How to Teach Basic Math for Free Anytime and Everywhere

Chinese math resources for kids

I believe that children can learn basic math for free anywhere.  Math is all around us, and children are born with the desire to learn. 

Parents are often worried about the cost of store-bought resources, time for creating activities, and pressure of academics. I hope this post can give reassurance, and a 1-page printable summary can be found at the end of the post.

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While I enjoy sharing learning games and quality Montessori materials, my children are usually learning basic math skills with little effort.

When my kids were younger, we didn’t have special manipulatives, and we’ve rarely used workbooks and apps. Currently, my 6-year-old daughter has been placed in 3rd grade math. Meanwhile, my 3-year-old has been learning to count and add.

Their math foundations have been established from daily routine and everyday experiences.

How I'm Teaching My Children Basic Math For Free and Without Workbooks

6 Important facts about teaching math to kids

  1. Many parents and caregivers are capable of teaching their kids math basics.
  2. Concrete concepts should mastered before interpreting symbols (eg, numerals, equations).
  3. Every child learns at their own pace. My 2 children are perfect examples of hitting milestones often a year or more apart.
  4. Basic math can be taught anywhere: indoors / outdoors, home / school / play.
  5. A short spontaneous lesson can be highly effective.
  6. Children can learn how to count and do math in multiple languages simultaneously.
  7. Learning is often spiral rather than linear.

Although many of us grew up with workbooks and feel the pressure of progressing to the next page, reviewing the same concept can deepen our child’s knowledge.

How to teach kids basic math for free - counting, addition, subtraction, multiplication, division, fractions

Teaching math at home series

This post is part of a series on teaching math at home:

  1. How I Taught My Daughter Basic Math For Free and Without Workbooks (This article)
  2. How to Count in Chinese and English with Montessori Materials
  3. 10+ Ways to Use a Wooden Hundred Board
  4. 10+ Ways to Use a Printable Hundred Chart
  5. Multiplication Chart and Pythagoras Board
  6. Teach Kids Time with Hands-On Clock Activities
  7. Interactive Calendar Learning Printables

How to teach counting for free

When kids first learn to count, they are usually counting by rote, for example 一, 二, 三, 四, 五, 六… (yī, èr, sān, sì, wǔ, liù / 1, 2, 3, 4, 5, 6…).

Both of my kids mastered rote counting from hide-and-seek, and this fun game offers ample opportunity for counting practice!

Initially, they would rush through the number sequence and lose count. This is common when kids have memorized numbers without knowing what they represent.  No worries!

To encourage my kids to improve their counting, I encourage them to count to a high number slowly and demonstrate this myself.

Shhh… let me share a secret with you: I tell them that it’s for “more hiding time” and don’t reveal my intent for counting practice.

Half of teaching is about how you sell a lesson in a way that fits a child’s worldview.

How I taught my children basic math for free - Counting practice with painted rocks
Counting practice with painted rocks

Everyday counting opportunities

Along with rote counting, counting specific quantities and one-to-one correspondence should be introduced.

  • When to start: Before they speak! Kids are absorbing everything from the start. Count fingers and toes, hugs and kisses – this helps them associate numbers with love and affection!
  • What to count – anything that’s around!
    • Objects: fingers, toes, food (Cheerios, fruit), toys, nature finds (eg, stones, leaves, twigs, pinecones), clothes, utensils, recycled bottle caps and paper rolls
    • Motions: steps, stairs, claps, hugs, jumps, swings at the playground.
  • Tips for starting:
    • Begin with lower quantities: “1…2…” And then stop. “That’s it! 2!”
    • Then gradually increase the amount.
    • Organize what your counting in a line so you can show the start and end.
    • For large amounts, show how to group objects by 5s or 10s so that it’s easier to keep track.
    • Kids love to be active, and counting a large staircase for example can leave emphasizes the grandiosity of big numbers!

Note: you don’t need to buy those popular plastic bears or other counters that will eventually end up in a landfill.

Size, shape, length, patterns

Another skill that can be taught anywhere is comparing object characteristics:

  • Size
  • Length
  • Color
  • Texture
  • Pattern

This type of math involves grasping and touching everything and moving one’s body to figure out the distance.

For example, my kids like to sort big and small nature finds and call them “mommies and daddies” and “babies”!

You can find anything in your house and group them in the aforementioned ways. This also teaches them organization skills!

Reaching for window shade chain and learning that it's too far away!
Letting my son learn that the window shade chain is too far away

I love the moment in the above picture, because the window chain is obviously way out of reach for my son. But he’s so determined to try and doesn’t even come close. I let him try, because he’s developing spatial awareness

Teach basic addition and subtraction for free

Math at mealtime

After counting is established, next comes addition and subtraction.

For example, when my kids ask for strawberries, we can count the number of pieces on their plate.

If they think it’s not enough and ask for more, this becomes an addition learning opportunity. As they eat, we can practice subtraction.

Baking is another natural way to teach math. With measuring cups, you can teach addition and subtraction by looking at volume measurements. They learn that precision can affect taste, and hopefully the result will be delicious!

Addition and subtraction of volume with the Thermos Foogo straw water bottle
Addition and subtraction of volume with the Thermos Foogo straw water bottle

Take notice of what draws your child’s attention, because that is what your child wants to learn.

On our occasional restaurant dates, my daughter likes to keep track of the table numbers, and she does subtraction by considering how many more tables we have to wait for.

As you model addition and subtraction in different settings, your children will discover more ways to apply math on their own!

Addition and subtraction at the park

The playground is a treasure trove of child-led learning opportunities. 

When my daughter is climbing a ladder and has reached the 3rd rung, I might ask, “How many more steps do you need to climb to reach the top?” 

The countdown before going home is always an alarmingly effective way to reinforce subtraction! For example, “You can go down the slide 10 more times.  Now you went 3 times, so you have 7 more changes before we go home.”

How to teach basic multiplication and division for free

Skip-counting, multiplication, and division can be taught in a child-led way, too!

Remember: work with what’s in front of you, and try not to stress about making anything special.

How I'm teaching my children basic math for free - Multiplication with painted rocks
Multiplication with painted rocks

For example, we can group rocks by 2s and demonstrate that 3 groups of 2 rocks is equal to 6 rocks (3 x 2 = 2 + 2 + 2 = 6), and then by 3s, 4s, and so forth.

Last year, my daughter learned to skip count and multiply by 5 with a simple hand counting activity!

Other times, you can incorporate it with whatever your child is working on.

Just this week, we did a quick multiplication “lesson” with a cute turtle weaving craft that my daughter wanted to make.

We needed 3 craft sticks per turtle, and my daughter wanted to make 3 turtles.  In less than 30 seconds, we reviewed that 3 x 3 = 9.

The next day, she decided to make 2 more turtles, so we discussed that since 3 x 3 = 9 and 3 x 2 = 6,  9 + 6 = 15, so 3 x 5 must equal 15!

Craft stick turtle Yarn Weaving God's Eye Craft
Learning multiplication with crafts

We have also introduced division through every day life.

For example, when we are sharing food or toys and want to allocate equally, this is relevant example of division.

Most commonly, we are dividing by 2 (between siblings), and also by 3 and 4, depending on how many family members are at home!

Cutting watermelon in half - teaching fractions math at home Montessori

Fractions

When we are baking, I might deliberately select a smaller volume of a measuring spoon to review fractions. If we scoop 1/4 tsp twice, we can review 1/4 tsp + 1/4 tsp = 1/2 tsp!

We can also practice fractions when cutting whole food (eg, pie, sandwich, quesadilla, pancake) into equal portions.

Through the act of cutting, my daughter realized that dividing her sandwich into 1/7 portions was difficult!

Have fun with verbal word problems

Verbal word problems are a fun way to integrate storytelling and math!

We make up funny stories such as:

  • “姐姐 has 73 dresses, 弟弟 pooped on 11 dresses, how many dresses are clean?”
  • “If we bought 12 strawberries from the market, and everybody in our family wants the same amount, how many strawberries should each person get?”
  • “妈妈 When you are 100 years old, I will be 70, and 弟弟 will be… 67!!”

Introducing numerals and equations

In all of the above examples of counting and basic math, the concepts did not require number symbols.

Children must hold math in their hands before they can hold it in their head.

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This is similar to how learning a language begins with listening and speaking before reading and decoding text.

How to introduce number symbols

  • Point them out in the environment: houses, in elevators, mailboxes, page numbers
  • Making numbers with pipe cleaners, play dough

Encouraging a love of learning math

Here is one of my favorite pictures of my daughter, looking for the smallest and largest numbers at the Post Office.

Counting practice at the post office - Math is all around us, and children are born with the desire to learn. Before I made any printables and collected educational toys, we established math foundations from routine, everyday experiences. My oldest child has learned everything from counting to multiplication through the simple, free ways detailed in this post. #math #preschool #kindergarten #firstgrade #homeschool
Child-led counting at the post office

While she called out various numbers in Chinese, my son ran along from mailbox-to-mailbox and tried to mimic what she said.

I had to suppress my urge to rush onto the next task.

I’m grateful that my children remind me to take pause and see the amazing world of learning from their perspective.

When the rest of the world seems to be worrying about which workbook or app get, please remember that free, meaningful lessons can be found throughout a regular day.

Chinese math learning for kids

Printable summary of basic math teaching tips

Click below to download a 1-page printable summary when you need a quick reference!

Have questions about teaching math?

I’d love to hear your thoughts about teaching math at home and how it’s been going for your family.

Feel free to leave a comment with any concerns or thoughts about your family’s learning journey, and I’ll try my best to find a solution for you.

In the meantime, I hope the following articles can be helpful!

More hands-on math resources

Happy learning, friends!

4 Comments

  1. This is very helpful, thanks Betty! I’d like to print the one pager out to remind myself, but the download doesn’t seem to work, could you please take a look? Thanks!

    1. Link doesn’t work for me either. Is there somewhere else to find the summary?

      Also, thank you for providing such useful tips in the blog post. Much appreciated!

      1. Hi Jennifer and Diana! Thanks for letting me know about the broken link – I have just fixed it. Please let me know if I can help with anything else!

  2. I was looking for some good blogs related to maths hopefully your article will help to solve my children problems in this subject.Thanks for sharing.

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