High School – Geometry Quilt Amelia is making a quilt for her bed. Her bed is 60 inches wide and 78 inches long. She wants the quilt to hang over on each side and on the end by at least 12 inches. On the finished quilt, the blocks will be 6-inch squares with 1.5-inch strips between them and around the outside edges. What is the minimum number of squares she will need to make? Amelia está haciendo un edredón para su cama. Su cama mide 60 pulgadas de ancho y 78 pulgadas de largo. Ella desea que el edredón quede colgando a cada lado y en la parte de los pies por lo menos 12 pulgadas. En el edredón acabado, los bloques serán cuadrados de 6 pulgadas con bandas de 1.5 pulgadas entre ellos y alrededor de los bordes exteriores. ¿Cuál es el número mínimo de cuadrados que necesitará hacer? Алла шьёт покрывало на свою кровать. Размеры её кроватисоставляют 60 инчей в ширину и 78 инчей в длину. Ей хочется, чтобы покрывало свисало с каждойстороны ис конца кровати по крайней мере на 12 инчей. На готовом покрывале рисунок будет состоять из квадратов со сторонойв 6 инчей с полосками в 1.5 инча между ними и вдоль внешних краёв. Какое минимальное количество квадратов ей нужно нашить?

3 – Geometry Quilt Amelia is making a quilt for her bed. Her bed is 60 inches wide and 78 inches long. She

wants the quilt to hang over on each side and on the end by at least 12 inches. On the finished quilt, the blocks will be 6-inch squares with 1.5-inch strips between them and around the outside edges. What is the minimum number of squares she will need to make?

HS – 3 – 1 CU 6 The translation of the key concepts (a 2-dimensional array, the extension of

the dimensions, accounting for the strips and borders, a minimum number of squares) occurs within all 4 attempts. Initially, when forgetting the overlap of the strips, then in translating to either of the two possible dimensions for the quilt – a thoroughly developed translation is evident. This becomes enhanced when s/he extends the translation to the generalized form.

PS 6 The process of determining the dimensions of the quilt, then drawing a strip,

a square, a strip . . . until the running total is equal to or greater than the desired dimension, and finally using the number of squares needed for each dimension to find the total number of squares needed is thoroughly developed. This becomes enhanced when s/he extends the process to the generalized form.

V 6 The review shown in step G (and possibly step F, for the other possible

translation) uses a different perspective (the generalized approach) to review the translation of the key concepts, the process of finding the number of squares, and finally the total number of squares needed for each interpretation – making it enhanced. Although s/he doesn’t review the 84, 90, or 102 – these could be done mentally.

C 6 The connecting path is enhanced by labeling each step, referring to a

previous step when a concept is used, using pictures with running totals to show the connection between the translation and the process, using prose to explain the connections between the process and each part of the review, and finally declaring which response s/he thinks the state thinks is correct! ☺

Acc. 5 132 squares is a mathematically justifiable solution supported by the work.

3 – Geometry Quilt Amelia is making a quilt for her bed. Her bed is 60 inches wide and 78 inches long. She

wants the quilt to hang over on each side and on the end by at least 12 inches. On the finished quilt, the blocks will be 6-inch squares with 1.5-inch strips between them and around the outside edges. What is the minimum number of squares she will need to make?

HS – 3 – 2 CU 6 The translation of the key concepts (a 2-dimensional array with the original

dimensions increased, accounting for the strips and borders, a minimum number of squares) is thoroughly developed when s/he is able to translate the task to solve with the original approach and enhanced when s/he translates it into a generalized format (for this task) – making the conceptual understanding a 6.

PS 5 The process of starting with simple area and finding the need for 12x12

squares, then accounting for the overlap of the strips in his/her drawing to find the need for only 11 x 12 squares is made thoroughly developed with the help of the generalized form in the verification.

V 6 The initial second look was when s/he changed from the 12x12 array to the

11x12 array after accounting for the overlap of the strips. The generalized second look (after “check”) provides a thoroughly developed review of the key concepts, using a different perspective on the process and needed calculations and supports the original solution – together the review is enhanced.

C 5 The arrows and labels help the connecting path to flow from the original

translation to the series of additions to the adjusted array and to the check – making it thoroughly developed.

Acc. 5 132 squares is a mathematically justifiable solution supported by the work.

3 – Geometry Quilt Amelia is making a quilt for her bed. Her bed is 60 inches wide and 78 inches long. She

wants the quilt to hang over on each side and on the end by at least 12 inches. On the finished quilt, the blocks will be 6-inch squares with 1.5-inch strips between them and around the outside edges. What is the minimum number of squares she will need to make?

HS – 3 – 3 CU 2 The translation of the key concepts (extending the dimensions and

accounting for the strips) is complete. Using area divided by area instead of a 2-dimensional array, and ignoring the border, along with drawing a 6” square with strips all around leading to a 7.5” square, are inappropriate. Together, these make the conceptual understanding underdeveloped. Without any evidence of a rectangular array – this work must be less than partially displayed.

PS 2 Finding the area of the extended dimension quilt and dividing by the area of

the extended dimension squares to find the total number of squares needed is ineffective. S/he does however extend the dimensions of the quilt and the square, and acknowledges “at least” making the overall process sketchy.

V 3 The prose provides a review of the overall translation of the task, s/he also

reviews each of the calculations – together these make the review partially effective. (There was no review of the process evident.)

C 3 A significant gap is created between the process used to solve the task –

resulting in an area of 8568 for the quilt and the verification resulting in an area of 8588 for the quilt – and the difference being ignored.

Acc. 1 152 squares is not a mathematically justifiable solution to the task.