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

1.1: Understand and apply concepts and procedures from number sense.

1.1.2: Understand the relative values of integers and non-negative rational numbers.

1.1.2.a: Compare different representations of non-negative rational numbers by implementing strategies (e.g., like denominators, changing to the same form).

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

1.1.2.b: Identify equivalence between non-negative integers, fractions, percents, and decimals.

Improper Fractions and Mixed Numbers
Percents, Fractions and Decimals

1.1.2.c: Compare and order integer values and explain which is greater and why (e.g., place the integers on a number line).

Comparing and Ordering Integers
Real Number Line - Activity A

1.1.2.d: Represent and identify integers on a model (e.g., number line, fraction line, or decimal grid).

Comparing and Ordering Integers
Real Number Line - Activity A

1.1.4: Understand the concepts of ratio and percent.

1.1.4.a: Write ratios in part/part and part/whole relationships using objects, pictures, and symbols (e.g., using /, :, or “to” as representations for ratios).

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood

1.1.4.b: Represent equivalent ratios using objects, pictures, or symbols.

Part:Part and Part:Whole Ratios
Polling: Neighborhood

1.1.4.c: Represent equivalent percentages using objects, pictures, and symbols.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.1.4.d: Identify percent as 100 equal-size parts of a set (e.g., 1% of 200 items is 2 items).

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.1.4.e: Explain ratio and percents and give examples of each.

Estimating Population Size
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood

1.1.5: Understand the meaning of multiplication and division on non-negative rational numbers.

1.1.5.a: Explain the meaning of multiplying and dividing non-negative fractions and decimals using words or visual or physical models (e.g., sharing a restaurant bill, cutting a board into equal-sized pieces, drawing a picture of an equation or situation).

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying with Decimals

1.1.5.b: Explain why multiplication of fractions can be done by multiplying denominators while addition of fractions requires finding common denominators.

Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

1.1.5.c: Use technology to demonstrate how multiplication and division with decimals affects place value.

Multiplying with Decimals

1.1.6: Apply computational procedures with fluency for addition and subtraction on non-negative rational numbers.

1.1.6.a: Find the sums or differences of nonnegative fractions or decimals.

Fractions with Unlike Denominators
Sums and Differences with Decimals

1.1.6.b: Write and solve real-world problem situations to find sums or differences of decimals or fractions.

Fractions with Unlike Denominators
Sums and Differences with Decimals

1.1.6.d: Use addition and subtraction to solve real-world problems involving non-negative rational numbers.

Sums and Differences with Decimals

1.1.7: Understand and apply strategies and tools to complete tasks involving addition and subtraction on non-negative rational numbers.

1.1.7.c: Use calculators to add and subtract with decimal numbers with precision to the thousandths place and beyond.

Sums and Differences with Decimals

1.1.8: Apply estimation strategies to predict or determine the reasonableness of answers in situations involving addition and subtraction on non-negative rational numbers.

1.1.8.b: Apply estimation strategies prior to computation on whole numbers, decimals, and fractions to approximate an answer.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

1.1.8.e: Describe various strategies used during estimation involving fractions and decimals.

Estimating Sums and Differences

1.2: Understand and apply concepts and procedures from measurement.

1.2.1: Understand the concepts of volume and extend the concept of area to surface area of rectangular prisms.

1.2.1.b: Represent the volume for given rectangular prisms using pictures or models.

Prisms and Cylinders - Activity A

1.2.1.c: Compare the surface area of two different rectangular prisms.

Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.2.1.d: Describe and provide examples for surface area measurement (e.g., gift wrapping, painting a room, amount of material needed to build a box).

Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.2.1.e: Explain and give examples of how the area and surface area are related (e.g., surface area is the sums of the areas of all the sides of a rectangular prism).

Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.2.1.f: Describe and compare the use of area and volume (e.g., covering and filling).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.2: Understand the differences between square and cubic units.

1.2.2.d: Explain why volume is measured in cubic units.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.2.e: Explain how the selected unit of length affects the size of cubic units (e.g., centimeter versus inch).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.4: Understand and apply systematic procedures to measure volume and capacity for solid shapes.

1.2.4.c: Select and use tools that match the unit.

Triple Beam Balance

1.2.4.d: Count or compute to obtain the volume or capacity and label the measurement.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.4.e: Use volume and capacity to describe and compare figures (e.g., fill containers with cubes to find which has a greater volume).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.4.f: Measure the capacity of containers using appropriate tools and label (e.g., graduated cylinders, measuring cups, tablespoons).

Triple Beam Balance

1.2.6: Understand and apply strategies to obtain reasonable estimates of volume or capacity.

1.2.6.b: Estimate volume or capacity.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.6.c: Use estimation to justify reasonableness of a volume of a rectangular prism.

Prisms and Cylinders - Activity A

1.2.6.d: Estimate a measurement of volume or capacity using standard or non-standard units (e.g., estimate the capacity of a bowl in cups and handfuls).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.6.e: Use or describe a process to find a reasonable estimate of volume or capacity (e.g., fill a container with rice or popcorn).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.3: Understand and apply concepts and procedures from geometric sense.

1.3.1: Understand the characteristics of circles and rectangular prisms.

1.3.1.a: Name and sort circles or rectangular prisms according to their attributes (faces, edges, radii, base, parallel faces).

Circles
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.3.1.b: Draw a figure with given characteristics (e.g., the set of points equidistant from a given point).

Classifying Triangles

1.3.1.c: Identify lines of symmetry in rectangular prisms.

Holiday Snowflake Designer
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.3.1.d: Explain lines of symmetry for circles.

Circles
Holiday Snowflake Designer

1.3.2: Apply understanding of angles and polygons.

1.3.2.a: Identify geometric figures and concepts in nature and art (e.g., triangle in architecture, rhombus in beadwork, culturally relevant textiles, quilts).

Classifying Quadrilaterals - Activity A
Classifying Triangles

1.3.2.c: Create a three-dimensional shape given its net or draw the net of a given threedimensional shape.

Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.3.2.d: Find the missing measure of an angle using the properties of parallel lines, perpendicular lines, vertical and corresponding angles.

Investigating Angle Theorems - Activity A

1.3.3: Understand the relative location of integers on a number line.

1.3.3.a: Show the order of a given set of integers on a number line.

Comparing and Ordering Integers
Real Number Line - Activity A

1.3.3.b: Identify the point of final destination given directions for movement on a number line including positive and negative numbers (vertical or horizontal) (e.g., temperature variation at different times of the day, bank accounts, gain and loss of weight).

Real Number Line - Activity A

1.3.3.c: Determine the distance between any two integers on a number line.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Real Number Line - Activity A

1.3.3.d: Describe relative location of points and objects on a number line with both positive and negative numbers.

Real Number Line - Activity A

1.3.3.e: Identify objects on a number line based on given numeric locations.

Real Number Line - Activity A

1.3.4: Apply understanding of rotations (turns) to two-dimensional figures.

1.3.4.a: Apply rotations (turns) of 900 or 1800 to a simple two-dimensional figure.

Rotations, Reflections and Translations

1.3.4.b: Create a design using (900, 1800, 2700, 3600) rotations (turns) of a shape.

Rotations, Reflections and Translations

1.3.4.c: Show how a shape has been rotated by 900 or 1800.

Rotations, Reflections and Translations

1.3.4.d: Describe a rotation so that another person could draw it

Rotations, Reflections and Translations

1.3.4.e: Identify the coordinates of objects that have been rotated 900, 1800, or 2700 on a coordinate grid.

Rotations, Reflections and Translations

1.3.4.f: Determine whether an object has been translated or rotated on a coordinate grid.

Rotations, Reflections and Translations

1.4: Understand and apply concepts and procedures from probability and statistics.

1.4.1: Understand probability as a ratio between and including 0 and 1.

1.4.1.b: Express probabilities as fractions or decimals between 0 and 1 and percents between 0 and 100.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

1.4.2: Understand various ways to determine outcomes of events or situations.

1.4.2.a: Determine and use the probabilities of the outcome of a single event.

Geometric Probability - Activity A

1.4.2.c: Calculate probability for an event (e.g., pulling colored or numbered balls from a bag, drawing a card, rolling a six on a number cube, spinning a spinner, etc.).

Geometric Probability - Activity A
Probability Simulations

1.4.3: Analyze how data collection methods affect the data collected.

1.4.3.d: Compare data collection methods for a given situation to determine fairness of the method (e.g., compare a phone survey, a web survey, and a personal interview survey).

Populations and Samples

1.4.4: Apply measures of central tendency to interpret a set of data.

1.4.4.a: Determine when it is appropriate to use mean, median, or mode and why a specific measure provides the most useful information in a given context.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.b: Use mean, median, and mode to explain familiar situations (e.g., the heights of students in the class, the hair color of students in the class).

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.c: Find the missing number given a mean for a data set with a missing element (e.g., given a set of homework scores and the desire to earn an average score of 80%, determine what score the student must earn on the next assignment).

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.5: Understand how to organize, display, and interpret data in text from single line graphs and scatter plots.

1.4.5.a: Justify a choice of a graph type for a given situation using information about the type of data.

Box-and-Whisker Plots
Line Plots
Stem-and-Leaf Plots

1.4.5.b: Read and interpret data from single line graphs and scatter plots, and determine when the use of these graphs is appropriate.

Scatter Plots - Activity A

1.4.5.c: Use an appropriate representation to display data (e.g., table, graphs) given a particular situation and audience.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

1.4.5.f: Use technology to generate bar graphs, line graphs, and scatter plots from tables of data.

Scatter Plots - Activity A

1.4.6: Evaluate a data set to determine how it can be, or has been, used to support a point of view.

1.4.6.a: Compare graphs to data sets (e.g., given unlabeled graphs and data sets, match the appropriate data to a graph).

Box-and-Whisker Plots
Line Plots
Stem-and-Leaf Plots

1.4.6.d: Explain whether the scale on a graph accurately represents the data.

Box-and-Whisker Plots
Line Plots
Stem-and-Leaf Plots

1.4.6.e: Compare or evaluate two or more interpretations of the same set of data for accuracy.

Populations and Samples

1.5: Understand and apply concepts and procedures from algebraic sense.

1.5.1: Apply rules for number patterns based on two arithmetic operations.

1.5.1.a: Recognize or extend patterns and sequences using operations that alternate between terms.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.1.b: Create, explain, or extend number patterns involving two related sets of numbers and two operations including addition, subtraction, multiplication, or division.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.1.c: Use rules for generating number patterns (e.g., Fibonacci sequence, bouncing ball) to model real-life situations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

1.5.1.e: Supply missing elements in a pattern based on two operations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.1.f: Select or create a pattern that is equivalent to a given pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.2: Apply understanding of patterns involving two arithmetic operations to develop a rule.

1.5.2.a: Describe the rule for a pattern with combinations of two arithmetic operations in the rule.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.2.b: Identify patterns involving combinations of operations in the rule, including exponents (e.g., 2, 5, 11, 23).

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.2.c: Represent a situation with a rule involving a single operation (e.g., presidential elections occur every four years; when will the next three elections occur after a given year?).

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.3: Apply understanding of equalities and inequalities to interpret and represent relationships between quantities.

1.5.3.a: Express relationships between quantities (decimals, percents, and integers) using =, not equal to, <, >, less than or equal to, and greater than or equal to.

Comparing and Ordering Decimals
Comparing and Ordering Integers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

1.5.3.b: Match a given situation to the correct inequality or equality.

Using Algebraic Equations

1.5.3.c: Express relationships between nonnegative rational numbers using symbols.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

1.5.3.d: Write an inequality with a single variable to match a particular situation.

Using Algebraic Equations

1.5.4: Apply understanding of tables, graphs, expressions, equations, or inequalities to represent situations involving two arithmetic operations.

1.5.4.a: Translate a situation involving multiple arithmetic operations into algebraic form using equations, tables, and graphs.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.b: Identify or describe a situation involving two arithmetic operations that matches a given graph.

Distance-Time Graphs

1.5.4.c: Represent an equation, expression, or inequality using a variable in place of an unknown number.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.e: Represent an equation or expression using a variable in place of an unknown number.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.f: Identify a situation that corresponds to a given equation or expression.

Using Algebraic Equations

1.5.6: Understand and apply a variety of strategies to solve one-step equations.

1.5.6.a: Solve one-step equations using pictures and symbols.

Modeling One-Step Equations - Activity A

1.5.6.b: Solve one-step single variable equations using any strategy (e.g., what number goes in the mystery box?).

Modeling One-Step Equations - Activity A

1.5.6.c: Solve real-world situations involving single variable equations.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
Using Algebraic Equations
Using Algebraic Expressions

1.5.6.d: Explain a strategy for solving a single variable equation.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

1.5.6.e: Write and solve one-step single variable equations for a given situation.

Modeling One-Step Equations - Activity A
Using Algebraic Equations
Using Algebraic Expressions

3: The student uses mathematical reasoning.

3.1: Analyze information.

3.1.1: Analyze information from a variety of sources to interpret and compare information.

3.1.1.b: Read and interpret data from single line graphs and scatter plots and determine when the use of these graphs is appropriate.

Scatter Plots - Activity A

3.1.1.c: Use volume and capacity to describe and compare figures (e.g., fill containers with cubes to find which has a greater volume).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

3.2: Make predictions, inferences, conjectures, and draw conclusions.

3.2.1: Apply prediction and inference skills to make or evaluate conjectures.

3.2.1.b: Predict a future element in a relation (e.g., find the fifteenth term in a pattern).

Introduction to Functions

3.2.2: Apply the skills of drawing conclusions and support those conclusions using evidence.

3.2.2.a: Draw conclusions from displays, texts, or oral discussions and justify those conclusions with logical reasoning or other evidence (e.g., read a newspaper article or ad; draw a conclusion and support that conclusion with evidence from the article or elsewh

Biconditional Statement
Conditional Statement

3.3: Verify results.

3.3.1: Analyze procedures and information used to justify results using evidence.

3.3.1.a: Find and compare rectangular prisms that have a given volume (e.g., if two rectangular prisms have the same volume and one has twice the height of the other, determine how the areas of their bases compare).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

3.3.1.b: Apply estimation strategies prior to computation of whole numbers, decimals, and fractions to determine reasonableness of answers.

Estimating Population Size
Estimating Sums and Differences

3.3.1.c: Identify different ways of selecting a sample (e.g., convenience sampling, response to a survey, random sampling) and which method makes a sample more representative for a population.

Polling: Neighborhood

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

4.1: Gather information.

4.1.1: Apply a planning process to collect information for a given purpose.

4.1.1.a: Use mean, median, and mode to explain familiar situations (e.g., the heights of students in the class; the hair color of students in the class).

Describing Data Using Statistics
Mean, Median and Mode

4.1.2: Understand how to extract information from multiple sources using reading, listening, and observation.

4.1.2.a: Use mean, median, and mode to explain situations (e.g., the heights of students in the class; hair color of students in the class; favorite movie of students in the class; most watched movie in a specific time frame).

Describing Data Using Statistics
Mean, Median and Mode

4.2: Organize, represent, and share information.

4.2.1: Apply organizational skills for a given purpose.

4.2.1.a: Show the order of the set of integers on a number line with both positive and negative numbers (e.g., organize the given birth years of the following Arabic kings on a number line).

Comparing and Ordering Integers
Real Number Line - Activity A

4.2.2: Apply communication skills to clearly and effectively express or present ideas and situations using mathematical language or notation.

4.2.2.a: Articulate various strategies used during estimation involving fractions and decimals.

Estimating Sums and Differences

4.2.2.c: Use an appropriate representation to display data (e.g., table, graphs) given a particular situation and audience.

Describing Data Using Statistics

5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

5.1: Relate concepts and procedures within mathematics.

5.1.1: Apply concepts and procedures from a variety of mathematical areas in a given problem or situation.

5.1.1.a: Translate a situation involving multiple arithmetic operations into algebraic form using equation, table, and graphs.

Distance-Time Graphs
Using Tables, Rules and Graphs

5.1.1.b: Given a set of data, compare various representations (e.g., table, graph, rule) for a given situation.

Populations and Samples

5.1.2: Apply different mathematical models and representations to the same situation.

5.1.2.a: Represent equivalent ratios or given percentages using objects, pictures, and symbols.

Part:Part and Part:Whole Ratios
Percents, Fractions and Decimals
Polling: Neighborhood

5.2: Relate mathematical concepts procedures to other disciplines.

5.2.1: Analyze mathematical patterns and ideas to extend mathematical thinking and modeling to other disciplines.

5.2.1.b: Show the order of the set of integers on a number line with both positive and negative numbers (e.g., organize and graph on a number line the given birth years of the given Arabic kings).

Comparing and Ordering Integers
Real Number Line - Activity A

5.2.1.c: Read a micrometer to the nearest hundredth of an inch or centimeter, depending on the tool.

Triple Beam Balance

5.3: Relate mathematical concepts and procedures to real-world situations.

5.3.1: Understand that mathematics is used in daily life and extensively outside the classroom.

5.3.1.a: Write and solve real-world problem situations to find sums or differences of decimals or fractions (e.g., explain how to find the change received from a $50.00 bill when a given amount of CD's and tapes with prices are bought).

Fractions with Unlike Denominators
Sums and Differences with Decimals