Kindergarten Spring Math — Compose/Decompose to 10, Addition & Subtraction within 10, Teen Numbers as Ten-and-Ones, Measurement, and Classification

Overview

Kindergarten Spring Math is the term in which children first do arithmetic. Building on the K-Fall foundation (counting to 100, subitizing, cardinality, one-to-one, numeral writing, ten-frames, shapes, patterns, sorting), the Spring unit teaches addition and subtraction within 10, composition and decomposition of numbers to 10, the foundational place-value structure of teen numbers (11-19 as 'ten and some ones'), direct comparison of length/weight/capacity, classification by category and counting within categories, and shape composition from parts.

Singapore CPA is the structural backbone: every skill is met first in the hands (two-color counters, rekenrek, ten-frame mat, linking cubes, balance pan), then on the page (number-bond diagram, part-part-whole bar, drawn ten-frame, drawn equation), and only then in symbolic notation (numerals, +, −, =, expressions, equations).

The number bond — Singapore's signature representation — is introduced in Lesson 1 and used throughout the unit; it is the visual that ties together composition (two parts make a whole), decomposition (a whole splits into two parts), and the inverse relationship between addition and subtraction. CGI's word-problem taxonomy structures the problem-solving thread: Join Result Unknown (Lesson 5), Separate Result Unknown (Lesson 8), Part-Part-Whole Whole Unknown (Lesson 11), and Compare Difference Unknown (Lesson 14) — four problem types children meet with manipulatives, drawings, and finally equations.

Teen numbers (11-19) are taught explicitly as ten-and-some-ones (CCSS K.NBT.A.1) using double ten-frames and ten-and-extras decompositions — this is the seed of place value, the structural foundation for Grade 1's work with 11-120.

Counting continues — daily routines (Calendar Circle, attendance count, line-up count, transition counts) keep counting-to-100 fluent and introduce skip-counting by 5s and 10s at the concrete tier. Measurement work introduces direct comparison only (no rulers) — children align two objects at a common baseline to compare length, place two objects on a balance pan to compare weight, and pour from one cup to another to compare capacity.

Classification deepens K-Fall's sorting-by-one-attribute work to multi-category counting (sort by one attribute, then count how many in each category — the seed of categorical data). Shape composition extends K-Fall's shape-naming work: children compose larger shapes from smaller ones (two triangles make a square; a triangle + a square = a house; six triangles = a hexagon) — the foundation for fraction work in later grades.

Manipulatives are concrete and specific — 20 two-color counters per child, 10-bead rekenrek per child or per pair, 5x2 ten-frame mats (2 per child for double-ten-frame work), 20 linking cubes per child, balance pan, identical capacity cups — never generic 'math manipulatives.' Every CPA-required skill specifies its C/P/A tier explicitly; misconceptions are named (e.g., 'counts both parts AND the whole when checking a number bond — triple-counting,' 'reads 14 as 4 and 1 because the 4 is heard first,' 'compares lengths from non-aligned baselines,' 'thinks more cups = more capacity even when cups are different sizes').

The unit closes with a portfolio-style summative in which each child decomposes 10 in three ways, solves three CGI word problems within 10, identifies the ten-and-ones structure of a teen number (e.g., 13 = 10 + 3), directly compares two objects by length AND by weight, classifies a collection of 12 objects into 2-3 categories and counts each, and composes a target shape from parts.

Depth bar

CCSS K by introducing the make-ten strategy as a pictorial bridge to Grade-1 1.OA.C.6 'add within 20 using strategies such as making ten' at the concrete and pictorial tiers only, by previewing skip-counting by 5s and 10s on a 100-chart (CCSS Grade-1 1.NBT.A.1 stretch — concrete tier only), and by introducing equal-share decomposition of 10 into two equal groups of 5 as a fair-share intuition foundation for Grade-2 division readiness (CCSS Grade-2 2.OA.C.3 stretch)