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A. NUMBER: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately. Estimation should always be used when computing with numbers or solving problems. 
WHOLE NUMBER





No performance indicator. It is expected that students continue to use prior concepts and skills in new and familiar contexts. 




RATIONAL NUMBER  



A.1. Students use negative and positive rational numbers expressed as integers, fractions and decimals.
 a. Recognize rational numbers as quotients of integers with a nonzero denominator and recognize that rational numbers can be negative or positive.
 (Connected Mathematics ProjectAccentuate the Negative) Develop algorithms for adding, subtracting, multiplying and dividing integers.
(Grade 8:LFP students recognize rational numbers)   classroom tests
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 b. Compare signed rational numbers and place them on the number line.
 (ATN) Compare and order rational numbers and locate them on the number line.
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A.2. Students compute with signed rational numbers.
 a. Use and interpret exponents.
 (ATN & comp sheets) Calculate values of exponential numbers and write them in both expanded and standard notation.
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 b. Follow conventions of order of operations including exponents.
 (ATN & comp sheets) Evaluate expressions including parenthesis, exponents, multiplication, division, addition and subtraction following the order of operations.
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 c. Solve problems using signed rational numbers.
 (ATN) Model and answer questions about problem situations using integers and rational numbers.
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A.3. Students understand that when the ratio of two varying quantities is constant, the two quantities are in direct proportion.
 a. Use ratios to compare quantities and use comparison to solve problems.
 (Stretching & Shrinking) Identify similar figures using side ratios, and determine missing measurements.
(Comparing & Scaling) Name equivalent forms of given ratios and rates and use them to make comparisons   classroom tests
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 b. Identify proportional relationships.
 (S&S) Identify proportional relationships in geometric figures to determine similarity.
(C&S) Determine situations in which data is proportionate   classroom tests
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 c. Use proportions to solve problems.
 (S&S) Use proportions to find missing values on similar figures.
(C&S) Set up and solve proportions. Use proportional reasoning to solve problems.
(Comp sheets) Solve proportions for missing values.   classroom tests
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A.4. Students interpret and use percents to solve problems.
 a. Use percents when comparing fractional parts of sets of unequal size.
 (C&S) Compare quantities of differing amounts using percents and fractions.
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 b. Solve practical problems involving percents.
 (Variables & Patterns) Calculate sales tax and discounts.
(S&S) Express scale factors as percentages to figure out sizes of similar figures.   classroom tests
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REAL NUMBERS


 

No performance indicator. Although no performance indicators are stated, students are expected to have instructional experiences in which they use rational numbers including rational approximations for pi or square roots.


 

B. DATA: Students make measurements and collect, display, evaluate, analyze and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students:
 understand that most measurements are approximations and that taking repeated measurements reveals this variability;
 understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement;
 understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.

MEASUREMENT AND APPROXIMATION


 

Although no performance indicators are stated at this level, it is expected that students continue to use prior concepts and skills in new and familiar concepts. 

 

DATA ANALYSIS





B.1. Students use graphs and charts to represent, organize, interpret, and draw inferences from data.
 a. Create tables, pictograms, bar graphs, line graphs, pie charts, stem and leaf plots, box and whiskers plots, and histograms using pencil and paper and electronic technologies.
 (V&P) Create tables, line graphs and pie charts using pencil and paper and electronic technologies.
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 b. Draw conclusions based on graphs and charts including tables, pictograms, bar graphs, line graphs, pie charts, stem and leaf plots, box and whiskers plots, and histograms.
 (V&P) Evaluate tables and graphs to solve problems.
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PROBABILITY


 

B.2 .Students understand and apply concepts of probability to simple events.
 a. Describe events as likely or unlikely and discuss the concept of likelihood using such words/phrases as "certain", "equally likely", and "impossible".
 (review problems) Express probabilities as both fractions and percents to describe the likelihood of given events.
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 b. Predict the probability of outcomes of simple experiments and verify predictions using the understanding that the probability of an occurrence is the ratio of the number of actual occurrences to the number of possible occurrences. 
 

 c. Interpret probabilities between and including zero and one and explain why zero and one are the upper and lower limits for probability values. 
 

C. GEOMETRY: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct twodimensional and threedimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures, students use estimation to check the reasonableness of results. 
GEOMETRIC FIGURES


 

C.1. Students understand angle properties of lines in the plane.
 a. Identify and name straight angles, angles at a point, and vertical angles and use these measures to find the measures of unknown angles.
 (comp sheets, review problems) Categorize angles as straight, obtuse, right, and acute.
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 b. Recognize that the measures that form straight angles add to 180 degrees and the measures of angles at a point add up to 360 degrees and apply this to property to solve problems.
 (S&S) Calculate missing measurements of angles along a straight line or in a triangle.
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 c. Recognize that vertical angles are congruent and apply this property to solve problems.
 (S&S) Recognize that vertical angles are congruent in order to prove similarity of triangles.
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GEOMETRIC MEASUREMENT


 

C.2. Students solve problems involving perimeter and area.
 a. Solve problems involving the area and perimeter of regions in the plane bounded by line segments and circular arcs.
 (Filling & Wrapping, comp sheets) Calculate perimeter, area and surface area of geometric figures.
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 b. Solve problems involving the area of combined figures.
 (F&W) Calculate surface area of prisms by calculating and adding the area of all faces.
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TRANSFORMATIONS


 

C.3. Students understand and use the concept of scale drawings to enlarge or reduce two dimensional plane figures.
 a. Use the concept of scale factors when enlarging or reducing and recognize the invariance of shape.
 (S&S) Calculate scale factors from side ratios of similar figures. Calculate values of missing sides given similar figures, or one figure and a scale factor.
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 b. Apply the understanding that enlargement or reduction by a scale factor leaves angle measures unchanged.
 (S&S) Prove that figures are similar by showing congruence of angles and calculating a scale factor.
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 c. Identify similar figures and name corresponding parts.
 (S&S) Identify similar figures and name corresponding sides and angles.
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D. ALGEBRA: Students use symbols to represent or model quantities, patterns and relationships and use symbolic manipulation to evaluate expressions and solve equations. Students solve problems using symbols, tables, graphs and verbal rules choosing the most effective representation and converting among representations. 
SYMBOLS AND EXPRESSIONS


 

D.1. Students create and evaluate expressions.
 a. Create and evaluate expressions using integers.
 (Comp sheets, V&P, ATN) Write equations given a situation. Evaluate an algebraic expression for integer values of variables.
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 b. Create and evaluate expressions using rational numbers.
 (Comp sheets, V&P, ATN) Write equations given a situation. Evaluate an algebraic expression for rational values of variables.
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EQUATIONS AND INEQUALITIES


 

D.2. Students understand and solve problems involving linear equations and know that a linear equation can be written in the form 0= ax + b.
 a. Solve equations of the form ax + b = c where a, b, and c are positive rational numbers or positive or negative integers.
 (V&P, ATN) Solve first degree equations for the variable.
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 b. Convert equations to 0 = ax + b form.
 (ATN) Recognize that equivalence does not change if you do the same action to both sides of an equation. Use inverse operations to manipulate equations.
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FUNCTIONS AND RELATIONS


 

D.3. Students understand and use directly proportional relationships, y = kx.
 a. Recognize directly proportional relationships by information in a table, graph, or formula.  (V&P) Convert proportional relationships to and from tables, graphs and equations.   classroom tests
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 b. Translate common directly proportional relationships into symbolic statements and graphs.
 (V&P) Write proportional relationships as equations given either a table or a situation.
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 c. Interpret the slope and yintercept of the graph of y = kx in terms of a given context.
 (V&P) Understand and explain the relationship between the speed of a vehicle and the "steepness" (slope) of the graph, and the equation of the direct variation.
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