โ† All courses

Numbers, Shapes, and Stories: Kindergarten Mathematics

Grade K ยท Christian ยท NGSS/CCSS-aligned

You run this one, and we hand you the words. Every lesson opens with a short story you tell out loud and ends with your child tapping a picture to answer, so nothing has to be read or typed at any point. It is kindergarten math done with things a child can pick up: blocks, buttons, fingers, pictures on a screen. By June they can count to 100, count out and compare groups of things, add and subtract by acting out little stories with real objects, say why 14 means one ten and four ones, and name the basic flat and solid shapes wherever they turn up. First grade assumes a child arrives already counting and comparing, and already sure that numbers stand for real amounts of real things. That is the year this builds.

What your child will learn

The whole year, in plain English. Tap any unit to see every skill inside, nothing is hidden.

How Many? Counting and Matching to 10peek inside โ–ธ

This is where it all starts. Your child learns that counting only works if every single object gets exactly one number word, said once, in the right order โ€” no skipping, no double-counting. You'll move from counting objects in a neat line (easiest) to a scattered pile (harder) to objects arranged in a circle (hardest, because there's no clear start or stop point).

  1. The counting word sequence 1-10

    Child recites the counting sequence 1-10 in order, without touching objects.

  2. One-to-one correspondence between touches and number words, first introduced with a small set of 3

    Child touches each of 3 lined-up objects exactly once while saying one number word per touch.

  3. One-to-one correspondence between touches and number words

    Child touches each object exactly once while saying one number word per touch, for a line of up to 10 objects.

  4. Cardinality: the last count word names the total

    Child states that the last number word said while counting a group tells how many objects are in it, without recounting.

  5. Counting objects arranged with no fixed path

    Child counts a scattered (non-lined-up) group of up to 10 objects and gives one final count.

  6. Counting objects in a closed circular arrangement

    Child counts objects arranged in a circle and correctly identifies where they started to avoid double-counting.

  7. Conservation of number under rearrangement

    Child predicts that recounting the same rearranged group of objects will give the same total, then checks by counting.

  8. Errors in one-to-one correspondence during counting

    Child identifies which of two counting attempts (shown by an adult) counted correctly and which skipped or double-counted an object.

  9. Counting to 10 applied in a novel picture context

    Child counts a scattered group of 10 objects presented in an unfamiliar picture (not toys or blocks used all unit) and gives the correct total.

Counting Further: To 20 and by Tens to 100peek inside โ–ธ

This unit stretches the counting-and-touching skill from Unit 1 up to 20, then teaches counting by tens (10, 20, 30...100) as a faster way to count โ€” using a 'ten-bag' of ten objects as one countable unit โ€” and teaches counting on from a number other than 1.

  1. One-to-one correspondence counting for sets up to 10, as a foothold into this unit's extension past 10

    Child touch-counts a set of 10 objects, saying one number word per object, and states the total.

  2. One-to-one correspondence counting extended to sets of 11-15

    Child touch-counts a scattered set of 11-15 objects, saying one number word per object, and states the total.

  3. One-to-one correspondence counting extended to sets of 16-20

    Child touch-counts a scattered set of 16-20 objects, saying one number word per object, and states the total.

  4. The rote number-word sequence to 20

    Child recites the counting sequence from 1 to 20 without objects present.

  5. The rote counting-by-tens sequence to 100

    Child recites the counting-by-tens sequence (10, 20, 30 ... 100) while pointing at pictured ten-groups.

  6. Correspondence between a tens-count word and a quantity of grouped tens

    Child matches a spoken count-by-tens number (e.g., 'thirty') to a picture showing the correct number of full ten-bags.

  7. Counting on from a number other than 1

    Child counts on from a stated number between 5 and 15 to reach a target total, without recounting from 1.

  8. The ten-and-some-more structure of teen numbers

    Child explains, using a ten-bag and loose objects, why 13 is 'ten and three more.'

  9. Tens-and-ones structure applied to an unfamiliar grouped picture

    Child determines, for a new mixed picture of ten-bags and loose objects never shown before (e.g., 4 bags and 6 loose in an unfamiliar layout, with a distractor group nearby), which spoken total it matches.

More, Fewer, or Same: Comparing Groupspeek inside โ–ธ

This unit teaches a genuinely different way to compare two groups: matching objects one-to-one instead of counting them. Your child learns the words 'more,' 'fewer,' and 'same number as' โ€” words that get reused, not retaught, for the rest of the year.

  1. One-to-one correspondence between two groups of objects

    Given two groups of up to 10 objects arranged in a line, the child draws a line connecting each object in one group to one object in the other group.

  2. Leftover objects as evidence of 'more' after matching

    After matching two unequal groups (up to 10 objects each), the child identifies which group has a leftover object and names that group as having 'more'.

  3. The 'same number as' case in one-to-one matching

    Given two matched groups with no leftover objects, the child taps the 'same number as' picture rather than choosing 'more' or 'fewer'.

  4. Choosing between matching and counting to compare scattered groups

    Given two scattered (unmatched, not pre-lined) groups of up to 10 objects each, the child decides to either match or count and then states which group has more, fewer, or whether they are the same.

  5. Comparing two written numerals 1-10 using their represented quantities

    Given two numeral cards from 1-10, each shown next to a picture of that many dots, the child taps the numeral that represents the larger amount.

  6. Comparing two written numerals 1-10 without a visible quantity model

    Given two numeral cards from 1-10 with no object pictures shown, the child states which numeral is larger by recalling the represented quantity.

  7. Testing a visual/perceptual claim about quantity using matching or counting

    Given a real-world claim like 'the tall skinny cup has more water' about two unequal, differently-shaped groups of objects placed in unfamiliar containers, the child uses matching or counting to check whether the claim is true.

  8. Constructing/recognizing a group with one fewer than a reference group

    Given a group of objects and told it has 'one fewer' than a shown group, the child selects which of two candidate groups matches that description.

Writing and Reading Numbers to 20peek inside โ–ธ

This unit attaches written numerals โ€” the actual squiggles 0 through 20 โ€” to amounts your child can already count and compare. The rule all unit long is: count or build the quantity first, show the numeral second, never the other way around.

  1. Correspondence between a counted set of 0-10 objects and its written numeral

    Child taps the numeral (0-10) that matches a counted set of objects shown on screen.

  2. The just-demonstrated numeral as a record of a small counted set (0-5)

    Given a set of 0-5 objects the child has just finger-counted with the parent, child taps the one numeral (from 2 choices) that was shown as the record of that exact count moments earlier.

  3. Correspondence between a teen-quantity (ten-stick plus loose ones) and its two-digit numeral

    Child taps the numeral (11-20) that matches a counted set built as a ten-stick plus some loose objects.

  4. The fixed sequence of numerals 0-10 as a record of the counting sequence

    Child places scattered numeral cards 0-10 into counting order.

  5. Orientation as a defining feature of numeral identity, unlike physical objects

    Child distinguishes correctly-formed numerals from mirror-reversed versions (e.g., correct 6 vs. reversed 6 that looks like 9's mirror) for a target numeral named aloud.

  6. The stroke sequence used to form each written numeral 0-20

    Child physically traces numerals 0-20 following a modeled stroke path, checked by the parent against a printed model.

  7. The ten-and-some-more structure represented inside a two-digit teen numeral

    Child explains, using a built ten-stick and loose objects, why the numeral for a teen number has a '1' even though the amount is more than one.

  8. Numerals as symbols that appear consistently across contexts outside the taught counting materials

    Given a numeral card shown alone with no counted objects present, child selects which of two real-world photos (e.g., a house number, a page in a counting book) contains that same numeral.

  9. Numeral order as a stand-in for quantity comparison without a visible count

    Child taps the larger or smaller numeral of two shown, both presented WITHOUT accompanying object sets, using only the numerals themselves.

Joining and Separating: Addition and Subtraction Stories to 10peek inside โ–ธ

This is the first time counting describes something changing, not just a fixed pile sitting still. Your child acts out stories โ€” things arriving, things leaving โ€” with real objects before ever seeing a number sentence like 5-2=3, which gets introduced afterward as a record of what already happened.

  1. Joining (putting-together) action within 10 objects

    Child acts out a joining story with real or pictured objects and states how many are in all, for totals to 10.

  2. Separating (taking-apart) action within 10 objects

    Child acts out a separating story with real or pictured objects and states how many are left, for starting amounts to 10.

  3. The join-versus-separate event structure in a spoken story

    Child determines whether a spoken story describes something coming (join) or something going (separate), before any number is mentioned.

  4. The number sentence as a record of a completed action, using 'is the same as' for the equals sign

    Child records a completed joining or separating action as a number sentence (e.g. 5 - 2 = 3) after acting it out with objects.

  5. Decomposition of numbers to 10 into two parts

    Given a number to 10 shown with objects, child finds a decomposition into two parts (e.g. 5 = 4+1) using the objects.

  6. Multiple decompositions of the same number

    Given one number to 10 shown with objects, child finds two different decompositions of that same number.

  7. Missing-addend stories (total and one part known)

    Given a spoken story mentioning a total and one known part, child finds the missing part using objects, for totals to 10.

  8. Discrimination among join, separate, and decompose story types

    Child chooses the numeral that shows the result of a mixed set of join, separate, and decompose stories presented in random order within the same session.

Ten and Some More: Decomposing 11-19peek inside โ–ธ

This unit gives every teen number the same structure: a full ten plus some loose ones, always. Your child already counts to 20 fluently and has used ten-frames โ€” this unit puts that fluency to work naming and building teen numbers rather than teaching counting itself.

  1. The ten-and-ones structure of teen numbers 11-19

    Given a built ten-frame (fully filled) plus a small group of loose objects (1-9), the child names the total as 'ten and ___ more' matching the count of loose objects.

  2. Physical construction of a teen number as a ten-group plus ones

    The child builds a physical model (one full ten-group plus loose ones) for any spoken teen number 11-19.

  3. Correspondence between a teen numeral and its ten-and-ones object model, generalized across surface variation

    The child matches a written teen numeral (11-19) to an object model showing its correct ten-and-ones decomposition, where the model's surface features (object color/type, ten-frame orientation, or arrangement) differ from any pairing directly drilled in a worked example, choosing among 2-3 pictured models.

  4. Invariance of a teen number's total across different spatial arrangements

    The child compares two different-looking arrangements of the same teen number (e.g., spread out vs. grouped into ten-and-ones) and states that the count is the same.

  5. Counting-on-from-ten as a strategy for finding a teen total

    The child counts on aloud from ten to reach a teen total, starting at 'ten' rather than restarting at 'one,' when shown a built ten-group plus loose ones.

  6. The fixed relationship between a teen number's name and its ones-count

    Given only the spoken teen number, the child predicts how many loose ones will be needed before building the model, then checks by building.

  7. Application of the ten-and-ones decomposition strategy to an unfamiliar object type and layout, observed as a single low-n classroom probe

    Presented with a new context never used in instruction, a ten-frame of buttons plus a scattered pile of buttons outside a frame of a different color, with no verbal cue that this is a 'teen number' task, the child taps the numeral matching the total, on a novel-context probe treated as low-stakes and formative rather than as proof of transfer.

  8. The count sequence 11-19 in order

    The child recalls, from memory without a model present, the number word that comes immediately after a given teen number up to 19.

Comparing Length and Weightpeek inside โ–ธ

This unit takes the matching-and-comparing logic from Unit 3 โ€” built for comparing amounts โ€” and points it at two new things: length and weight. Your child learns to compare length by lining up starting points, then order three objects at once, and to read a balance-scale picture to compare weight.

  1. Direct pairwise comparison of length using endpoint alignment

    Given two objects with aligned endpoints shown on screen, the child taps the one that is longer (or shorter).

  2. Direct pairwise comparison of weight using balance-scale dip direction

    Given two objects on a balance-scale picture where one side clearly dips, the child taps the heavier (or lighter) object.

  3. Justification of a length comparison by naming the endpoint evidence

    Given a new pair of objects whose length difference is subtler than the worked examples, the child names which is longer and states that it 'stops further out' with reduced parent prompting.

  4. The distinction between 'same length' and 'close but different length'

    Given two objects with matching start and stop points, the child classifies the pair as 'same length' rather than 'longer' or 'shorter', distinguishing this from pairs that merely look close.

  5. Seriation (transitive ordering) of three objects by length

    Given three objects of differing length, the child orders them from shortest to longest by comparing each new object against the objects already placed, not just its nearest neighbor.

  6. The possible mismatch between visual size and actual weight

    Given a big-looking but light object paired against a small-looking but heavy object on a balance picture, the child predicts an outcome from appearance, compares it to the balance result, and identifies that appearance and weight disagreed.

  7. Discrimination between length-comparison and weight-comparison task types

    Given a mixed, unlabeled set of length and weight comparison pictures, the child identifies which attribute each picture concerns (a stick picture vs. a balance picture) before answering.

  8. The level (equal-weight) state of a balance-scale picture

    Given a balance picture with both sides level, the child recalls that this means the two objects weigh the same, distinguishing it from a picture with any visible dip.

  9. The shared direct-comparison logic underlying quantity comparison (Unit 3) and length/weight comparison (this unit)

    Given a description comparing sticks' lengths and a description comparing block piles' amounts, the child explains how the two comparisons use the same 'look and match' idea without counting.

Naming and Building 2D and 3D Shapespeek inside โ–ธ

The last unit of the year. Your child names 5 flat shapes (circle, square, triangle, rectangle, hexagon), 4 solid shapes (sphere, cube, cone, cylinder), describes position with words like above and beside, and builds bigger shapes out of smaller ones. The core idea repeated all unit: a shape's name comes from its sides and corners, not its size, color, or which way it's turned.

  1. Identity of the 5 named 2D shapes across changes in size, color, and orientation

    Child names a circle, square, triangle, rectangle, or hexagon shown at an unfamiliar size, color, or rotation, by tapping the matching name/picture.

  2. Names of circle and square immediately after their first worked introduction

    Child names a circle or square shown in a size and color like the ones just demonstrated, by tapping the matching name.

  3. Names of the 4 named 3D solids

    Child recalls the spoken name for a sphere, cube, cone, or cylinder when shown a real object or picture of that solid.

  4. Side-count and corner-count as the defining attribute distinguishing 2D shapes

    Child counts the number of sides and corners on a given 2D shape and states whether that count matches another shape's count.

  5. The flat/solid (2D/3D) distinction independent of size and color

    Child sorts a mixed pile of 2D and 3D shape pictures into flat and solid groups, regardless of the shapes' size or color.

  6. Position words describing an object's location relative to a second object

    Child identifies whether one object is above, below, beside, in front of, or behind a second (reference) object shown in a picture.

  7. Composition of a target 2D shape from smaller component shapes

    Child builds a given larger 2D shape (e.g., a hexagon or rectangle) out of two or three smaller pattern-block shapes.

  8. The 5 named 2D shapes' identity in an unfamiliar real-world context

    Child selects the correct name for a 2D shape presented in a context never used anywhere in this unit's instruction (e.g., a hexagon-shaped floor tile pattern, or a triangle-shaped kite), with no size/color/orientation cue matching a taught example.

  9. Addition/subtraction story answers (Unit 5-6) interleaved with current shape-naming items

    Child recalls a previously taught addition or subtraction story answer (Units 5-6) and a shape name in the same mixed practice set without confusing the two response formats.

From the parent guide

You run this one, and we hand you the words. Every lesson opens with a short story you tell out loud and ends with your child tapping a picture to answer, so nothing has to be read or typed at any point. It is kindergarten math done with things a child can pick up: blocks, buttons, fingers, pictures on a screen. By June they can count to 100, count out and compare groups of things, add and subtract by acting out little stories with real objects, say why 14 means one ten and four ones, and name the basic flat and solid shapes wherever they turn up. First grade assumes a child arrives already counting and comparing, and already sure that numbers stand for real amounts of real things. That is the year this builds.

Unit 1 ยท what to expect

This is where it all starts. Your child learns that counting only works if every single object gets exactly one number word, said once, in the right order โ€” no skipping, no double-counting. You'll move from counting objects in a neat line (easiest) to a scattered pile (harder) to objects arranged in a circle (hardest, because there's no clear start or stop point).

The full guide covers all 8 units: where kids get stuck, what to say, and how to tell it's working. Included with the course.

Ready when you are

Free for 30 days ยท then $29/mo or $290/yr for the whole family ยท Cancel anytime, no questions asked.

Start your family's account
Numbers, Shapes, and Stories: Kindergarten Mathematics, Grade K Homeschool Curriculum