Array Building Workshop
Teacher: Demo Teacher | Grade: 3 | Subject: Math | Duration: 45 minutes
📝 Description: Students build rectangular arrays with counters to visualize multiplication facts and transition from skip counting to understanding equal groups.
Standards
- 3.OA.A.1 - Interpret products of whole numbers as total number of objects in equal groups
- 3.OA.A.3 - Use multiplication and division within 100 to solve word problems involving equal groups and arrays
- 3.OA.B.5 - Apply properties of operations as strategies to multiply and divide
Learning Objectives
Students will be able to:
- Create rectangular arrays using counters to represent multiplication problems
- Identify rows and columns in an array and connect them to multiplication factors
- Write multiplication equations based on arrays they build and observe
- Explain how arrays show equal groups more clearly than skip counting alone
Materials Needed
- Grid paper (1 sheet per student)
- Counters (20-25 per student or pair)
- Dry erase boards and markers (1 per student)
- Array recording sheet (teacher-created simple template)
- Chart paper for class examples
- Document camera or projection capability
Lesson Structure
Opening (5 minutes)
Display 12 counters scattered randomly on document camera. Ask: "If I want to arrange these 12 counters in equal rows, what are some ways I could do it?" Allow 2-3 student suggestions, then demonstrate arranging them into a 3x4 rectangle. Introduce the term "array" and explain today's goal of using arrays to understand multiplication better than just skip counting.
Main Activity (35 minutes)
Step-by-step instructions:
- Guided Array Building (8 minutes): Give each student 15 counters. Call out "Make an array with 2 rows of 3." Walk around checking arrays. On chart paper, draw the array and write "2 rows × 3 in each row = 6 total." Repeat with 3 rows of 4 counters.
- Grid Paper Transfer (7 minutes): Show students how to place their 2×3 counter array on grid paper, with each counter covering one square. Have them trace around the rectangle shape and remove counters. Demonstrate writing "2 × 3 = 6" below the drawn rectangle.
- Independent Array Practice (10 minutes): Students work with partners. Give multiplication problems: 2×5, 3×3, 4×2, and 1×8. For each problem, students build the array with counters, transfer to grid paper, and write the equation on their dry erase board.
- Array Rotation Activity (8 minutes): Students discover that 2×3 and 3×2 both equal 6 by physically rotating their arrays. Have them build both versions with counters and discuss what they notice. Connect to "rows and columns can switch places."
- Word Problem Arrays (2 minutes): Present: "There are 4 rows of desks with 5 desks in each row. How many desks total?" Students build the array and write the equation. Check answers using dry erase boards held up simultaneously.
Closing (5 minutes)
Have students create one final array of their choice using exactly 16 counters. They draw it on grid paper and write the multiplication equation. Share 2-3 different arrays for 16 (1×16, 2×8, 4×4) and discuss how arrays help us see multiplication as "groups of groups" rather than just counting by numbers.
Quick Check: Show a 3×6 array and ask: "What multiplication equation does this show? How many total objects? How is this different from skip counting by 3s six times?"
Formative Assessment
During the lesson, look for:
- Students correctly building arrays with the specified number of rows and columns (not random groupings)
- Accurate transfer from physical arrays to grid paper representations
- Students connecting the array structure to multiplication factors when writing equations
Differentiation Strategies
Support for Struggling Students:
- Start with smaller arrays (2×2, 2×4) and provide guided hand-over-hand support for building
- Use colored counters to emphasize rows (red row, blue row) and reinforce the pattern
- Allow continued use of skip counting while building arrays to bridge understanding
Challenge for Advanced Learners:
- Explore larger multiplication facts (6×7, 5×9) and find multiple array arrangements
- Introduce the concept of square arrays and prime numbers that only make 1×n rectangles
- Create word problems for classmates based on their array discoveries
ELL/ELD Support:
- Emphasize vocabulary with gestures: point to rows horizontally, columns vertically, repeat "equal groups"
- Provide sentence frames: "I see ___ rows with ___ in each row, so ___ × ___ = ___"
- Pair ELL students with strong English speakers for partner array building activities