4.OA: Operations and Algebraic Thinking

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

4.OA.1.i: Interpret a multiplication equation as a comparison.

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

1.1.1.1: Example: Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.

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

4.OA.1.ii: Represent verbal statements of multiplicative comparisons as multiplication equations.

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

4.OA.2.i: Use drawings and equations with a symbol for the unknown number (variable) to represent the problem.

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

4.OA.2.ii: Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.

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

4.OA.3.i: 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.

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.ii: Represent these problems using equations with a letter standing for the unknown quantity (variable).

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.iii: 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.i: Find all factor pairs for a whole number in the range 1-36.

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

4.OA.4.ii: 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.iii: Determine whether a given whole number in the range 1-36 is a multiple of a given one-digit number.

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

4.OA.4.iv: Determine whether a given whole number in the range 1-36 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.i: Generate a number or shape pattern that follows a given rule.

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

4.OA.5.ii: Identify apparent features of the pattern that were not explicit in the rule itself.

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

4.NBT: Number and Operations 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)
Rounding Whole Numbers (Number Line)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)
Whole Numbers with Base-10 Blocks

4.NBT.2.i: Read and write multi-digit whole numbers to the one millions place using base-ten numerals, 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.ii: 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)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Whole Numbers with Base-10 Blocks

4.NBT.3: Use place value and/or understanding of numbers 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 to the one millions place using strategies flexibly, including 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)
Whole Numbers with Base-10 Blocks

4.NBT.5.i: Using strategies based on place value and the properties of operations, multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.

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

4.NBT.5.ii: 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.i: 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.

No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

4.NBT.6.ii: 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.i: Using visual fraction models, explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b). 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.1.ii: Attention should focus on how the number and size of the parts differ even though the two fractions themselves are the same size.

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.i: By creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2, compare two fractions with different numerators and different denominators.

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.ii: Recognize that comparisons are valid only when the two fractions refer to the same whole.

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.iii: Record the results of comparisons with symbols >, =, or <, and justify the conclusions, 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)

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 unit fractions 1/b.

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)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

4.NF.3.b.i: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation.

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.b.ii: Justify decompositions by using a visual fraction model or other strategies.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
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.

Fractions Greater than One (Fraction Tiles)

4.NF.3.d: Using visual fraction models and equations, 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)

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

4.NF.5.i: Express a fraction with denominator 10 as an equivalent fraction with denominator 100.

Modeling Decimals (Area and Grid Models)

4.NF.6: Use decimal notation for fractions with denominators 10 or 100.

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

4.NF.7.i: Compare two decimals to hundredths by reasoning about their size.

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.NF.7.ii: Recognize that comparisons are valid only when the two decimals refer to the same whole.

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.NF.7.iii: 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: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

4.MD.1.i: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec.

Cannonball Clowns (Number Line Estimation)

4.MD.1.ii: Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.

Cannonball Clowns (Number Line Estimation)

4.MD.1.iii: Record measurement equivalents in a two-column table.

Cannonball Clowns (Number Line Estimation)

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

4.MD.2.ii: Using diagrams such as number line diagrams that feature a measurement scale, to represent measurement quantities.

Elapsed Time
Road Trip (Problem Solving)

4.2: Represent and interpret data.

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.i: 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.

Polygon Angle Sum

4.MD.7.ii: Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

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.i: Draw and label points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

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

4.G.1.ii: Identify these in two-dimensional figures.

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

4.G.2.i: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of specified size.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions

4.G.2.ii: Recognize right triangles as a category, and identify right triangles.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions

4.G.3.i: 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.

Quilting Bee (Symmetry)

4.G.3.ii: Identify line-symmetric figures.

Quilting Bee (Symmetry)

4.G.3.iii: Draw lines of symmetry.

Quilting Bee (Symmetry)