Grade K · fall math.gK.f

Kindergarten Fall Math — Counting to 100, Subitizing, Cardinality, Shapes, and Pattern

18 weeks 150 min/week 16 lessons 14 skills 39 exercises 2 assessments

Overview

Kindergarten Fall Math launches the K-8 mathematics sequence on a Singapore-CPA foundation: every concept is met first in the hands (concrete manipulatives), then on the page (pictorial representations), and only then in symbolic notation (abstract numerals and signs). The unit's three intertwined arcs are NUMBER (counting to 100, subitizing 1-10, cardinality, one-to-one correspondence, numeral writing 0-20, comparing quantities), SHAPE (2D and 3D shape names, attributes, position words), and PATTERN (AB / ABB / AAB extension and creation, sorting and classifying).

Number Talks anchor each lesson's warm-up beginning in week 2, building from dot-image subitizing through ten-frame flash to scattered-collection counts. Counting forward to 100 by ones is the headline goal; backward counting from 10 and skip-counting by 2s, 5s, and 10s appear at the concrete tier as stretch.

Shape work moves from naming (circle, square, triangle, rectangle, hexagon, oval; sphere, cube, cone, cylinder) to attribute description (sides, vertices, flat faces, curved surfaces) — children sort and classify physical shape collections.

Patterns and sorting introduce algebraic thinking at its earliest: pattern is a relationship, and sorting reveals categories. Across the term, daily routines (calendar counting, attendance counting, line-up counting, transition counts) embed practice without adding instructional time.

Manipulatives are concrete and specific — 20 unifix cubes per pair, two-color counters, pre-printed ten-frame mats, dice, dot-pattern cards, attribute-block sets, geosolids — never generic 'math manipulatives.' The QC bar is that every skill has a real CPA tier triple and every misconception is named (e.g., 'recites the count-word sequence but does not coordinate one word to one object,' 'last-number-said is treated as a label not a total,' 'counts the same object twice when objects are in a circle').

Frameworks anchor: CCSS-Math K (full), Singapore MOE Primary-1 baseline (K is the foundation layer), English NC EYFS + Y1 transition, NCTM PreK-2 Principles & Standards. The unit ends with a portfolio-style summative in which each child performs a count to 50 (with skip to 100 as stretch), composes a 5-shape sort with one chosen attribute, extends and creates one AB and one ABB pattern, and writes numerals 0-10.

Essential questions

Why does the last number we say when we count tell us how many there are?
How can we 'see' how many without counting one by one?
What makes a square a square and not just a rectangle?
How do mathematicians know one pile has more than another?
What is a pattern, and how can we know what comes next?
How do people in different parts of the world show numbers?

Enduring understandings

Counting is a coordinated act: one word for each thing, in order, with the last word naming the total (cardinality).
Quantities can be represented in many ways — fingers, dots, ten-frames, tallies, numerals, words — and the same number means the same amount no matter how we show it.
Shapes have names and attributes; the same shape stays the same shape no matter how we turn it or how big it is.
Comparing two groups (which is more, less, or equal) is a foundational mathematical move, supported by one-to-one matching before abstract symbols.
Patterns are rules; once we find the rule, we can extend the pattern and even create our own.
Mathematics is a human activity practiced in many cultures with many tools — finger-counting, abacus, ten-frame, tally, vigesimal dots-and-bars — and all of them count the same things.

Visual reference library 8 assets


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Illustration

Unit-opener splash: a kindergarten classroom 'math corner' with labeled bins of unifix cubes (red, blue, yellow, green), two-color counters in a translucent caddy, a 5x2 ten-frame mat on the rug, dice in a clear cup, attribute blocks fanned out, and a wall-mounted 100-chart. Style: warm watercolor, child's-eye perspective at rug height. Caption banner reads 'Counting, Shapes, and Patterns — Kindergarten Math.'


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Chart Physical / non-image

Master 100-chart anchor chart: 10x10 grid, numerals 1-100, large 28-pt font, multiples of 10 highlighted in yellow, multiples of 5 outlined in red. Mounted at child-height on the math wall. Used daily for calendar counting and 100th-day-of-school countdown.


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Chart

Ten-frame poster set: six 18"x12" laminated ten-frame mats showing 0, 3, 5, 7, 8, 10 dots in standard top-row-fills-first arrangement. Used for daily ten-frame flash subitizing routine.


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Chart

Number representation card set: for each of 0-10, an 8.5"x5.5" card showing four representations in quadrants — numeral (top-left, large), finger configuration photo (top-right), ten-frame (bottom-left), tally marks (bottom-right). Posted as a number line at child-height.


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Chart Physical / non-image

2D shape attribute anchor chart: six panels for circle, square, triangle, rectangle, hexagon, oval. Each panel shows the shape outline (bold black, 4"x4"), a child-friendly attribute list ('3 sides, 3 vertices' or 'curved, no vertices'), and one real-world photo example (e.g., stop sign for octagon-variant, slice of bread for square).


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Chart Physical / non-image

3D solid attribute anchor chart: four panels for sphere, cube, cone, cylinder. Each panel shows a photo of the solid, names faces (curved/flat), edges, and vertices, and lists one real-world example (sphere → orange, cube → die, cone → ice-cream cone, cylinder → soup can).


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Chart Physical / non-image

Position-words anchor chart: a cartoon bear with a box, showing the bear in 6 positions (above the box, below the box, beside the box, in front of the box, behind the box, on top of the box), each labeled in large 24-pt text.


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Chart Physical / non-image

Pattern anchor chart: shows AB, AAB, ABB, and ABBA patterns using colored beads (red and blue), each pattern labeled with letter-naming convention ('A is red, B is blue') and a 'what comes next?' prompt-arrow at the end of each row.

Lessons (16)

#	Title	Min	Skills
1	Counting to 10 — meeting the count sequence	25	1
2	Counting from 11 to 20 — the trickiest numbers	25	1
3	Number Talk — dot flash subitizing 1-5	25	1
4	One-to-one correspondence — count and tag	25	1
5	How many? — the cardinality principle	25	1
6	Writing numerals 0 to 5 — stroke order and tracing	30	1
7	Writing numerals 6 to 10 — the tricky curls	30	1
8	Meet the ten-frame — the math superpower	25	1
9	Ten-frame to ten — and matching representations	30	2
10	Comparing quantities — more, less, equal	30	1
11	Sort and classify — by one attribute	25	1
12	Patterns — AB and ABB, extend and create	30	1
13	2D shapes — names and attributes (circle, square, triangle, rectangle)	30	1
14	2D shapes — hexagon and oval, plus shape hunt	25	1
15	3D solids — sphere, cube, cone, cylinder	30	1
16	Position words, comparing review, and mathematical-thinking close	30	3

Skills (14)

Strand · AT

Recognize, extend, and create repeating patterns (AB, AAB, ABB) K

Strand · DS

Sort and classify objects by one attribute (color, shape, size) and count each category K

Strand · GM

Strand · NS

Strand · PS

Mathematical practices at K — explain thinking, use tools, model with math K

Assessments (2)

Summative Portfolio week 18 30 min covers 13 skills
Formative Summative Blend week 9 20 min covers 5 skills

Standards alignment

Framework

Common Core State Standards — Mathematics

            K.CC.A.1K.CC.A.2K.CC.A.3K.CC.B.4.aK.CC.B.4.bK.CC.B.4.cK.CC.B.5K.CC.C.6K.CC.C.7K.G.A.1K.G.A.2K.G.A.3
            + 9 more
          

Framework

Singapore MOE Mathematics Syllabus — Primary 1 (K baseline)

            P1-Whole-Numbers-Counting-to-100P1-Whole-Numbers-Number-Notation-Read...P1-Whole-Numbers-Comparing-OrderingP1-Geometry-2D-ShapesEYFS-Number-and-Numerical-Patterns
            
          

Framework

English National Curriculum — EYFS + Year 1 transition

            EYFS-ELG-NumberEYFS-ELG-Numerical-PatternsEYFS-ELG-Shape-Space-MeasuresY1-Number-Number-and-Place-ValueY1-Geometry-Properties-of-Shapes
            
          

Framework

NCTM Principles and Standards for School Mathematics — Pre-K-2

            PreK-2.NUM.A-Count-with-UnderstandingPreK-2.NUM.B-CardinalityPreK-2.GEO.A-Recognize-Name-Compare-ShapesPreK-2.ALG.A-PatternsPreK-2.DATA.A-Sort-Classify
            
          

Pedagogical anchors

Singapore CPA — Concrete to Pictorial to Abstract (Bruner / Singapore MOE)
PRIMARY anchor. Every skill in this unit declares cpa_required=true with named concrete_form (unifix cubes, two-color counters, ten-frames, dice, finger configurations), pictorial_form (drawn dot arrangements, ten-frame stamps, drawn shapes), and abstract_form (numerals 0-20, comparison symbols >, <, =, shape names as words). Every lesson explicitly opens at Concrete (manipulatives in hands), bridges to Pictorial (drawing or picture cards), and only then introduces Abstract notation.
NCTM Effective Mathematics Teaching Practices (NCTM 2014, 8 practices)
Practice 1 'Establish mathematics goals to focus learning' opens every lesson (objective stated as a child-friendly 'I can' statement). Practice 3 'Use and connect mathematical representations' anchors every CPA bridge. Practice 4 'Facilitate meaningful mathematical discourse' shapes every Number Talk warm-up (lessons 1, 4, 7, 10, 13, 16). Practice 5 'Pose purposeful questions' drives checks_for_understanding. Practice 6 'Build procedural fluency from conceptual understanding' is the explicit C-to-P-to-A ordering.
Cognitively Guided Instruction (Carpenter, Fennema, Franke, Levi, Empson 1999/2014)
Children's intuitive counting strategies are surfaced and named. Lessons 4, 7, 11 explicitly ask children to share their own counting strategies (count-all / count-on / known-fact) before the teacher names the strategy. CGI student-strategy inventory is the teacher's mental model in formative_assessment scoring.
Liljedahl Building Thinking Classrooms — Visibly Random Groups (light at K)
Lessons 6 and 12 use VRG via color-sticker partner draws (developmentally adapted from Liljedahl's middle-school protocol — at K the 'group' is a pair). Children stand at vertical non-permanent surfaces (whiteboards or chart paper taped at child-height) for the shape-sort and pattern-extend tasks.
Clements & Sarama Learning Trajectories (Building Blocks / 'Learning and Teaching Early Math' 2014/2021)
The counting trajectory (Pre-Counter → Reciter → Corresponder → Counter (Small Numbers) → Producer → Counter and Producer) directly informs skill sequencing for math.gK.f.ns.count_to_100, math.gK.f.ns.cardinality, math.gK.f.ns.one_to_one. Shape trajectory (Pre-Recognizer → Recognizer → Constructor) informs math.gK.f.gm.shapes_2d / 3d.
Number Talks (Parrish 2010 / Humphreys & Parker 2015)
Daily 5-minute Number Talk routine in warm_up of lessons 1, 4, 7, 10, 13, 16. Dot-image flash subitizing, ten-frame flash, and 'how do you see it?' prompts.

Depth bar

Covers

CCSS

K.CC.A.1: count to 100 by ones and tens
K.CC.A.2: count forward from a given number
K.CC.A.3: write 0-20
K.CC.B.4.a-c: one-to-one correspondence, cardinality, +1 successor
K.CC.B.5: count to answer how many, configurations to 10 / scattered to 20
K.CC.C.6: compare two groups
K.CC.C.7: compare written numerals 1-10
K.G.A.1-3: positions, 2D/3D names, flat vs solid
K.G.B.4: describe shapes by attributes
K.MD.B.3: classify and sort, in full

Exceeds

CCSS by introducing K.NBT.A.1 'compose ten ones into one ten' as a Spring foundation lesson preview (CCSS Grade-1 expectation 1.NBT.B.2), by extending counting backward from 10 (CCSS Grade-1 1.NBT.A.1 backward-count expectation) at the concrete tier, and by exposing skip-counting by 2s and 5s through pictorial-tier dot patterns (a Grade-1 1.NBT.A.1 stretch) — all introduced concretely-only with no abstract-tier mastery required at K