4.OA: Operations and Algebraic Thinking

1.1: Use the four operations with whole numbers to solve problems.

4.OA.1: Use and interpret multiplicative equations.

4.OA.1.a: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal or written 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, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), and distinguish multiplicative comparison from additive comparison.

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

4.OA.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. 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)

1.2: Gain familiarity with factors and multiples.

4.OA.4: Using whole number in the range 1–100.

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

4.OA.4.a: Find all factor pairs for a given whole number.

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

4.OA.4.b: Recognize that a whole number is a multiple of each of its factors.

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

4.OA.4.c: Determine whether a given whole number is a multiple of each of a given one-digit number.

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

4.OA.4.d: Determine whether a given whole number is prime or composite.

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

1.3: Generate and analyze 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.

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

4.NBT: Number and Operation in Base Ten

2.1: Generalize place value understanding for multi-digit whole numbers.

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.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

4.NBT.2: Read and write multi-digit whole numbers.

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

4.NBT.2.a: Read and write multi-digit whole numbers using base-ten numerals (standard form), number names (word form), and expanded form.

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

4.NBT.2.b: Compare two multi-digit numbers based on values of the digits in each place, using <, >, and = symbols to record the results of comparisons.

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

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

Rounding Whole Numbers (Number Line)

2.2: Use place value understanding and properties of operations to perform multi-digit arithmetic.

4.NBT.4: Fluently add and subtract multi-digit whole numbers using an algorithm including, but not limited to, the standard algorithm.

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

4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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

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)
Pattern Flip (Patterns)

4.NF: Number and Operations—Fractions

3.1: Extend understanding of fraction equivalence and ordering.

4.NF.1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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, 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 <, >, =, and justify the conclusions.

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)

3.2: 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.

4.NF.3.a: Add and subtract of fractions e.g., joining and separating parts referring to the same whole.

Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

4.NF.3.b: Decompose a fraction into a sum of fractions with like denominators in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., 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, e.g., 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, e.g., by using visual fraction models and equations to represent the problem.

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)

3.3: Understand decimal notation for fractions, and compare decimal fractions.

4.NF.6: Read and write decimal notation for fractions with denominators 10 or 100. Locate these decimals on a number line.

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.

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

4.1: Solving 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 one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. 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, including problems involving fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Elapsed Time
Road Trip (Problem Solving)

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

Chocomatic (Multiplication, Arrays, and Area)

4.3: Geometric measurement: understand concepts of angle and measure angles.

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

Polygon Angle Sum

4.G: Geometry

5.1: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

4.G.1: Draw points, lines, line segments, rays, angles (right, acute, 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, and identify categories of right, acute, and obtuse triangles.

Classifying Quadrilaterals

4.G.3: Recognize and draw lines of symmetry for two-dimensional figures.

Quilting Bee (Symmetry)