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Kindergarten Math: Counting, Shapes, and Numbers to 20, Talked Through
This page covers kindergarten math as laid out in the Common Core standards: counting to 100 and counting objects correctly, comparing numbers, early addition and subtraction within 10, understanding teen numbers as ten ones plus more ones, comparing length and weight, sorting objects, and naming and building 2D and 3D shapes. It does not include first-grade work like place value to 100 or fact fluency beyond 10.
A lesson sounds like a conversation. The tutor might lay out five counters and ask how many there are, then ask what happens if one more is added, rather than explaining the rule first. If a child says '14 has a 1 and a 4' but can't yet say that means a ten and four ones, the tutor builds from the counting a child already shows, using objects, dots, and simple drawings, then checks a few days later that the idea is still there.
Who it is for
- Kindergartners starting formal math, including those just learning to recognize numerals
- Parents who want to sit nearby and hear how their child explains numbers and shapes
- Teachers looking for extra one-on-one practice to go with classroom lessons
- Homeschooling families following Common Core kindergarten math
- Children who can count aloud but need practice connecting counting to quantity
What you will be able to do
- Count forward to 100 by ones and count on from any number
- Count a set of up to 20 objects accurately and say how many without recounting
- Add and subtract within 10 using objects, fingers, or drawings
- Explain that teen numbers are ten ones and some more ones
- Compare numbers, lengths, weights, and shapes using the right words
- Sort objects into groups, name 2D and 3D shapes, and combine shapes to make new ones
A taste of a lesson on Teen numbers as ten ones and some more ones
The tutor asks, you answer, and it works from what you actually said. No videos to sit through.
The 20 topics in Kindergarten Math
Each topic builds on the ones before it. The tutor checks what you already know and starts there.
Counting forward to 100
Say the number names in order from 1 to 100, starting from any number less than 100, and count in ones. Students learn the pattern of tens (10, 20, ... 90) and that the teen and decade names follow regular patterns. Real understanding: the student can keep counting correctly past 20 and recognize where a count breaks down.
Counting objects with one-to-one correspondence
Count a set of up to 20 objects by touching or moving each object exactly once while saying one number name per object, with the last number said giving the total. Students learn that the same objects counted in any order give the same total. Real understanding: the student matches each number name to exactly one object without skipping or double counting.
Builds on Counting forward to 100
Writing and recognizing numerals 0 to 20
Recognize and write the numerals 0 through 20 and connect each numeral to a quantity shown with objects or dots. Students learn to read numerals in any order and to write them with correct formation. Real understanding: the student can match a numeral to the matching number of objects and write the numeral for a given count.
Builds on Counting objects with one-to-one correspondence
Cardinality: the last number counted is the total
Understand that the last number said when counting a set tells how many are in the set, and that counting a set again in a different order gives the same answer. Students learn to answer 'how many?' by counting and to answer without recounting when a set is small. Real understanding: the student can explain why the last count is the total, not just state it.
Builds on Counting objects with one-to-one correspondence
Counting on from a given number
Starting from any number within 100 (for example, start at 37 and count 5 more), continue the count forward and identify the number reached. Students also count a given quantity of objects starting from a number other than one. Real understanding: the student knows the next number after any number in the count sequence without restarting at one.
Builds on Counting forward to 100, Writing and recognizing numerals 0 to 20
Comparing numbers and sets to 10 and beyond
Compare two sets of objects, or two numbers, to tell which has more, fewer, or the same number, using matching, counting, or the position of numerals in the count sequence. Students learn the words greater than, less than, and equal to, and use the symbols >, <, = appropriately. Real understanding: the student can justify a comparison by matching or by counting, and knows that the number later in the count is greater.
Builds on Cardinality: the last number counted is the total, Counting on from a given number
Modeling addition and subtraction stories
Represent situations in which items are added to or taken away from a group, using objects, drawings, and simple equations such as 3 + 2 = 5 and 5 - 2 = 3. Students learn the words add, plus, take away, minus, equals, and that the equal sign means both sides have the same value. Real understanding: the student can act out or draw a story problem and write the matching equation.
Builds on Writing and recognizing numerals 0 to 20, Cardinality: the last number counted is the total
Adding and subtracting within 5
Solve addition and subtraction problems with totals up to 5 using objects, fingers, drawings, counting on, and counting back, and know the basic facts within 5 from memory. Real understanding: the student can find sums and differences quickly and check them with a model.
Builds on Counting on from a given number, Modeling addition and subtraction stories
Decomposing numbers to 10 and 5 and 10 relationships
Show all the ways a number up to 10 can be split into two parts (for example, 7 = 3 + 4 = 2 + 5 = 6 + 1 = 0 + 7), using objects, drawings, and equations. Students learn the pairs that make 5 and 10, and that a part and its partner make the whole. Real understanding: the student sees that the parts can be rearranged and that knowing one part gives the other.
Builds on Adding and subtracting within 5
Adding and subtracting within 10
Solve addition and subtraction problems with totals up to 10 using counting on, counting back, making ten, number bonds, and the relationship between addition and subtraction (for example, knowing 4 + 3 = 7 helps find 7 - 3). Real understanding: the student chooses a strategy for each problem, explains it, and checks the answer with a model or a related fact.
Builds on Decomposing numbers to 10 and 5 and 10 relationships
Teen numbers as ten ones and some more ones
Understand that the numbers 11 to 19 are each made of one group of ten and some ones, with the numeral showing a 1 in the tens place and the ones digit showing the extra ones (for example, 14 is 10 and 4 ones). Students build teen numbers with ten-frames and bundled objects and write them with equations such as 10 + 4 = 14. Real understanding: the student can explain why 14 is 'ten and four' and not 'four and ten'.
Builds on Counting on from a given number, Decomposing numbers to 10 and 5 and 10 relationships
Counting and writing numbers to 20 in tens and ones
Read, write, and represent numbers from 11 to 20 using ten-frames and place-value vocabulary, and compare teen numbers by looking at the tens and ones. Students know that a teen number with more ones is greater, and they can decompose a teen number into 10 and some ones. Real understanding: the student can use the tens and ones structure to order and compare numbers to 20.
Builds on Comparing numbers and sets to 10 and beyond, Teen numbers as ten ones and some more ones
Describing and comparing measurable attributes
Describe measurable attributes of objects such as length, weight, capacity (how much a container holds), and height, using words like long, short, tall, heavy, light, full, and empty. Students compare two objects directly by lining them up or holding them to see which is longer, taller, heavier, or holds more. Real understanding: the student knows which attribute is being compared and can justify the comparison with a direct method.
Builds on Comparing numbers and sets to 10 and beyond
Ordering objects by length, height, and weight
Order three or more objects from shortest to longest, tallest to shortest, or lightest to heaviest, using direct comparison and a chain of pairwise comparisons. Real understanding: the student can justify an ordering of three objects by comparing pairs and recognizes that if A is longer than B and B longer than C, then A is longer than C.
Builds on Describing and comparing measurable attributes
Classifying objects into categories and counting them
Sort a group of objects into categories by a chosen attribute such as color, size, or shape, and count how many are in each category. Students learn to name the attribute used and to say how many are in each group, and they compare the counts with more, fewer, or same. Real understanding: the student can sort the same set in two different ways and explain the rule for each group.
Builds on Cardinality: the last number counted is the total, Comparing numbers and sets to 10 and beyond
Describing positions and directions
Use words such as above, below, next to, in front of, behind, beside, inside, outside, and between to describe where an object is relative to another object. Students also name directions such as up, down, left, and right. Real understanding: the student can describe the location of an object relative to a reference object and can locate an object from a verbal description.
Identifying and naming 2D shapes
Name and recognize circles, triangles, squares, rectangles, and hexagons regardless of size, orientation, or whether the shape is drawn in a different way. Students learn that a square is a special rectangle with four equal sides and that shapes have sides and corners. Real understanding: the student can recognize a shape from its features (sides, corners) and not only its usual picture.
Builds on Describing positions and directions
Identifying and describing 3D shapes
Name and recognize spheres, cubes, cones, cylinders, and rectangular prisms (boxes), and describe them by their faces, edges, and corners in simple terms such as flat, curved, round, and pointy. Students compare 3D shapes with 2D shapes found on their faces. Real understanding: the student can tell whether a solid has flat faces, curved surfaces, or both, and can find a 2D shape on a 3D object.
Builds on Identifying and naming 2D shapes
Analyzing and comparing 2D and 3D shapes
Compare 2D and 3D shapes by their similarities and differences, including how many sides or corners they have, and sort them into groups. Students also use shape names to describe parts of other objects, such as a rectangle-shaped door. Real understanding: the student can explain why a given shape belongs in a category and how two shapes differ.
Builds on Identifying and naming 2D shapes, Identifying and describing 3D shapes
Composing shapes from other shapes
Combine simple shapes to make a new shape, such as two triangles making a rhombus or a square with a triangle making a rectangle, and take a larger shape apart into smaller shapes. Students use pattern blocks, paper, or drawings. Real understanding: the student can see a larger shape as made of smaller shapes and can name the new shape made from pieces.
Builds on Identifying and naming 2D shapes, Analyzing and comparing 2D and 3D shapes
Practice questions in Kindergarten Math
A few of the kinds of questions you will work through, with answers.
Count these stars one at a time: ★ ★ ★ ★ ★ ★. How many are there?
See the answer
6
Touching each star once while saying one number per star and stopping at the last star gives 6.
One plate has 5 crackers and another plate has 8 crackers. Which plate has more?
See the answer
The plate with 8 crackers
8 comes after 5 when counting, so 8 is greater than 5.
There are 6 ducks in a pond. 2 more ducks swim in. How many ducks are in the pond now?
See the answer
8
Counting on from 6 by 2 more (7, 8) gives a total of 8 ducks.
What is 16 made of, in terms of tens and ones?
See the answer
1 ten and 6 ones
The numeral 16 shows a full group of ten and 6 extra ones.
Find two ways to make 7 using two parts, for example 7 = 5 + 2. Give one more way.
See the answer
7 = 4 + 3 (or any valid pair)
Any two whole numbers that add to 7, such as 4 and 3, show a valid decomposition.
If you put two triangles together along one matching side, what new shape can you make?
See the answer
A square or a rectangle (depending on the triangles)
Two right triangles joined along their longest side can form a rectangle or square, showing how shapes combine into a new one.
Questions about this subject
My child can count to 20 but doesn't know what the numbers mean. Is this still the right place to start?
Yes. Counting aloud is the starting point the course assumes, and early lessons focus on connecting that counting to actual quantities of objects, which is exactly the gap this addresses.
Does this cover first-grade topics like two-digit addition?
No. The course stops at Common Core kindergarten standards: numbers to 20, addition and subtraction within 10, and does not include place value to 100 or fact fluency beyond 10.
How does the tutor handle a child who isn't reading yet?
Lessons rely on spoken questions, objects, dots, and simple pictures rather than long written text, since kindergarten math standards don't assume independent reading.
What if my child gets an answer wrong?
The tutor asks a follow-up question based on what the child actually said, such as recounting with objects, rather than simply giving the correct answer.
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