### 1: Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, and symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.

#### 1.1: Number sense

1.1.1: Decompose and recompose whole numbers up to 10,000 using a variety of one, two- and three-digit combinations

1.1.2: Determine factor pairs that make up a given number

1.1.3: Develop an understanding of fractions as parts of unit wholes and division of whole numbers

1.1.4: Demonstrate equivalent forms of common fractions using physical models, pictures, and number lines

1.1.5: Compare and order fractions using physical models, pictures, and number lines

#### 1.2: Operations

1.2.2: Add and subtract larger numbers (e.g., three digits + two digits) and explain how the operation works

1.2.3: Demonstrate mastery of mental math strategies for multiplying numbers (e.g., 25 * 8)

1.2.4: Show how multiplication and division facts up to 50 are related, using arrays, skip counting, and area models

1.2.5: Master multiplication facts and the related division facts up to the 10s tables

1.2.7: Develop and use strategies to estimate the results of operations on whole numbers

1.2.8: Use physical models and pictures to add and subtract benchmark fractions

1.2.9: Find 1/3, 1/4, and 1/5 of a given set or area using models

1.2.11: Select and use appropriate methods and tools for computing (e.g., mental computation, estimation, calculators, paper and pencil) depending on the context and nature of the computation

### 2: Algebraic Reasoning: Students will develop Algebraic Reasoning and an understanding of Patterns and Functions by solving problems in which there is a need to recognize and extend a variety of patterns; to progress from the concrete to the abstract using physical models, equations, and graphs; to describe, represent, and analyze relationships among variable quantities; and to analyze, represent, model, and describe real-world functional relationships.

#### 2.1: Patterns and change

2.1.3: Interpret tables, graphs and real-world events based on how they change over time

#### 2.2: Representations

2.2.1: Model situations that involve the addition, subtraction, multiplication and division of whole numbers using objects, pictures, geometric model, and symbols

#### 2.3: Symbols

2.3.2: Develop an understanding of the Commutative and Associative Properties of whole number multiplication as a tool to solve problems (e.g., is 4 × 5 always the same as 5 × 4?)

### 3: Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree pf accuracy by selecting appropriate tools and units.

#### 3.1: Classification

3.1.1: Identify and classify two-dimensional and three-dimensional shapes according to their properties

#### 3.2: Location and transformation

3.2.1: Identify line and rotational symmetry in two-dimensional shapes

#### 3.3: Measurement

3.3.4: Find the distance around a geometric figure to the nearest whole number (perimeter)

3.3.5: Find the number of square units it takes to cover a rectangle (area)

3.3.6: Count the number of cubes it takes to fill a three-dimensional figure (volume)

3.3.8: Estimate and then measure the mass of an object to the nearest whole unit

### 4: Quantitative Reasoning: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.

#### 4.1: Collect

4.1.1: Pose questions that can be answered with data; systematically collect and organize both categorical and numerical data

#### 4.2: Represent

4.2.1: Construct and use data displays (e.g., tables, scaled pictographs, bar graphs, line plots) in order to answer a question

#### 4.3: Analyze

4.3.1: Describe a set of data as a whole, noting important features such as concentration of values, spread of the values, and extreme values

4.3.2: Find and use measures of center (mode and median) to summarize and interpret data

#### 4.4: Probability

4.4.1: Describe the outcomes of an experiment or event (e.g., possible/impossible, certain/uncertain, less likely/equally likely/more likely)

### G: Geometry

#### G.8: Students shall analyze characteristics and properties of 2 and 3 dimensional geometric shapes and develop mathematical arguments about geometric relationships.

G.8.5.1: Identify and model regular and irregular polygons including decagon

#### G.9: Students shall apply transformations and the use of symmetry to analyze mathematical situations.

G.9.5.1: Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchanged

#### G.10: Students shall specify locations and describe spatial relationships using coordinate geometry and other representational systems.

G.10.5.1: Use geometric vocabulary (horizontal/x-axis, vertical/ y-axis, ordered pairs) to describe the location and plot points in Quadrant I

### M: Measurement

#### M.12: Students shall use attributes of measurement to describe and compare mathematical and real-world objects.

M.12.5.5: Model the differences between covering the faces (surface area/nets) and filling the interior (volume of cubes)

#### M.13: Students shall identify and use units, systems and processes of measurement.

M.13.5.1: Solve real world problems involving one elapsed time, counting forward (calendar and clock)

M.13.5.3: Draw and measure distance to the nearest cm and ¼ inch accurately

M.13.5.4: Develop and use strategies to solve real world problems involving perimeter and area of rectangles

### DAP: Data Analysis and Probability

#### DAP.14: Students shall formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.

DAP.14.5.1: Develop appropriate questions for surveys

DAP.14.5.2: Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stem-and-leaf plots

DAP.14.5.3: Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs

#### DAP.15: Students shall select and use appropriate statistical methods to analyze data.

DAP.15.5.1: Interpret graphs such as line graphs, double bar graphs, and circle graphs

DAP.15.5.2: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data

#### DAP.17: Students shall understand and apply basic concepts of probability.

DAP.17.5.2: List and explain all possible outcomes in a given situation

M.13.4.9: Use strategies for finding the perimeter of a rectangle

M.13.4.10: Use strategies for finding the area of a rectangle

M.13.4.11: Use strategies to find the volume (cubic units) of rectangular prisms and cubes

DAP.14.4.1: Create a data collection plan after being given a topic and collect, organize, display, describe and interpret simple data using frequency tables or line plots, pictographs and bar graphs

DAP.15.4.1: Represent and interpret data using pictographs, bar graphs and line graphs in which symbols or intervals are greater than one

DAP.15.4.2: Match a set of data with a graphical representation of the data

DAP.17.4.2: Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcome (roll number cubes, pull tiles from a bag, spin spinner, or determine the fairness of the game)

Correlation last revised: 5/9/2018

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