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Mathematics - Secondary Curriculum Secondary Mathematics I
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Strand: NUMBER AND QUANTITY - Quantities (N.Q)

Reason quantitatively and use units to solve problems. Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions (Standards N.Q.13).
  • Access Ramp - Student Task
    This task has students design an access ramp, which complies with the Americans with Disabilities Act (ADA) requirements and include pricing based on local costs.
  • Accuracy of Carbon 14 Dating I
    This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating.
  • Accuracy of Carbon 14 Dating II
    This Illustrative Mathematics task is a refinement of "Carbon 14 dating" which focuses on accuracy. While the mathematical part of this task is suitable for assessment, the context makes it more appropriate for instructional purposes. This type of question is very important in science and it also provides an opportunity to study the very subtle question of how errors behave when applying a function: in some cases the errors can be magnified while in others they are lessened.
  • Bus and Car
    This Illustrative Mathematics task operates at two levels. In part it is a simple exploration of the relationship between speed, distance, and time. Part (c) requires understanding of the idea of average speed, and gives an opportunity to address the common confusion between average speed and the average of the speeds for the two segments of the trip.
  • Calories in a sports drink
    This Illustrative Mathematics task involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. An unexpected surprise awaits in this case, however, as no reasonable interpretation of the level of accuracy makes sense of the information reported on the bottles in parts (b) and (c). Either a miscalculation has been made or the numbers have been rounded in a very odd way.
  • Dinosaur Bones
    The purpose of this Illustrative Mathematics task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.
  • Felicia's Drive
    This Illustrative Mathematics task provides students the opportunity to make use of units to find the gas need to make some sensible approximations.
  • Fences - student task
    This task has students design a fence that meets the city ordinances and the client's specifications.
  • Framing a House - student task
    This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed.
  • Fuel Efficiency
    Sadie has a cousin Nanette in Germany. Both families recently bought new cars and the two girls are comparing how fuel efficient the two cars are. Sadie tells Nanette that her family's car is getting 42 miles per gallon. Nanette has no idea how that compares to her famiy's car because in Germany mileage is measured differently. She tells Sadie that her family's car uses 6 liters per 100 km. Which car is more fuel efficient?
  • Giving raises
    A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine you are in charge of deciding how the raises should be determined.
  • Harvesting the Fields
    This is a challenging Illustrative Mathematics task, suitable for extended work, and reaching into a deep understanding of units. The task requires students to exhibit MP1, Make sense of problems and persevere in solving them.
  • How Much is a Penny Worth?
    The price of copper fluctuates. Between 2002 and 2011, there were times when its price was lower than $1.00 per pound and other times when its priace was higher than $4.00 per pound. Copper pennies minted between 1962 and 1982 are 95% copper and 5% zinc by weight, and each penny weighs 3.11 grams. At what price per pound of copper does such a penny contain exactly one cent worth of copper?
  • Ice Cream Van
    The purpose of this Illustrative Mathematics task is to engage students, probably working in groups, in a substantial and open-ended modeling problem. Students will have to brainstorm or research several relevant quantities, and incorporate these values into their solutions.
  • Introduction to the Materials (Math 1)
    Introduction to the Materials in the Mathematics One of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
  • Lesson Starter: Solving Math Problems with a Team
    Students will work in teams to solve mathematical problems; they listen to the reasoning of others and offer correction with supporting arguments; they modify their own arguments when corrected; they learn from mistakes and make repeated attempts at solving problems.
  • Module 1: Sequences - Student Edition (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 1, Sequences is written as two intertwined learning cycles that begin by alternating from arithmetic sequence to geometric sequences, so students can compare and contrast features as they represent both types of sequences with tables, graphs, story contexts, diagrams, and equations.
  • Module 1: Sequences - Teacher Notes (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 1 Teacher Notes, Sequences is written as two intertwined learning cycles that begin by alternating from arithmetic sequence to geometric sequences, so students can compare and contrast features as they represent both types of sequences with tables, graphs, story contexts, diagrams, and equations.
  • Module 4: Equations & Inequalities - Student Edition (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 4, Equations and Inequalities, students use units in combinations to define new variables for use in modeling with equations and inequalities, and interpret expressions that are the result of combining units.
  • Module 4: Equations & Inequalities - Teacher Notes (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 4 Teacher Notes, Equations and Inequalities, students use units in combinations to define new variables for use in modeling with equations and inequalities, and interpret expressions that are the result of combining units.
  • New Cuyama
    The purpose of this Illustrative Mathematics task is to provide a fun context to examine the pitfalls of disregarding units when reporting and manipulating quantities. Teachers might use this as a discussion-starter about appropriate and careful use of units.
  • NUMBER & QUANTITY - Quantities (N.Q) - Sec Math I Core Guide
    The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics I - Quantities (N.Q).
  • Runners' World
    This Illustrative Mathematics task provides students with an opportunity to engage in Standard for Mathematical Practice 6, attending to precision. It intentionally omits some relevant information. The incompleteness of the problem statement makes the task more amenable to having students do work in groups.
  • Secondary I Textbook
    Secondary I Textbook is composed of modules that are aligned with the Utah Core State Standards for Mathematics. Each lesson begins with a worthwhile task that has been designed to develop mathematical understanding, solidify that understanding, or allow for practice of the new concepts, while focusing on the mathematical goals of the chosen learning cycle.
  • Selling Fuel Oil at a Loss
    This Illustrative Mathematics task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the business.
  • Solar Radiation Model
    The task is a seemingly straightforward modeling task that can lead to more involved tasks if the instructor expands on it. In this task, students also have to interpret the units of the input and output variables of the solar radiation function.
  • Storage Shed - student task
    Students are going to build storage sheds as a fund raising project, but before they can start they must determine the best dimensions for the shed, make scale drawings and decide on how much to charge for each shed.
  • Student Task: Leaky Faucet
    The student's task is to determine how much water a dripping faucet might waste in a year.
  • Student Task: Yogurt
    In this task, students must calculate how much yogurt is produced by a machine at a food company.
  • Traffic Jam
    Last Sunday an accident caused a traffic jam 12 miles long on a straight stretch of a two lane freeway. How many vehicles do you think were in the traffic jam? Explain your thinking and show all calculations.
  • Weed killer
    The principal purpose of this Illustrative Mathematics task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.


UEN logo http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.