A: 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.

A.1: Students use negative and positive rational numbers expressed as integers, fractions, and decimals.

A.1.a: Recognize rational numbers as quotients of integers with a non-zero denominator and recognize that rational numbers can be negative or positive.

Adding and Subtracting Integers

A.2: Students compute with signed rational numbers.

A.2.b: Follow conventions of order of operations including exponents.

Order of Operations

A.3: Students understand that when the ratio of two varying quantities is constant, the two quantities are in direct proportion.

A.3.a: Use ratios to compare quantities and use comparison to solve problems.

Rational Numbers, Opposites, and Absolute Values

A.3.c: Use proportions to solve problems.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

A.4: Students interpret and use percents to solve problems.

A.4.b: Solve practical problems involving percents.

Percent of Change
Percents, Fractions, and Decimals
Real-Time Histogram

B: 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.

B.1: Students use graphs and charts to represent, organize, interpret, and draw inferences from data.

B.1.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.

Box-and-Whisker Plots
Distance-Time Graphs
Elevator Operator (Line Graphs)
Forest Ecosystem
Graphing Skills
Histograms
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

B.1.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.

Box-and-Whisker Plots
Forest Ecosystem
Graphing Skills
Histograms
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

B.2: Students understand and apply concepts of probability to simple events.

B.2.a: Describe events as likely or unlikely and discuss the concept of likelihood using such words phrases as "certain", "equally likely", and "impossible".

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)

C: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct two-dimensional and three-dimensional 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.

C.1: Students understand angle properties of lines in the plane.

C.1.a: Identify and name straight angles, angles at a point, and vertical angles and use these measures to find the measures of unknown angles.

Investigating Angle Theorems
Triangle Angle Sum

C.1.c: Recognize that vertical angles are congruent and apply this property to solve problems.

Triangle Angle Sum

C.2: Students solve problems involving perimeter and area.

C.2.b: Solve problems involving the area of combined figures.

Area of Triangles
Fido's Flower Bed (Perimeter and Area)

C.3: Students understand and use the concept of scale drawings to enlarge or reduce two-dimensional plane figures.

C.3.a: Use the concept of scale factors when enlarging or reducing and recognize the invariance of shape.

Dilations
Similar Figures

C.3.b: Apply the understanding that enlargement or reduction by a scale factor leaves angle measures unchanged.

Dilations
Similar Figures

D: 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.

D.1: Students create and evaluate expressions.

D.1.a: Create and evaluate expressions using integers.

Order of Operations

D.1.b: Create and evaluate expressions using rational numbers.

Compound Interest
Order of Operations

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.

D.2.b: Convert equations to 0 = ax + b form.

Standard Form of a Line

D.3: Students understand and use directly proportional relationships, y = kx.

D.3.b: Translate common directly proportional relationships into symbolic statements and graphs.

Direct and Inverse Variation