#### Why don’t you show how many cookies are in a stack, box, carton, crate, pallet, or truck?

We decided not to do that because we want to encourage students to use benchmarks and then apply their understanding to move up or down in place value. For example, if a student knows (has memorized) that a box = 100 cookies and a truck = 1,000,000 cookies, then the student can use that knowledge to figure out that 1,000 cookies = a carton or 100,000 cookies = a pallet. While automaticity is good, at this stage, we want students applying what they know to reason things out. This is no different than how an adult might read a large number like 500,000,000,000,000. Most of us probably can’t read that number on sight. We would have to figure out that we are in the trillions, then read the number as 5 hundred trillion.

We also decided not to list the number of coookies in each container anywhere in the game. This wasn’t to help the students to learn place value better. We just thought it would be more fun if the student had the opportunity to discover the number of cookies in each container for themselves by trial-and-error.

#### Why don’t you line up the digits in addition orders vertically?

We do that in levels 5 and 6 where numbers get into the millions and digits can be difficult to visually track; and we are considering doing this in earlier levels as well. Right now, we are presenting addition orders horizontally so that students need to use place value to pick out digits to add (and can discover the advantages of lining up digits vertically for themselves). We encourage students to print out one of our blackline masters (Place Value Columns (3-Digits) or Place Value Columns (5-Digits)) and to use it to re-write problems if it makes things easier. This can be done in practice mode, but there is enough time in the early rounds to do this in the game mode also.

#### Can you have the count flash on the screen or be spoken outloud when you tap on a cookie, stack, box, carton or crate on the conveyor belt screens?

We considered doing that. We noticed that when we played the game, we were reluctant to shift our eyes from the conveyor belts to the counter until we made a mistake or lost track of the count in our head. We also noticed that we tended to read the count outloud when playing the game with younger students: it is nice reinforcement for them and enables them to focus more on what they are doing by reducing the cognitive load of trying to maintain a mental count. However, the count could be distracting when working with addition and multiplication orders (keeping track of the actual count is not necessary on those levels) and, most importantly, a worker on the factory floor would not have the benefit of those cues either!

We did make the count more prominent in version 1.3 by making the text larger and placing the count directly beneath the order. This reduces the distance that our eyes need to travel between the order, the converyor belts, and the count: encouraging us to use the counter more frequently.

#### Can you have the option to slow down the conveyor belts for students still working on their fine motor skills? Can you make the game adaptive so that new problems are based on how the student did on earlier problems?

We like both of these ideas but decided not to implement them because we decided to make this a game first and an educational tool second. Hand-eye coordination and fine motor skills are simply part of the game mechanics and making the game more adaptive would mean that players could not compare their sales records head-to-head. If we decide to release a new version of the game focused on the school market, we would definitely include these features, along with the ability to use the game with at least 30 players and more detailed progress monitoring (e.g., how many problems a student did, which problems a student got correct/incorrect, how long it took to complete each problem, and if a student had trouble with a particular type of problem).

If you’d like to see a school-based version of this game, please let us know through our contact form!

#### Why do the subtraction levels seem more like counting levels?

That happens because we have decided to separate the operational side of addition, subtraction, multiplication, and division from the accounting side. Too often, operations appear to be mysterious black boxes to students. To get the “answer,” they have to follow a series of memorized “rules.” But the operations of addition, subtraction, multiplication, and division are actually incredibly intuitive and grounded in everyday real-world experiences. To add, we combine. To subtract, we take away. The first conceptual stage for multiplication is repeated addition. And to divide, we… well, divide. By conflating the accounting side with the operational side, we make arithmetic appear harder and more abstract than it really is and impede conceptual understanding and schema-development. See our learning guide to learn more about linking the accounting side to the operational side once the operational side of arithmetic has been made transparent.