Show students the following visual math talk prompt and be prepared to pause the video where indicated:

Then ask students:

How many bottles are there?
Craft a convincing argument without the use of a calculator.

Similar to Day 1 of the Stack ‘Em Up problem based unit, students will be presented with a crate of drink bottles organized in an 8 x 14 multiplication array and will be tasked to determine how many bottles there are in total.

Since we are aiming to build fluency and flexibility multiplying one- and two-digit numbers we are going to ensure students are not leveraging the calculator as a tool.

As the facilitator, we are going to do our best to work from an array or open array (or area model) to highlight the strategies students are using to multiply these two factors.

Some students may choose to employ a doubling and halving strategy such as halving the 8 rows and doubling the 14 columns which employs use of the identity property (i.e.: any quantity multiplied by 1 keeps its identity or remains unchanged) and our understanding of fraction equivalence (i.e.: 1 = 1 whole = 2 halves = 2 one-halves) and the associative property to reassociate one-half with the 8 rows and 2 with the 14 columns.

This use of the associative and commutative properties allows us to see that 8 rows of 14 columns is equivalent to 4 rows of 28 columns.

Of course, these visuals can support your facilitation of this visual number talk, but it would be most effective if the facilitator draws the models both as arrays or area models and represents symbolically as the thinking emerges.

It is important for you to also determine how far symbolically you believe is beneficial for students given their current entry point. The symbolic representation here is more helpful for educators to understand what is actually happening through the use of the identity, commutative and associative properties.

A student who is using a doubling and halving strategy can continue to use this strategy to make one of the factors smaller and smaller and one of the factors larger and larger until they are comfortable determining the product.

A student who continues to utilize this strategy will eventually arrive at a 1 by 112 array which results in a total of 112 bottles.

It should be noted that some students may choose to leverage the distributive property instead by breaking down 8 x 14 into 8(10 + 4) or some other variation that decomposes the factors down into more manageable chunks. This approach should also be modelled with an array and/or area model.