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: Locate commonly used positive rational numbers including terminating decimals through hundredths, fractions (halves, thirds, fourths, eighths, and tenths), mixed numbers, and percents on a number line.

Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

1.1.b: Using physical materials or pictures to demonstrate the meaning and equivalence of fractions, decimals and/or percents (for example, write the fractions, decimal, and percent value for the shaded portion of a partially shaded circle).

Improper Fractions and Mixed Numbers

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

1.2.a: Read, write, order and compare common fractions, decimals, and percents in a variety of forms.

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

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

1.3.a: Identify and use the concepts of factor, multiple, prime, composite, and square numbers.

Finding Factors with Area Models

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

1.4.a: Demonstrate equivalence relationships among fractions, decimals and percents in problem-solving situations (for example, two students out of eight is the same as 25%)

Percents, Fractions and Decimals

1.6: Use number sense to estimate and justify the reasonableness of solutions to problems involving inteters, rational numbers, and common irrational numbers such as square root of 2, square root of 5 and pi.

1.6.a: Use number sense to estimate, determine, and justify the reasonableness of solutions involving whole numbers, decimals, and common fractions (only sums and differences for fractions and decimals). For example: Is 1/2 + 1/3 closer to 0, 1/2 or 1?

Fractions with Unlike Denominators
Sums and Differences with Decimals

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 geometric and numeric patterns using tables, words, symbols, concrete objects, or pictures.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.b: Use a variable to represent an unknown (letter, box, symbol).

Using Algebraic Equations

2.2: Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.

2.2.a: Solve problems by representing and analyzing patterns using tables, words, concrete objects, or pictures.

Arithmetic 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 (for example, A creature gains 3 oz. a day, how much will it have gained over 10 days?)

Distance-Time Graphs
Using Tables, Rules and Graphs

2.4: Distinguish between linear and nonlinear functions through informal investigations.

2.4.a: Explain whether data presented in a chart or graph is changing at a constant rate.

Distance-Time 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 problems using tables, concrete objects, or pictures involving linear relationships with whole numbers.

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

3.2: 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: Find and use measures of central tendency including mean, median, and mode.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

3.2.b: Find and use the range from a given set of data (for example, find the range from 2 to 12. Note: the range is 10).

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots

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

3.6.a: Using a chance device, such as a number cube or spinner, design a fair game and an unfair game, and explain why they are fair and unfair respectively.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

3.6.b: Make predictions based on data obtained from simple probability experiments.

Geometric Probability - Activity A
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).

3.7.a: Determine the number of possible outcomes for simple events using a variety of methods such as: organized lists or tree diagrams.

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: Identify, compare, and analyze the attributes of two-and three-dimensional shapes and develop vocabulary to describe the attributes (for example, acute, obtuse, right angle, parallel lines, perpendicular lines, intersecting lines, and line segments).

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

4.4: Solve problems using coordinate geometry.

4.4.a: Plot points on a coordinate graph in quadrant 1

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.b: Solve problems involving area of polygons (square, rectangle, parallelogram, rhombus, triangle)

Area of Parallelograms - Activity A

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

4.6.a: Identify congruent shapes using reflections, rotations, and translations.

Constructing Congruent Segments and Angles
Rotations, Reflections and Translations

4.6.b: Show lines of symmetry on a two-dimensional figure.

Holiday Snowflake Designer

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.

5.1.c: Estimate the area of a polygon.

Area of Parallelograms - Activity A

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

5.3.b: Select the appropriate scale for a given problem (for example, using the appropriate scale when setting up a graph or determining the order of numbers on a number line).

Real Number Line - Activity A

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

5.4.a: Use formulas and/or procedures to solve problems involving the perimeter of a polygon.

Rectangle: Perimeter and Area

5.4.b: Use formulas and/or procedures to solve problems involving the area of squares, rectangles, parallelograms, rhombus, and triangles.

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: Demonstrate how changing one of the dimensions of a rectangle or triangle affects its perimeter and area using concrete materials or graph paper.

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

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.

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

6.2.a: Demonstrate conceptual meaning of addition and subtraction of fractions and decimals, in problem solving situations.

Fractions with Unlike Denominators
Sums and Differences with Decimals

6.2.b: Use and explain strategies to add/subtract decimals and fractions in problem-solving situations (common fractions with like and unlike denominators, mixed numbers, and decimals to thousandth.)

Fractions with Unlike Denominators
Sums and Differences with Decimals

6.2.c: Find equivalent representations by decomposing and composing whole numbers (for example, 48 x 12 = (48 x 10) + (48 x 2)).

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and 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.a: 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.

Estimating Population Size
Estimating Sums and Differences

6.4: Select and use appropriate methods for computing with commonly used fractions and decimals, percents, and integers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator, and computer methods, and determining whether the results are reasonable.

6.4.a: Apply appropriate computation methods to solve problems involving whole numbers, common fractions, and decimals (use only addition and subtraction of fractions and decimals).

Adding Real Numbers
Adding and Subtracting Integers
Fractions with Unlike Denominators
Order of Operations
Sums and Differences with Decimals