Building Foundational Math Skills in Primary Grades: The Importance of Hands-On Learning

Building Foundational Math Skills in Primary Grades: The Importance of Hands-On Learning

Introduction

Mathematics education in the primary grades (preschool through second grade) must focus on building a strong foundation of number sense through hands-on, concrete learning experiences. Unfortunately, many classrooms have shifted toward digital apps, paper-pencil worksheets, and standardized testing preparation, leaving students with gaps in their mathematical understanding. Research has shown that students who lack foundational numeracy skills struggle with advanced concepts later on, creating a cycle of mathematical deficiency.

This article explores essential primary math skills that should be developed through manipulatives such as a 10-frame, a 100-bead counting frame (100 BB), and number lines. These tools are crucial for conceptual understanding, problem-solving, and mental math development.

Essential Primary Math Skills and Hands-On Methods

1. Number Sense and Subitizing

Concept: Number sense is the ability to understand, relate, and connect numbers. Subitizing is the ability to instantly recognize the number of objects in a set without counting them one by one. Hands-On Method: Use a 10-frame or a 100-bead counting frame with alternating colors (five red, five white) to develop visual recognition of numbers. For example, show students a 10-frame with 7 dots and ask, "How many?" without counting individually. Encourage them to see 5 and 2 rather than counting 1,2,3, etc.

2. Counting On and Counting Back

Concept: Adding or subtracting from a given number rather than starting from one each time. Hands-On Method: Using a 100-bead counting frame, ask students to start at 8 and count on 3 more. Visually tracking movement of beads reinforces number sequencing and addition. Similarly, for subtraction, have them move backward to see number relationships.

3. Part-Whole Relationships, Partitioning, and Subordinating Partitioning

Concept: Understanding how numbers can be broken into parts and combined. Subordinating partitioning involves breaking a number into hierarchical smaller parts to build fluency. Hands-On Method: Use a 10-frame with counters to show how 7 can be made from 3 and 4 or 5 and 2. With a 100 BB, show partitioning of numbers like 25 into 20 and 5, and further break it down into 10+10+5. This helps students see relationships between numbers and supports mental math strategies.

4. Greater Than, Less Than, and Comparing Quantities

Concept: Recognizing which numbers are larger or smaller. Hands-On Method: Use number lines and bead counting frames to compare numbers. Have students slide beads on two different 100 BBs to see which has more or less. Similarly, place numbers on a number line and discuss which is further along.

5. Associative and Commutative Properties of Addition

Concept:

• Associative Property: (a + b) + c = a + (b + c)

• Commutative Property: a + b = b + a Hands-On Method: Use manipulatives to show that grouping doesn’t affect sum. For example, using a counting frame, illustrate that moving groups of 2 and 3 beads results in the same total whether you count (2+3) first or (3+2) first.

6. One More, Two More, Three Less Strategy

Concept: Understanding incremental increases or decreases in number sequences. Hands-On Method: Start at a number on a number line and physically hop forward or backward. On a counting frame, slide beads to show how numbers grow or shrink.

7. Conceptual vs. Perceptual Subitizing

Concept:

• Perceptual Subitizing is recognizing small amounts instantly (e.g., knowing 3 dots without counting).

• Conceptual Subitizing is breaking larger sets into familiar groups (e.g., seeing 8 as two groups of 4). Hands-On Method: Show quick flashes of a 10-frame or counting frame arrangement and ask students to describe how they see the number.

Glossary of Terms with Exemplars

1. Subitizing – Instantly recognizing a number without counting (e.g., knowing a 5-group on a 10-frame without counting each dot).

2. Counting On – Starting from a known number and adding more (e.g., "Start at 7 and add 2" using a counting frame).

3. Partitioning – Breaking a number into parts (e.g., "10 is 6 and 4").

4. Subordinating Partitioning – Hierarchically breaking numbers into smaller components for better number sense (e.g., "25 is 20+5, and 20 is 10+10").

5. Number Line – A visual representation of numbers in order, used for operations.

6. One More, Two More – Understanding incremental increases (e.g., "What is one more than 9?").

7. Associative Property – Grouping numbers in any order for addition (e.g., "(3+4)+5 is the same as 3+(4+5)").

8. Commutative Property – Switching numbers in addition without changing the sum (e.g., "4+3 is the same as 3+4").

9. Greater Than, Less Than – Comparing numbers (e.g., "9 is greater than 6 because it is farther on the number line").

10. Conceptual Subitizing – Seeing larger numbers as groups of smaller ones (e.g., recognizing 9 as two groups of 4 and 5 on a counting frame).

11. Perceptual Subitizing – Instantly recognizing small amounts (e.g., "I see 3 dots without counting").

Conclusion

The shift away from hands-on, concrete math experiences in primary education has resulted in significant gaps in foundational numeracy skills. Tools like 10-frames, 100-bead counting frames, and number lines must be reintroduced into classrooms to support early mathematical understanding. Without these foundational skills, students will struggle with fluency, problem-solving, and higher-level math concepts. A return to research-based, manipulative-driven instruction will build a stronger mathematical foundation, ensuring students develop the necessary number sense and reasoning skills for long-term success.