Population Ratios

SCORE Mathematics

Standards Connections

Population Ratios

Introduction: An interdisciplinary project (mathematics, social studies) where students choose a county in the United States and using ratios convert the statistics into meaningful numbers.

Prior Knowledge: Students need to know how to set up and solve ratios.

Grade Level: 4-7

Task: Students will retrieve data from Internet; set up and solve ratios to answer questions.

Resources: Government Information Sharing Project, Worksheet (HTML) / Worksheet (PDF)

Process: Students access web site and record various population statistics pertaining to a county in the USA of their choice. Students then use this data to set up and solve ratios. Students compare data to make meaning of the numbers.

Learning Advice: Check computations on calculator. Answers will be approximate.

Evaluation:

4- Data is complete. Computations are accurate. Mathematical reasoning is correct.
3- Data is complete. Computations are reasonable. Mathematical reasoning is apparent.
2- Data is partial. Correct formulas are used. Mathematical reasoning is lacking.
1- Data is incomplete

Extensions: Do area comparisons.

Make travel brochure for the county.

Conclusion: Students will be able to make real-life applications and meanings of ratios!

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California Mathematics Academic Standards:

Grade 4:
Mathematical Reasoning
2.0 Students use strategies, skills, and concepts in finding solutions.
2.2 apply strategies and results from simpler problems to more complex problems

3.0 Students move beyond a particular problem by generalizing to other situations.

3.3 develop generalizations of the results obtained and apply them in other circumstances

Grade 5:
Number Sense
1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers.

1.2 interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number

Statistics, Data Analysis and Probability
1.0 Students display, analyze, compare, and interpret different data sets, including data sets of different sizes.

1.3 use fractions and percentages to compare data sets of different size

Mathematical Reasoning
2.0 Students use strategies, skills and concepts in finding solutions.

2.6 make precise calculations and check the validity of the results from the context of the problem

Grade 6:
Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.

1.3 use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as multiplication of both sides of an equation by a multiplicative inverse.

Algebra and Functions
2.0 Students analyze and use tables, graphs and rules to solve problems involving rates and proportions.

2.2 demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity

Statistics, Data Analysis and Probability
3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events.

3.1 represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome
3.5 understand the difference between independent and dependent events

Grade 7:
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms.

1.6 calculate the percentage of increases and decreases of a quantity

Mathematical Reasoning
1.0 Students make decisions about how to approach problems.

1.2 formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed

3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations.

3.3 develop generalizations of the results obtained and the strategies used and apply them to new problem situations

NCTM 5-8:

STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 4: MATHEMATICAL CONNECTIONS
STANDARD 5: NUMBER AND NUMBER RELATIONSHIPS
STANDARD 7: COMPUTATION AND ESTIMATION
STANDARD 9: ALGEBRA
STANDARD 10: STATISTICS

NCTM 9-12:

STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 4: MATHEMATICAL CONNECTIONS
STANDARD 5: ALGEBRA
STANDARD 10: STATISTICS