Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Middle School
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [7.RP]

OREGON MATH STANDARDS (2021): [7.RP]

Overview

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. 

Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

2021 Oregon Math Guidance: 7.RP.A.1

ODE and Oregon Math Project Logo

Cluster: 7.RP.A - Analyze proportional relationships and use them to solve mathematical problems in authentic contexts.

STANDARD: 7.RP.A.1

 Standards Statement (2021):

Solve problems in authentic contexts involving unit rates associated with ratios of fractions.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.RP.A.2

8.AEE.B.5

HS.NQ.B.3, HS.GM.C.11

7.RP.A.1

7.RP.A Crosswalk

 Standards Guidance:

Terminology

  • Ratios of fractions refers to complex fractions where the numerator and/or denominator of a ratio includes a fraction, such as ¼ ÷ ½ is also the ratio of (¼)/(½)

Teaching Strategies

  • This includes ratios of lengths, areas and other quantities measured in like or different units.
  • Students should have opportunities to create visual representations to solve complex ratio problems.
  • Students should build upon their understanding of fractions as a form of division.
  • Students should build upon their fluency in division of fractions.
  • Students should be able to solve problems involving unit rate presented in practical, real-life situations.

Examples

2021 Oregon Math Guidance: 7.RP.A.2

 ODE and Oregon Math Project Logo

Cluster: 7.RP.A - Analyze proportional relationships and use them to solve mathematical problems in authentic contexts.

STANDARD: 7.RP.A.2

 Standards Statement (2021):

Recognize and represent proportional relationships between quantities in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Identify the constant of proportionality (unit rate) within various representations.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.RP.A.2, 6.RP.A.3

7.RP.A.3, 8.AEE.B.5, 8.AEE.B.6, 8.AFN.A.1, 8.AFN.A.2, 8.AFN.B.4

7.AEE.B.4, 7.GM.A.1

7.RP.A.2

7.RP.A Crosswalk

 Standards Guidance:

Clarifications

  • Students should demonstrate a conceptual understanding of slope.
  • Students should recognize equations in the form y = mx are proportional.
  • Students should know that a graph with a straight line through the origin is proportional.
  • Explain what a point (𝑥,) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,𝑟) where 𝑟 is the unit rate.
  • This standard builds on students' understanding of unit rates from 6th grade.

Boundaries

  • In seventh grade, students are expected to understand that unit rate and constant of proportionality are the same.

Teaching Strategies

  • Have students represent proportional relationships using equations, and decide whether two quantities are in a proportional relationship.

Progressions

  • Students identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Recognize the constant of proportionality as both the unit rate and as the multiplicative comparison between two quantities.  (Please reference page 9 in the Progression document).

Examples

2021 Oregon Math Guidance: 7.RP.A.3

 ODE and Oregon Math Project Logo

Cluster: 7.RP.A - Analyze proportional relationships and use them to solve mathematical problems in authentic contexts.

STANDARD: 7.RP.A.3

 Standards Statement (2021):

Use proportional relationships to solve ratio and percent problems in authentic contexts.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.RP.A.3, 7.RP.A.2

7.RP.B.5, 7.RP.B.6, 7.RP.B.7

HS.AEE.A.2

7.RP.A.3

7.RP.A Crosswalk

 Standards Guidance:

Terminology

  • Simple interest – a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.  Simple Interest = (principal) * (rate) * (# of periods)
  • Markups and markdowns - increase and decrease in the amount of a quantity

Boundaries

  • This includes solving multi step problems involving simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
  • Students should be able to represent proportional relationships using equations.

Teaching Strategies

  • Students should be able to analyze and make decisions about relationships using proportional reasoning strategies, which may include but not limited to graphing on a coordinate plane and/or observing whether a graph is a straight line passing through the origin
  • Students may use flexible strategies such as a + 0.05a = 1.05a with the understanding that adding a 5% tax to a total is the same as multiplying the total by 1.05.

Progressions

  • Student should be able to identify, represent, and use proportional relationships between quantities using verbal descriptions, tables of values, equations, and graphs to model contextual, mathematical problem and translate from one representation to another. (Please reference page 10 in the Progression document).

Examples

2021 Oregon Math Guidance: 7.RP.B.4

 ODE and Oregon Math Project Logo

Cluster: 7.RP.B - Investigate chance processes and develop, use, and evaluate probability models.

STANDARD: 7.RP.B.4

 Standards Statement (2021):

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Represent probabilities as fractions, decimals, and percents.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.RP.A.3, 7.RP.A.2

HS.DR.E.14

 N/A

7.SP.C.5

7.RP.B Crosswalk

 Standards Guidance:

Terminology

  • Descriptions may include impossible, unlikely, equally likely, likely, and certain.
  • Know that a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is equally likely, and a probability near 1 indicates a likely event.

Teaching Strategies

  • Students should be able to represent the probability as a fraction, decimal numbers, or percent.

Progressions

  • In Grade 7, students build their understanding of probability on a relative frequency view of the subject, examining the proportion of “successes” in a chance process—one involving repeated observations of random outcomes of a given event, such as a series of coin tosses.
  • “What is my chance of getting the correct answer to the next multiple choice question?” is not a probability question in the relative frequency sense. “What is my chance of getting the correct answer to the next multiple choice question if I make a random guess among the four choices?” is a probability question because the student could set up an experiment of multiple trials to approximate the relative frequency of the outcome. And two students doing the same experiment will get nearly the same approximation. These important points are often overlooked in discussions of probability. (Please reference page 7 in the Progression document).

Examples

 

2021 Oregon Math Guidance: 7.RP.B.5

 ODE and Oregon Math Project Logo

Cluster: 7.RP.B - Investigate chance processes and develop, use, and evaluate probability models.

STANDARD: 7.RP.B.5

 Standards Statement (2021):

Use experimental data and theoretical probability to make predictions. Understand the probability predictions may not be exact.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.RP.A.3

HS.DR.E.14

 N/A

7.SP.C.6

7.RP.B Crosswalk

 Standards Guidance:

Terminology

  • Approximate the (theoretical) probability of a chance event by collecting data and observing its long-run relative frequency (experimental probability). Predict the approximate relative frequency given the (theoretical) probability.

Teaching Strategies

  • Students should draw upon understanding of proportional relationships to make predictions.
  • Students should be able to predict the approximate, relative frequency given the theoretical probability.

Progressions

  • It must be understood that the connection between relative frequency and probability goes two ways. If you know the structure of the generating mechanism (e.g., a bag with known numbers of red and white chips), you can anticipate the relative frequencies of a series of random selections (with replacement) from the bag.
  • If you do not know the structure (e.g., the bag has unknown numbers of red and white chips), you can approximate it by making a series of random selections and recording the relative frequencies. This simple idea, obvious to the experienced, is essential and not obvious at all to the novice. The first type of situation, in which the structure is known, leads to “probability”; the second, in which the structure is unknown, leads to “statistics.” (Please reference page 7 in the Progression document).

Examples

  • When rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
  • When drawing chips out of a bag containing an unknown number of red and white chips, estimate the probability of selecting a particular chip color given 50 draws.

2021 Oregon Math Guidance: 7.RP.B.6

  ODE and Oregon Math Project Logo

Cluster: 7.RP.B - Investigate chance processes and develop, use, and evaluate probability models.

STANDARD: 7.RP.B.6

 Standards Statement (2021):

Develop a probability model and use it to find probabilities of events. Compare theoretical and experimental probabilities and explain possible sources of discrepancy if any exists.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.RP.A.3

HS.DR.E.14, HS.DR.E.15

 N/A

7.SP.C.7

7.RP.B Crosswalk

 Standards Guidance:

Clarification

  • Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
  • Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Teaching Strategies

  • Probability models may include various random generation devices including, but not limited to, bag pulls, spinners, number cubes, coin toss, and colored chips.
  • Students should have multiple opportunities to collect data using physical objects, graphing calculators, or web-based simulations.

Progressions

  • A probability model provides a probability for each possible nonoverlapping outcome for a chance process so that the total probability over all such outcomes is unity. The collection of all possible individual outcomes is known as the sample space for the model. For example, the sample space for the toss of two coins (fair or not) is often written as {TT, HT, TH, HH}.
  • The probabilities of the model can be either theoretical (based on the structure of the process and its outcomes) or empirical (based on observed data generated by the process). In the toss of two balanced coins, the four outcomes of the sample space are given equal theoretical probabilities of 1/4 because of the symmetry of the process—because the coins are balanced, an outcome of heads is just as likely as an outcome of tails. (Please reference page 7 in the Progression document).

Examples

  • Find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
  • Kim calculates the probability of landing on heads when tossing a coin to be 50%. She uses this to predict that when Tiffany tosses a coin 20 times, the coin will land on heads 10 times.  When Tiffany performed the experiment, the coin landed on heads 7 times. Explain possible reasons why Kim’s prediction and Tiffany’s results do not match.
  • Illustrative Mathematics:

2021 Oregon Math Guidance: 7.RP.B.7

  ODE and Oregon Math Project Logo

Cluster: 7.RP.B - Investigate chance processes and develop, use, and evaluate probability models.

STANDARD: 7.RP.B.7

 Standards Statement (2021):

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.RP.A.3

HS.DR.E.14, HS.DR.E.15

 N/A

7.SP.C.8

7.RP.B Crosswalk

 Standards Guidance:

Clarifications

  • Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Teaching Strategies

  • Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
  • Design and use simulations to generate experimental frequency data for compound events.

Progressions

  • The product rule for counting outcomes for chance events should be used in finite situations like tossing two or three coins or rolling two number cubes. There is no need to go to more formal rules for permutations and combinations at this level.
  • Students should gain experience in the use of diagrams, especially trees and tables, as the basis for organized counting of possible outcomes from chance processes. For example, the 36 equally likely (theoretical probability) outcomes from the toss of a pair of number cubes are most easily listed on a two-way table. (Please reference page 8 in the Progression document).

Examples