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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# High School Math A & B

CLASSROOM IDEAS
EXAMPLES FOR
Math A

The following ideas for lessons and activities are provided to illustrate examples of each performance indicator. It is not intended that
teachers use these specific ideas in their classrooms; rather, they should feel free to use them or adapt them if they so desire. Some of
the ideas incorporate topics in science and technology. In those instances the appropriate standard will be identified. Some classroom
ideas exemplify more than one performance indicator. Additional relevant performance indicators are given in brackets at the end of
the description of the classroom idea.

2C.
• Have students make multiplication and addition charts for a 12-hour clock, using only the numbers 1-12.
• Have students determine if the system is closed under addition and multiplication. If not, they should give a counterexample.
• Have students determine if multiplication and addition are commutative under the system, and if not, give a counterexample.
• Have students determine if there is an identity element for addition and multiplication, and if so, what are they?
• Have students determine if addition and multiplication are associative under the system, and if not, give a counterexample.
• Does each element have an additive and multiplicative inverse?
• Determine if multiplication is distributive over addition (if not give a counterexample) and if addition is distributive
over multiplication (if not, give a counterexample). [Also 3D.]

3D.
Identify the field properties used in solving the equation 2(x - 5) + 3 = x + 7.

4B.
Explain why the basic construction of bisecting a line segment is valid.

5B.
While watching a TV detective show, you see a crook running out of a bank carrying an attachÃ© case. You deduce from
the conversation of the two stars in the show that the robber has stolen \$1 million in small bills. Could this happen?
Why or why not?

Hints: 1. An average attachÃ© case is a rectangular prism (18” x 5” x 13”).
2. You might want to decide the smallest denomination of bill that will work.
[Also 5A.]

5H.
An odometer is a device that measures how far a bicycle (or a car) travels. Sometimes an odometer is not adjusted accurately
and gives readings which are consistently too high or too low.

Paul did an experiment to check his bicycle odometer. He cycled 10 laps around a race track. One lap of the track is
0.4 kilometers long. When he started, his odometer read 1945.68 and after the 10 laps his odometer read 1949.88.
Compare how far Paul really traveled with what his odometer read.
Make a table that shows numbers of laps in multiples of 10 up to 60 laps, the distance Paul really travels, and the distance
the odometer would say he traveled.

Draw a graph to show how the distance shown by the odometer is related to the real distance traveled.

Find a rule or formula that Paul can use to change his incorrect odometer readings into accurate distances he has gone
from the start of his ride.

An odometer measures how far a bicycle travels by counting the number of times the wheel turns around. It then multiplies
this number by the circumference of the wheel. To do this right, the odometer has to be set for the right wheel circumference.
If it is set for the wrong circumference, its readings are consistently too high or too low. Before Paul’s experiment,
he estimated that his wheel circumference was 210 cm. Then he set his odometer for this circumference. Use the
results of his experiment to find a more accurate estimate for the circumference.

6A.
A box contains 20 slips of paper. Five of the slips are marked with a “X,” seven are marked with a “Y,” and the rest are
blank. The slips are well mixed. Determine the probability that a blank slip will be drawn without looking in the bag on
the first draw. Have students determine the probability theoretically and then have each conduct the experiment with
ten trials and see how close the empirical probability was to the theoretical probability. Combine data from all students
in the class to see if a larger number of trials will result in an empirical probability that more closely resembles the
theoretical probability. [Also 6B.]

## Math B

Key Idea 1
Mathematical Reasoning

Students use mathematical reasoning to analyze mathematical situations,
make conjectures, gather evidence, and construct an argument.

 PERFORMANCE INDICATORS INCLUDES EXAMPLES 1A. Construct proofs based on deductive reasoning. • Euclidean and analytic direct proofs. See Classroom Activity 1A. 1B. Construct indirect proofs. • Euclidean indirect proofs. See Classroom Activity 1B.

Key Idea 2
Number and Numeration

Students use number sense and numeration to develop an understanding of the
multiple uses of numbers in the real world, the use of numbers to communicate
mathematically, and the use of numbers in the development of mathematical
ideas.

 PERFORMANCE INDICATORS INCLUDES EXAMPLES 2A. Understand and use rational and irrational numbers. • Determine from the discriminant of a quadratic equation whether the roots are rational or irrational. • Rationalize denominators. • Simplifying of algebraic fractions with polynomial denominators. • Simplify complex fractions. See Classroom Activity 2A. 2B. Recognize the order of the real numbers. • Give rational approximations of irrational numbers to a specific degree of accuracy. See Classroom Activity 2B. 2C. Apply the properties of the real numbers to various subsets of numbers. • Use the properties of real numbers in the development of algebraic skills. See Classroom Activity 2C. 2D. Recognize the hierarchy of the complex number system. • Subsets of complex numbers. See Classroom Activity 2D. 2E. Model the structure of the complex number system. • Imaginary unit of complex numbers. • Standard form of complex numbers. See Classroom Activity 2E.

Key Idea 3
Operations

Students use mathematical operations and relationships among them to understand
mathematics.

 PERFORMANCE INDICATORS INCLUDES EXAMPLES 3A. Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions. • Operations with fractions with polynomial denominators. • Add and subtract rational fractions with monomial and binomial denominators. See Classroom Activity 3A. 3B. Develop an understanding of and use the composition of functions and transformations. • Understand the general concept and symbolism of the composition of transformations. • Apply the composition of transformations (line reflections, rotations, translations, glide reflections). • Identify graphs that are symmetric with respect to the axes or origin. • Isometries (direct, opposite). • Applications to graphing (inverse functions, symmetry). • Define and compute compositions of functions and transformations. See Classroom Activity 3B. 3C. Use transformations on figures and functions in the coordinate plane. • Apply transformations (line reflection, point reflection, rotation, translation, and dilation) on figures and functions in the coordinate plane. • Use slope and midpoint to demonstrate transformations. • Use the ideas of transformations to investigate relationships of two circles. • Use translation and reflection to investigate the parabola. See Classroom Activity 3C. 3D. Use rational exponents on real numbers and all operations on complex numbers. • Absolute value of complex numbers. • Evaluate expressions with fractional exponents. • Basic arithmetic operations with complex numbers. • Simplify square roots with negative radicands. • Use the product of a complex number and its conjugate to express the quotient of two complex numbers. • Cyclic nature of the powers of i. • Solving quadratic equations. • Laws of rational exponents. See Classroom Activity 3D. 3E. Combine functions, using the basic operations and the composition of two functions. • Determine the value of compound functions. • Pairs of equations. See Classroom Activity 3E.

Key Idea 4 Math B
Modeling/Multiple Representation

Students use mathematical modeling/multiple representation to provide a means
of presenting, interpreting, communicating, and connecting mathematical information
and relationships.