Kindergarten · printable course

Numbers, Shapes, and Stories: Kindergarten Mathematics

Kindergarten · 262 pages · 69 lessons · PDF, print at home

A full-year kindergarten math course delivered by a parent, built entirely on objects a child can point at and count: counting to 100, one-to-one correspondence to 20, comparing groups and measurable attributes, addition and subtraction acted out with real things, decomposing teen numbers into ten and some ones, and naming 2D and 3D shapes. Every lesson opens with a short spoken story the parent reads aloud and closes with the child tapping a picture answer. No reading or typing is ever required of the child. The course starts by checking where each child actually is, since some arrive already counting to ten and others do not.

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What is inside

Every unit and lesson in this book, in order. The same lessons are taught online at lettersanddevotion.com, so a family can move between paper and screen.

Numbers, Shapes, and Stories: Kindergarten Mathematics

69 lessons · try a lesson online free

Unit 1: How Many? Counting and Matching to 109 lessons
  1. 1.The counting word sequence 1-10
  2. 2.One-to-one correspondence between touches and number words, first introduced with a small set of 3
  3. 3.One-to-one correspondence between touches and number words
  4. 4.Cardinality: the last count word names the total
  5. 5.Counting objects arranged with no fixed path
  6. 6.Counting objects in a closed circular arrangement
  7. 7.Conservation of number under rearrangement
  8. 8.Errors in one-to-one correspondence during counting
  9. 9.Counting to 10 applied in a novel picture context
Unit 2: Counting Further: To 20 and by Tens to 1009 lessons
  1. 10.One-to-one correspondence counting for sets up to 10, as a foothold into this unit's extension past 10
  2. 11.One-to-one correspondence counting extended to sets of 11-15
  3. 12.One-to-one correspondence counting extended to sets of 16-20
  4. 13.The rote number-word sequence to 20
  5. 14.The rote counting-by-tens sequence to 100
  6. 15.Correspondence between a tens-count word and a quantity of grouped tens
  7. 16.Counting on from a number other than 1
  8. 17.The ten-and-some-more structure of teen numbers
  9. 18.Tens-and-ones structure applied to an unfamiliar grouped picture
Unit 3: More, Fewer, or Same: Comparing Groups8 lessons
  1. 19.One-to-one correspondence between two groups of objects
  2. 20.Leftover objects as evidence of 'more' after matching
  3. 21.The 'same number as' case in one-to-one matching
  4. 22.Choosing between matching and counting to compare scattered groups
  5. 23.Comparing two written numerals 1-10 using their represented quantities
  6. 24.Comparing two written numerals 1-10 without a visible quantity model
  7. 25.Testing a visual/perceptual claim about quantity using matching or counting
  8. 26.Constructing/recognizing a group with one fewer than a reference group
Unit 4: Writing and Reading Numbers to 209 lessons
  1. 27.Correspondence between a counted set of 0-10 objects and its written numeral
  2. 28.The just-demonstrated numeral as a record of a small counted set (0-5)
  3. 29.Correspondence between a teen-quantity (ten-stick plus loose ones) and its two-digit numeral
  4. 30.The fixed sequence of numerals 0-10 as a record of the counting sequence
  5. 31.Orientation as a defining feature of numeral identity, unlike physical objects
  6. 32.The stroke sequence used to form each written numeral 0-20
  7. 33.The ten-and-some-more structure represented inside a two-digit teen numeral
  8. 34.Numerals as symbols that appear consistently across contexts outside the taught counting materials
  9. 35.Numeral order as a stand-in for quantity comparison without a visible count
Unit 5: Joining and Separating: Addition and Subtraction Stories to 108 lessons
  1. 36.Joining (putting-together) action within 10 objects
  2. 37.Separating (taking-apart) action within 10 objects
  3. 38.The join-versus-separate event structure in a spoken story
  4. 39.The number sentence as a record of a completed action, using 'is the same as' for the equals sign
  5. 40.Decomposition of numbers to 10 into two parts
  6. 41.Multiple decompositions of the same number
  7. 42.Missing-addend stories (total and one part known)
  8. 43.Discrimination among join, separate, and decompose story types
Unit 6: Ten and Some More: Decomposing 11-198 lessons
  1. 44.The ten-and-ones structure of teen numbers 11-19
  2. 45.Physical construction of a teen number as a ten-group plus ones
  3. 46.Correspondence between a teen numeral and its ten-and-ones object model, generalized across surface variation
  4. 47.Invariance of a teen number's total across different spatial arrangements
  5. 48.Counting-on-from-ten as a strategy for finding a teen total
  6. 49.The fixed relationship between a teen number's name and its ones-count
  7. 50.Application of the ten-and-ones decomposition strategy to an unfamiliar object type and layout, observed as a single low-n classroom probe
  8. 51.The count sequence 11-19 in order
Unit 7: Comparing Length and Weight9 lessons
  1. 52.Direct pairwise comparison of length using endpoint alignment
  2. 53.Direct pairwise comparison of weight using balance-scale dip direction
  3. 54.Justification of a length comparison by naming the endpoint evidence
  4. 55.The distinction between 'same length' and 'close but different length'
  5. 56.Seriation (transitive ordering) of three objects by length
  6. 57.The possible mismatch between visual size and actual weight
  7. 58.Discrimination between length-comparison and weight-comparison task types
  8. 59.The level (equal-weight) state of a balance-scale picture
  9. 60.The shared direct-comparison logic underlying quantity comparison (Unit 3) and length/weight comparison (this unit)
Unit 8: Naming and Building 2D and 3D Shapes9 lessons
  1. 61.Identity of the 5 named 2D shapes across changes in size, color, and orientation
  2. 62.Names of circle and square immediately after their first worked introduction
  3. 63.Names of the 4 named 3D solids
  4. 64.Side-count and corner-count as the defining attribute distinguishing 2D shapes
  5. 65.The flat/solid (2D/3D) distinction independent of size and color
  6. 66.Position words describing an object's location relative to a second object
  7. 67.Composition of a target 2D shape from smaller component shapes
  8. 68.The 5 named 2D shapes' identity in an unfamiliar real-world context
  9. 69.Addition/subtraction story answers (Unit 5-6) interleaved with current shape-naming items

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