Walk Through Video

Watch this “Walk Through” video of the entire math talk portion of the lesson to gain a better understanding of the intentionality behind this string of related problems:

String of Related Problems

For today’s Math Talk, we will build on the Shot Put context from day 1. Continue the context storyline by recalling how last day, we used 4 red measuring sticks plus 12 feet to measure a throw of 76 feet and model this on the double number line: Problem #1: Set-up the context for today’s math talk by stating:

Today, a younger thrower had thrown a distance of 38 feet.  How many red sticks and additional feet would be needed to measure the 38 foot throw?

We recommend that you model the scenario by drawing the representation by hand of a number line and jumps to represent each measuring stick, plus the additional 12 feet. Some students may recall or calculate the length of the red measuring stick again with the learning from last day. Problem #2:

What about a 19 foot throw?

Facilitator Notes

For today’s Math Talk, we will build on the Shot Put context from day 1. Continue the context storyline by recalling how last day, we used 4 red measuring sticks plus 12 feet to measure a throw of 76 feet and model this on the double number line: Set-up the context for today’s math talk by stating:

Today, a younger thrower had thrown a distance of 38 feet.  How many red sticks and additional feet would be needed to measure the 38 foot throw?

We recommend that you model the scenario by drawing the representation by hand of a number line and jumps to represent each measuring stick, plus the additional 12 feet. Some students may recall or calculate the length of the red measuring stick again with the learning from last day. When we ask students where 38 feet should go on the number line, they should place it at the midpoint between 0 feet and 76 feet. For some students, they may need to decompose 76 into 70 + 6 to half both quantities separately as 35 + 3. Alternatively, some students may choose to decompose 76 into 60 + 10 + 6 and half each quantity to get 30 + 5 + 3 to confirm that 38 is in fact the halfway point. From here, students will likely be able to see without too much trouble that you will need 2 red measuring sticks plus some number of additional feet. The goal is that students will be able to realize that when we half the distance of 76 feet to 38 feet, we will need to half the number of red measuring sticks as well as the 12 additional feet. By applying the idea of scaling both units, 76 feet and 4r + 12, by one half, our equation will remain equivalent. Now we can ask students the next question in the string of related problems:

What about a 19 foot throw?

If we come to the conclusion that 19 feet is half of 38 feet, students may choose to use a similar strategy to how we modelled scaling in tandem in the last scenario. Consider using your double number line model from the first day to show how we can scale for these new throws. If students are struggling to follow your hand drawn representation of the number line and feel showing a less abstract representation, you might consider sharing this silent solution animation and/or the following still frame images: When students work on the 38 foot throw, take note of which students recognize that the total distance is half of the first throw, resulting in half the number of red sticks and half the number of additional feet required to measure. Be sure to highlight this strategy with the whole group. This strategy reveals the big idea that both sides of an equation can be scaled as a single unit in tandem. Note that the 19 foot throw is half of the 38 foot throw and a similar discussion can take place. You might consider using the following visuals to assist in this math talk if none of the students are able to “see” or arrive at the fact that 38 feet is half of 76 feet, and half of 38 feet is 19 feet. We would encourage the use of visuals only after you’ve attempted to ask students purposeful questions that will help them plot where each of those distances would go approximately on the number line.

Big Idea

When students work on the 38 foot throw, take note of which students recognize that the total distance is half of the first throw, resulting in half the number of red sticks and half the number of additional feet required to measure. Be sure to highlight this strategy with the whole group. This strategy reveals the big idea that both sides of an equation can be scaled as a single unit in tandem. Note that the 19 foot throw is half of the 38 foot throw and a similar discussion can take place. You might consider using the following visuals to assist in this math talk if none of the students are able to “see” or arrive at the fact that 38 feet is half of 76 feet, and half of 38 feet is 19 feet. I would encourage the use of visuals only after you’ve attempted to ask students purposeful questions that will help them plot where each of those distances would go approximately on the number line.