NS: Number Sense

NS.1: Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers:

NS.1.2: Order and compare whole numbers and decimals to two decimal places.

Adding Decimals (Base-10 Blocks)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

NS.1.3: Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.

Rounding Whole Numbers (Number Line)

NS.1.4: Decide when a rounded solution is called for and explain why such a solution may be appropriate.

Rounding Whole Numbers (Number Line)

NS.1.5: Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see Standard 4).

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

NS.1.7: Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

NS.1.9: Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Fractions (Area Models)
Treasure Hunter (Decimals on the Number Line)

NS.2: Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals:

NS.2.1: Estimate and compute the sum or difference of whole numbers and positive decimals to two places.

Adding Decimals (Base-10 Blocks)
Subtracting Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)

NS.3: Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations:

NS.3.1: Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.

Cargo Captain (Multi-digit Subtraction)
Number Line Frog Hop (Addition and Subtraction)

NS.3.2: Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results.

Function Machines 3 (Functions and Problem Solving)

NS.4: Students know how to factor small whole numbers:

NS.4.1: Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)

NS.4.2: Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

Factor Trees (Factoring Numbers)

AF: Algebra and Functions

AF.1: Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences:

AF.1.5: Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given.

Road Trip (Problem Solving)

MG: Measurement and Geometry

MG.1: Students understand perimeter and area:

MG.1.1: Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm²), square meter (m²), square kilometer (km²), square inch (in²), square yard (yd²), or square mile (mi²).

Fido's Flower Bed (Perimeter and Area)

MG.1.2: Recognize that rectangles that have the same area can have different perimeters.

Fido's Flower Bed (Perimeter and Area)

MG.1.3: Understand that rectangles that have the same perimeter can have different areas.

Fido's Flower Bed (Perimeter and Area)

MG.1.4: Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.

Fido's Flower Bed (Perimeter and Area)

MG.2: Students use two-dimensional coordinate grids to represent points and graph lines and simple figures:

MG.2.1: Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line).

Function Machines 2 (Functions, Tables, and Graphs)

MG.2.2: Understand that the length of a horizontal line segment equals the difference of the x-coordinates.

City Tour (Coordinates)

MG.2.3: Understand that the length of a vertical line segment equals the difference of the y-coordinates.

City Tour (Coordinates)

MG.3: Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems:

MG.3.2: Identify the radius and diameter of a circle.

Measuring Trees

MG.3.4: Identify figures that have bilateral and rotational symmetry.

Quilting Bee (Symmetry)

SDAP: Statistics, Data Analysis, and Probability

SDAP.1: Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings:

SDAP.1.1: Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

SDAP.1.2: Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets.

Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

SDAP.1.3: Interpret one- and two-variable data graphs to answer questions about a situation.

Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

SDAP.2: Students make predictions for simple probability situations:

SDAP.2.2: Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3 /4).

Spin the Big Wheel! (Probability)

MR: Mathematical Reasoning

MR.1: Students make decisions about how to approach problems:

MR.1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

Pattern Flip (Patterns)

MR.2: Students use strategies, skills, and concepts in finding solutions:

MR.2.1: Use estimation to verify the reasonableness of calculated results.

Target Sum Card Game (Multi-digit Addition)

MR.3: Students move beyond a particular problem by generalizing to other situations:

MR.3.1: Evaluate the reasonableness of the solution in the context of the original situation.

Reaction Time 2 (Graphs and Statistics)