Standard K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).


Progression of Skills
koa3.png


About the Math
In order for students to decompose numbers they must first understand the Part Part Whole Relationships. Students see that numbers are made up of other numbers. Then they can see that a number can be broken apart into smaller quantities. Begin with numbers 4 and 5 and give students two-color counters, connecting cubes and ask them to build the number so that five can be 4 and 1, 2 and 3 and 5 and 0. Students can record their findings by drawing. Some students may be able to represent the relationships with numerals. This is a goal for the end of the year. Connect this concept to the five and ten frame. Some students may need to see the representation of the quantity.


Essential Skills and Knowledge (from MSDE Common Core Frameworks)

  • Knowledge that decomposition involves separating a number into two parts and understanding that there is a relationship between the sum of the parts and the whole
  • Knowledge that there are a variety of combinations that represent a given number
  • Ability to begin with the whole when decomposing numbers into pairs. Knowledge that when writing an equation to represent the decomposition of a number, the values on each side of the equal sign are the same (e.g., 7 = 2 + 5)

Rich Instructional Tasks

How Many Ways? - Activity 10.13: Teaching Student-Centered Mathematics Grades K-3 (289).
For further Instructional Activities from this text, refer to Activity 10.20 (note: modify to decompose numbers less than or equal to 10; 299), Activity 10.21 (300), and Activity 6.1 (note: modify with numbers that decompose to less than or equal to 10; 165)
VDW-k-3.png

Four to Score - Math Intervention: Building Number Power with Formative Assessments, Differentiation, and Games (61-63)
For further Instructional Activities from this text, refer to Big Top Twelve (96-99) and Funny Bunny (note: use bunnies to decompose numbers less than or equal to 10; 133-135)

Online Resources

Hide the Cubes


Connecting Children's Literature

mouse_count.png Mouse Count Task
fireflies.png Ten Fireflies Task


Formative Assessments

Matching Sets



Print Resources

Teaching Student-Centered Mathematics, Grades K-3: Chapter 6, Strategies for Whole-Number Computation (157-185) and Chapter 10, Algebraic Reasoning (275-309)
Math Intervention: Building Number Power with Formative Assessments, Differentiation, and Games, PreK-2
Teaching Student-Centered Mathematics
  • Activity 3.1 Equations and Number Patterns (pg. 73) (add pdf)
Developing Number Concepts Book 1: Counting, Comparing, and Pattern
  • Activity 1-11 Peek and Count (pg. 39)
  • Activity 1-13 Tell Me Fast (pg 42) BLM 20-27.pdf
Developing Number Concepts Book 2: Addition and Subtraction
  • Activity 1-9 Writing Equations (pg. 29) BLM 2-6.pdf
  • Activity 1-12 Counting Boards (pg. 33) BLM 64-73.pdf
  • Activity 1-14 Plus and Minus Train (pg. 35) BLM 98.pdf
  • Activity 2-1 Snap It (pg. 56) BLM 1.pdf
  • Activity 2-8 Working With Number Arrangements (pg. 65) BLM 76-82.pdf
  • Activity 3-2 Instant Rec. of Number Arrangements (pg. 115)
  • Activity 3-3 Instant Rec. of Number Arrangements (pg. 117) BLM 76-82.pdf

Hands on Standards
  • Lesson 12, Part-Part-Whole (pg. 38)
  • Lesson 15, Decomposing Numbers (pg. 44)
  • Lesson 9, Arranging Sets of Objects (pg. 108)

Investigations Alignment

Quarter 1 Quarter 2 Quarter 3 Quarter 4
Unit 4: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9
Unit 6: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5A.2, 5A.4, 5A.5