## Why this topic?

The Common Core State Standards for Mathematics references the use of arrays at every elementary grade level. Arrays are used for counting as well as for organization, measurement, multiplication, and representation of fractions. As adults we have a well-developed understanding of both discrete (separate objects) and continuous (area model) arrays. It is sometimes difficult for us to see when children don’t observe features of an array that are obvious to us. .

## What should we consider?

Arranging discrete items into rows of equal numbers of elements to assist in counting is probably one of the earliest experiences young students have with arrays. Helping children to understand the counting and repeated addition possibilities of these arrangements is important to address early in the learning process.

The multiplicative features of an array will probably not be perceived by students until later, so teachers should be aware of differences between their own understanding of “obvious features” and children’s developing awareness of those same features. Transitioning from discrete arrays to continuous area models is another step that requires some assistance from the teacher. Using individual units to “cover” the area of a rectangle may not lead to an understanding of the multiplicative aspect of such a measurement. Students need time and assistance to discover for themselves the relationship of equal numbers of units in each row and a specific number of rows.

## What should we do?

Providing many activities and spending time talking with students to determine their level of understanding is important at the early stages because arrays will be used later for both measurement activities and fraction activities. Some of the resources included in this collection will provide examples of the types of activities students need to develop the deep understanding of the features of both discrete and continuous arrays. Teachers will want to help young students see and use the characteristics of arrays to organize and count objects. Allow students to discover how arrays provide information about factors, how they can be used to identify prime numbers, even vs. odd numbers, or square numbers. Work with older students to be sure that they see the relationship between arrays of discrete objects and continuous area models. Explore the resources in this collection for ideas and strategies that ensure your students develop expertise in recognizing and using the characteristics of arrays.

## Collection Discussion

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