1: Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

1.1: Demonstrate meanings for integers, rational numbers, percents, exponents, square roots and pi using physical materials and technology in problem-solving situations.

1.1.a: Recognize and use equivalent representations of positive rational numbers.

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

1.2: Read, write and order integers, rational numbers and common irrational numbers such as square root of 2, square root of 5, and pi.

1.2.a: Read, write, order and compare positive rational numbers and integers.

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

1.2.b: Locate positive rational numbers and integers on a number line.

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
Real Number Line - Activity A

1.4: Use the relationships among fractions, decimals, and percents, including the concepts of ratio and proportion, in problem-solving situations.

1.4.a: Use the relationships among fractions, decimals and percents. including the concepts of ratio and proportion, in problem-solving situations.

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

2: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.

2.1: Represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation.

2.1.a: Represent, describe, and analyze numeric or geometric patterns involving common positive rational numbers or integers using tables, graphs, rules, or symbols.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.3: Analyze functional relationships to explain how a change in one quantity results in a change in another (for example, how the area of a circle changes as the radius increases, or how a person's height changes over time).

2.3.a: Predict and describe how a change in one quantity results in a change in another quantity in a linear relationship.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

2.5: Solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, and graphical) and a variety of tools (physical materials, calculators, and computers).

2.5.a: Solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, or graphic).

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

2.5.b: Translate written words to algebraic expressions/equations and conversely, algebraic expressions/equations to words.

Using Algebraic Equations

3: Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.

3.1: Read and construct displays of data using appropriate techniques (for example, line graphs, circle graphs, scatter plots, box plots, stem-and-leaf plots) and appropriate technology.

3.1.a: Construct a histogram or stem and leaf from a set of given data.

Histograms
Populations and Samples
Stem-and-Leaf Plots

3.1.b: Read, interpret and draw conclusions from histograms, circle graphs, stem and leaf plots, and scatter plots.

Correlation
Histograms
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

3.2: Display and use measures of central tendency, such as mean, median and mode and measures of variability, such as range and quartiles.

3.2.a: Given a display of data (for example, line plot, stem and leaf plot, list of data), determine the mean, mode, median and range.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Stem-and-Leaf Plots

3.3: Evaluate arguments that are based on statistical claims.

3.3.a: Evaluate arguments that are based on measures of central tendency or data displays.

Mean, Median and Mode

3.4: Formulate hypotheses, drawing conclusions, and making convincing arguments based on data analysis.

3.4.a: Analyze data and draw conclusions to predict outcomes based on data displays such as histograms and stem and leaf plots.

Histograms
Stem-and-Leaf Plots

3.6: Make predictions and compare results using both experimental and theoretical probability drawn from real-world problems.

3.6.a: Report the probability of an event in fraction, decimal and percent form.

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

3.6.b: Determine the probability of simple independent events (for example, tossing a coin and rolling a die).

Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Geometric Probability - Activity A
Independent and Dependent Events

3.6.c: Make predictions based on theoretical probability.

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

3.7: Using counting strategies to determine all the possible outcomes from an experiment (for example, the number of ways students can line up to have their picture taken).

3.7.a: Determine the number of possible outcomes from a given event using a variety of strategies, such as: tree diagrams, or organized lists.

Permutations and Combinations

4: Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.

4.2: Describe, analyze and reason informally about the properties (for example, parallelism, perpendicularity, congruence) of two- and three-dimensional figures.

4.2.a: Describe, analyze and reason informally about the attributes of two- and three-dimensional shapes (for example, angles, sides, edges, faces, vertices).

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

4.3: Apply the concept of ratio, proportion and similarity in problem-solving situations

4.3.a: Identify and compare similar shapes using ratio, proportion, or scale factor.

Similar Figures - Activity A

4.4: Solve problems using coordinate geometry.

4.4.a: Construct a coordinate graph and plot ordered integer pairs in all four quadrants.

Introduction to Functions
Points in the Coordinate Plane - Activity A

4.5: Solving problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions.

4.5.a: Solve problems involving the circumference of a circle (formulas not provided).

Circle: Circumference and Area

4.5.b: Solve problems involving the areas of circles, triangles, and parallelograms (formulas not provided).

Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

4.5.c: Solve problems involving the surface area of rectangular prisms (formulas not provided).

Surface and Lateral Area of Prisms and Cylinders

4.6: Transforming geometric figures using reflections, translations, and rotations to explore congruence.

4.6.a: Use reflections, translations, and/or rotations, to determine congruence between figures.

Constructing Congruent Segments and Angles
Reflections
Rotations, Reflections and Translations

5: Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.

5.3: Read and interpret various scales including those based on number lines, graphs, and maps.

5.3.a: Read and interpret scales on number lines, graphs and maps (for example, given a map and a scale, determine the distance between two points on the map).

Real Number Line - Activity A

5.4: Develop and use formulas and procedures to solve problems involving measurement.

5.4.a: Develop and use procedures or formulas to solve problems involving area of polygons (for example, trapezoids, regular hexagons, regular octagons).

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

5.5: Describe how a change in an object's linear dimensions affects its perimeter, area, and volume.

5.5.a: Describe how a change in an object’s linear dimensions affects its perimeter and area (for example, how a change in the radius or diameter will affect the circumference and area of a circle).

Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

5.6: Select and use appropriate units and tools to measure to the degree of accuracy required in a particular problemsolving situation.

5.6.a: Select and use appropriate units and tools to measure to the degree of accuracy required in a particular problemsolving situation (for example, reconstruct a replica of a given figure).

Triple Beam Balance

6: Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.

6.1: Use models to explain how ratios, proportions, and percents can be used to solve real-world problems.

6.1.a: Use concrete materials or pictures to explain how ratios, proportion, and percents can be used to solve real world problems.

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

6.2: Construct, use and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers.

6.2.a: Apply order of operations (including exponents with positive rational numbers.

Order of Operations

6.2.b: Add, subtract, multiply, and divide positive rational numbers or integers.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Order of Operations
Sums and Differences with Decimals

6.2.c: Explain strategies to add, subtract and multiply positive rational numbers.

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

6.3: Develop, apply and explain a variety of different estimation strategies in problem-solving situations, and explain why an estimate may be acceptable in place of an exact answer.

6.3.b: Solve problems using estimation and justify choice of techniques.

Estimating Population Size
Estimating Sums and Differences