Mathematics · Year 2

Active learning ideas

The Structure of Arrays

Arrays offer a tangible way for Year 2 students to grasp multiplication concepts. Moving beyond rote memorization, active learning with arrays allows students to physically build and explore the spatial relationships inherent in multiplication, solidifying their understanding of equal groups.

• National Curriculum Attainment Targets
• KS1: Mathematics - Multiplication and Division

• 15–25 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 20 min · Small Groups

Array Construction Station

Provide students with manipulatives like counters, blocks, or even dried beans. Give them multiplication sentences (e.g., 2 x 5) and have them build the corresponding array. Encourage them to draw their arrays and label the rows and columns.

Analyze how rotating an array changes the way we describe it with numbers.

Facilitation Tip

During the Stations Rotation, ensure students have enough time at each station to fully engage with the materials and the specific task related to array construction.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 15 min · Pairs

Array Rotation Challenge

Students create an array for a given multiplication fact, then rotate their paper or mat 90 degrees. They then write the new multiplication sentence that represents the rotated array, reinforcing the commutative property.

Justify why multiplication is a more efficient way of counting than repeated addition.

Facilitation Tip

During the Gallery Walk, circulate to prompt students to explain their reasoning for identifying an object as an array and how it relates to multiplication.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 25 min · Whole Class

Array Hunt

Take students on a walk around the classroom or school to find real-world examples of arrays, such as egg cartons, window panes, or seating arrangements. Have them record or sketch their findings and write the corresponding multiplication sentence.

Explain how we can use an array to show that multiplication can be done in any order.

Facilitation Tip

During the Array Hunt, encourage students to sketch or photograph their findings and be prepared to explain why each example fits the definition of an array.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Focus on arrays as a visual model for multiplication, emphasizing the connection between equal groups, rows, and columns. Avoid presenting multiplication solely as repeated addition; instead, use arrays to show how multiplication is a more efficient way to represent these equal groupings. Explicitly model how to construct arrays and relate them to number sentences, including demonstrating the commutative property.

Students will demonstrate understanding by accurately constructing arrays for given multiplication facts and by identifying arrays in their environment. They will be able to articulate how an array represents equal rows and columns and connect it to a multiplication sentence.

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Watch Out for These Misconceptions

• During Array Construction Station, watch for students who consistently build arrays with the first number representing rows and the second number representing columns, struggling to see the alternative orientation.

  Prompt students to physically rotate their constructed array or the paper it's on, asking them to recount the rows and columns to see that 3 rows of 4 objects is the same total as 4 columns of 3 objects.

• During Array Rotation Challenge, students might focus only on the total number of objects rather than the structure of equal groups within the array.

  Ask students to explain how their rotated array still represents the same multiplication sentence by pointing out the equal number of objects in each row and column.

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Methods used in this brief

• Stations Rotation