Making Arrays

In order to gain a better understanding of the relationship between multiplication and division, we began studying arrays.  We looked at them in different ways and learned to see the multiplication and division facts they could represent.  In this activity, each team of students created an array with objects in the classroom.  Then they visited other teams' arrays and discussed the fact family they saw.  Students took along their white boards and wrote down the facts they discussed. 

Making arrays

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Multiplying Large Numbers

We learned several different algorithms for multiplying multi-digit numbers - partial products, lattice, and the traditional approach.  But I want my students to go beyond learning the algorithm.  I want them to really understand what is happening when we multiply these large numbers.  When our study of multiplication began, we spent a lot of time exploring repeated addition and arrays.  So I built on this knowledge and asked our kids to build BIG arrays - like 23 x 34 - using base ten blocks.  We then were able to connect the array to the 4 partial products we made when using the partial products algorithm.  Our kids were actually able to see what happens when we multiply large numbers together. 

In the video below, you'll see kids solving problems using the partial products algorithm and "building" the array using base-ten blocks.  But the important step comes after creating the array.  You'll see kids making a connection between the numbers on their white boards and the actual base ten blocks.