### 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.

#### A.2: Students compute with signed rational numbers.

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

#### 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.

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

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

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

### 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.

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.

#### 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".

### 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.

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

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

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

#### 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.

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

### 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.

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

#### 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.

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

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

Correlation last revised: 5/11/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.