Mathematics in Action

The Consortium for Foundation Mathematics is a team of fourteen co-authors, primarily from the State University of New York and the City University of New York systems. Using the AMATYC Crossroads standards, the team developed an activity-based approach to mathematics in an effort to reach the large population of college students who, for whatever reason, have not yet succeeded in learning mathematics.

Chapter 1. Whole Numbers

Activity 1.1 Education Pays

Objectives:

1. Read and write whole numbers.

2. Compare whole numbers using inequality symbols.

3. Round whole numbers to specified place values.

4. Use rounding for estimation.

5. Classify whole numbers as even or odd, prime, or composite.

6. Solve problems involving whole numbers.

Activity 1.2 Bald Eagle Population Increasing Again

Objectives:

1. Read tables.

2. Read bar graphs.

3. Interpret bar graphs.

4. Construct graphs.

Activity 1.3 Bald Eagles Revisited

Objectives:

1. Add whole numbers by hand and mentally.

2. Subtract whole numbers by hand and mentally.

3. Estimate sums and differences using rounding.

4. Recognize the associative property and the commutative property for addition.

5. Translate a written statement into an arithmetic expression.

Activity 1.4 Summer Camp

Objectives:

1. Multiply whole numbers and check calculations using a calculator.

2. Multiply whole numbers using the distributive property.

3. Estimate the product of whole numbers by rounding.

4. Recognize the associative and commutative properties for multiplication.

Activity 1.5 College Supplies

Objectives:

1. Divide whole numbers by grouping.

2. Divide whole numbers by hand and by calculator.

3. Estimate the quotient of whole numbers by rounding.

4. Recognize that division is not commutative.

Activity 1.6 Reach for the Stars

Objectives:

1. Use exponential notation.

2. Factor whole numbers.

3. Determine the prime factorization of a whole number.

4. Recognize square numbers and roots of square numbers.

5. Recognize cubed numbers.

6. Apply the multiplication rule for numbers in exponential form with the same base.

Activity 1.7 You and Your Calculator

Objective:

1. Use order of operations to evaluate arithmetic expressions.

What Have I Learned?

How Can I Practice?

Chapter 1 Summary

Chapter 1 Gateway Review

Chapter 2. Variables and Problem Solving

Activity 2.1 How Much Do I Need to Buy?

Objectives:

1. Recognize and understand the concept of a variable in context and symbolically.

2. Translate a written statement (verbal rule) into a statement involving variables (symbolic rule).

3. Evaluate variable expressions.

4. Apply formulas (area, perimeter, and others) to solve contextual problems.

Activity 2.2 How High Will It Go?

Objectives:

1. Recognize input/output relationship between variables in a formula or equation (two variables only).

2. Evaluate variable expressions in formulas and equations.

3. Generate a table of input and corresponding output values from a given equation, formula, or situation.

4. Read, interpret, and plot points in rectangular coordinates that are obtained from evaluating a formula or equation.

Activity 2.3 Are You Balanced?

Objectives:

1. Translate contextual situations and verbal statements into equations.

2. Apply the fundamental principle of equality to solve equations of the forms x + a = b, a + x = b and x - a = b.

Activity 2.4 How Far Will You Go? How Long Will It Take?

Objectives:

1. Apply the fundamental principle of equality to solve equations of the form ax = b, a ≠ 0.

2. Translate contextual situations and verbal statements into equations.

3. Use the relationship rate · time = amount in various contexts.

Activity 2.5 Web Devices for Sale

Objectives:

1. Identify like terms.

2. Combine like terms using the distributive property.

3. Solve equations of the form ax + bx = c.

Activity 2.6 Make Me an Offer

Objectives:

1. Use the basic steps for problem solving.

2. Translate verbal statements into algebraic equations.

3. Use the basic principles of algebra to solve real-world problems.

What Have I Learned?

How Can I Practice?

Chapter 2 Summary

Chapter 2 Gateway Review

Chapter 3. Problem Solving with Integers

Activity 3.1 On the Negative Side

Objectives:

1. Recognize integers.

2. Represent quantities in real-world situations using integers.

3. Represent integers on the number line.

4. Compare integers.

5. Calculate absolute values of integers.

Activity 3.2 Maintaining Your Balance

Objectives:

1. Add and subtract integers.

2. Identify properties of addition and subtraction of integers.

Activity 3.3 Whats the Bottom Line?

Objectives:

1. Write formulas from verbal statements.

2. Evaluate expressions in formulas.

3. Solve equations of the form x + b = c and b - x = c.

4. Solve formulas for a given variable.

Activity 3.4 Riding in the Wind

Objectives:

1. Translate verbal rules into equations.

2. Determine an equation from a table of values.

3. Use a rectangular coordinate system to represent an equation graphically.

Activity 3.5 Are You Physically Fit?

Objectives:

1. Multiply and divide integers.

2. Perform calculations involving a sequence of operations.

3. Apply exponents to integers.

4. Identify properties of calculations that involve multiplication and division with zero.

Activity 3.6 Integers and Tiger Woods

Objectives:

1. Use order of operations with expressions that involve integers.

2. Apply the distributive property.

3. Evaluate algebraic expressions and formulas using integers.

4. Combine like terms.

5. Solve equations of the form ax = b, where a ≠ 0, that involve integers.

6. Solve equations of the form ax + bx = c, where a + b ≠ 0, that involve integers.

What Have I Learned?

How Can I Practice?

Chapter 3 Summary

Chapter 3 Gateway Review

Chapter 4. Problem Solving with Fractions

Activity 4.1 Are You Hungry?

Objectives:

1. Identify the numerator and the denominator of a fraction.

2. Determine the greatest common factor (GCF).

3. Determine equivalent fractions.

4. Reduce fractions to equivalent fractions in lowest terms.

5. Determine the least common denominator (LCD) of two or more fractions.

6. Compare fractions.

Activity 4.2 Get Your Homestead Land

Objectives:

1. Multiply and divide fractions.

2. Recognize the sign of a fraction.

3. Determine the reciprocal of a fraction.

4. Solve equations of the form ax = b, a ≠ 0, that involve fractions.

Activity 4.3 On the Road with Fractions

Objectives:

1. Add and subtract fractions and with the same denominators.

2. Add and subtract fractions and with different denominators.

3. Solve equations in the form x + b = c, and x - b = c that involve fractions.

Activity 4.4 Hanging With Fractions

Objectives:

1. Calculate powers and square roots of fractions.

2. Evaluate equations that involve powers.

3. Evaluate equations that involve square roots.

4. Use order of operations to calculate numerical expressions that involve fractions.

5. Evaluate algebraic expressions that involve fractions.

6. Use the distributive property with fractions.

7. Solve equations of the form ax + bx = c with fraction coefficients.

What Have I Learned?

How Can I Practice?

Chapter 4 Summary

Chapter 4 Gateway Review

Chapter 5. Problem Solving with Mixed Numbers and Decimals

Cluster 1 Mixed Numbers and Improper Fractions

Activity 5.1 Food for Thought

Objectives:

1. Determine equivalent fractions.

2. Add and subtract fractions and mixed numbers with the same denominators.

3. Convert mixed numbers to improper fractions and improper fractions to mixed numbers.

Activity 5.2 Mixing with Denominators

Objectives:

1. Determine the least common denominator (LCD) for two or more mixed numbers.

2. Add and subtract mixed numbers with different denominators.

3. Solve equations in the form x + b = c and x - b = c that involve mixed numbers.

Activity 5.3 Tiling the Bathroom

Objectives:

1. Multiply and divide mixed numbers.

2. Evaluate expressions with mixed numbers.

3. Calculate the square root of a mixed number.

4. Solve equations of the form ax + b = 0, a ≠ 0, that involve mixed numbers.

Cluster 1 What Have I Learned?

Cluster 1 How Can I Practice?

Cluster 2 Decimals

Activity 5.4 What Are You Made Of?

Objectives:

1. Identify place values of numbers written in decimal form.

2. Convert a decimal to a fraction or a mixed number and vice versa.

3. Classify decimals.

4. Compare decimals.

5. Read and write decimals.

6. Round decimals.

Activity 5.5 Dive into Decimals

Objectives:

1. Add and subtract decimals.

2. Compare and interpret decimal numbers.

3. Solve equations of the type x + b = c and x - b = c that involve decimals.

Activity 5.6 Quality Points and GPA: Tracking Academic Standing

Objectives:

1. Multiply and divide decimals.

2. Estimate products and quotients involving decimals.

Activity 5.7 Tracking Temperature

Objectives:

1. Use the order of operations to evaluate expressions that include decimals.

2. Use the distributive property in calculations that involve decimals.

3. Evaluate formulas that include decimals.

4. Solve equations of the form ax = c and ax + bx = c that involve decimals.

Activity 5.8 Think Metric

Objectives:

1. Know the metric prefixes and their decimal values.

2. Convert measurements between metric quantities.

Cluster 2 What Have I Learned?

Cluster 2 How Can I Practice?

Chapter 5 Summary

Chapter 5 Gateway Review

Chapter 6. Problem Solving with Ratios, Proportions, and Percents

Activity 6.1 Everything is Relative

Objectives:

1. Understand the distinction between absolute and relative measure.

2. Write a ratio in its verbal, fraction, decimal, and percent formats.

Activity 6.2 Four out of Five Dentists Prefer the Brooklyn Dodgers?

Objectives:

1. Recognize that equivalent fractions lead to a proportion.

2. Use a proportion to solve a problem that involves ratios.

Activity 6.3 The Devastation of AIDS in Africa

Objectives:

1. Use proportional reasoning to apply a known ratio to a given piece of information.

2. Write an equation using the relationship ratio · total = part and then solve the resulting equation.

Activity 6.4 Who Really Did Better?

Objectives:

1. Define actual and relative change.

2. Distinguish between actual and relative change.

Activity 6.5 Dont Forget the Sales Tax

Objectives:

1. Define and determine growth factors.

2. Use growth factors in problems that involve percent increases.

Activity 6.6 Its All on Sale!

Objectives:

1. Define and determine decay factors.

2. Use decay factors in problems that involve percent decreases.

Activity 6.7 Take an Additional 20% Off

Objective:

1. Apply consecutive growth and/or decay factors to problems that involve two or more percent changes.

Activity 6.8 Fuel Economy

Objectives:

1. Apply rates directly to solve problems.

2. Use proportions to solve problems involving rates.

3. Use unit analysis or dimensional analysis to solve problems that involve consecutive rates.

What Have I Learned?

How Can I Practice?

Chapter 6 Summary

Chapter 6 Gateway Review

Chapter 7. Problem Solving with Geometry

Activity 7.1 Walking around Bases, Gardens, and Other Figures

Objectives:

1. Recognize perimeter as a geometric property of plane figures.

2. Write formulas for, and calculate perimeters of, squares, rectangles, triangles, parallelograms, trapezoids, and

ygons.

3. Use unit analysis to solve problems that involve perimeter.

Activity 7.2 Circles Are Everywhere

Objectives:

1. Measure the lengths of the diameter and circumference of circles.

2. Develop and use formulas for calculating circumferences of circles.

Activity 7.3 Lance Armstrong and You

Objectives:

1. Calculate perimeters of many-sided plane figures using formulas and combinations of formulas.

2. Use unit analysis to solve problems that involve perimeters.

Activity 7.4 Baseball Diamonds, Gardens, and Other Figures Revisited

Objectives:

1. Write formulas for areas of squares, rectangles, parallelograms, triangles, trapezoids, and polygons.

2. Calculate areas of polygons using appropriate formulas.

Activity 7.5 How Big Is That Circle?

Objectives:

1. Develop formulas for the area of a circle.

2. Use formulas to determine areas of circles.

Activity 7.6 A New Pool