### 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.

#### 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.

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

#### 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.

### 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.

#### 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.

#### 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).

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

### 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.

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

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.

#### 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.

#### 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.

#### 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.

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

3.6.c: Make predictions based on theoretical 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.

### 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).

#### 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.

#### 4.4: Solve problems using coordinate geometry.

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

#### 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).

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

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

#### 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.

### 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).

#### 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).

#### 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).

#### 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).

### 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.

#### 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.

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

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

#### 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.

Correlation last revised: 1/24/2009

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