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 use physical materials and technology in problem-solving situations;

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Square Roots

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;

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values

1.3: apply number theory concepts (for example, primes, factors, multiples) to represent numbers in various ways;

Chocomatic (Multiplication, Arrays, and Area)

1.4: use the relationships among fractions, decimals, and percents, include the concepts of ratio and proportion, in problem-solving situations;

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Fraction, Decimal, Percent (Area and Grid Models)
Geometric Probability
Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Road Trip (Problem Solving)

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;

Pattern Flip (Patterns)

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);

Function Machines 1 (Functions and Tables)
Points, Lines, and Equations
Translating and Scaling Functions

2.4: distinguish between linear and nonlinear functions through informal investigations; and

Absolute Value with Linear Functions
Linear Functions

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

Solving Two-Step 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;

Box-and-Whisker Plots
Correlation
Distance-Time Graphs
Graphing Skills
Least-Squares Best Fit Lines
Mascot Election (Pictographs and Bar Graphs)
Prairie Ecosystem
Reaction Time 2 (Graphs and Statistics)
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter 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;

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

3.4: formulate hypotheses, draw conclusions, and make convincing arguments based on data analysis;

Polling: City
Polling: Neighborhood
Real-Time Histogram

3.5: determine probabilities through experiments or simulations;

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

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

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

3.7: use 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).

Probability Simulations

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 ;

Classifying Quadrilaterals
Rock Art (Transformations)

4.3: apply the concepts of ratio, proportion, and similarity in problem-solving situations;

Beam to Moon (Ratios and Proportions)
Circles
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

4.5: solve problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions; and

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

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

Dilations
Holiday Snowflake Designer
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
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.

5.1: estimate, use, and describe measures of distance, perimeter, area, volume, capacity, weight, mass, and angle comparison;

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Beam to Moon (Ratios and Proportions)
Cannonball Clowns (Number Line Estimation)
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Measuring Trees
Perimeter and Area of Rectangles
Pyramids and Cones

5.2: estimate, make, and use direct and indirect measurements to describe and make comparisons;

Cannonball Clowns (Number Line Estimation)
Estimating Population Size

5.4: develop and use formulas and procedures to solve problems involving measurement;

Area of Triangles

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

Perimeter and Area of Rectangles

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;

Direct and Inverse Variation
Estimating Population Size
Fraction, Decimal, Percent (Area and Grid Models)
Part-to-part and Part-to-whole Ratios

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

Fractions with Unlike Denominators
No Alien Left Behind (Division with Remainders)

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; and

Cannonball Clowns (Number Line Estimation)
Estimating Sums and Differences
Multiplying Decimals (Area Model)

6.4: select and use appropriate algorithms for computing with commonly used fractions and decimals, percents, and integers in problem-solving and determine whether the results are reasonable.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Dividing Mixed Numbers
Estimating Sums and Differences
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)