High School – Algebraic Relationships Sally’s Driving Sally is going to college 320 miles away. Her dad is taking her furniture in a moving van and she’ll be driving her car. Her dad can only drive 55 miles per hour, but Sally can drive at 65 miles per hour. Sally lets him leave half-an-hour earlier than her. How far from home will she catch up with him? Sally asistirá al colegio que se encuentra a 320 millas de distancia. Su papá transporta sus muebles en un camión de mudanza y ella manejará su automóvil. Su papá sólo puede conducir a 55 millas por hora, pero Sally puede conducir a 65 millas por hora. Sally permite que su papá salga media hora antes que ella. ¿A cuánta distancia de su casa lo alcanzará? Света уезжает в колледж, расположенный на расстоянии 320 миль от её дома. Её отец повезёт её мебель в автофургоне для перевозки мебели, а она поведёт свою машину. Отец может ехать со скоростью только 55 миль в час, а Салли может ехать со скоростью 65 миль в час. Салли даёт отцу выехать на полчаса раньше, чем выезжает сама. На каком расстоянии от дома она его догонит?

2 – Algebraic Relationships Sally’s driving Sally is going to college 320 miles away. Her dad is taking her furniture in a moving van and she’ll be driving her car. Her dad can only drive 55 miles per hour, but Sally can drive at 65 miles per hour. Sally lets him leave half-an-hour earlier than her. How far from home will she catch up with him? HS – 2 – 2 CU 6 The student shows an understanding of the key concepts of rate,

different rates for Sally and Dad, differences in time traveled, and catching up. This is enhanced through the translation between differences in miles Dad is ahead of Sally and in the verification, the equation to find the time Sally has driven when they are both in the same place. The translation shows an extension with the flexibility to go between the two major parts of the task (and when the negative value is interpreted).

PS 6 The original approach to the task, using Sally’s driving time and

recording the miles Dad is ahead of her until Sally is ahead of Dad – and identifying the decrease by increments of 10 – followed by the translation of that information into time is elegant. The first approach is enhanced by the generalization in the equation for the differences in location, so that no difference would be “they should be at the same place”.

V 6 The review is related to the original approach, but then uses an

enhanced different perspective as a defense (this is a nice touch just in case the reader was confused with the first conversion from miles ahead to time).

C 5+ The connecting path does not allow the reader to move easily from

one thought to another (from the differences in mileage to the time traveled by Sally) – the student requires the reader to think about that relationship – both in the original approach as well as in the different perspective in the verification. Once the reader understands this relationship, the paper flows smoothly from one connection point to the next. This struggle makes the path thoroughly developed instead of enhanced.

Acc. 5 2 and 3/4 hours out from home is a mathematically justifiable

solution to the task and is supported by the student work.

2 – Algebraic Relationships Sally’s driving Sally is going to college 320 miles away. Her dad is taking her furniture in a moving van and she’ll be driving her car. Her dad can only drive 55 miles per hour, but Sally can drive at 65 miles per hour. Sally lets him leave half-an-hour earlier than her. How far from home will she catch up with him? HS – 2 – 1 CU 5 The paper shows an understanding of the key concepts of rate,

different rates (found by both adding and subtracting the difference of travel time) and driving times for Dad and Sally, as well as catching up meaning an equal distance from home. The translation of the task into two perspectives is thoroughly developed.

PS 5 The overall strategy of establishing an equation with one unknown

and solving it then using that information to find the distance from home is complete. The work is made thoroughly developed by his/her working the two equations (and telling us s/he knows they are both processes for the task, just from two points of view); along with the verbiage letting the reader know what the mathematics is doing.

V 4 The verification is both embedded: working both equations to get

the same time for Sally’s driving, and the verbiage along the way; as well as identified: where s/he says “let’s check it with Sally’s Dads” and gets the same distance from home for both Sally and Dad. This particular paper MIGHT have been thoroughly developed with a purposeful review of the key concepts, instead of only having that review embedded.

C 5 The path connecting the key concepts to the strategy used to the

verification and the final solution is thoroughly developed with both the mathematics and the verbiage along the way describing the mathematics (not just a record of the steps used).

Acc 5 178.75 miles from home is a mathematically justifiable solution that

is supported by this work.

2 – Algebraic Relationships Sally’s driving Sally is going to college 320 miles away. Her dad is taking her furniture in a moving van and she’ll be driving her car. Her dad can only drive 55 miles per hour, but Sally can drive at 65 miles per hour. Sally lets him leave half-an-hour earlier than her. How far from home will she catch up with him? HS – 2 – 3 CU 2 The translation of the key concept of different rates is attempted in

the chart, but the key concepts of “catching up” (meaning traveled the same miles) and the connection between miles and time are just more than minimal, making the overall translation underdeveloped.

PS 2 The overall process of creating a chart to record miles traveled over

periods of time and comparing Sally’s to Dad’s is useful, but underdeveloped – especially when s/he subtracts miles from miles and gets minutes “left over” (ineffective). (The calculation errors are a part of the score for accuracy.)

V 1 Although the “check” is evident, it is definitely minimal. C 2 A series of “crater sized gaps” exist, between the concept of Dad

having a head-start but traveling in the same time periods as Sally, between the process used in the chart and the “catching up” when she is actually ahead sometime before 2 hours, the statement “her dad got __ miles a head so I just add those on and see” and the answer of 3 hrs and 3.5 minutes.

Acc 1 Even allowing for the numerous calculation errors, there is definitely

evidence that further instruction in the key concepts is needed, and 3 hours and three and a half minutes is not correct.