Show the next visual math talk prompt and be ready to pause the video once prompted:

Show the following visual math talk prompt and be ready to pause the video once prompted:

In the video, students are presented with visuals and a text prompt to set the context involving an equal quantity of caterpillars stored in large containers plus an additional two caterpillars in a smaller container.

You’ll notice that this first prompt attempts to make this context very visual and scaffolds students toward an algebraic equation that could be used to represent this situation, 4m + 2 = 30.

It is worth noting that this context is going to require the use of partitive division as the unknown variable represents the rate of caterpillars per large container while the number of large containers is known.

Some students might immediately begin using trial and error to determine the value of m. For example, some students might try m = 5 and will skip count to 20 (or multiply 4 large containers by 5 caterpillars) plus 2 caterpillars is 22. Therefore, they might adjust up until they land on the value of m that will result in a total of 30 caterpillars.

Other students might leverage a linear model like a stacked bar model beginning with 30 caterpillars and working backwards to reveal how many caterpillars must be in the 4 large containers. By subtracting the two additional caterpillars, students will quickly realize that there must be 28 caterpillars divided equally across the 4 large containers.

Now that the 2 additional caterpillars have been removed from the equation, we now have a simple one step equation involving partitive division to solve. Some students might choose to scale down by halving twice, or other students might immediately partition the quantity into 4 groups representing the 4 large containers.

Ensure that students are able to connect how multiplying by 1 fourth (or by 1 half and again by 1 half) is equivalent to dividing by 4. This idea can be helpful for students to solidify their understanding of how dividing by a quantity is equivalent to multiplying by the reciprocal.

Facilitator Note:

Be sure to ask students about what they notice when they analyze the equation 4(m) + 2 = 30 and the operations they used to solve for the unknown number of caterpillars per large container, m. Some students may be able to recognize that we are using opposite operations to undo or work backwards to find the value of m. Ensure this is explicitly highlighted.