## BOXED COUNTERS—FIND FACTORS WITH AN ARRAY MODEL

Students investigate numbers and their factors by manipulating arrays of counters. Students select the number of counters for their array and then observe what happens as they change its dimensions while keeping the total number of counters the same. They pose and explore questions such as, “If I can represent 12 as a 3 × 4 array, can I also show it as a 4 × 3 array? What numbers form square arrays? How many ways can I arrange 23 counters so that every row of my array contains an equal number of counters? Do larger numbers have more factors than smaller factors?”

OBJECTIVES
• Students will use a rectangular array model to find all factors of given numbers.
• Students will see the relationship between the pictorial representation of multiplication and its symbolic form.
• Students will make and record observations about relationships and patterns between numbers and their factors.
COMMON CORE CONNECTIONS
Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (5) Use appropriate tools strategically; (7) Look for and make use of structure.

Content Standards

3.OA5, 6, 7, 9; 4.OA4, 5 