Kindergarten Readiness- Math

Due to COVID-19, most of us have lost access to pre-school and other childcare options that supported our children’s learning. While this is frustrating for students already in school, it is even more nerve wracking for parents of students entering Kindergarten.

Many parents of pre-school aged kids are wondering if their children are on track or falling behind. What are children expected to know when they walk into their first day of Kindergarten? How do we, as parents, make sure they are meeting those expectations?

To help solve this issue, I am starting a series on what kindergartens expect your child to know before they walk in the doors and how you as the parent can support that development. As always, the first step to solving any problem is to define it. So over the next few weeks, I will be going over the expectations in each of the 4 major developmental domains for this area: social-emotional, language and literacy, math, and English language development (English as a Second Language, ESL). I am taking these standards from the California Preschool Learning Foundations Volume 1. While these are California standards, the rest of the country has similar standards and expectations. In any case, they are a good guideline for us parents.

After I have outlined the standards, I will then post a series of activities you can do with your toddler to help them be ready for school (skip to the activities). Those posts will be scaffolded with activities to support earlier learners as well as those about to enter Kindergarten next year.

This week we will be talking about Math.

Math, ugh?

Creating a solid math foundation is important for a child’s future success as an adult. Being able to count and understand numbers and shapes is vital for every adult career.

Because nothing happens in a bubble, these skills are scaffolded. We start looking for signs of readiness in the 3.5- 4 year age span, then we look for those skills to have grown in the 4.5-5 year age range.

Remember, we start looking for these behaviors at the beginning of the age range, so if your child displays none of them at 3.5 years old or only displays the 4-year-old skills at almost 5 that is okay! They have plenty of time to develop the skills we are looking for.

If your child is a little bit behind, that is okay; that is why the buffer is there. Children have a tendency to develop in leaps in one domain and stagnate in the others. They often rotate through where these great gains are made.

If you are concerned that your child is falling too far behind, consult your doctor. Early intervention is key if there is a problem. The sooner you start intervention, the faster the problem corrects itself and the less likely it is to turn into a disadvantage later.

One more disclaimer: children all express themselves differently. The examples below are only a few ways children can demonstrate readiness in this domain. Furthermore, readiness is evaluated in the child’s mother tong. So a child who speaks a different language at home should display readiness in that language, but may not display readiness in an English environment.

A quick note: anywhere I say the child should tell you a number, I mean they should indicate they know the number. They can show this any number of ways from handing you the number of objects you asked for, holding up fingers, to saying the number verbally.

4 Years Old

Number Sense

At 4, children should really be getting a feel for numbers and amounts. They aren’t always super accurate, but they clearly understand the concept of numbers and they should demonstrate it often.

Children of this age should be getting really good at counting to 10, and they should do it often without prompting. They may point to and count blocks after stacking them, count their steps, sing counting songs, and group toys together to count them. Remember, they may not always get it right. You could hear the child sing “One, two, three, four, five, seven, nine, ten!” occasionally, but they should get it right more than they get it wrong.

Beyond counting out loud, they should be recognizing some written numbers. Maybe they pick out the number 3 in a book, or they can draw and identify “2”. They may not recognize all the numerals we use for counting (0-9), but they should recognize more than three numerals. At this point, they are not expected to understand or identify higher numbers. So they may be able to identify “1” but when confronted with “11” they may say “Look mommy! Two ones!” instead of recognizing it as eleven.

After counting a group of objects, they should be able to tell you the number of objects without recounting. For example, you could count the number of bears in a picture together, and then if you ask “how many bears was that” the child should immediately respond “six.” And when asked how many dolls they are playing with, they should either count them out and tell you the highest number or be able to look at the group of dolls and tell you the answer (”three!”).

Around 4 they should also be recognizing common groupings. In groups of items fewer than 5, they should be able to identify the number of objects without counting. For standard objects in common configurations, they should be able to pick out groupings of up to 6 without counting. What does this look like? They should no longer need to count the dots on a 6-sided die, or if they have three dolls in front of them they should be able to tell you “three” without counting.

As they start to fully understand groups, they should show they understand that we can compare groups of items. If they have 3 blocks, and their friend has two blocks, they could decide to group them so they have “more” blocks. They may recognize that a friend had more gummy bears in their fruit snack than they do and then ask for more so it is even, or they could give one of their dolls to a sibling/ friend and then say “I have less dolls.” In some circumstances, they may even try to make things even (”Look! Now everyone has 4 crayons!”)

While they are pulling groups of objects together, they should recognize the larger group is counted as a whole just like their smaller grouping of items was before. For example, if they have 3 crayons, and their friend brings 2 crayons to the table, they should now recognize there are 5 crayons on the table. They should not only count their three original crayons.

Algebra, Classifications, and Patterns

Sorting and matching are difficult skills, but our 4-year-olds should be well on their way towards mastering them. They should be sorting items by one attribute. In a pile of vehicles they may only pick up the trains, or they could pick cars of a certain color. They may not sort the whole pile, but they are definitely choosing items of specific attributes.

Given a pile of laundry, they may be able to sort out one specific item without help at a time. So maybe they pull out all the shirts into a new pile, and then all the socks, and then all the pants. Once they have their piles, they can then go through a pile and sort it based on a new attribute, like size.

They should also be able to identify and create a simple repeating pattern. Stacking blocks in a red-blue-red-blue pattern, or making a bracelet with black-white-black-white beads. They should clap in a pattern with a group during circle time at school, and anticipate patterns in stories (with some help). Or they could make a double-decker sandwich of cracker-cheese-cracker-cheese-cracker at snack time.

Measurement

Just like they can compare groups of objects, they can compare less concrete attributes. They should be able to compare weights, lengths, and volumes.

For example, they may compare themselves to others: “I’m taller than my brother,” or “Susie is heavier than me.” Or they could compare the lengths and heights of toys: “My tower is tallest,” or “the blue train is longer than the green train, but the red train is longer than both of them!”

When playing they may sort toys by size or match a larger doll to the larger bottle and a smaller doll to the smaller bottle. While pretending, daddy may get the big bowl, mommy the medium bowl, and baby the small bowl.

Geometry

Children at this age should be able to identify common shapes in their environment. They may pick up a block and call it a square, or pick up a ball and point out that its a circle. If you draw common shapes, like a rectangle or a triangle, they should be able to name them. And when presented with a pile of multiple different sized shapes they should be able to sort by shape; pulling out all the triangles or circles. It is important they can recognize shapes can be different sizes.

They should also be using different simple shapes to represent complex concepts while drawing or pretending. While drawing, a circle could represent the sun, or a square could represent a house. While pretending a rectangular cushion could be a raft or a box could be… well anything…..

Finally, they should understand how objects exist in space. That means they should be regularly demonstrating they understand in, on, under, up, down, inside, and outside. Instructions using these words “Your doll is under the table,” or “Please put the plate on the table,” should be easy for the child to understand and follow.

Mathematical Reasoning

Mathematical reasoning is the beginning of logic and complex problem-solving. It includes logical ideas like the base of the tower is more stable if it is wider than the top or comparing things for size.

They may display the beginnings of mathematical reasoning by ordering a ring stacker from the largest ring to smallest or by building a tower will all rectangular blocks at the base and triangular blocks at the top. When playing with friends, they may divide resources so everyone in the group has the same number of crayons; or set up the paint so every paint has its own paintbrush.

Sorting will be based on ever more complex criteria as well. Maybe they sort objects by what can roll and what can’t, or they sort blocks by both size and color. And when faced with a container that is not big enough to hold what they want it to, they will go search for a larger container.

At Around 5 Years Old

Number Sense

At 4, children can mostly count to 10. Now, they should have the same success counting to 20 as they did to 10 a year ago. They may mix up or skip some of the numbers, but they should mostly be able to count to 20 and they should be excited to do so in everyday circumstances.

Maybe your child has counting contests with other children, or counts all the stairs in a staircase, or counts how many jumps they can do. No matter how they do it, you should hear them frequently count to 20.

Not only can they count numbers or objects to 20, but now they should be able to recognize written numbers to 20. They may point out page numbers or use alphabet/number blocks to make numbers. And recognizing written numbers is only the start. They should be able to recognize how many objects are in a small pile without needing to count them for groups up to 4 objects. They may hold up fingers to indicate you have three dolls or shout about how they only have 2 pieces of bacon on their plate without needing to count the objects individually.

And speaking of counting, at this point they should be able to count out 10 objects without help. They could point to and count out 10 blocks, or point at and count the children they are playing duck-duck-goose with. If you ask them to get 5 napkins while setting the table, they should be able to go count out 5 napkins without help and bring them to the table.

At 4 we were setting up their math foundation by helping them understand the concepts of more or less, now they should have mastered more/ less and moved on to actual simple arithmetic. They can divide 6 pieces of fruit among 6 people so everyone has a piece of fruit, and divide 8 crayons between 4 people evenly. If I have 5 rocks, and the child has 5 rocks, they can count the rocks in each pile and determine we have the same amount. If I add a rock to the child’s pile, they will now recognize they have one more rock than me. The child may even go find another rock to add to my pile so we have the same number of rocks again.

The concepts of addition and subtraction are becoming more and more clear. If there are 6 bananas on the counter, and then the child eats one, they should be able to answer how many bananas are left. For larger numbers of objects, or combining 2 groups of objects together, the child may need to re-count the objects. If you are adding or subtracting by one (you have 5 grapes, here is one more) they should not need to count all the objects again and should know the number of objects has changed by exactly one object.

Algebra, Classifications, and Patterns

Up until now, children have mostly been sorting items by one attribute. Those attributes can be complex (does it roll?) or concrete (is it red?) but now they should be able to sort by multiple attributes to make multiple piles. If they are sorting the laundry, they may be able to pull out all the shirts and sort them by who’s shirt it is. They could sort their blocks by shape or sort buttons by both size and color.

Pattern recognition is up too. They should more easily recognize and complete patterns, and may even make patterns themselves without prompting. Pattern songs are particularly fun for this age, including songs like the hokey-pokey. You should see them using patterns during art while making a necklace or while building with blocks. They could also clap or move in patterns (clap, hop, wiggle, clap, hop, wiggle, etc.)

Measurement

Before, when the child was comparing objects, they did it directly. They would put their shoes together to determine who has a longer shoe, or stand back to back to figure out who is taller. While they should still do that, they should also be bringing in a third object to do their comparisons. Maybe they use a string to determine if one apple is bigger around than another, or they stand against a wall and compare their marks on the wall to determine who is taller. While they may not use an actual ruler yet, they will use found objects as ways to measure and compare two other objects.

If they don’t have an object long enough to compare the two objects they are looking at, they may use units of a different object. For example, they could measure the diameter of a plate and a cup by stacking goldfish nose to tail and determine the plate is 15 goldfish wide and the cup is 6. Or maybe they determine the distance between two objects by walking toe to heel and counting steps.

They are also getting good at comparing the sizes of objects. At the pouring station, they can line up all the bowls and cups by size from largest to smallest (or vice versa). In the ball pit they can pull out different sized balls and line them up. When playing with their stuffed animals, they line them up from smallest to largest.

Geometry

At 4, children can identify common shapes. At 5 they should be able to construct them as well. Maybe they fold paper in half and make a triangle, or they use playdough to make a shape. They can also combine common objects (like blocks) to make a new shape (I used these squares to make a rectangle).

It should also be easier for them to find common shapes in their environment. They should know the TV is a rectangle, or the clock is a circle without prompting.

When doing art or building, they should also be combining shapes to make something new. A square with a triangle on top is a house, or maybe they use pieces of paper to make a collage.

Their understanding of objects in spaces is also expanding. They are the ones who can now give directions to find things in complicated places. When asked, “where are your shoes” they can direct you to under the table or behind the couch. And if they can’t find their book, you can say it is on the table and they will understand without any other prompting (like pointing).

Mathematical Reasoning

The 5-year-olds ability to problem solve and communicate the solution to a problem is also expanding rapidly.

They may notice, at a glance, that there are not enough crayons for everyone in a group to have one and then seek a teacher for the exact number of crayons they need. When setting the table, if they have too many napkins they may return the extra and tell you how many were left. When building, if they run out of the blocks they were using, they may use smaller blocks, or turn a larger block on its side without prompting.

And their estimation skills are beginning to develop. If shown a ball, they should be able to estimate how many of that ball could fit in a small box. They could also estimate how many carrots mom packed for lunch.

How to Improve

Creating a strong math foundation is very important to helping our children be sucessful adults. After all, we need math for everything from finances to measuring furniture.

The first thing you can do to help them develop math skills is to count. Count everything. If there are 6 fish on a page of the book you are reading, count them. Count the steps on the stairs. Count the number of eyes and ears you have. Just count.

Then give them numbers to play with. There are number puzzles, mats you can print off so they can trace the numbers with play dough, coloring books where they can recognize numbers. And anytime you see a number written, point to it and say the number.

If you notice a group of 6 or less, start by saying “there are 6 fish” and then count them. This helps them recognize groups. Play with dice and arrange objects they are playing with into easily recognizable groups and then identify how many there are. Then add and subtract from the group and count the new sum.

Play games and sing songs that use numbers. Hopscotch, 5 little monkeys, 5 little ducks, 99 bottles of juice on the wall. Whatever songs you know that count, sing and dance to them.

Play with shapes. Once they know their shapes a little, point to a common object and name its shape. Holding a ball? The ball is round like a circle. The box they are coloring on is a rectangle, etc. Help them learn their shapes and then point out as many shapes as you can.

Play games like “I spy” but tell them the shape. “I spy a circle” or “I spy a rectangle.” Start with cards or puzzle pieces that are the shapes and then expand the game to include common objects. You can also draw a shape, tape it to the floor, and sort common objects in the room to their shape.

Finally, don’t dumb down your language. Instead of saying “Your shoe is over there” say “Your shoe is under the table” and point to give them an extra cue. Use words like under, above, over, in, and through as often as they are applicable. Narrate the child’s actions as they are learning these concepts “You put the red block on top of the blue block.”

Don’t overthink it, just guide them through just like you would for any new vocabulary. We are just laying a foundation.

What are your favorite math learning tricks? Leave them in the comments below,. Let me know if you want a full post on how to teach math to toddlers. Don’t forget to like and share 🙂

Related Posts