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Mathematics

Mathematics Year 1 Inclusion Tasks

Inclusion tasks are tasks designed specifically for use by students and are eligible for inclusion in a Collection of Evidence. These tasks have been created by teachers throughout the State of Washington. They have undergone a peer review process and are edited to assure alignment with state standards. The inclusion tasks have been set apart from the Classroom Practice Tasks for a number of reasons and are therefore not to be used for instructional purposes. The tasks are assured to be aligned to a number of Reporting Strands and will address at least two Performance Expectations in two different strands. The tasks and resulting work samples are built and developed around important mathematics skills. These are the same skills assessed on the state assessment through the End of Course (EOC) exam. With inclusion tasks, teachers will need to limit their assistance so the work sample is truly a reflection of student work. Inclusion tasks will be in PDF format and are not to be edited. The goal is to have enough tasks in the inclusion bank so that the students have a wide variety of tasks and topics to choose from.

Only inclusion tasks are eligible for inclusion in a student Collection of Evidence to be submitted for scoring. These tasks are not to be used for classroom instructional purposes.

All of the extracts found here are for review purposes only.

The extracts below are intended to give you an overview of the task, understand all PEs addressed in the task, and the overall context of the task.

Full access to the Mathematics Year 1 and Year 2 tasks are available through the secure EDS account established in your district. Once an EDS account has been established, you can print all of the complete tasks by assigning them to students.

For more information about inclusion tasks please contact coemath@k12.wa.us.
Bacteria Growth                                                                                                                                        

(M1.2.C; M2.5.A; M1.7.A,B)
(A1.3.C; A1.2.E; A1.7.A,B)

Shauna is studying the growth of two colonies of bacteria in a lab.  Colony A starts with 12 bacteria and Colony B starts with 6 bacteria.  She notices that, after 2 hours, Colony A has grown to 108 bacteria.  For Colony B, Shauna finds that after 3 hours, the colony has grown to 384 bacteria.
Betty’s Borders

(M1.2.B, M1.7.D, M1.6.D)
(A1.3.B, A.1.7.C,D)

Betty is landscaping her large front yard this spring.  She will use square stepping-stones to create a design.  She is not sure how many stepping-stones she will need, so she drew the first three stages of the design, as shown in the table.  She will continue to add stepping-stones to create additional stages of the design.

Big Box

(M1.2.B,C; M1.6.C, M1.8.B)
(A1.3.B,C; A1.2.B, A1.8.B)                                                                                                          

You are the manager of a packaging company responsible for manufacturing congruent boxes in the shape of rectangular prisms from rectangular sheets of cardboard. The rectangular boxes will be created by cutting congruent squares from each corner of the cardboard sheet and folding the remaining material to form an open box (bottom and 4 sides, without a top). You need to determine what size congruent squares to cut out of each corner of the rectangular sheets to form an open box that will have the maximum volume possible.

Building a House

(M1.3.D, M1.2.C, M1.8.E)
(A1.4.B, A1.3.C, A1.8.E) 

Don is two weeks away from finishing building a house and needs to hire one or more workers.  He reads through the local paper and finds two people, Wendy and John, who are advertising for construction work.  Wendy has construction experience and charges $15 per hour.  John has less experience than Wendy and is charging $10 per hour.

CD Recording Contract

(M1.2.C, M1.3.F, M1.6.D)
(A1.3.C, A1.6.D, A1.7.D)

You have just signed a recording contract with a major record label.  Before you start recording the tracks for your first CD, you decide to do some research on recent best-selling CDs.  You start by selecting 10 CDs and record the number of tracks on the CD and the total playing time of the CD in a scatterplot.

Cell Phones

(M1.2.C, M1.7.A&B, M1.8.E)
(A1.3.C, A1.7.A&B, A1.8.E)

In 1990, approximately 2 out of 100 people in the United States owned a cell phone.  During the years 1990 to 1995, the number of people was 145% of the previous year.  (Source: U.S. Census Bureau.)  A function that models this situation is f(x) = 2(1.45)x where f(x) is the number of people and x is the years since 1990.

Conner’s Touchdown

(M1.3.F, M1.8.G)
(A1.6.D, A1.8.G)                                                                                                                    

Conner is a very fast running back on the football team. The coach recorded his times during a play that resulted in a touchdown. The play started on the 10-yard line. The data for Conner’s run is given in the table below.

Costs of Essentials

(M1.2.B, M1.3.F, M1.8.B)
(A1.3.B, A1.6.D, A1.8.B)

Many items that were considered essential 40 years ago are still considered essential today.  Some of these essential goods include bread, milk, eggs, and gasoline.  These essential goods, along with mean income and minimum wage, are indicators of economic strength and stability.

Football Kickoff

(M2.2.B,F; M1.2.C, M1.8.E)
(A1.5.B,D; A1.3.C, A1.8.E)                                                                                                           

The path a football travels during a kickoff can be modeled by the equation f(x) = -0.0124 (x2-180x) where f(x) is the height of the ball above the ground, in feet, and x is the horizontal distance traveled by the ball, in feet.

How Close is Lightning?

(M1.1.B, M1.3.F, M1.2.C)
(A1.1.B, A1.6.D, A1.3.C)

During a thunderstorm, Cindy uses a stopwatch to time (in seconds) from when she sees a flash of lightning to when she hears the crash of thunder. The next day, she uses a map and a ruler to determine the distances to the lightning strikes.  The time between the lightning and the thunder, in seconds, and the distance from Cindy, in meters, are graphed in the scatterplot.

Hydraulophone

(M1.6.C, M2.2.F, M1.8.B)
(A1.2.B, A1.5.D, A1.8.B)                                                                                                                   

A hydraulophone is a musical instrument, like a pipe organ, where music is made by controlling water flow.  Water is shot in a parabolic path and collected in a reservoir to be recycled through the instrument.  The path of the water stream determines the location and width of the reservoir.

Marble Canyon

(M2.1.C, M1.6.C, M1.8.B)
(A1.1.D, A1.2.B, A1.8.B)

A tourist is walking on the Navajo Bridge over the Marble Canyon and accidentally drops a cell phone.  A nearby sign shows that the Navajo Bridge is 1,617 feet above the canyon floor.

Mass and Force
 
(M1.2.A&B, M1.5.C)
(A1.3.A&B, A1.6.B)
 
An athletic trainer is studying the relation between the mass of an object and the force needed to accelerate the object.  She decides to conduct some experiments with several objects. 
Math Club

(M1.3.D, M1.3.F, M1.8.C,G)

(A1.4.B, A1.6.D, A1.8.C,G)
 
The Brickhouse High School Mathletes are raising funds for an upcoming field trip to the “Experience Math Project”. They will be selling candy. Their advisor checks in with various students at different times and asks them how much money they have raised up to that day. The advisor’s notes are below.
The Potlatch

(M1.3.A, M1.5.C)
(A1.4.A, A1.6.B)

The Kwakwaka’wakw are preparing a potlatch for Thunderbird Park, Victoria, British Columbia.  Datsa is making gifts for guests.  

Pre-Season Football

(M1.1.C, M1.5.C, M1.8.A)

(A1.1.C, A1.6.B, A1.8.A)
 
Bob and Jim are getting ready for football season. Bob wants to lose weight but Jim wants to gain weight. Trainer Sue weighed both players and developed weight loss and gain plans for each player.
Safe Driving

(M1.1.C, M2.1.C, M1.2.B, M1.6.D)
(A1.1.C&D, A1.3.B, A1.7.D)

Different roads have different speed limits for various reasons.  The primary reason is the relationship between the speed of a vehicle and the time it takes the vehicle to come to a full stop.  Other factors that affect the stopping time include road conditions and braking efficiency.         

A Salmon Population Study 

(M1.3.F, M1.8.G)

(A1.6.D, A1.8.G)

You have been asked to present your findings and make recommendations for fishing regulations regarding the adult salmon in Big Beef Creek. Examine the data in the table and respond to each item below.
Skate Park

(M2.2.A, M1.6.C, M1.8.A-B)
(A1.5.A, A1.2.B, A.1.8.A-B)           

At the Rotary skate park, Taryn and Jaden are practicing their ramp skills.  At the top of the ramp, their potential energy is given by the formula PE = 9.8mh where PE is potential energy in Joules, m is mass in kilograms, and h is height in meters.  At the bottom of the ramp, their kinetic energy is given by the formula KE = ½mv2 where KE is kinetic energy in Joules, m is mass in kilograms, and v is velocity in meters per second.
Sprinkler and a Horse

(M1.6.D, M1.2.C, M1.8.E)
(A1.7.D, A1.3.C, A1.8.E)

Farmer John has a rectangular shed in one of his fields.  He wants to water part of the field by putting a sprinkler on one corner of the shed.  The area watered by the sprinkler depends on the distance the water sprays from the sprinkler.  John drew a sketch showing the shed, the location of the sprinkler, and the distance the water sprays from the sprinkler, which he labeled using w.