### 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.

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).

#### 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.

#### 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.

#### 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%)

#### 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?

### 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.

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

#### 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.

#### 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?)

#### 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.

#### 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.

### 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.

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).

#### 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.

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

#### 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.

### 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).

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

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

#### 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)

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

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

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

### 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.

#### 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).

#### 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.

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

#### 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.

### 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.

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.)

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

#### 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.

#### 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).

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.