1: Number and Operations

1.1: Develop an understanding of multiplication and division concepts and strategies for basic multiplication facts and related division facts.

1.1.1: Develop concepts of multiplication and division through the use of different representations (e.g. equal-sized groups, arrays, area models, and skip counting on number lines for multiplication, and successive subtraction, partitioning, and sharing for division).

Chocomatic (Multiplication, Arrays, and Area)
Multiplying Decimals (Area Model)
No Alien Left Behind (Division with Remainders)

1.1.2: Use commutative, associative, and distributive properties to develop strategies and generalizations to solve multiplication problems. These strategies will evolve from simple strategies (e.g. times 0, times 1, doubles, count by fives) to more sophisticated strategies, such as splitting the array.

Chocomatic (Multiplication, Arrays, and Area)

1.1.3: Relate multiplication and division as inverse operations and learn division facts by relating them to the appropriate multiplication facts.

Factor Trees (Factoring Numbers)
Function Machines 3 (Functions and Problem Solving)

1.1.4: Consider the context in which a problem is situated to select the most useful form of the quotient for the solution, and they interpret it appropriately.

No Alien Left Behind (Division with Remainders)

1.1.5: Be able to make comparisons involving multiplication and division, using such words as "twice as many" or "half as many".

Multiplying Decimals (Area Model)
No Alien Left Behind (Division with Remainders)

1.2: Develop fluency and quick recall of multiplication facts and related division facts and fluency with multi-digit multiplication and division.

1.2.1: Extend their work with multiplication and division strategies to develop fluency and recall of multiplication and division facts.

Factor Trees (Factoring Numbers)

1.2.2: Apply their understanding of models for multiplication (i.e. equal-sized groups, arrays, area models), place value, and properties of operations (in particular, the distributive property) as they develop, discuss, and use efficient, accurate, and generalizable methods to multiply multidigit whole numbers.

Cannonball Clowns (Number Line Estimation)
Chocomatic (Multiplication, Arrays, and Area)
Number Line Frog Hop (Addition and Subtraction)

1.2.3: Apply their understanding of models for division (partitioning, successive subtraction) place value, properties, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multidigit dividends.

Function Machines 3 (Functions and Problem Solving)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)

1.3: Develop the ability to estimate the results of computation with whole numbers, fractions or decimals and be able to judge reasonableness.

1.3.1: Generalize patterns of multiplying and dividing whole numbers by 10, 100, and 1000 and develop understandings of relative size of numbers.

Pattern Flip (Patterns)

1.3.2: Be able to estimate sums and differences with whole numbers up to three digits.

Target Sum Card Game (Multi-digit Addition)

1.3.4: Select and apply appropriate strategies (mental computation, number sense and estimation) for estimating products and quotients or determining reasonableness of results, depending on the context and numbers involved.

No Alien Left Behind (Division with Remainders)
Target Sum Card Game (Multi-digit Addition)

1.3.5: Make reasonable estimates of fraction and decimal sums and differences.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Measuring Motion
Subtracting Decimals (Base-10 Blocks)

1.4: Extend place value concepts to represent and compare both whole numbers and decimals.

1.4.1: Extend their understanding of place value to numbers up to 10,000, 100,000 and millions in various contexts and depending on grade level.

Cannonball Clowns (Number Line Estimation)
Modeling Decimals (Base-10 Blocks)

1.4.2: Understand decimal notation as an extension of the base-ten system of writing whole numbers through place-value patterns and models (place-value charts and base-ten blocks) from tenths to hundredths and thousandths, depending on grade level.

Modeling Decimals (Area and Grid Models)
Modeling Decimals (Base-10 Blocks)

1.5: Use benchmarks to help develop number sense.

1.5.2: Learn about the position of numbers in the base-ten number system (763 is 7 x 100 plus 6 x 10 plus 3 x 1) and its relationship to benchmarks such as 500, 750, 800 and 1000.

Cannonball Clowns (Number Line Estimation)
Modeling Decimals (Base-10 Blocks)

1.5.4: Understand and use common benchmarks such as 1/2 or 1 to compare fractions.

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)

1.6: Develop an understanding of commonly used fractions, decimals, and percents, including recognizing and generating equivalent representations.

1.6.1: Develop an understanding of the meanings and uses of fractions to represent parts of a whole, parts of a set, or points or distances 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)
Toy Factory (Set Models of Fractions)

1.6.2: Understand that the size of a fractional part is relative to the size of the whole, and use fractions to represent numbers that are equal to, less than, or greater than 1.

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)

1.6.3: Solve problems that involve comparing and ordering fractions by using models, benchmark fractions, or strategies involving common numerators or denominators.

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)
Toy Factory (Set Models of Fractions)

1.6.4: Understand and use models, including the number line, to identify equivalent fractions including numbers greater than one.

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)

1.6.5: Connect and extend their understanding of fractions to modeling, reading and writing decimals (tenths, hundredth and thousandths), that are greater than or less than 1, identifying equivalent decimals, and comparing and ordering decimals. Connect fractions (initially halves, fourths, and tenths, and then fifths, thirds, and eighths) and their equivalent decimals through representations including word names, symbols and models (10 x 10 grids and number lines).

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Decimals (Base-10 Blocks)

1.6.6: Recognize and generate equivalent forms of commonly used fractions, decimals and percents.

Fraction, Decimal, Percent (Area and Grid Models)

1.7: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.

1.7.1: Apply their understandings of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators.

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)
Toy Factory (Set Models of Fractions)

1.7.2: Apply their understandings of decimal models, place value, and properties to develop strategies to add and subtract fractions and decimals.

Adding Fractions (Fraction Tiles)
Chocomatic (Multiplication, Arrays, and Area)

1.7.3: Develop fluency with standard procedures for adding and subtracting fractions and decimals.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Subtracting Decimals (Base-10 Blocks)

1.7.4: Add and subtract fractions and decimals to solve problems and use number sense to determine reasonableness of results.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Subtracting Decimals (Base-10 Blocks)

2: Algebra

2.1: Represent and analyze patterns and relationships involving multiplication and division to introduce multiplicative reasoning.

2.1.1: Build a foundation using multiplicative contexts for later understanding of functional relationships with such statements as, "The number of legs is 4 times the number of chairs" or "A quarter is five times the value of a nickel."

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

2.1.2: Make generalizations by reasoning about the structure of the pattern to determine if the patterns are nonnumeric growing, repeating, or multiplicative patterns.

Pattern Flip (Patterns)

2.2: Identify the commutative, associative, and distributive properties and use them to compute with whole numbers.

2.2.1: Explore the commutative and associative properties through models and examples to determine which properties hold for multiplication and division facts and develop increasingly sophisticated strategies based on these properties and the distributive property to solve multiplication problems involving basic facts.

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

2.2.2: Use properties of addition and multiplication to multiply and divide whole numbers and understand why these algorithms work.

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

2.3: Understand and apply the idea of a variable as an unknown quantity and express mathematical relationships using equations.

2.3.2: Develop an understanding of the use of a rule to describe a sequence of numbers or objects.

Pattern Flip (Patterns)

2.4: Represent and analyze patterns and functions, using words, tables, and graphs.

2.4.1: Describe patterns verbally and represent them with tables or symbols.

Pattern Flip (Patterns)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

2.4.2: Continue to identify, describe, and extend numeric patterns involving all operations and nonnumeric growing or repeating patterns.

Pattern Flip (Patterns)

2.4.3: Identify patterns graphically, numerically, or symbolically and use this information to predict how patterns will continue.

Pattern Flip (Patterns)

2.4.5: Be able to use various techniques including words, tables, numbers and symbols for organizing and expressing ideas about relationships and functions.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

3: Geometry and Measurement

3.3: Predict and describe the results of sliding (translation), flipping (reflection), and turning (rotation) two-dimensional shapes.

3.3.1: Investigate, describe, and reason about decomposing, combining, and transforming polygons to make other polygons.

Quilting Bee (Symmetry)
Rock Art (Transformations)

3.3.2: Investigate and describe line and rotational symmetry.

Quilting Bee (Symmetry)

3.3.3: Extend their understanding of two-dimensional space by using transformations to design and analyze simple tilings and tessellations.

Quilting Bee (Symmetry)
Rock Art (Transformations)

3.4: Use ordered pairs on a coordinate grid to describe points or paths (first quadrant).

3.4.1: Learn how to use two numbers to name points on a coordinate grid and know this ordered pair corresponds to a particular point on the grid.

City Tour (Coordinates)

3.4.2: Make and use coordinate systems to specify locations and to describe paths.

City Tour (Coordinates)

3.5: Use geometric models to solve problems, such as determining perimeter, area, volume, and surface area.

3.5.1: Develop measurement concepts and skills through experiences in analyzing attributes and properties of two- and three-dimensional objects.

Measuring Motion

3.5.4: Connect area measure to the area model that has been used to represent multiplication, and use this connection to justify the formula for the area of a rectangle.

Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

3.5.8: Develop strategies to determine the volumes of prisms by layering.

Balancing Blocks (Volume)

3.6: Select and apply appropriate standard (customary and metric) units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.

3.6.1: Select appropriate units, strategies, and tools to solve problems that involve estimating and measuring perimeter, area and volume.

Fido's Flower Bed (Perimeter and Area)

3.6.2: Develop facility in measuring with fractional parts of linear units.

Measuring Motion
Measuring Trees

3.6.4: Understand that a cube that is 1 unit on an edge is the standard unit for measuring volume.

Balancing Blocks (Volume)
Measuring Motion

3.7: Select and use benchmarks (1/2 inch, 2 liters, 5 pounds, etc.) to estimate measurements.

3.7.1: Develop strategies for estimating measurements using appropriate benchmarks, both standard units such as 1 foot and nonstandard units such as the length a book.

Measuring Motion

3.7.2: Learn to use strategies involving multiplicative reasoning to estimate measurements (i.e. estimating their teacher?s height to be one and a quarter times the student?s own height).

Measuring Motion

3.7.3: Estimate angle measure using a right angle as the benchmark.

Measuring Motion

4: Data Analysis and Probability

4.1: Represent and analyze data using tallies, pictographs, tables, line plots, bar graphs, circle graphs and line graphs.

4.1.1: Recognize the differences representing categorical and numerical data.

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

4.1.2: Construct and analyze frequency tables, bar graphs, picture graphs, and line plots and use them to address a question.

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)

4.1.3: Compare different representations of the same data and evaluate how well each representation shows important aspects of the data.

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

4.1.4: Use their understanding of whole numbers, fractions, and decimals to construct and analyze circle graphs and line graphs.

Elevator Operator (Line Graphs)
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.1.5: Apply their understanding of place value to develop and use stem-and-leaf plots.

Cannonball Clowns (Number Line Estimation)
Modeling Decimals (Base-10 Blocks)

4.2: Describe the distribution of the data using mean, median, mode or range.

4.2.1: Learn to compare related data sets, noting the similarities and differences between the two sets and develop the idea of a "average" value.

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

4.2.2: Learn to select and use measures of center: mean, median and mode and apply them to describing data sets.

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

4.2.3: Build an understanding of what the measures of center tells them about the data and to see this value in the context of other characteristics of the data such as the range.

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

4.2.4: Begin to conceptually explore the meaning of mean as the balance point for the data set.

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

4.3: Propose and justify conclusions and predictions based on data.

4.3.2: Learn to collect data using observations, surveys and experiments and propose conjectures.

Graphing Skills
Histograms
Mascot Election (Pictographs and Bar Graphs)
Populations and Samples

4.3.4: Design investigations to address a question and consider how data collection methods affect the nature of the data set.

Probability Simulations
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Theoretical and Experimental Probability

4.4: Predict the probability of simple experiments and test predictions.

4.4.1: Examine the probability of experiments that have only a few outcomes, such as game spinners (i.e., how likely is it that the spinner will land on a particular color?), by first predicting the probability of the desired event and then exploring the outcome through experimental probability.

Spin the Big Wheel! (Probability)

4.4.2: Learn to represent the probability of a certain event as 1 and the probability of an impossible event as 0.

Histograms
Spin the Big Wheel! (Probability)

4.4.3: Learn to use common fractions to represent events that are neither certain nor impossible.

Spin the Big Wheel! (Probability)

4.5: Describe events as likely or unlikely and discuss the degree of likelihood using words like certain, equally likely and impossible.

4.5.1: Understand probability as the measurement of the likelihood of events.

Spin the Big Wheel! (Probability)

4.5.2: Learn to estimate the probability of events as certain, equally likely or impossible by designing simple experiments to collect data and draw conclusions.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Histograms
Permutations
Permutations and Combinations
Reaction Time 2 (Graphs and Statistics)

4.3.1: Learn how to describe data, make a prediction to describe the data, and then justify their predictions.

Polling: City
Polling: Neighborhood

4.3.3: Design simple experiments to examine their conjectures and justify their conclusions.

Geometric Probability - Activity A
Polling: City
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.5.3: Estimate the probability of simple and compound events through experimentation and simulation.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.5.4: Use a variety of experiments to explore the relationship between experimental and theoretical probabilities and the effect of sample size on this relationship.

Geometric Probability - Activity A
Polling: City
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability