Turned Arrays
About This Worksheet
Turned Arrays is a third grade multiplication activity that helps students see what happens when an array is turned. Each problem shows two arrays that contain the same total number of objects but have their rows and columns switched. Students write a multiplication equation for Array A and another for Array B, then look for the pattern between the two equations. For example, 3 × 4 and 4 × 3 both have a product of 12. This gives students a visual introduction to the idea that changing the order of the factors does not change the product.
Curriculum and Grade Alignment
This worksheet is intended for third grade learners who are building connections between arrays and multiplication properties. The main goal is to help students recognize that a rotated array represents the same total even though the factors switch places. Before beginning, your child should be comfortable writing multiplication equations from arrays. The next step is naming and using the Commutative Property of Multiplication more formally. This activity supports multiplication concepts, factor relationships, and visual reasoning.
Student Tasks
Students will study four pairs of arrays. For each pair, they write the multiplication fact represented by Array A and the fact represented by Array B. The arrays use dots, squares, and triangles and show the same product arranged in two different directions. After completing the equations, students finish a rule stating what happens to the factors and product when an array is turned. This builds understanding of factor order and equivalent multiplication facts.
Common Challenges and Misconceptions
Some students may think the turned array represents a different total because it looks different. Others may count the objects again correctly but miss the relationship between the two factor orders. A child may also confuse rows and columns when writing the equations. Encourage your child to compare the two equations side by side and ask, “What changed, and what stayed the same?” This makes the commutative relationship easier to notice.
Implementation Guidance
Teachers can use this worksheet when transitioning from array models to the Commutative Property of Multiplication. It works especially well in guided groups because students can physically rotate a drawn or tiled array. Parents can build a small array with coins or blocks and turn the paper or tray sideways. Ask the child to write the multiplication fact before and after turning it. This makes the relationship very concrete.
Details and Features
This worksheet includes four paired array comparisons in a blue grid. Each pair shows the same product with the rows and columns reversed. Students write both multiplication equations and complete a short rule at the bottom. The printable supports multiplication properties, array interpretation, factor order, and equivalent facts.