Understanding Arrays in Mathematics
An array is a powerful tool that helps children see quantities in organized patterns, which fosters understanding of numbers as groups rather than isolated units. Arranging objects or numbers in rows and columns is a way to help students begin to see patterns and structure. This visual representation helps them grasp the concept of multiplication as repeated addition, reinforcing the idea of equal groups and how numbers can be organized. Introducing arrays early on also sets the stage for students to later connect these concepts to more abstract mathematical operations.
Key Ideas for Teaching Arrays
Using Hands-On Models to Teach Arrays
Students learn best when they can work with physical models to explore mathematical concepts. Arrays are particularly effective in this way because they help students visualize and organize numbers. Start with simple objects, like counters, square tiles, or Unifix cubes, and have students arrange them in rows and columns. This setup allows students to explore the patterns in arrays, such as counting rows or columns to find the total number of objects, which connects directly to multiplication.
In addition to supporting multiplication, arrays are a powerful tool for exploring division. By dividing objects into equal rows or columns, students can visually determine how many rows or columns can be created for a given group size, or how many objects fit into each row or column. This hands-on approach deepens their understanding of division as both grouping and sharing.
Building Arrays:
Provide students with a set number of counters or cubes, 24 for example, and encourage them to explore the different arrays they can create with the given quantity. Students can represent their arrays using repeated addition equations or multiplication equations. This activity also provides an opportunity to introduce and explore the concepts of prime and composite numbers.
Using Visual Representations to Teach Arrays
Students can transition from creating concrete arrays to representing them visually on grid paper.
Capturing Arrays:
This simple game helps students deepen their understanding of arrays and their connection to multiplication. Two students play against each other. On each turn, a student rolls two dice, and the numbers rolled determine the dimensions of their array. The student then draws the array on grid paper, writes the dimensions as a multiplication expression, calculates the total number of unit squares inside the array, and records the total inside the array. Play continues until neither player can fit another array on the grid paper. The winner is the player who captures the highest total area (number of unit squares) on the grid.
Building Math Vocabulary Around Arrays
When students are working with arrays, it’s important for them to know the difference between rows and columns and to use the vocabulary accurately. Rows go across, and columns go up and down. Learning this early prepares students for future math topics like working with tables, graphs and coordinate grids, where mixing up rows and columns can cause confusion.
