Anya agrees to look after her younger brother every day for 1 hour before dinner Her parents agree to pay her $15 per week, starting in September. If she does a spectacular job, her parents agree that on the first Monday of each month she will get a raise of $2 per week. So far, Anya has done a spectacular job. Anya's parents have a monthly household budget. In the budget, they estimate fferent things each month. Determine the how much they will be spending on di first month when her parents should estimate spending more than $100 per month for paying Anya to babysit. Justify your answer. Week Problem A Room to Grow Ada Lovelace Public School needs to add a new wing to its main building that includes a classroom, library, staff room, and washroom. The plans for the addition are shown, with all new rooms being rectangular; however, some of the measurements are missing. 10 m 8 m Staff Library Room Classroom 3 m Washroom 6 m Fortunately, the contractor remembered the following extra details: The length of the classroom is three times the width of the washroom. The width of the staff room is half the length of the library. When describing the dimensions of a rectangle, the contractor uses length to describe the longer side, and width to describe the shorter side. (a) What are the missing dimensions of the classroom and the staff room? (b) What is the total floor area of the four new rooms? THEMES GEOMETRY & MEASUREMENT, NUMBER SENSEProblem B Fraction Fun A large rectangle is in the first quadrant of the Cartesian plane with its four vertices at (0, 0), (8, 0), (8, 4), and (0, 4). It is divided into eight regions labelled A, B, C, D, E, F, G, and H, as shown. 3 C B 2 1 A H F G D 5 6 7 8 2 3 What fraction of the area of the large rectangle is the area of region A? the area of region B? the area of region C? the area of region D? THEMES GEOMETRY & MEASUREMENT, NUMBER SENSECEMC.UWATERLOO.CA | The CENTRE for EDUCATION in MATHEMATICS and COMPUTING Problem of the Week Problem B Jordyn's Garden Jordyn's neighbourhood is building a community garden to grow some vegetables. They would like the garden bed to have an area of 48 square metres, and plan to put wooden fence boards around the edges of the garden bed. To reduce the cost of the project, they would like the garden bed to have the smallest possible perimeter. (a) Determine the length and width of Jordyn's community garden bed. Assume the side lengths are whole numbers, in metres. (b) The community decided to double the area of the garden bed, but would still like it to have the smallest possible perimeter. Again, assume the side lengths are whole numbers, in metres. Determine the length and width of the garden bed now. THEMES GEOMETRY & MEASUREMENT, NUMBER SENSENAME: DATE: Permutations VS Combinations PERMUTATION: order matters COMBINATION: order does not matter n Pr = 7 n! n! (n - r ) ! .C. = [n-r) !r! Determine whether the situation requires a permutation or combination and solve. Problem P or C? Use the formula Answer How many ways can 8 people finish a P marathon? C N How many ways can a class of 225 students, P elect two class representatives? C How many ways can 10 students fill the P student government positions of president, vice president, secretary, treasurer, and communications officer? C C How many ways can 4 people be selected for P the customer service department from 30 applicants? C 5 How many ways can 6 cereal boxes be P chosen from a store that carries 22 cereal boxes? C How many ways can 13 gymnasts finish first, P second, and third place? C How many distinct words can be formed from P the letters in the word MULTIPLY? C You volunteer five days in the month of P November. How many ways can you choose the days to volunteer? C Algebra and Beyond 2021