A: Number and Operations

A.1: Students will understand numerical concepts and mathematical operations

A.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

A.1.1.1: Exhibit an understanding of the place-value structure of the base-ten number system by:

A.1.1.1.a: reading, modeling, writing, and interpreting whole numbers up to 10,000

Modeling Decimals (Base-10 Blocks)

A.1.1.1.b: comparing and ordering numbers up to 1,000

Fraction Garden (Comparing Fractions)

A.1.1.1.c: recognizing the position of a given number in the base-ten number system and its relationship to benchmark numbers such as 10, 50, 100, 500

Modeling Decimals (Base-10 Blocks)

A.1.1.2: Use whole numbers by using a variety of contexts and models (e.g., exploring the size of 1,000 by skip-counting to 1,000 using hundred charts or strips 10 or 100 centimeters long).

Modeling Decimals (Base-10 Blocks)

A.1.1.4: Identify the relationship among commonly encountered factors and multiples (e.g., factor pairs of 12 are 1 x 12, 2 x 6, 3 x 4; multiples of 12 are 12, 24, 36).

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Pattern Flip (Patterns)

A.1.1.5: Use visual models and other strategies to recognize and generate equivalents of commonly used fractions and mixed numbers (e.g., halves, thirds, fourths, sixths, eighths, and tenths).

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

A.1.1.6: Demonstrate an understanding of fractions as parts of unit wholes, parts of a collection or set, and as locations on a number line.

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)
Toy Factory (Set Models of Fractions)

A.1.1.7: Use common fractions for measuring and money (e.g., using fractions and decimals as representations of the same concept, such as half of a dollar = 50 cents)

Modeling Decimals (Area and Grid Models)

A.1.2: Understand the meaning of operations and how they relate to one another.

A.1.2.1: Use a variety of models to show an understanding of multiplication and division of whole numbers (e.g., charts, arrays, diagrams, and physical models [i.e., modeling multiplication with a variety of pictures, diagrams, and concrete tools to help students learn what the factors and products represent in various contexts]).

Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)

A.1.2.2: Find the sum or difference of two whole numbers between 0 and 10,000.

Adding Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)

A.1.2.3: Solve simple multiplication and division problems (e.g., 135 ÷.(ٱ= 5

Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
Multiplying Decimals (Area Model)
No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

A.1.2.4: Identify how the number of groups and the number of items in each group equals a product.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
Multiplying Decimals (Area Model)

A.1.2.5: Demonstrate the effects of multiplying and dividing on whole numbers (e.g., to find the total number of legs on 12 cats, 4 represents the number of each [cat] unit, so 12 x 4 = 48 [leg] units).

Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
Multiplying Decimals (Area Model)
No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

A.1.3: Compute fluently and make reasonable estimates.

A.1.3.1: Choose computational methods based on understanding the base-ten number system, properties of multiplication and division, and number relationships.

Factor Trees (Factoring Numbers)
No Alien Left Behind (Division with Remainders)

A.1.3.2: Use strategies (e.g., 6 x 8 is double 3 x 8) to become fluent with the multiplication pairs up to 10 x 10.

Factor Trees (Factoring Numbers)

A.1.3.4: Demonstrate reasonable estimation strategies for measurement, computation, and problem solving.

Cannonball Clowns (Number Line Estimation)
Multiplying Decimals (Area Model)

B: Algebra

B.1: Students will understand algebraic concepts and applications.

B.1.1: Understand patterns, relations, and functions.

B.1.1.5: Recognize and use the commutative property of multiplication (e.g., if 5 x 7 = 35, then what is 7 x 5?).

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)

B.1.1.6: Create, describe, and extend numeric and geometric patterns including multiplication patterns.

Function Machines 1 (Functions and Tables)
Pattern Flip (Patterns)

B.1.1.7: Represent simple functional relationships:

B.1.1.7.a: solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit)

Function Machines 1 (Functions and Tables)

B.1.2: Represent and analyze mathematical situations and structures using algebraic symbols.

B.1.2.2: Recognize and use the commutative and associative properties of addition and multiplication (e.g., "If 5 x 7 = 35, then what is 7 x 5? And if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?").

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)

B.1.2.3: Explore the ways that commutative, distributive, identity, and zero properties are useful in computing with numbers.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)

B.1.3: Use mathematical models to represent and understand quantitative relationships.

B.1.3.1: Model problem situations with objects and use representations such as pictures, graphs, tables, and equations to draw conclusions.

Graphing Skills

C: Geometry

C.1: Students will understand geometric concepts and applications.

C.1.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

C.1.1.1: Describe and compare the attributes of plane and solid geometric figures to show relationships and solve problems:

C.1.1.1.a: identify, describe, and classify polygons (e.g., pentagons, hexagons, and octagons)

Classifying Quadrilaterals

C.1.1.1.b: identify lines of symmetry in two-dimensional shapes

Quilting Bee (Symmetry)

C.1.1.1.c: explore attributes of quadrilaterals (e.g., parallel and perpendicular sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square)

Classifying Quadrilaterals

C.1.1.1.d: identify right angles

Classifying Quadrilaterals

C.1.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

C.1.2.2: Use ordered pairs to graph, locate specific points, create paths, and measure distances within a coordinate grid system.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

C.1.3: Apply transformations and use symmetry to analyze mathematical situations.

C.1.3.1: Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.

Rock Art (Transformations)

C.1.3.2: Identify and describe the line of symmetry in two- and three-dimensional shapes.

Quilting Bee (Symmetry)

D: Measurement

D.1: Students will understand measurement systems and applications.

D.1.1: Understand measurable attributes of objects and the units, systems, and process of measurement.

D.1.1.3: Identify time to the nearest minute (elapsed time) and relate time to everyday events.

Elapsed Time

D.1.2: Apply appropriate techniques, tools, and formulas to determine measurements.

D.1.2.2: Estimate measurements.

Cannonball Clowns (Number Line Estimation)

E: Data Analysis and Probability

E.1: Students will understand how to formulate questions, analyze data, and determine probabilities.

E.1.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

E.1.1.1: Collect and organize data using observations, measurements, surveys, or experiments.

Graphing Skills
Reaction Time 2 (Graphs and Statistics)

E.1.1.2: Represent data using tables and graphs (e.g., line plots, bar graphs, and line graphs).

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)

E.1.1.3: Conduct simple experiments by determining the number of possible outcomes and make simple predictions:

E.1.1.3.a: identify whether events are certain, likely, unlikely, or impossible

Spin the Big Wheel! (Probability)

E.1.1.3.b: record the outcomes for a simple event and keep track of repetitions

Spin the Big Wheel! (Probability)

E.1.1.3.d: use the results to predict future events

Spin the Big Wheel! (Probability)

E.1.2: Select and use appropriate statistical methods to analyze data.

E.1.2.1: Apply and explain the uses of sampling techniques (e.g., observations, polls, tally marks) for gathering data.

Reaction Time 2 (Graphs and Statistics)

E.1.4: Understand and apply basic concepts of probability.

E.1.4.1: Discuss the degree of likelihood of events and use terminology such as "certain," "likely," "unlikely".

Spin the Big Wheel! (Probability)