ply at your school. This will help students keep their rows and columns even. Pose a problem and allow students to use manipulatives you have available to construct the array. If you say, “Build an array for this multiplication problem: 3 x 5,” do they know the 3 refers to # of rows and the 5 refers to the number in each row?
- Turn the paper after building the above array to see the commutative property. Now the picture shows 5 x 3 (5 rows with 3 in each row). The product is still 15.
- Use the manilla grid paper along with bingo dobbers to create the array. The grids can also be completed with mini stickers (I get them all the time in junk mail) or drawings.
- When using pictures of arrays, direct your students to always label 2 sides of the array (the rows and columns). Try to label different sides of the array so it’s not always presented in the same format.
- Find the product: The whole point of using an array as a multiplication strategy is to visualize the rows and columns to help calculate the product. If students create rows and columns and then just count the objects one-by-one, then this does not accomplish the objective. Show students how to skip count using the # of objects in the rows or columns. Believe me, students don’t always know to do this without a hint from the teacher. Or better yet, before actually telling them to do this, ask students this question: “How did you get the total number of objects?” When you pose this question, you are honoring their strategy while secretly performing an informal assessment. Then when the student who skip counted to find the total shares their strategy, you give them the credit: “That is an efficient and fast way to count the objects, thank you for sharing! I’d be interested to see if more of you would try that with the next problem.” Plus now students have 2 strategies.
- Use the distributive property to find the product: Let’s suppose the array was 6 x 7. Maybe your students are trying to count by 6’s or 7’s to be more efficient – but the problem is that counting by 6’s or 7’s is difficult for most students. Break up (decompose) the array into smaller sections in which the student can use their multiplication skills. Decomposing into rows or columns of 2’s and 5’s would be a good place to start. This is the distributive property in action – and now the students have 3 strategies for using an array!! This is a great way to use known facts to help with those being learned.Here is a link to Math Coach’s Corner (image credited above) and a great array resource: Multiplication arrays activities from TPT $5.50. Here is my FREE guided teaching activity to help students decompose an array into 2 smaller rectangles. Click HERE for the free blank template.
- Use the online geoboard I described a few posts back to create arrays using geobands. Click here for the link: Online geoboard Click here for the previous post: Geometry websites (blog post)
- Try these freebies: Free array activities from k-5mathteachingresources.com. Here’s a sample.
- Play this game I call “Block-It.” This is a competitive partner game in which students must create arrays on grid paper. Click here for a FREE copy of the directions: Block-It Game Directions
- Relate use of arrays when learning strategies for division and area.
In a future post I will show some ways to use manipulatives and pictures arrays for double digit multiplication problems. Stay tuned!!