**List of Necessary Math Manipulatives**

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I know I’m a total geek, but I really love math! It’s my favorite subject to teach in my homeschool.

The other day we were trying to finish up school quickly to go somewhere fun, and I overheard one of my daughters tell a younger daughter, “No! Don’t go ask mom for help! She’ll have to get out the math manipulatives and show you ten different ways to solve the problem — it will take forever. Just let me help you!”

I have a reputation.

My children actually do like math (for the most part) they just wanted to make sure we didn’t miss our fun outing. I attribute a huge portion of their enjoyment of math to my use of math manipulatives over the years.

**What are math manipulatives?**

Math manipulatives are objects learners can use to represent abstract pieces of mathematical information, providing a hands-on way to explore and understand math problems. Abstract concepts can be difficult for young minds to understand, but manipulatives make them relatable because children can better visualize the concept.

For example, when you use fraction strips to show your child visually that 1/2 is larger than 1/3, the concept of fractions gets a whole lot easier because he can now “see” it with his brain. That denominator can be confusing until kids can really see that a fraction is just a piece of a whole, and that the denominator tells you about the size of the piece and the numerator tells you how many you have.

In addition to helping children “see” math problems, manipulatives also provide tactile understanding. Tactile learning builds a deeper, more profound understanding of math concepts. The more of your child’s senses you can involve in learning, the better.

Further, math manipulatives make math FUN! A certain amount of drill is necessary to attain math fluency, and let’s face it — flashcards are boring. But kids are happy to “play math” using blocks or fun games with manipulatives.

**How do I use math manipulatives?**

I make things easy on myself by keeping all of my math manipulatives together in a plastic storage bin. I keep it on the highest shelf in a kitchen cabinet so my kids can’t reach it, and so I have easy access to it, since we study at the kitchen table. The easier it is for me to grab the math manipulatives, the more likely I am to use them daily!

Because I’m homeschooling several children at various levels of math, I don’t actually teach lessons. Instead, my children read through the daily lesson (we primarily use Saxon, but it doesn’t matter what curriculum you use) and the example problems, then start on their daily problems.

They ask me for help as problems arise, and I also help them work through missed problems after we check their assignment. No matter the problem or the level, all the way up through Algebra and Geometry, I use manipulatives to explain missed concepts. I then let my children use the manipulatives to practice the concept or solve their problems.

I’ll provide specific examples with each of my favorite math manipulatives in the list below, but there are also lots of youtube videos that explain how to use any of the manipulatives you purchase.

## Must-Have Math Manipulatives List & Ways to Use Them

I’ll just tell you upfront that I use a lot of homemade math manipulatives. They work great and since they’re mainly objects from around my house, they’re practically free! A pencil and paper also work great for drawing math problems, which helps them to be more easily understood.

But the items on the list below are my favorite math manipulatives that I pull out and use almost daily (and have over the last 18 years of homeschooling) so I still consider them very cost effective. Numbers 1-6 are necessary for effective learning during the elementary grades. The rest are just helpful.

Here’s the list of my favorite math manipulatives!

**1. Counters**

Beware purchasing the super cute counters! It took me three years of purchasing new counters each year to learn that my kids would never leave packages of adorable, colored dinosaurs or cats or bears alone, no matter how much I pleaded nor how high I hid them.

So now I just purchase the boring, flat, colored counters, and I find the largest, cheapest set I can whenever I need them. I also bought a 1″ circle punch so I can make paper counters. My kids prefer the plastic discs, though, because they’re easier to manipulate than small paper circles.

Things like dried beans, pennies, or colored beads work, too. Occasionally, I’ll purchase a bag of skittles or m&m’s to use as counters for a fun change. You’ll find a hundreds chart to use with your counters in these homemade math manipulatives.

**Math concepts to teach with counters:**

- Counting
- Number recognition
- Number correspondence
- Ordinal numbers
- More, less and equivalence
- The concept of ten (use counters with ten frames)
- Addition and subtraction
- Multiplication and division

**2. Pattern Blocks**

Pattern blocks are flat shapes designed so all of the sides of all the shapes are the same length, except for the trapezoid, which has 1 side that is twice as long. Their shapes make them easy to nest together to build 2D patterns and figures.

Pattern blocks help students develop spatial reasoning, which is an essential part of a good math foundation. As students become more familiar with composition and decomposition of shapes, they recognize patterns more easily.

I keep a bucket of them in our manipulatives kit, so I have enough for all of my children to work with at the same time. I like to print activity cards with colored designs for my kiddos to figure out, and we also use them right in the Saxon books 1-3 and for free play. Sometimes we even pick out all the squares and use them like color tiles for graphing.

**Concepts to teach with pattern blocks:**

- Patterns
- Shapes
- Geometric designs
- Spatial Relations
- Types of angles
- Area, parallel and perpendicular lines, and other geometry concept

**3. Base Ten Blocks**

Since our entire number system is based on the number ten, it’s critical that kids develop a good understanding of the number ten and how place value affects numbers. Base Ten blocks help kids “see” the concept of place value, and they can manipulate these blocks to “build” numbers for deep and thorough understanding.

They also help with regrouping, as you can “trade” your child a 10 block for 10 ones, or a 100-block for 10 tens. This is really helpful when your child starts adding large numbers and has to regroup multiple numbers in a row.

**Concepts to teach with Base Ten blocks:**

- Place Value
- Regrouping
- Addition
- Subtraction
- Multiplication
- Division
- Division with remainders
- Zero as place holder
- Fractions
- Decimals
- Expanded notation

**4. Bucket Balance **

A balance will help students explore measurement and mass.

I have this one and it isn’t exactly precise. If you’re looking for a high quality, tightly calibrated scale for scientific experimentation, keep looking.

Strangely, I find I almost use this more to teach Algebra than I do with my younger children. I write the components of algebraic equations on legos and add them to both sides of the balance to model balancing equations.

**Concepts to teach with a bucket balance:**

- Explore volume and
- Compare solids and liquids
- Measure mass
- Measuring
- Estimating
- Cause and effect
- Explore volume vs. mass

**5. Fraction Tiles & Fraction Circles**

I remember walking home from school with a friend in either 4th or 5th grade and arguing about fractions. She *insisted* that her 1/5 acre yard was bigger than my 1/4 acre yard, because 1/5 is bigger than 1/4. I explained over and over why a bigger denominator made a smaller piece, or fraction, and she got madder and madder and we parted mortal enemies.

Luckily, as neighbors we couldn’t hate each other forever. But I learned an important lesson about trying to teach my friends math. Just don’t! Ever!

Fractions aren’t intuitive, so it really helps to show kids that wholes divided into more pieces have smaller pieces and thus bigger denominators. The more kids can visualize the process, the better they’ll understand it.

Multiplication and division of fractions is another very counterintuitive concept that will be made much easier with manipulatives. The manipulatives make it easy to show them that multiplying a number by a fraction creates a smaller number, while dividing by a fraction results in a larger number.

I have two sets of fraction tiles and fraction circles. One set is plastic and the other set is magnetic. I prefer the magnetic set and so do my kiddos! We usually play with them on a cookie sheet to make it easier to get pieces to stay in place.

**Concepts to teach with Fraction Tiles and Circles:**

- the meaning of numerators and denominators
- how fractions work
- fraction addition and subtraction
- equivalent fractions
- multiplication and division of fractions

**6. ****Linking Cubes**

You’ll find many different types of linking cubes. My favorite are the ones that can snap together on all sides (so you can build geometric figures) rather than the type that just snap together at the bottom on top, building a tower.

If you bought enough sets of these to build a 10x10x10 cube, a couple of 100’s, several 10-trains and still have several singles, they could even replace your Base Ten set. But that’s a whole lot of linking cubes! Still you could teach most of the base ten concepts with this set, even without a 1000-cube.

**Concepts to teach with linking cubes:**

- Patterns
- Number correspondence
- Counting
- Skip counting
- Comparisons
- Measurement
- Regrouping
- Sorting
- Addition and subtraction
- Multiplication and division
- Squared and cubed numbers
- Graphing

**7. Judy Clock**

When your math curriculum talks about using a geared clock, this is what they’re talking about. I don’t know why it’s called a Judy clock, but it’s great for beginners just learning to tell time!

The minutes hand is the same color as the minutes and the hour hand is the same color as the hours, making it easy to read. The hands are synced together with gears, too, so they move together naturally anytime you move either of them, with the same mechanism as a real clock.

Mine is made from heavy duty masonite, and has miraculously survived all eight of my children in perfect condition, so it’s worth the investment. That said, I don’t think it’s completely necessary. If you have an analog wall clock you could take down to use a teaching tool, that would work. Or you could print the free clock in these homemade math manipulatives.

Telling time will be a much smaller portion of your children’s math curriculum than place value or arithmetic, so if you have limited funds, spend them on numbers 2-6 above, and then just use counters like coins or dried beans or such that you already have around your house.

**Concepts to teach with a Judy clock:**

- telling time
- schedules
- calendars
- counting by 1’s, 5’s and 15’s
- time terminology (quarter past, half past, etc…)

**8. Ten Frames**

Ten Frames are one of the simplest, yet most effective tools for teaching number sense. Since our number system is based on ten, a thorough understanding of ten and all the components of ten is critical.

Luckily, ten frames are easy peasy (it’s a 2 x 5 array of identical boxes) and don’t require an outlay of cash. You can print some up using the link to the free printable below, you can make your own by cutting off the two end cups of an egg carton, or you can just draw one. I actually like to draw them on our dry-erase boards and then use cute magnets as the counters.

I don’t have enough room her to tell you ALL the reasons Ten Frames are one of my favorite math manipulatives, but I tell ya — they are magical. Learn more about them at this link.

**>>> Get your FREE Printable Ten Frames & Games! <<<**

**Concepts to teach with Ten Frames:**

- Counting
- Subitization
- Number correspondence
- More, less and equivalence
- Addition and subtraction
- Components of ten
- Regrouping
- Decomposition of large numbers
- Problem solving

**9. Geoboards**

Geoboards are square boards with elevated pegs from which students stretch rubber bands to form various shapes. They come in various sizes, from 5-by-5 arrays to 10-by-10 arrays. I prefer the larger size to work with.

Though not strictly essential, geoboards are a lot of fun — especially for kinesthetic and tactile learners! When I bought our first set of Saxon Math Manipulatives (eons ago) the first thing my daughter opened and played with and played with and played with was the geoboard set.

I actually use mine more for teaching Geometry concepts, like rotation and translation, than I do for my younger kids. If you don’t have a geoboard, graph paper or dot paper will also work to learn these concepts, though it won’t be as much fun.

**Concepts to teach with Geoboards:**

- Plane Shapes (squares, rectangles, triangles, parallelograms, trapezoids, etc…)
- Symmetry
- Rotation
- Translation
- Reflection
- Coordinate Planes
- Graphing
- Types of angles
- Problem solving
- Spatial relations

**Are all of the math manipulatives on this list really necessary?**

There are so many cool looking math manipulatives out there, but what is *really necessary*? The short answer is no. As a veteran homeschool mom and penny pincher extraordinaire, I can assure you that you don’t really need everything in the list above.

I use numbers 1-6 almost daily in my own homeschool, but you could really teach math well and effectively with only numbers 2, 3, 5 and 6, plus a few free, printable, math manipulatives and things from around your house (listed below). The other things on the list are just cream.

You might be tempted to compare this list to a commercial set of math manipulatives, or the ones recommended by the publisher of your math curriculum, and find it lacking. But I promise you’ll be fine with just these few items and a few things you probably already have on hand!

**Math Manipulatives You Probably Already Own**

A few other math manipulatives I use frequently, but I just print my own or gather them up from around my house:

**Hundreds Chart:** You’ll use this daily to teach counting, skip counting, prime numbers, number patterns, squared numbers and more. Find a free, printable hundreds chart at that link.

**Paper Base Ten Set:** It’s nice to have a 2 dimensional base ten set when teaching or demonstrating a problem on a white board. I just print them myself. You’ll find a free set at that link.

**Money:** I’m too frugal to pay real money for play money that my kiddos will just play with and lose. So I just throw all of our pocket change into a jar, which we use when we learn about money.

**Measuring Tools:** ruler, yard stick, measuring cups and spoons, quart and gallon pitchers, whatever you’ll need to teach your child about measuremtn.

**Craft sticks:** These work well in place of a base ten set if needed. You can group them into bundles of 100 and 10 with rubber bands to teach place value and regrouping.

**Counters:** The counters above are handy, but you can use just about anything as counters: pennies, pom poms, dried beans, colored beads, or even edibles like marshmallows, cereal pieces, m&m’s or skittles. My kiddos favorite counters are the consumable kind!

**Dominoes:** Dominoes are a fun way to teach counting, subitization and other math skills.

**Dice:** You could pilfer a few from your game cabinet or buy a package from the dollar store. I recently purchased a couple of 6-packs of regular dice and a 5-pack of ten-sided dice (necessary for ten frame games) at my local dollar store.

**Deck of cards:** Playing cards with just the numbers (remove the face cards) or number cards like Uno or Rook work equally well. Card games are great for working on mental math, number correspondence, and drilling facts in a fun way!

**>>> Make Your Own Math Manipulatives Kit FREE! <<<**

I hope this helps! I remember feeling bamboozled by all the math manipulatives available (and shocked by the prices of the kits our math curriculum suggested) when I first started homeschooling.

### Pin this list of favorite math manipulatives for later!

What are your favorite math manipulatives from this list? Please share in the comments below!

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This is an awesome list of math manipulatives! I have never used the ten frame, but I’m going to print that out for my daughter. Thanks! I think all my kids’ favorite manipulatives are the counting bears. They are probably not a “must-have,” but my kids totally love them.

We love the counting bears, too. Actually, I love all of the adorable counters out there, I just don’t love that my kids can’t manage to leave them alone! Aren’t math manipulatives fun?