4.MP: Mathematical Practices

(Framing Text): Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes

4.MP.1: Make sense of problems and persevere in solving them.

Biconditional Statements
Conditional Statements
Estimating Population Size
Pattern Flip (Patterns)

4.MP.1.a: Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. When a solution pathway does not make sense, look for another pathway that does. Explain connections between various solution strategies and representations. Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Improper Fractions and Mixed Numbers
Linear Inequalities in Two Variables
Modeling One-Step Equations
Multiplying with Decimals
Pattern Flip (Patterns)
Polling: City
Solving Equations on the Number Line
Using Algebraic Expressions

4.MP.2: Reason abstractly and quantitatively.

Conditional Statements
Estimating Population Size

4.MP.3: Construct viable arguments and critique the reasoning of others.

Biconditional Statements

4.MP.3.a: Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.

Biconditional Statements
Conditional Statements

4.MP.4: Model with mathematics.

Estimating Sums and Differences

4.MP.5: Use appropriate tools strategically.

Elapsed Time

4.MP.5.a: Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.

Segment and Angle Bisectors

4.MP.6: Attend to precision.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Using Algebraic Expressions

4.MP.6.a: Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.

Arithmetic Sequences
Finding Patterns
Fraction, Decimal, Percent (Area and Grid Models)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

4.MP.7: Look for and make use of structure.

Pattern Flip (Patterns)

4.MP.7.a: Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.

Arithmetic Sequences
Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

4.MP.8: Look for and express regularity in repeated reasoning.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Pattern Finder
Pattern Flip (Patterns)

4.MP.8.a: Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

4.OA: Operations and Algebraic Thinking

(Framing Text): Use the four operations with whole numbers (addition, subtraction, multiplication, and division) to solve problems.

4.OA.1: Interpret a multiplication equation as a comparison (for example, interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations.

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

4.OA.2: Multiply or divide to solve word problems involving multiplicative comparison, for example, by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

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

4.OA.3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.

Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)

4.OA.3.a: Represent these problems using equations with a letter standing for the unknown quantity.

Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)

4.OA.3.b: Assess the reasonableness of answers using mental computation and estimation strategies, including rounding.

Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)

(Framing Text): Gain familiarity with factors and multiples.

4.OA.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Factor Trees (Factoring Numbers)

(Framing Text): Generate and analyze numeric and shape patterns.

4.OA.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Finding Patterns
Pattern Flip (Patterns)

4.NBT: Number and Operations in Base Ten

(Framing Text): Generalize place value understanding for multi-digit whole numbers by analyzing patterns, writing whole numbers in a variety of ways, making comparisons, and rounding.

4.NBT.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Cannonball Clowns (Number Line Estimation)
Whole Numbers with Base-10 Blocks

4.NBT.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Cannonball Clowns (Number Line Estimation)

4.NBT.3: Use place value understanding to round multi-digit whole numbers to any place.

Rounding Whole Numbers (Number Line)

(Framing Text): Use place value understanding and properties of operations to perform multi-digit addition, subtraction, multiplication, and division using a one-digit divisor.

4.NBT.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Cargo Captain (Multi-digit Subtraction)
Target Sum Card Game (Multi-digit Addition)
Whole Numbers with Base-10 Blocks

4.NBT.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

No Alien Left Behind (Division with Remainders)

4.NF: Number and Operations—Fractions

(Framing Text): Extend understanding of equivalence and ordering of fractions.

4.NF.1: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
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)

4.NF.2: Compare two fractions with different numerators and different denominators, for example, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, for example, by using a visual fraction model.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
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)

(Framing Text): Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.3: Understand a fraction a/b with a >1 as a sum of fractions 1/b. In other words, any fraction is a sum of unit fractions.

4.NF.3.a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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

4.NF.3.b: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, for example, by using a visual fraction model.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
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)

4.NF.3.c: Add and subtract mixed numbers with like denominators, for example, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Fractions Greater than One (Fraction Tiles)

4.NF.3.d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators,

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

4.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

4.NF.4.a: Understand a fraction a/b as a multiple of 1/b.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Modeling Fractions (Area Models)

4.NF.4.b: Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Modeling Fractions (Area Models)

(Framing Text): Understand decimal notation to the hundredths and compare decimal fractions with denominators of 10 and 100.

4.NF.6: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100, describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)

4.NF.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, for example, by using a visual model.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

4.MD: Measurement and Data

(Framing Text): Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

4.MD.1: Know relative sizes of measurement units within each system of units (standard and metric), including kilometers, meters, and centimeters; liters and milliliters; kilograms and grams; pounds and ounces; hours, minutes, and seconds. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

Cannonball Clowns (Number Line Estimation)

4.MD.2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money.

Elapsed Time
Road Trip (Problem Solving)

4.MD.2.a: Include problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Elapsed Time
Road Trip (Problem Solving)
Toy Factory (Set Models of Fractions)

4.MD.2.b: Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Elapsed Time
Road Trip (Problem Solving)

(Framing Text): Apply knowledge of area and perimeter to solve real-world and mathematical problems.

4.MD.3: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

Chocomatic (Multiplication, Arrays, and Area)

(Framing Text): Understand various concepts of angles and angle measurement.

4.MD.7: Recognize angle measure as additive.

Polygon Angle Sum

4.MD.7.a: Understand that when an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.

Polygon Angle Sum

4.MD.7.b: Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, for example by using an equation with a symbol for the unknown angle measure.

Polygon Angle Sum

4.G: Geometry

(Framing Text): Draw and identify lines and angles, as well as classify shapes by properties of their lines and angles.

4.G.1: Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

City Tour (Coordinates)
Classifying Quadrilaterals
Elevator Operator (Line Graphs)

4.G.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions

4.G.3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Quilting Bee (Symmetry)