When you first begin homeschooling it can be difficult to figure out what you need to teach your kids to keep them “on track” as they approach first grade.
We are here to come alongside you with our brand-new Kindergarten program, which meets three times a week for just twenty minutes. This program is built around small, bite-sized chunks of learning that keep your children engaged and eager for more!
Below you will find a checklist of “essentials” that a child should know in order to successfully begin most first-grade curriculum. In this post, I focused specifically on arguably the most mysterious subject, Math, and then added a little more.
Mathematical Thinking Happens Naturally
Math is a natural process that children begin to explore at a young age.
As they sort toys into different arrangements, count things, recognize patterns, and otherwise make sense of the mathematical world around them, they are validating Galileo Galilei’s famous observation that “Mathematics is the language with which God has written the universe.”
The inherent order, intricate detail, and mathematically precise structure of our world all point to the nature of our Creator, and even the youngest children can see how wonderfully God has made all things.
Sometimes, however, our kids struggle to see the relationship between this beautiful world of natural math and the numbers and symbols that represent them. Math can seem abstract when represented by numbers and symbols. By making it visual and hands-on, we can bring their natural ability to understand math back into play.
Preschool Math Skills
There are many math skills that can be accomplished without paper and pencils that will prepare your child for a more formal math curriculum. Use this list of preschool Math skills to introduce fundamental math skills into your child’s play:
- Identifying colors (if your child struggles with identifying colors after age 5, and especially if colorblindness runs in your family, you may want to consult your doctor about the possibility of colorblindness)
- Identifying numbers (0-9 initially)
- Counting by rote (saying numbers, not counting objects) – start with counting to 10, then 20, then up to 100
- Counting objects (up to 10)
- Understanding one-to-one correspondence – that the last item counted is the quantity represented (if child counts ducks, 1, 2, 3 – he understands that there are three ducks)
- Subitizing — being able to identify the number of objects without counting (up to 5)
- Sorting by color, size, texture, or other feature
- Making simple patterns (block, car, block, car…)
- Doing simple addition and subtraction problems using objects (2 bears sat in the car, 1 more bear got in, how many are in the car now?)
- Saying/singing days of the week and months of the year
- Identifying seasons
- Using counting books, shape books, and other math concept books to gently introduce math concepts
Laying a Solid Foundation in Number Sense
Once kids are able to count to 20 by 1’s, to 100 by 10’s, and understand the idea of one-to-one correspondence, they are ready to move up into the next level of developing number sense.
If you can help your kids develop number sense from the very beginning of their educational journey, you will set them up for success as they develop Mathematical reasoning skills throughout their life.
What is Number Sense?
Number sense refers to the ability to work flexibly and confidently with numbers based on a deep understanding of how numbers work, which largely depends on seeing numbers in groups of 1, 10’s, 100’s, etc.
Since our mathematical system is built on a base-ten framework, it is imperative that children see numbers grouped in 10’s from their first encounter with Math.
There are three key concepts that all children need to know in order to truly understand HOW Math works, rather than skating on the surface of fact memorization and a few highly recommended Math tools (manipulatives) that help reinforce these concepts.
Three Key Concepts:
Subitizing refers to the ability to see groups of numbers at a glance without counting. When kids first begin counting, it will serve them well for years to come if they can learn to arrange the objects they are counting in groups of 10’s which are further broken up into sub-groups of 5’s.
For example, instead of counting a random pile of eight raisins, they should practice laying out the raisins in a line of five with a line of three more underneath.
The sub-groups of five are key because that is what allows our brains to instantly see amounts without counting individual objects. For example, a random pile of nine toys is not instantly countable, but an ordered group of five and four can be instantly recognized – with a little bit of training.
This ties in directly with the skill of composing and decomposing numbers – that is, grouping objects in their base ten values and breaking them back apart in meaningful ways.
If you can make this type of exercise a regular part of their play, it will help them intuitively begin to “see numbers” in instantly recognizable amounts – so that ultimately when they think of the number eight, they see groupings of five and three more, or visualizing the number twenty-six as two groups of tens, a group of five, and one more.
This basis of intuitive number sense leads spontaneously into a solid understanding of addition, subtraction, fact families, place value, estimation, and much more!
As they practice this “instant recognition” skill of seeing numbers in groups of tens with sub-groups of fives, they will find themselves adding and subtracting before they even realize what’s going on.
With a bit of intentional practice, you can help them master all the combinations of “ten” which is key to everything else in the Math Facts world, as well as develop fluency in their single-digit addition facts.
Then you can overlay “Math Talk” equations onto the familiar hands-on play-based experience and show them how subtraction is a simple extension of addition. For instance, asking how many more you need to add to six to make nine should prompt a visual image where three missing spaces “light up.” This also opens the door to early algebraic reasoning!
The Best Math Manipulatives
Anything that helps kids see numbers grouped in “10’s” is useful. The best tools, however, take this a step further and focus intentionally on the sub-groups of 5’s within every 10. This simple aspect turns every number into an instantly recognizable amount.
For young kids, ten frames serve as the perfect tool for this. You can purchase plastic or magnetic ten frames and use them to develop number sense as described above, or you can simply draw a 5×2 grid and use it repeatedly to group objects that you count.
As kids get older and are ready to work with larger numbers, you can extend all these ideas by using an abacus (if the rows of ten are differentiated into different colors in groups of five) or a rekenrek. A rekenrek is essentially a rod or string of ten beads with five in one color and five in another color. There are usually at least two of these rows to help with subitizing and adding/subtracting within twenty, but you can also get a 10-row rekenrek (which is similar to an abacus with ten rows of ten beads on each.)
You can easily DIY these Math tools, and the hands-on experience of making these may be just what kids need in order to solidify these Math concepts!
In Developing Number Sense and Mastering Math Facts Level 1, we cover all these ideas and use these tools very strategically to help walk kids step-by-step through a fundamental, lifelong understanding of HOW Math works.
This class focuses on helping kids enjoy learning as they lay a solid foundation for all future Math skills through:
- hands-on activities,
- Math games,
- creative practice (making mini-books, completing color-by-number worksheets, solving picture puzzles, using note-taking guides, etc.),
- digital activities,
- quizzes focused on ensuring skill mastery at each level, and
- ongoing conversations about the HOW and WHY of Mathematical problem-solving skills.
For Parents of Older Kids
If you have older kids who have some gaps in their understanding (or fluency and self-confidence!) of how multi-digit addition and subtraction with re-grouping works and are ready to begin their journey into multiplication and division in a way that builds on deep understanding, not memorization or “tricks,” then you may be interested in Level 2 of this same class.
To round out the discussion of subjects and topics kids can learn before first grade, refer to this list of ideas and this blog post on What My Child Needs to Learn Before First Grade.
Before First Grade, Science, Social Studies, and even foreign languages can be explored through educational shows, books, and by exploring the world through nature, museums, zoos, and other field trips. Have fun! Learn about the world around you with your preschoolers!
Here are some ideas:
- Community Helpers – fire, police, construction workers, store clerks, servers, food service, doctors, dentists
- Lakes and ponds
- Flowers and grass
- Animals (zoo, pet shop, etc)
- Reading/exploring signs in multiple languages (around here a lot of things are in Spanish and English, or have Braille on them)
- Visiting hands-on museums and exhibits
- Finding family-friendly festivals and cultural events in your area
You will prepare your young children for future learning by providing them with active educational adventures. Those will give them an understanding of the world around them and joy in exploring it that will lead to a lifelong love of learning.
About the Author: Sandra, formerly a Math teacher (M.A.), now homeschools her three kids and funnels her passion for teaching into creating engaging, hands-on Math curriculum, courses, and activities that help kids develop a deep understanding of how Math works and enjoy the learning process. Her dream is to help raise a generation of Math Superstars who have never heard of Math anxiety and are confident in their own ability to make sense of Math. She teaches K-6th grade math including Math Art, Number Sense Addition & Subtraction, and Number Sense Multiplication & Division through True North Homeschool Academy.