Greece Central Middle School Mathematics Unit Essential Questions 2007-08

Prime Time How are factors, multiples, divisors, and products related? How can factors and products be modeled geometrically? How can strategies using factors and multiples be used in solving real world problems?

Data Around Us How do we read, write and interpret large numbers that occur in real life measurements?

Bits and Pieces II What are benchmarks? How can they help us solve problems? How can we use a variety of strategies to perform operations (addition, subtraction, multiplication, and division) on rational numbers? How do operations with rational numbers help in problem solving?

Shapes and Designs What are the defining characteristics of polygons? How do we sort and classify polygons? Why do we need to measure shapes?

Bits and Pieces III How are fractions, decimals, and percents related? How can estimation strategies using decimals and percents be used in solving real world problems? How can decimals and percents be used to solve real world problems?

Covering and Surrounding Why do we need to measure shapes? Can we use numbers to describe two-dimensional shapes? How does measurement of two-dimensional shapes help in problem solving?

Data About Us (or mini-unit on Statistics) How does mathematics help us collect, display, analyze and interpret data? How do we use measures of center and spread to describe data?

What Do You Expect? How can experimental and theoretical probability be used to represent and solve problems using uncertainty? Accentuate the Negative What are integers? How are integers used in real world situations? What are rational numbers? What is absolute value?

Variables and Patterns How can relationships among variables be represented? How can a pattern be used to understand the relationship between variables? How can patterns help in problem solving?

Stretching and Shrinking What is similarity? How do similar relationships help in problem solving?

Filling and Wrapping How does mathematics quantify space shapes? How does measurement of space shapes help in problem solving?

Data Around Us (Inv. 4.3) How big is big? How small is small?

Comparing and Scaling How does mathematics help us to make comparisons? How does proportional reasoning help in problem solving?

Moving Straight Ahead How can multiple representations be used to express relationships among variables? What are the defining characteristics of a linear relationship? What is rate of change? How do linear relationships help in problem solving?

Looking for Pythagoras How do we sort and classify real numbers? How can measurement be used to create models for real numbers?

Proportional Reasoning (mini-unit) How does proportional reasoning help in problem solving? How can proportional reasoning be used in real-life situations? Operations with Monomials (mini-unit) How do we use number properties to perform operations with algebraic expressions? How is working with numbers similar to and different from working with algebraic expressions?

Operations with Polynomials (mini-unit) How do we use number properties to perform operations with algebraic expressions? How is working with numbers similar to and different from working with algebraic expressions?

Kaleidoscopes, Hubcaps and Mirrors What are transformations? What effect do transformations have on geometric figures?

Algebraic Reasoning (mini-unit) How can real world situations be represented symbolically? How can symbolic representation help in problem solving?

Thinking with Mathematical Models How can mathematics be used to model real world situations? How can multiple representations be used to express relationships among variables?

Growing, Growing, Growing How can multiple representations be used to express relationships among variables? What are the defining characteristics of an exponential relationship? How do exponential relationships help in problem solving?

Frogs, Fleas and Painted Cubes How can the roots of a quadratic equation be found graphically? How can a geometric model assist us in understanding the symbolic manipulation of factoring? What are the defining characteristics of a parabola?

Inequalities How can inequalities be used to model real world situations? How can multiple representations be used to express relationships among variables? How can multiple solutions to an inequality be represented?