GRADE 10

GOAL: The student understands and applies the concepts and procedures of mathematics.

Washington State Essential Academic Learning Requirements	Meridian School District Math Framework	Assessment Strategies
The learner will: Understand and apply concepts and procedures from number sense BENCHMARKS Number and Numeration Understand and use properties and symbolic representations of rational numbers Explain the magnitude of numbers by comparing and ordering rational numbers Understand concepts of and use processes involving prime and composite numbers, factors and multiples, and divisibility Understand and apply the concepts of ratio and both direct and indirect proportion. Computation Understand operations on real numbers Compute with rational numbers, powers, and roots Use mental arithmetic, pencil and paper, calculator, or computer as appropriate to the task involving real numbers Estimation Identify situations involving whole numbers in which estimation is useful Use estimation to predict computation results and to determine the reasonableness of answers, for example, estimating a grocery bill	To meet this standard the learner will: 1.1.6 Use negative, zero, and fractional exponents (2-6) 1.1.2 Find the number of ways to select some items from a group (6-5) Use the multi-counting principle to find a number of possible arrangements of items (6-2) 1.1.4 Use quadratic formula to solve quadratic equation.	1	2	3	4	5
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GOAL: The student understands and applies the concepts and procedures of mathematics.

Suggested Instructional Strategies / Activities

Resources & Materials

2-6 Do pg. 99 “Exploration” Integrated II text. Uses a graphing calculator to explore how a calculator treats fractional and negative exponents. Students use graphics calculators to explore negative and zero exponents and come up with definition. 6-5 Do pg. 328 “Talk it over” As partner activity. 6-2 Do pg. 302 “Exploration” Uses letters on note cards to manipulate them into all possible arrangements. Negative, Zero, and Fractional exponents. Q: 2^2(2^3)=? A:2^5(a^x.a^y=a^x+y) Q: 2^5/2^3=? A:2^2(a^x/a^y=a^x-y) 1=2^3/2^3=2^3-3=2^0 Similar argument for negative and fractional exponents. Reinforce by using calculator.

TI-82 Calculator & Int. II text Int. II text and TI-82 Calculator Int. II text 4 index cards & a partner. Whiteboard, paper, pencil, calculator.

GOAL: The student understands and procedures of mathematics.

Washington State Essential Academic Learning Requirements	Meridian School District Math Framework	Assessment Strategies
The learner will: Understand and apply concepts and procedures from measurement BENCHMARKS Attributes and dimensions Understand how changes in dimension affect perimeter, area, and volume Measure objects and events directly or use indirect methods such as finding the volume of a cone given its height and diameter Calculate rate and other derived and indirect measurements Approximation and precision Understand that measurement is approximate Estimate to predict and determine when measurements are reasonable, for example, estimating how much paint is needed to paint the walls of a classroom Systems and tools Understand the benefits of standard units of measurement and the advantages of metric systems Select and use tools that will provide an appropriate degree of precision, for example, using kilometers vs. light years	To meet this standard the learner will: 1.2.2 Find the surface area and volume of spheres (2-6,2-4) Find the distance between two points in three dimensions (10-5)	1	2	3	4	5
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GOAL: The student understands and applies the concepts and procedures of mathematics.

Suggested Instructional Strategies / Activities	Resources & Materials
2-6 Use Lenart Spheres to “deduce” formulas related to spheres. Surface area and volume of spheres. -Actually use oranges and manila folder to create a cylinder that just barely contacts the orange compare volume of the cylinder to the volume of the orange. See page 4 in the text.	Lenart sphere classroom set. Oranges, manila folders, scissors, and tape. Integrated II text

GOAL: The student understands and applies the concepts and procedures of mathematics.

Washington State Essential Academic Learning Requirements	Meridian School District Math Framework	Assessment Strategies
The learner will: Understand and apply concepts and procedures from geometric sense BENCHMARKS Properties and relationships Use geometric properties and relationships to compare, contrast, describe, and classify 2- and 3- dimensional geometric figures Construct geometric models and scale drawings using tools as appropriate, for example, building a model of a bridge Locations and transformations Understand and use coordinate grids Understand and apply multiple geometric transformations using combinations of translations, reflections, and/or rotations.	To meet this standard the learner will: 1.3.1 Discover properties of 45° -45° -90° and 30° –60° –90° triangles (8-8) Visualize space figures (10-1) 1.3.2 Apply properties of similar triangles (8-3) Describe space figures that are formed by rotating plane figures around a line (10-2) Describe the location of points in space using three coordinates (10-4) 1.3.3 Describe the graphs of functions (2-1) Represent figures on a coordinate plane using as few variables for coordinates as possible (5-5) 1.3.6 Use matrices to represent changes in the size or position of a polygon (3-6) Transform geometric figures and learn how transformations affect their properties (5-4)	1	2	3	4	5
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GOAL: The student understands and applies the concepts and procedures of mathematics.

Suggested Instructional Strategies / Activities

Resources & Materials

10-1 Play-Doh activities: Must make prisms, pyramids, etc. Build stellated icosahedron with origami 2-1 Do pg 59 “Talk it over” Uses the topography of a trail to discuss slopes, Linear & non linear concepts. 5-4 Use graphing Calculator to transform figures using matrix multiplication -Create Escher-like tessellations -Create and make tangrams Discover properties of 45.45-90 & 30-60-90. -Patty paper explorations (folds, etc.) Visualize space figures Exploration: What does a space figure look like in two dimensions? -Students work with a partner to create space figures & analyze. Performance assessment pg. 558

Play-Doh Int II text TI-82 calculator Stiff paper, rulers, protractors and scissors. Integrated II text.

GOAL: The student understands and applies the concepts and procedures of mathematics.

Washington State Essential Academic Learning Requirements	Meridian School District Math Framework	Assessment Strategies
The learner will: Understand and apply concepts and procedures from probability and statistics BENCHMARKS Probability Understand the properties of dependent and independent events Understand and use appropriate counting procedures to determine probabilities Statistics Collect data using appropriate methods and technology Organize and display data in appropriate forms such as tables, graphs, scatter plots, and box plots Calculate and use the different measures of central tendency, variability , and range as appropriate in describe data Use statistics to support different points of view, for example, in a debate or a position paper Prediction and inference Design and conduct experiments to verify or disprove predictions Understand and make inferences based on the analysis of experimental results	To meet this standard the learner will: 1.4.5 Learn about different ways to select a sample (1-3) 1.4.8 Use an experiment to simulate the results of a survey (1-2) Find probability of an event and of mutually exclusive events (6-3) Relate probability to odds. Find probability of independent and dependent events (6-4) Find probability of independent and dependent events (6-7,8) Use diagrams and tables to count possibilities (6-1)	1	2	3	4	5
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GOAL: The student understands and applies the concepts and procedures of mathematics.

Suggested Instructional Strategies / Activities

Resources & Materials

1-3 Do pg. 18 “Talk it over” Discusses deciding how to choose a particular type sample. 1-2 Students create question & survey classmates 6-7.8 Use Pascal’s triangle to illustrate n ^c r. Learn different ways to select a sample. -Use random sampling to select a sample by using the random number generator on a TI-82 calculator. See pg. 19 in the text. Find the probability of an event. Play the game of skunk. -Roll two dice. Play 5 rounds, one for each letter in the word skunk. Roll the dice until a 1 is rolled. That ends a round. While students stand, they get points shown on dice. If a 1 is rolled, they lose all points for that round. They may sit down after the first roll of a round, but they get no points if they sit. They also do not lose points if a 1 is rolled. Student with the most points wins. Also, if two 1’s are rolled “Snake eyes” and a student is standing, they lose all points from all rounds. Ask students what the probability is of rolling a 1 or snake eyes.

Integrated II text TI-82 Calculator. Integrated II textbook.

GOAL: The student understands and applies the concepts and procedures of mathematics.

Washington State Essential Academic Learning Requirements	Meridian School District Math Framework	Assessment Strategies
The learner will: Understand and apply concepts and procedures from algebraic sense BENCHMARKS Patterns Recognize, create, extend complex patterns and sequences. Generalize and express rules describing patterns and sequences. Representations Translate among tabular, symbolic, and graphical representations of relations, for example, displaying information from a table as a graph Represent situations that involve variable quantities with expressions, formulas, and equations, and inequalities Operations Simplify and evaluate expressions and formulas. Write and solve equations and inequalities.	To meet this standard the learner will: 1.5 Find powers of binomials (6-9) Model real world situations with equation (9-1) Classify expressions (9-1) Analyze graphs of polynomial functions written in factored form (9-4) Solve rational equations that simplify to linear or quadratic equations (9-3) Solve cube equations by various methods (9-5) Use matrices to represent data sets and use matrix operations (3-5) 1.5.3 Describe graphs of functions (2-1) Review linear functions, slope of a line, and direct variation (2-2) Understand and use the relationships between the slopes of parallel and perpendicular lines (3-3) Understand how the coefficients of a quadratic function influence its graph (4-1) Explore translations of parabolas (4-2) 1.5.4 Explore situations that involve constant products (2-3) Model and apply relationships in which one quantity is proportional to the square or cube of another (2-5) 1.5.6 Solve systems of linear equations by graphing and graph systems of linear inequalities (3-1) Solve systems of equations by substitution (3-2) Solve quadratic equations by graphing and factoring	1	2	3	4	5
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GOAL: The student understands and applies the concepts and procedures of mathematics.

Suggested Instructional Strategies / Activities	Resources & Materials
6-9 Use of Pascal’s triangle to illustrate binomial thm. 3-5 Use TI-82 calculators to multiply large matrics 4-2 Do pg. 193 Exploration. -Using multiple graphs on a graphing calculator to explore translating parabolas Explore translations of parabolas -Use a graphing calculator to see how changing the equation affects the graph of a parabola. Exploration on pg. 193 in the text	TI-82 calculator TI-82 Calculator & Int. II text book TI-82 Calculator some quadratic equations. Integrated II text.

GOAL: The student uses mathematics to define and solve problems.

Washington State Essential Academic Learning Requirements	Meridian School District Math Framework	Assessment Strategies
The learner will: 2.1 Investigate situations BENCHMARKS Search systematically for patterns in complex situation Analyze and use multiple strategies Identify what information is missing or extraneous and compensate for it Analyze an unproductive approach and attempt to modify it or try a new approach 2.2 Formulate questions and define the problem BENCMARKS Identify questions to be answered in complex situations Define problems in complex situations Identify the unknown in complex situations 2.3 Construct solutions BENCMARKS Organize and synthesize information from multiple sources Select and use appropriate mathematical tools Apply viable strategies, concepts, and procedures to construct a solution.	To meet this standard the learner will: 2.1 Explore situations in which quantities repeatedly double or split in half (2-7) 2.3.2 Solve systems of equations using additions or subtraction and choose a method for solving a system of equations (3-4) Use technology to find inverse matrices and use them to solve systems of equations (3-8)	1	2	3	4	5
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GOAL: The student uses mathematics to define and solve problems.

Suggested Instructional Strategies / Activities	Resources & Materials
3-8	TI-82 Calculators

GOAL: The student uses mathematical reasoning.

Washington State Essential Academic Learning Requirements	Meridian School District Math Framework	Assessment Strategies
The learner will: 3.1 Analyze information BENCHMARKS Interpret and integrate information from multiple sources Validate thinking and mathematical ideas using models, known facts, patterns, relationships, counter-examples, and proportional reasoning 3.2 Predict results and make inferences BENCHMARKS Make conjectures and inferences based on analysis of problem situations 3.3 Draw conclusions and verify results BENCHMARKS Test conjectures and inferences by formulating a proof or by constructing a counter-example Support arguments and justify results using inductive and deductive reasoning Check for reasonableness of results Reflect on and evaluate procedures and results and make necessary revisions	To meet this standard the learner will: 3.1 3.3.2 Know how a survey of part of a population can be used to predict results (1-1) Apply inductive reasoning to many situations and realize the limitations of inductive reasoning (1-5) Apply deductive reasoning and learn how it differs from inductive (1-6, 5-6) 3.3.3 Recognize errors in mathematical and logical reason (1-7) Learn to raise questions about surveys (1-4)	1	2	3	4	5
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GOAL: The student uses mathematical reasoning.

Suggested Instructional Strategies / Activities

Resources & Materials

GOAL: The student communicates knowledge and understanding in both everyday and mathematical language.

Washington State Essential Academic Learning Requirements	Meridian School District Math Framework	Assessment Strategies
The learner will: 4.1 Gather information BENCHMARKS Develop or select and efficient system for collecting information Use reading, listening, and observation skills to access and extract mathematical information from multiple, , self-selected sources such as pictures, diagrams, physical models, and narratives, and symbolic representations Integrate the use of a variety of available technologies to browse, select, and retrieve mathematical information from multiple sources 4.2 Organize and interpret information BENCHMARKS Express complex ideas and situations using mathematical language and rotation in appropriate and efficient forms Express or present mathematical ideas clearly and effectively using both everyday and mathematical language appropriate to audience 4.3 Represent and share information Express complex ideas and situations using mathematical language and notation in appropriate and efficient forms Explain or represent complex mathematical ideas in ways appropriate for audience and purpose.	To meet this standard the learner will: 4.1 Learn about different ways to select a sample (1-3)	1	2	3	4	5
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