarly to the number cards with some differences. Number tiles are multiple tiles of 1, 10, 100, and 1000. As in the Montessori Stamp Game, they are used as an alternative way to help children build numbers, solve math problems and move their understanding of place value to the next level.   For the number 218, in number cards the child would select 200, 10, and 8 cards. With our number tiles, the child would obtain 2 “100” cards, 1 “10” card and 8 “1” tiles. These are an excellent way to make the connection between decimal materials to building numbers, as well as to practice “exchanging” tiles from one place value for other place value tiles when completing math problems. Children take the solid foundation of number awareness they learned with the other two resources and use them throughout book 3.

# Moving Beyond Book 3.

While these materials are not included in our ShillerLearning Math Kit II, children can certainly still benefit from using these materials into middle school. (Plus, the decimal material make great building blocks for free time!). If your older child has dyscalculia or struggles with number sense and understanding place value, incorporating these materials can be extremely beneficial.

Feel free to reach out if you need additional guidance for teaching regrouping, place value or anything else with your child. Make sure to check out our upcoming webinar on Teaching Place Value with Montessori Materials for more tips and tricks to help incorporate multisensory place value learning into your homeschool day.

# See Inside Our Montessori-Based Kits

## Language Arts A - PreK to 1st Grade

### Amanda Osenga

Amanda is a former Montessori teacher, now homeschooling her dear son - an only child. Amanda and her family reside in an Airstream parked in Washington State. She loves Washington's outdoor opportunities. When not homeschooling, she also blogs, works as a virtual assistant, and loves creating hand-lettering pieces.

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# 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.

### Two kinds of (intermediate) failures may result:

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.

Photo Credit @ofnumbersandstars

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.

# Want to See Inside Our Montessori-Based Kits?

## Math Kit II (G4 - Pre-Algebra)

### Larry Shiller

Larry Shiller is President of ShillerLearning, whose mission is to help kids learn and fulfill their potential. Shiller has degrees from Massachusetts Institute of Technology and the Harvard Business School and is the author of Software Excellence (Prentice-Hall).

A father of three, Shiller is active in non-profits and his hobbies include working with local startups, music (Shiller is an accomplished violinist who - when not helping children learn math and language arts - performs in the NYC tri-state area), tennis (Shiller's team made it to the USTA national finals in his skill bracket), Quoridor (Shiller is a former USA Champion), backgammon (Shiller is the Voice of Backgammon, doing commentary on backgammon tournaments worldwide), table tennis, and flying (Shiller holds a private pilot's license).

# 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.

# See Inside Our Montessori-Based Kits

## Language Arts A - PreK to 1st Grade

### Amanda Osenga

Amanda is a former Montessori teacher, now homeschooling her dear son - an only child. Her family resides in an Airstream parked in Washington State and loves Washington's outdoor opportunities. When not homeschooling, Amanda blogs, loves reading, and creates hand-lettering pieces.

# Enhance your Math Lessons with these Fun Montessori Inspired Pi Day Math Lessons

My High School math teacher had all the digits of pi wrapped around the upper portion of the classroom wall like a border. Any student who had memorized them all by the 14th of March got bonus points in the class. Only a few kids were able to accomplish this feat. My teacher celebrated by bringing in pies and having a fun “pi-day” in class.

You can incorporate Pi-Day into your homeschooling as well.

## Here are a few ideas to get you started planning your "Pi Day" School Day:

• Talk about what Pi is: Bake a pie- math, reading skills, and snacks! What more could a homeschooler want??

• Cylinder works,

• Pi-digit matching,

• Fractions with circles (our Fraction Kit is a great option for this!),

• Use a compass to make different size circles,

• Measure out 3.14 inches or feet of string,

• Have pot pie for dinner,

• Number writing practice writing the digits of Pi,

• Read about famous mathematicians,

• Research how it got the name “Pi”,

• Take a field trip to a local pizza place and get a lesson on spinning the perfect pizza pie,

• Check out Pi day activities at your local library,

• Read the book Sir Cumference and the Dragon of Pi,

• Practice making the Pi symbol in rice, sand or with our grain set,

• Make the Pi symbol out of playdough or clay,

• Find Pi with a variety of circles!

### Math Kit 1:

Book 1

Lesson 2- Shapes

Lesson 10- Shapes Matching

Lesson 15- Comparisons Among 2

Book 2-

Lesson 42- Subtraction With Circles

### Math Kit 2:

Book 5

Lesson 10- Diameter and the Chord

Lesson 113- Angle Degrees

Lesson 114- Protractor and Radius

Book 6

Lesson 84- Planes

Lesson 85- Circles and Spheres

Lesson 118- Measuring a Circle’s Circumference

Lesson 119- Circle Circumference and Pi

## Happy Pi Day!

Like these ideas? We think you’ll love our free monthly printable packs too. Subscribe to our newsletter to be the first ones with access to the packs.

# See Inside Our Montessori-Based Kits

## Language Arts A - PreK to 1st Grade

### Amanda Osenga

Amanda is a former Montessori teacher, now homeschooling her dear son - an only child. Her family resides in an Airstream parked in Washington State and loves Washington's outdoor opportunities. When not homeschooling, Amanda blogs, loves reading, and creates hand-lettering pieces.

# The U.S Math Crisis

We have a math crisis in the U.S.

Maybe that's the least of our problems. But maybe not. Consider this:

• 80% of US 8th graders cannot calculate fractions, decimals and percentages.

• 40% of US 4th graders cannot tell NE from SW on a map.

It's really just us. The world does better:

• In Germany 35% of teens take and pass advanced placement exams; in the US it's 4%

• In Japan kids start algebra two years ahead of those in the US.

What are the repercussions?

• In the California State University system 60% of Freshman are required to take remedial math and science classes
• One in five adult Americans cannot:

Calculate the total of a purchase w/tax & tip

Locate an intersection on a road map

Enter background information correctly on a form

• MIT economist Lester Thurow says that only 20% of Americans have the work skills and education to be competitive in the global marketplace

And no one believes it! In a recent study 71% of high school parents say that they are satisfied with the math education their children are getting. Ouch.

The US has a math crisis. And the repercussions are serious. Join ShillerLearning and the Rising Stars Foundation in creating better outcomes for our children and country.

# See Inside Our Montessori-Based Kits

## Language Arts A - PreK to 1st Grade

### Larry Shiller

Larry Shiller is President of ShillerLearning, whose mission is to help kids learn and fulfill their potential. Shiller has degrees from Massachusetts Institute of Technology and the Harvard Business School and is the author of Software Excellence (Prentice-Hall).

A father of three, Shiller is active in non-profits and his hobbies include working with local startups, music (Shiller is an accomplished violinist who - when not helping children learn math and language arts - performs in the NYC tri-state area), tennis (Shiller's team made it to the USTA national finals in his skill bracket), Quoridor (Shiller is a former USA Champion), backgammon (Shiller is the Voice of Backgammon, doing commentary on backgammon tournaments worldwide), table tennis, and flying (Shiller holds a private pilot's license).

# 15+ Multisensory Multiplication Hacks for Homeschoolers

Children learn best when all of their senses are engaged. A multisensory approach in education is not simply a catchy trend. It’s a proven approach to enhance learning and cement concepts. Hands-on math education teaches concepts in a way no textbook ever could. By engaging the senses, our children can experience concepts in a more concrete way. This helps subjects that might feel extremely abstract, such as multiplication, become relatable and less intimidating.

# Multisensory Multiplication Games & Hacks for Your Homeschool

• Building equations with blocks- Children’s play blocks make the best manipulatives! Create a visual example of the equation you are solving with a set of blocks. By building the equation, children benefit from a tactile experience of physically feeling the numbers as well as the visual benefit of seeing the quantity. Children can also build a visual representation of the times table with blocks if they feel ambitious. This is a fantastic way to incorporate hands-on math into your home. [The ShillerLearning math curriculum does this with decimal material (base ten blocks), number cards, the operator set, and later number tiles (along with the lines of The Stamp Game].

• Draw out the equation- For example- Take the equation 4x6. Have the student draw a 4 by 6 grid of stars/circles/flowers/ etc. to visualize the equation and count the total number. You may use the ShillerLearning Graph sheet or Blank Number Grid for this.

• Dots or stickers- This is done similar to drawing as above. Using BINGO daubers or small stickers, children create a visual representation of the equation.

• Multiplication songs- Check out the ShillerLearning CD's for the “Multiples of Four”, “Count by Fives”, and “Powers of Ten” songs to use in your homeschool. Kids love to sing and dance to these songs!

• ShillerLearning’s base ten decimal materials- These are the blue manipulatives in our Math Kit I. Using the materials provides students with a concrete way to make a physical representation of numbers, equations, and value.

• Use art- Children with a creative streak can greatly benefit from incorporating art. Giving them a chance to make a beautiful multiplication table can help immensely. Turning equations into pictures is another approach for incorporating art.

• Tap numbers with fingers on the table- This can be an especially useful way to work on multiplication facts. The student taps one finger for each number. If they are working on counting by 3s, for example, they would tap their finger harder for each multiple of three.

• Jump it out- Similar to above. In this approach, children jump up for each number and do a jumping jack on the multiple.
• Money- Using cash is an excellent way to give kids a hands-on, real-life experience with multiplication. Allow them to figure out how much change is needed at the grocery store, to sort and count change, and other money experiences.

• Use a ball- Say an equation and toss the ball to your student. They can toss the ball back after answering the equation. Roleplay and have the student ask you the equation. Occasionally throw in a wrong answer to see if your student catches it. You can also write numbers on a ball. Toss the ball to one student who makes note of the number on top. The ball is then tossed to the next person who makes note of the number on top. Students then work together to solve the equation of those two numbers multiplied to one another.

• Food can sometimes be the answer to a problem- Use small snacks as manipulatives to eat after the equation has been solved. Students can build out the equation with their favorite treat and eat the answer!

• Completing multiplication tables- Proving a student with a blank multiplication table to fill out can have surprising benefits. Some children may need to fill our a table dozens of times along with incorporating other techniques listed here. You may print additional grids for your multiplication tables from your customer downloads.

• Number tiles- Another hallmark of ShillerLearning’s materials are our number tiles. You will recognize how these are used if you are familiar with the Montessori Stamp Game. Students use these to build equations as they move on from the base ten materials. The number tiles are the final transition in moving from concrete (base ten materials and number cards) to abstract work (just pencil and paper or mental math) in the basic operations. Instead of the unit cubes, we use the “1” tiles; instead of ten rods, we use the “10” tiles; instead of the hundreds of flats, we use “100” tiles; instead of the thousand cubes, we use “1000” tiles.

• Card games- Divide a deck of cards evenly between two players. Each player flips two cards at a time and multiples the amount shown on their cards. The player with the highest equation takes the other players cards. Play continues until someone runs out of cards, or for a set amount of time. Creating multiplication games with materials already on hand is an excellent way to build skills!

• Dominos- These already have two numbers on each piece. Multiply the two numbers together. Play a game similar to the approach above. You can also adapt the regular dominos game so that players can place a piece that has the same answer as one already on the board.

• Cooking- Following a recipe is an excellent way to work on multiplication skills. From measuring ingredients, adapting measurements, adjusting recipe size, and adjusting serving skills. Cooking together is an excellent way to work on math together.

• Flash cards- ShillerLearning’s flashcards are an excellent resource. These cards help children learn facts without just rote memorization. Each card demonstrates how to make the equation out of our base 10 materials as well.

Check out all our math songs on these albums:

Like this? Check out our Math Kits to help teach your children more about money. They help children understand the concept of money, make change, and other practical money skills.

# See Inside Our Montessori-Based Kits

## Language Arts A - PreK to 1st Grade

### Amanda Osenga

Amanda is a former Montessori teacher, now homeschooling her dear son - an only child. Her family resides in an Airstream parked in Washington State and loves Washington's outdoor opportunities. When not homeschooling, Amanda blogs, loves reading, and creates hand-lettering pieces.

# 3 Hacks to Expand the Life of Your Multisensory Fraction Materials

You love multisensory fraction materials. What to do with these materials once fractions have been learned? Creative hacks to expand their life for years.

There’s been an ongoing debate over “unitaskers” in the home. For those who don’t know, a “unitasker” is an item that only does one thing. These are often found in the kitchen. Egg slicers, cherry pitters, and melon ballers are common examples of “unitaskers.” Occasionally a few creative people will find additional uses for them. For the most part, they get used for only one task. As minimalism and simplifying become more popular, these “unitaskers” are getting more attention than ever.

## Helping Montessori Materials Find New Life

These items exist within the homeschool world too. Parents often shy away from purchasing materials because they struggle to see the investment in something they might only use for a short period of time. We want to get the best ‘bang for our buck’ in all our investments for home education. By purchasing high-quality Montessori materials, we can reuse them from child to child. This helps extend the life of less often used resources.

The Montessori Method is careful and intentional about the materials used. You’ll find the same materials used over a span of several years. Children will have a chance to become familiar and comfortable with items. They will be able to grow in how they’re used and teach younger siblings ways to use them. Within the Montessori setting, you’ll also find materials reused over and over. Intentionality is placed in being good stewards of resources and reusing anything possible in different ways.

A little bit of creativity can also go a long way. Finding ways to extend the life of our materials ensures we’re getting the most we can for our money. We’re always amazed at the amazing creations children make with our decimal materials, wooden shapes, and other manipulatives! Kids are so creative. Sometimes letting them loose with a shelf full of materials and a little bit of free time yields amazing results.

### 3 Ways to Use Fraction Circles Within Your Homeschool

Fraction circles are one material parent often shy away from. They are key multisensory fraction materials. Yet, home educators often worry they are not used long enough to justify the expense. We are often asked if the lessons in our Fraction Book can be completed without the fraction circles.

While it can be done, it’s not going to be especially easy. All our lessons are written with the fraction circles in mind. They are beautiful and children love using them. Made from durable plastic, they’re designed to last. We’ve also made sure to make them visually appealing with bright colors children love. The Fraction Kit will do an excellent job teaching your children fractions. It can be used interspersed with your lessons (we do “fraction Friday” at home). Or you can work through it completely after Math Kit I or book 4 in Math Kit II.

The fractions circles can be reused in other ways too! They don’t have to sit on the shelf until it’s fraction time.

Work on fine motor skills by using them for tracing. Obviously, you can get a perfect circle with the “whole” circle piece. Children also love tracing the smaller pieces. They will become pictures of pizza, pie, geometric patterns and designs, and more. Kids also love the challenge of getting all the pieces placed together to make an even circle. You’ll be amazed at what your child comes up with when they are shown how to trace fraction circles.

Provide your builder-in-training with new building materials. The pieces come apart to become awesome building blocks. Watch as your child delights in creating towers and building walls. They can be especially fun when combined with other building blocks to add color, texture, and even decoration! These multisensory fraction materials suddenly become so much more with your creative builder.

Try some mosaic work. Mosaics are an excellent way to work on visual-spatial skills, patterns, and creativity. The size of the fraction circle pieces makes them wonderful for beginner mosaics. The inner edges are already made to nestle together and the colors create beautiful works of art. While the rounded outer edge gives kids an interesting challenge to figure out how to build their layout. Try using them alongside the wooden shapes for even more options.

These are a few ideas to help get you thinking outside the box. We hope you’ll enjoy finding other uses for the fraction circles, and all your other Montessori materials.

# See Inside Our Montessori-Based Kits

## Language Arts A - PreK to 1st Grade

### Amanda Osenga

Amanda is a former Montessori teacher, now homeschooling her dear son - an only child. Her family resides in an Airstream parked in Washington State and loves Washington's outdoor opportunities. When not homeschooling, Amanda blogs, loves reading, and creates hand-lettering pieces.