Best Homeschool Math and How to Help Your Child Learn It

You can help your child learn math. You can make Math intentional, but Don’t take the Fun out of Math!

If you use a boilerplate curriculum you will just end up teaching your child in a way that lacks purpose and more often than not takes the fun out of math. Understanding math is understanding the world around you. Kids have an innate curiosity for understanding the world around them. I think they know they have to learn it in small doses as they go, because it’s too vast to try to take it all in. But when we start pushing math worksheets, word problems that don’t apply to their lives and do so while their minds are on play mode, we are sending the message that this “math” is more important than understanding how things work and also that Math is uninteresting and tedious.

In an effort to justify this, many people, moms, school teachers, school principles…tell kids that they will be smarter than other kids that don’t do worksheets and learn this kind of meaningless math. They are often told how smart they are getting because they can finish 10 pages of addition in a short time.

To quote Paul Lockhart “Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions. Math is not about following directions, it’s about making new directions.”

So how do I help my child learn math?

Understand where is math in the real world, how to find it. The challenge for you as the parent is to figure out when it’s too early for a child to understand math concepts and do certain calculations. From that wisdom,  just talk about them in small doses, and when your child is ready introduce the concept in more depth. And when she’s ready show her how to do the calculation.

What you need math for and how to learn it:

“Clocks tell time, but only if you know how to interpret them, which

uses math. In particular, telling time uses addition and subtraction.

How much longer until school gets out? How long did I sleep last

night? When’s my favorite TV show on? And if you know how to use it,

clocks involve what is called sexagesimal counting; that is, counting

by sixties. There are 60 seconds in a minute, 60 minutes in an hour.

So we think of 15 minutes as a quarter of an hour, for example.  That

uses fraction concepts.

We do a bit of math when we drive a car. We have an intuitive

understanding of speed, for example. 30 miles per hour is slow, you

might say, or 50 mph is too fast for barreling down local streets.

How long would it take to drive from Los Angeles to San Francisco?

It’s about 370 miles. Or could you determine your average speed if you

drove from Seattle to Tacoma in 20 minutes?

Same thing with sports, whether it’s running track or seeing how far

you can throw that football. How many yards is it to first down? How

would you keep score without using math?

Shopping involves lots of math. How much change would you get if you

paid for a $25.99 sweater with two twenties? How would you calculate

sales tax, or a 30% discount? Tons of math there.

Then again, maybe you love to build things, so you decide to get into

furniture design. You’ll use geometry like there’s no tomorrow….

How long do I need to make that cut, or what size should that dovetail

joint be? How many square yards of fabric do you need to upholster

that couch? What angle do I need to cut the panel by, to make it fit?

If you’re living in a technologically advanced society, just about

everything involves math of some sort. The computer you use is a

machine to do binary arithmetic incredibly fast; the house you live in

was constructed by architects who had to specify its dimensions, and

engineers who had to determine the loads the various parts could

withstand. You would be hard pressed to find something that didn’t

relate to math in some way.”  From – A Better Mathematics Curriculum, by Tom Davis, PhD

Math skills by age

4 to 5 year olds do not have any practical use for math other than showing how old they are with their fingers. It is possible they may be around older people that require them to “learn some math” in that case 4 -5 Year olds will practice counting 1 -20. And recognizing numbers from 1 -10.

Or they might learn by osmosis.

My daughter learned to count from 1 -30 when she was 5 only because during the summer months she played at the pool with other kids and they would count how long they could be under water. They also counted before they jumped in the water. Etc. I thought my daughter was advanced…but not in math, in swimming! The fact that she was swimming and jumping in the pool at 5 lead her to learn to count by osmosis.

6 year olds can practice shopping and reading the prices.

They can measure a space with their steps, they can estimate many things like how much salt a dish will need, how long a piece of string they’ll need to tie the doorknob to their bed, there will be a lot of hands-on trial and error in order to get to more accurate estimations. This is also called the scientific method.

They can learn the numbers from 0 – 30. They can learn some additions. They can tell what is half and they can be introduced to reading time on a clock.

You don’t need to drill your child with workbooks full of addition and subtraction pages. You can make them some pages as you go based on what you think they are ready for and what you know they know and can benefit from practicing on paper. If they are ready..if they are adding with their fingers, and making some simple calculations in their head then the paper ones will be very easy and fun for them.

There has been enough research studies by now to convince parents and teachers that IT IS IMPORTANT TO LET KIDS USE THEIR FINGERS TO COUNT, LET THEM USE THEIR FINGERS, THERE IS NO SHAME IN ADDING AND SUBTRACTING WITH THE FINGERS.

A 7 and 1/2 year old with a normal, social and rich life, may have learned all the above even if no one has “taught” him. You can help a 7 and a half to learn the following in a matter of weeks:

To count to 100

To recognize the numbers up to 100

To recognize all the hundreds

We used a stack of flashcards for the numbers. One side was for 1 -50 and the other side for 51 – 100). We helped her memorize them. We practiced a few times per week. We shuffled them and payed them on the table and arranged them in order. Etc.

We also counted money. At the time we happened to be in Europe so she learned to count Euro. Didn’t matter to her, she could go to the Kiosk and but candy.

To do two digit addition

To subtract with one and two digits

Solve problems that relate precisely to real life events such as: “The toy I want costs $10, I had $17 but I bought 4 things at the dollar store and I gave my friend enough to by 4 things also. That is $8 plus tax. So I have about $8 left. I need $3 more dollars to buy my toy.

They can follow a recipe to make pancakes or waffles.

 

By the time they are 8 years old they can use a ruler to measure accurately.

They understand giving change and can do simple change calculations.

They may understand the concept of multiplication and able to multiply.

They can estimate how much fabric they might need for a project.

They can follow a recipe to make cookies.

They can learn fractions with a visual.

PERSONAL FINANCE

6 – 7 year olds

Currency denominations:

There are so many ways to explain this, and all of them should be explained.

How many quarters make a $1? This is tangible. Take a bunch of quarters and make sets of two. Tell her two quarters make .50 c, and two .50 cents make $1.

Explain that 100 cents makes $1.

Explain quarters. 4 quarters make $1.

The above takes time, don’t expect your child to take it all in at once. Dish it out in small morsels that he can really savor.

6 – 8

Other denominations. Practice adding denominations.

Calculate change – Practice role playing at home, go shopping, buy things for themselves.

Staying within your budget.

Expenses.

What is Profit?

6 – 9 years old

Reading the prices, round up .99 cents to a dollar, adding how much a few things you want at the store would cost all together, figuring out if you have enough money to pay for something at the store, figuring out how much you need.

Remember to add a little bit for taxes.

Talk about taxes: what are taxes? What is sales tax used for? Some kids may have a problem with this at first -my daughter refused to pay sales tax for a long time but after a while it becomes a normal part of shopping.

9 – 11

Borrowing money. What is interest?

Expenses, profit.

Budgeting.

Saving money.

Banks.

Bank accounts.

Calculating taxes.

Talk bout taxes. They are familiar with sales tax. Talk about Income Tax. What are income taxes used for?

Tipping. Calculating how much tip to leave at a restaurant.

12 – 14

Loans. House, car, student loans. If you borrow a certain amount, how long will it take to pay it off? How much will your payments be? Talk about interest rates. Learn to calculate interests rates and payments at different loan terms.

PROBLEM SOLVING

This is the kind of skill that you gather through solving puzzles, working on projects, playing games, and is also applied to personal finance.

I think it is amusing that 4 and 5 year olds are encouraged to sort. Sorting little trinkets and meaningless objects by type, color, and size. It seems a little weird to me, that’s all. When I see kids sorting their trick or treating candy, trading candy, organizing a yard sale, organizing their supplies, they categorize everything! They are little masters of sorting by the most outlandish categories. They don’t need to be sat in front of a manipulative to help them learn this is skill.

They make up their own games and puzzles, solve problems, play with puzzles, they play store, they see things upside down and can draw or write letters upside down and backwards, their world is full of infinite possibilities -they live in a math world.

Once the problem appears, you can give them tips to solve it. It’s much easier to wrap your head around a math problem when it solves an immediate problem in your life. For example an 8 year old needs to quickly figure out how many party favors to have at his birthday if he’s inviting 6 friends and each kid gets 4 trinkets and treats. He might want to add them…This is a good time to introduce multiplication. He will probably thank you for the tip.

Continue looking for opportunities to use multiplication. Once your mind is on that, you will recognize the opportunities often, when applied to real life problem solving he will see the benefit of learning to multiply and at the same time he will be practicing “word problems”.

GAMES FOR MATH

Pattern Blocks and Board Set

Go Fish

War

Tic Tac Toe

Geoboards

4 in a Row

Hi Low

Darts:  is a game of multiplication, and subtraction.

Cribbage

Tetris

HANDS ON PROJECTS

Another way to get extra exposure to practicing arithmetic and word problems is by doing hands on projects.

My daughter is currently working on a business. She wants to sell string art kits at a one day market. She had to estimate how much wood we needed to buy. I had them cut the board into 2’x2’ boards so I could put them in my car. So she had to measure and count how many pieces each board could be divided into (she didn’t realize she was doing division, she was just measuring out 6”x8” pieces). Then she had to figure out how many pieces she would have total out of 4 boards (multiplication).

She has to do a lot more calculations. I suggest or explain and she may or may not understand. That’s ok. I am confident that it will come up again and again. She loves building things -multiplying, dividing and solving problems comes with the territory.

MEASUREMENTS

Measure things in inches, feet,  yards.

When we cook or bake we measure in cups and teaspoons.

We measure how fast we go in the car by miles per hour.

We measure time.

We measure weight in pounds and ounces.

It is very important to learn the metric system. It is sooo easy. It’s not worth putting it off until they are older or in case they go into a technical field. This is the kind of math that really needs to be learned, and not just because the rest of the world uses the metric system.

Exponential growth.

Reading graphs – charts and tables.

Measuring and telling time:

You can introduce reading time at 6 years old, but it may or may not click. Just keep referring to the clock and asking them to tell you what time it is. By 7 she’ll start getting the hang of it.

Measuring time uses a lot of arithmetic and can be practiced when trying to know how long until a friend comes over for a play date, how long to go to a birthday party, etc.

Telling time can be introduced by showing them the half and the quarters. Kids understand half, quarter and three quarters if you always point out when their age as 5 and 1/4, 5 and 1/2, 5 and 1/4. By the time they are 7 you can show them on a piece of paper with a graph like a circle (that resembles a clock) when they will be 7 and 1/2, 7 and 1/4…By the time they are 8 years old they can fill out the areas of the circle and figure out how to write it in fractions.

STATISTICS – Kids can be very good at estimating, but they live in a world of data. They, more than any other generation, should understand sooner than latter what are statistics, how they are used, what kinds of statistics are there, examples, etc.

ESTIMATION – Estimating amounts, measurements, financial transactions.

GEOMETRY – Very young kids start learning the shapes and the names of the shapes because they are everywhere. Geometry is a fun subject to learn and since it is visual it can be applied to anything around us. It can be like a game or a more creative activity.

Geometry is the one subject I would include in our Intentional Learning.

Math for the future

Kids can learn the math that will prepare them for all stages of their lives. Specially adulthood. Once they have a grasp on this math, independently of the math that is needed to function in society, as kids get older they may want to go into a field of Engineering, or perhaps mathematics, chemistry, physics, computer science, economics…

Any science requires math.

In addition to science there are many careers that require a good understanding of maths like architecture, product design, etc.

The problem with teaching algebra, calculus, trigonometry to kids is that they don’t know yet what they will be when they grow up. So the argument might go like this: Kids should have a good foundation of algebra, calculus, geometry because IF they want to be computer scientist, engineers or economists, whatever, they will need some of these skills.

The problem with that argument is that it is exactly what schools are doing. Does it work? Not really. Some kids are good at Math, very few have a special gift for mathematics and lap it all up, but most kids hate math by the time they are teenagers, and in a High School they hate it even more, so they cross a lot of careers off their list because they believe they are not good at math.

What Math Does My Teen Need for University?

If she is interested in a technical field that requires mathematics, she will be inclined towards learning the mathematics that is needed for the area of expertise. It takes different mathematics to be a computer scientist than an economist, an engineer, or a mathematician.

Algebra, trigonometry and geometry will be needed for most technical fields. As well as calculus depending on the field. But geometry is part of the Intentional Learning list and kids would know how to create and solve geometry problems by the time they go into their teens. Algebra can be learned easily if they like solving problems and puzzles. And it doesn’t take five years to learn calculus.

Therefore, I would not focus on a math curriculum that forces you to teach your kid the math that kids learn at school. I would focus on the math they will need through their lives and on their day to day through real life opportunities and projects, as well as geometry. And when they are 12 – 14 years old, I would encourage them to learn algebra and calculus on their own. And I would suggest chemistry and physics depending on the child’s interests and aptitude.

High School vs College is an article on how to get into college or university if you homeschool and what is required.

SCIENCE

Nurture a love for science and introduce physics whenever possible.Toys as well as real play is full of Physics, chemistry, biology, etc.

There are physics concepts that you can bring up or point out when they are playing like:

How electricity works, do some experiments, point out static electricity.

Force, speed, momentum, etc. Estimating where an object might land and how you would adjust the speed or force…Build a catapult. Make paper airplanes.

Build forts, things out of rocks, wood pieces, pillows…Science is experimentation.

The world around them is natural sciences. Read our Science at Home for 4 – 8 year olds.

LEARNING REAL MATHEMATICS

Of course I am not a mathematician and I use the term “math” the way I think you, (probably also not a mathematician otherwise you wouldn’t be here) expect me to use it. I talk about the real-life skills that are important for kids to learn. But I don’t talk about real mathematics because that would be way beyond what I am qualified to discuss.

I have met only two or three mathematicians in my life. People that have a love and a gift for math, so they decided to devote their life to thinking and practicing mathematics. One of them was a software engineer but his first and only love was Math. I guess it run in his family the way painting runs in mine. He could make calculus sweet and beautiful to someone who has thought all her life that she hated math. These real mathematicians call math Art.

Learning real mathematics sounds a lot like playful art. I can’t comprehend how but if you have an interest I would refer you to read The Mathematicians Lament and then go to websites that are run by real mathematicians that are concerned about how erroneously presented math is in schools/curricula and have free resources to present to kids so that you can focus on fostering a love for Math.

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

https://www.youcubed.org/

https://naturalmath.com/

Happy Maths!

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